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UCRL 7167 Rev. I

University of California

Ernest O. Lawrence Radiation Laboratory

THE VAPOR PRESSURES OF

30 INORGANIC LIQUIDS BETWEEN ONE

ATMOSPHERE AND THE CRITICAL POINT

Livermore, California

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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UCRL-7167 Rev. I

UNIVERSITY OF CALIFORNIA

Lawrence Radiation Labora tory

L ive rmore , California

Contract No. W-7405-eng-48

THE VAPOR PRESSURES OF 30 INORGANIC LIQUIDS BETWEEN

ONE ATMOSPHERE AND THE CRITICAL POINT

DAVID G. EDWARDS

June 17, 1964

0

CONTENTS

Abs t rac t . . . . . . . . .

Introduction . . . . . . . .

A. Vapor P r e s s u r e Deviations from the Claus ius-Clapeyron Equation . . . .

B. Exper imenta l Data

C. Scope of this Work

Vapor P r e s s u r e Deviation Curves

A. Construction of Deviation Curves

B. Shape of Curves

C. Slope of Curve at Normal Boiling Point

D. Relation to Liquid and Vapor Densi t ies Along Coexis tence Envelope . . . . . .

E. Correspondence of Maxima and Minima

F . Correspondence of Data with Deviation Curve

Deviation Curves and Tables of Interpolated Vapor P r e s s u r e s

A. P rocedure . . . . . . . .

B. Summarized Cr i t ica l P rope r ty and Vapor P r e s s u r e Values

C. Individual Substances

1. Hydrogen Isotopes

2. Neon

3. Nitrogen

4. Carbon Monoxide

5. Argon

6. Oxygen

7. Methane

8. Nitric Oxide

9. Krypton

- i i i -

CONTENTS (Continued)

10. Xenon

11. Silicon Tetrafluoride

12. Ni t rous Oxide

13. Carbon Dioxide

14. Hydrogen Chloride

15. Hydrogen Bromide

16. Sulfur Hexafluoride

17. Hydrogen Sulfide

18. Hydrogen Iodide

19- Chlorine

20. Ammonia

21. Cyanogen

22. Sulfur Dioxide

23. Hydrogen Fluor ide

24. Hydrogen Cyanide

25. Nitrogen Tetroxide

26. Bromine

27. Sulfur Trioxide

28. Carbon Tet rachlor ide

29. Tin Tet rachlor ide

30. Water

IV. Acknowledgments

V. References

- I V -

- 1 -

THE VAPOR PRESSURES OF 30 INORGANIC LIQUIDS BETWEEN

ONE ATMOSPHERE AND THE CRITICAL POINT*

DAVID G. EDWARDS

Lawrence Radiation Laboratory , Universi ty of California

L ive rmore , California

June 17, 1964

ABSTRACT

Li te ra tu re values of the vapor p r e s s u r e s of H , HD, D^, N^, O^, Ne,

Ar, K r , Xe, CO, NO, CH^, SiF^, N^O, CO^, HCl, HBr, HI, SF^, H^S, Cl^.

Br^ , NH^, C^N , SO^, SO^, HF, HON, N^O^, CCl , and SnCl have been

compared with the Kirchhoff formula

log PT^ = - A / T + B is.

between the normal boiling point and the cr i t ica l point, where A and B are de

te rmined for each liquid. Plots a re presented of the deviations computed by

the equation

K obs

Based on accura te ly de termined curves for 17 of these subs tances , e m

pi r ica l hypotheses were developed to allow the predict ion of the most probable

course of the deviation curve in ca ses where the data appeared to be unre l i

able . In addition, where p rec i se data were avai lable, the possibi l i ty of the

existence of f ine-s t ruc ture curvature has been demons t ra ted .

Work performed under the auspices of the U. S. Atomic Energy

Commission.

- 2 -

The deviation curves have been used to obtain tables of interpolated

vapor -p ressu re values which a r e , in most c a s e s , more accura te by one order

of magnitude than any now in the l i t e r a tu re , par t icu lar ly where smoothed

r e g r e s s i o n curves do not d i sc r imina te between random exper imenta l e r r o r s

and systemat ic deviations of an a r b i t r a r i l y chosen formula from the r ea l

v a p o r - p r e s s u r e curve . Since the deviation curve is invariably shown to

approach the ze ro ordinate at the cr i t ica l point with a large negative slope,

the correspondence between the cr i t ica l p r e s s u r e and t empera tu re is fixed

with a high degree of confidence. A par t icu lar resu l t of this work is that

the cr i t ica l p r e s s u r e of NH_ was shown to be about one a tmosphere higher

than the present ly accepted value. Our values for the cr i t ica l points of

CH. , C^N^, HCN, and Br^ have also resolved differences existing between

var ious author i t ies in the l i t e r a tu re .

I. INTRODUCTION

A. VAPOR PRESSURE DEVIATIONS FROM THE CLAUSIUS-

CLAPEYRON EQUATION

The approximate Claus ius-Clapeyron re la t ion (Eq. 3 below) predic ts

that the log of the vapor p r e s s u r e P should vary l inear ly with the inverse of

the absolute t empera tu re T. Actually, the rea l vapor p r e s s u r e deviates

from this re la t ionship , as shown in exaggerated form in Figure 1. The

origin of these deviations can be seen from a considerat ion of the exact

Claus ius-Clapeyron equation

dP/dT= A H / T (V - V ), (1)

where AH is the heat of vaporization at t empera tu re T, and V and V. a re g i

the vapor and liquid molar volumes, respect ive ly . At p r e s s u r e s below one

a tmosphere , V is substantial ly ze ro and V is given quite closely by the

ideal gas equation

V = R T / P . (2) g

Substituting Eq. 2 into 1, the famil iar form of the approximate Claus ius-Clapeyron

equation is obtained:

A H / R r e p r e s e n t s the slope of the line given by a plot of In P vs 1 / T . The

major deviation of the rea l vapor p r e s s u r e from this line below the boiling

point or iginates from the fact that AH is not a constant but va r i e s with T

according to a re la t ion such as Eq. 4:

AH = a + bT + cT^, (4)

where a, b , and c a r e constants . As T approaches the c r i t i ca l point, AH

goes to ze ro ; and above one a tmosphere , the deviation of V from the ideal

- 4 -

O

Crit ical point

nflection point

Boiling point

Tr ip le point

/T GLL-63ij--T25A

F i g . 1. The log P vs 1/T v a p o r - p r e s s u r e c u r v e e x a g g e r a t e d to show the v a r i o u s c u r v a t u r e s . (Adapted with p e r m i s s i o n f r o m I n d u s t r i a l and E n g i n e e r i n g C h e m i s t r y . )

- 5 -

gas equation becomes p rogress ive ly g rea t e r ; V also begins to increase

significantly. At the cr i t ica l point AV becomes ze ro ; although AH/AV is

indeterminate at the cr i t ica l point, it has a l imiting value of approximately

7P (111), c

Returning to an examination of Eq. I, it is seen that the inflection

point (shown between the boiling point and the cr i t ica l t empera tu re in F igure

1) a r i s e s from the necess i ty that the dew point line of the coexistence

envelope change di rect ion in order to attain c losure at the cr i t ica l point.

This general ly occurs for T / T between 0.75 and 0.85.

Thus the deviations of vapor p r e s s u r e from ideal behavior a r e seen to

be due to:

(1) Depar ture of dAH/dT from l inear i ty .

(2) Deviation of V from ideal behavior . g

(3) An inflection point in (dV /dT) at the saturated condition

(denoted by the subscr ipt s) .

Although the v a p o r - p r e s s u r e - t e m p e r a t u r e re la t ionship could be exactly

expressed by substituting a power s e r i e s in T for AH, and a power s e r i e s in

( 1 / T ) P for AV (as d iscussed by Lewis and Randall (66)), it has been shown by

Waring (111) that a four-constant equation of the form

log P = A + B / T + C T + DT^ (5)

is adequate to descr ibe the features of the rea l v a p o r - p r e s s u r e curve

i l lus t ra ted in Figure 1. Indeed, Miller (78) has shown that for the region be

tween one a tmosphere and the cr i t ica l point, which is the a r e a of in teres t in

this investigation, Eq. 5 could be fitted to the data for 23 of the compounds

given by this work to within 1.54% average ma^ximum e r r o r . F u r t h e r m o r e ,

according to Miller , even the simple Kirchhoff equation

log P =: - A / T + B (6)

- 6 -

(where A and B a re constants) fitted the same data with an average maximum

e r r o r of only 3.20%. This close fit between the boiling point and the cr i t ica l

point is a consequence of the fact that for many substances a line of constant

slope drawn between the boiling point and the cr i t ica l point b i sec ts the rea l

v a p o r - p r e s s u r e curve because of the existence of the inflection d i scussed

above. In addition, it develops that the slope A in Eq. 6 i s , for many of the

substances investigated he r e , quite close to the slope at the boiling point, as

is shown in Table I below; the a r i thmet ic sum of the maxinnum positive and

negative deviations of the vapor p r e s s u r e from Eq. 6 for these substances is

about 1 atm. or l e s s , as is seen in F igures 2-5 below. The derivat ion of the

modified Klein equation for predicting heats of vaporization (102) was based

on a recognit ion of this condition.

Thus it is seen that while Eq. 5 adequately follows the rea l vapor-

p r e s s u r e curve, it may be in e r r o r by as much as 1.5% when the constants a re

derived from a corre la t ion using T , P , and T (as shown by Miller (78)),

or by a few tenths of a percent if fitted by a r e g r e s s i o n curve to the exper imenta l

v a p o r - p r e s s u r e data between T and T , as done by many of the authors cited

in this work. For cr i t ica l p r e s s u r e s of 40 to 60 a tm. , e r r o r s of 1.5% amount

to absolute e r r o r s of 0.6 to 0.8 a tm. Even when fitted by r eg res s ion - l ine

t r ea tment , the result ing equation fails markedly to fit the data to the same

degree as the precis ion of the measu remen t s in the region of high curvature

between the inflection point and the cr i t ica l point. This situation has been

graphical ly demonst ra ted by Michels et_al. (73-77). F u r t h e r m o r e , F r i edman

and White (31) have specifically stated that Eq. 5 cannot be made to give a

good fit with the data for N- near both the boiling point and the cr i t ica l point.

This also has been recognized by Hoge (50), who fitted the data for oxygen

to five separate equations of the type of Eq. 6, and by Osborne et a.1. (85, 86),

- 7 -

T A B L E I

COMPARISON O F H E A T S O F V A P O R I Z A T I O N

S u b s t a n c e

n - H ^

Ne

^ 2 CO

A r

^ 2 CH^

NO

Kr

Xe

S i F ^

N^O

HCl

H B r

5 ^ 6 H^S

HI

^^2 NH3

^ 2 ^ 2 SO2

(HF)^

HCN

^ 2 ^ 4

B^2 SO3

CCI4

SnCl^

H^O

AH^

c a l . / m o l e

216

410

1333

1444

1558

1630

1955

3293

2158

3021

4460

3956

3860

4210

4080

4463

4724

4878

5581

5576

5955

5020^

6027

7040^

7030

9990

7170

8300

9717

AH, k c a l . / m o l e

258

442

1353

1446

1546

1631

1985

2988

2153

2995

3945

3768

3799

4090

3992

4285

4 6 0 1

4675

5340

5342

5677

6422

6478

8203

6826

7639

6918

7794

9147

^ ^ k - ^ ^ b c a l . / m o l e

42

32

20

2

-12

1

30

- 3 0 5

- 5

-26

- 5 1 5

- 1 8 8

- 6 5

-120

- 8 8

- 1 7 8

- 1 2 3

- 3 2 6

- 2 4 1

-234

- 2 7 8

1402

451

1163

-204

- 2 3 5 1

-252

-506

-570

^ \ / b c a l . / m o l e - " K .

13

16.7

18.0

18.3

18.3

18.6

18.3

25.4

18.5

18.7

22.9

21.0

20 .8

20.4

20 .1

20.7

19.9

20.2

23.0

21.9

22.2

22.6

22 .3

28 .8

21.2

24 .8

20.4

20 .7

25 .3

P e r r y , C h e m i c a l E n g i n e e r s Handbook, F o u r t h E d . p . 3 -107 , Ref. (91).

0.4

E 0.3 o 0.2 ^ 0.1

1 1

-

1 1

1 1 1

3^ ^ ^ ^ ^ ^ N 2 _ ^ ^

""^^ C 0 _ _ _ ^ 1 1 1

1

- ^ 2

1

1 1

y^ tC02,SF6

1 1

1

%

1

0 GLL-633-ij-itOB

20 80 40 60

% 1/T F i g . 2. D e v i a t i o n c u r v e s for H2. ^Z' ^ 2 ' ^ ^ ' ^ ' - ' 2 ' ^'^'^ S F ^ .

00

100

as 0.7

0.6

05

04

03

02

0.

0

I I I !

—

1 1 1 1

1 1 1 1

X

JY / ^

J^ J^

^ ^

^ ^

1 1 1

1

>xClS '̂'"'*

^ 2 ' * ' \ \ \ —

% -

¥ 1 1 \

1 0

GLL-633-436A

20 40 60 % 1/T

^

80 100

F i g . 3. Dev i a t i on c u r v e s for Xe , K r , CH4, O^. and A r .

-10

-

O

O

O

00

o

U ro

o

CO

O

O

<M

O

h-

\ MM

*

o

t--cf ro

oo

1

^

O (M

^

pq

(NJ

1—

1

u

r—1

U cq

u

m

> 3 u

0

•iH

•H

> 0) p

Th

hi

(ujp

) p

HF

, N

^O.

d (a

tm)

O

O

O

.—

.—

IV)

rv)

4^

O

-f̂

bo

no

CT)

o

-P̂

.O

o p

o —

—

no

'4̂

CD

bo

O

no

N0

,HC

Nd

(atm

) _

1 2

\ ^

o

o

2 \

^ CD

\

\

\. 1

1 $\

\ \V

\ \

^ \

2 1

—

X "n

—

\\

-\

\\ ro

1 o

oo

oo

op

p —

—

no

O

J -P̂

en

(J

) N

e,C

Cl4

,Sn

CL

d (a

tm)

-IT

-

-12 -

who fitted the data for the vapor p r e s s u r e of H2O with an equation utilizing

exponential functions. Manifestly, then, the experimental determinat ion of

vapor p r e s s u r e always will be capable of g r ea t e r prec is ion than can be ob

tained with simple equations containing up to four constants , and it is only

with considerable effort that special equations have been developed that have

sufficient flexibility to reliably smooth such h igh-precis ion data.

It appeared, there fore , that a deviation curve based on a relat ion as

s imple as Eq. 6 would:

1) Be capable of as g rea t a degree of prec is ion as m o r e complicated

equations.

2) Conform m o r e closely to the behavior of rea l v a p o r - p r e s s u r e curves

so as to more c lear ly define the magnitude of exper imental e r r o r s .

3) Establ ish prec ise ly the value of d P / d T at any t e m p e r a t u r e .

4) Es tabl i sh prec ise ly the value of the vapor p r e s s u r e above one a tmo-

shpere re la t ive to the boiling point as stated here in , and to the t empera tu re

scale used by the original investigator as t ransposed to an ice point of 273.15''C

5) Fix m o r e prec ise ly the correspondence between the cr i t ica l p r e s s u r e

and the cr i t ica l t empera tu re (as recognized by Picker ing (93)).

The above points will be further amplified in the discuss ion below.

B. EXPERIMENTAL DATA

In considering the need for a comprehensive investigation of the data r e

ported in the l i t e r a tu re , the following points were weighed. The most accura te

published corre la t ions of v a p o r - p r e s s u r e data above 1 a tm. , with the exception

of NBS Circular 564 (84), dated back to the Landol t -Bornste in "Physikal i sch-

Chemish Tabellen" (65), las t revised in 1936, and the International Cr i t ica l

Tables (54), published in 1928. Stull 's m o r e recent (1947) resu l t s (108) based

on Cox-Chart cor re la t ions had been shown by Mil ler (78) to be ser iously in

- 1 3 -

e r r o r because the cor re la t ion used was such that the v a p o r - p r e s s u r e curve

was made to approach the cr i t ica l point in the opposite direct ion from the rea l

v a p o r - p r e s s u r e curve shown in F igure 1. In addition, a considerable amount

of new v a p o r - p r e s s u r e data had been published.

A considerat ion of the data available indicated that initially our invest i

gation would be well served if r e s t r i c t ed to 30 or so inorganic subs tances .

For half of these data of high prec is ion had been repor ted; the remainder were

of sufficient industr ia l and scientific impor tance to justify a careful r e - e x a m i

nation of the data repor ted p r io r to 1947.

In addition to the works mentioned above, we would like to acknowledge

our indebtedness to the bibliographic works of Kelley (59) and of Picker ing (93);

these have been of invaluable help in searching the l i t e r a tu r e . The original

sources of all work relevant to the compounds considered by us have been

studied, but we have cited only those containing data on which our resul ts a r e

based or those represent ing e r r o r s or omiss ions in the previous l i t e ra tu re

s o u r c e s . Where the resu l t s of only the most recent invest igators have been

used, a thorough analysis of the work of the previous invest igators has been

given by one or m o r e of the authors ci ted.

Since the details of the experimental work pert inent to the data used he re

a r e d iscussed by the original au thors , only general comments need be given

he re regarding exper imental methods . It is well recognized that the prec is ion

of v a p o r - p r e s s u r e data will be governed by the following considerat ions: (1)

purity of sample; (2) prec is ion of p r e s s u r e measurement ; (3) prec is ion of

t empera tu re m e a s u r e m e n t s ; and (4) adequate prec is ion of t empera tu re control

and the design of the apparatus such as to insure the at tainment of t rue liquid-

vapor equi l ibr ium.

-14-

Until the relat ively recent advent of such powerful analytical tools as

m a s s spectrography and gas chromatography, the methods available for d e

terminat ion of the purity of sample were r e s t r i c t ed largely to s imple m e a

surements such as density, boiling point, and refract ive index. In the ear ly

days , invest igators making v a p o r - p r e s s u r e measu remen t s often pioneered in

the synthesis of the ma te r i a l itself; in notable c i r cums tances , as mentioned

below, these v a p o r - p r e s s u r e determinat ions have not been repeated even though

the purity of the original ma te r i a l is manifestly suspect in the light of more

recent synthetic work. Possibly the mos t r emarkab le case is that of a r s i n e ,

for which no h igh -p re s su re m e a s u r e m e n t s have been made since Fa raday ' s

work up to 13 a tm. , repor ted in 1845.

Since the development of the Keyes deadweight piston gage, for which the

vapor p r e s s u r e of CO^ at 0°C. has been established as the standard ca l ib ra

tion point, this ins t rument has been used ei ther as the working gage or as the

p r i m a r y standard for all prec is ion measu remen t s above 2 or 3 a tm. This gage

is sensi t ive to 0.001 a tm. at p r e s s u r e s up to 150 a tm.

The t empera tu re sensitivity corresponding to this degree of p r e s s u r e

sensitivity is 0.0007 °C. in the neighborhood of the cr i t ica l point, where d P / d T

is about 1.5 a t m . / ° C . This degree of sensitivity is attainable ei ther with mul t i -

junction thermocouples , which a r e to be general ly p re fe r red below lOO^K., or

with platinum res i s t ance t he rmomete r s above this t e m p e r a t u r e .

An important problem stil l unresolved is the fixing of the boiling points

of many well known liquids on the International Tempera tu re Scale. Until this

has been done, the reported v a p o r - p r e s s u r e values mus t be considered, at

bes t , to be only internally consistent with the boiling point as determined by

the invest igator . Indeed, much of the confusion existing in the l i t e ra tu re today

has been caused by the h is tor ica l fluctuation of the accepted value of the ice

- 1 5 -

point on the Kelvin scale and the impossibil i ty of using a simple additive r e l a

tionship to equate the many h is tor ic Kelvin scales which have been used.

Undoubtedly the g rea tes t source of e r r o r — both in frequency and degree

to be found in v a p o r - p r e s s u r e data has a r i s e n from poor t empera tu re control .

Poor thermosta t ing is general ly the cause of e r r o r when the repor ted t empera

ture does not correspond to the p r e s s u r e measu remen t ; this is par t icu lar ly a

cause of e r r o r near the c r i t i ca l point because of relat ively sluggish at tainment

of l iquid-vapor equil ibr ium. Where the heat of vaporizat ion is relat ively large

at t empera tu re s below the c r i t i ca l point, this heat exer ts a se l f -cor rec t ing ef

fect on measu remen t s which tends to check t empera tu re f luctuations. However,

near the cr i t ica l point, AH becomes smal le r ; in addition, the difference be

tween the liquid and vapor density dec r ea se s markedly , thus increasing the

difficulty in maintaining equil ibr ium.

Our examination of the deviation curves derived from the data convinced

us that the in te res t s of accuracy would be bes t served by:

1) Computing the deviations relat ive to the mos t accura te boiling point

available in the l i t e r a tu re .

2) Using the most accura te data to define a general behavior pat tern for

the deviation curve , including specifically a pat tern for the location

of the maximum and minimum and the re la t ive slopes of the var ious

portions of the deviation curve .

3) Est imat ing the accuracy of the data by thei r agreement with a smooth

curve conforming to this generally established pa t te rn .

Since there is a high conformity of the data to these r equ i r emen t s , we feel that

the precis ion of the method has been positively demonst ra ted and the existence

of situations where g r e a t e r - t h a n - n o r m a l e r r o r s had occur red could be d is t in

guished. We feel these c r i t e r i a a r e manifestly m o r e re l iable indica tors of the

-16-

prec is ion of the data than those claimed for the exper imenta l apparatus by the

original au thors . The general accuracy of the best values given in this repor t

re lat ive to the International Tempera tu re Scale is probably not bet ter than

±0.0 1°C. , with a corresponding p r e s s u r e var ia t ion at the t empera tu re in

question. The absolute accuracy of the values is generally to one less dec i

mal point than stated, but these values can be used for purposes of internal

compar ison (of d P / d T , for example) to the number of places quoted.

C. SCOPE OF THIS WORK

The usefulness of deviation curves to r ep resen t v a p o r - p r e s s u r e data

accurate ly from one a tmosphere to the c r i t i ca l point is well recognized.

There has been, however, no sys temat ic effort to compare data for different

substances with the same base function, each author adopting a mathemat ica l

function giving a p re fe r red fit to his data . In many ca se s , deviations from the

equations have not been plotted, and the problem of distinguishing between

potentially rea l effects, sys temat ic deviations from an assumed and perhaps

inadequate empir ica l equation, and random deviations due to exper imental

e r r o r has general ly been left to the r e a d e r . In cases where the precis ion of

the data is within 0.001 a tm. , and a corresponding t empera tu re prec is ion , this

problem is obviated. However, where exper imental e r r o r s and rea l effects

a r e given equal weight in r e g r e s s i o n - c u r v e t rea tment , the resu l t is inevitably

confused. Histor ical ly , then, the v a p o r - p r e s s u r e deviation curve has been

t rea ted as a mathemat ica l tool whose cha rac te r i s t i c s were imposed by the

special conditions of each individual problem.

The objective of this work was to de te rmine whether , if deviation curves

for a la rge number of inorganic liquids were plotted on a single bas i s , any

common cha rac t e r i s t i c s could be established for substances whose vapor p r e s

su res were accura te ly known, and whether curves having these common

-17 -

cha rac t e r i s t i c s would give a reasonable fit for other substances whose r e

ported vapor -pressure data were of questionable re l iabi l i ty .

In this work all data have been compared to the Kirchhoff equation

l°g ^K = - t ° C + l 7 3 . 1 5 + S , (^)

and the deviation has been expressed as

d - P . . - P , . (8)

K obs

Tempera tu res expressed in the Kelvin scale were converted to degrees Cel

sius on the basis of the ice point used by the invest igator , although we r ea l

ized that these h is tor ic Kelvin scales were not s t r ic t ly equivalent to the p r e s

ent 1954 Kelvin scale based on an ice point of 2 73.15°K. The A and B con

stants were evaluated using selected boiling points and cr i t ica l points, and

were expressed to six f igures . The considerat ions governing the select ion of

these values will be d iscussed in m o r e detail below. Equations 1 and 2 were

combined and the deviations were computed on a IBM 650 machine . The de

viations obtained were plotted to a scale consistent with the prec is ion of the

data, the mos t p rec i se plots being readable to 0.001 atm, and a corresponding

t empera tu re prec i s ion . II. VAPOR PRESSURE DEVIATION CURVES

A. CONSTRUCTION OF DEVIATION CURVES

In order to fully define the deviation curve using eqs . 1 and 2, the fol

lowing information was required:

1. The boiling point, T, ;

2. The cr i t ica l t e m p e r a t u r e , T ;

3. The cr i t ica l p r e s s u r e j P ; c

4. Vapor-pressure data between T, and T .

- 1 8 -

Satisfactory boiling point values based on accura te , low p r e s s u r e work

were found in the l i t e ra tu re for mos t of the subs tances . In a few c a s e s , the

boiling point used was determined by us from the h igh -p re s su re deviation

curve presented in this repor t .

By passing the l inear Kirchhoff equation through the boiling point and

cr i t ica l point, the value of d is necessa r i ly 0 at one a tmosphere and at the

cr i t ica l p r e s s u r e . In some cases minor cor rec t ions in P have been made ^ c

by adjusting d ra ther than by recalculat ing the constants in eq. 1. (See

tables in P a r t III.)

In cases where the cr i t ica l point was established by accura te PVT de

terminat ions of the coexistence envelope, in conjunction with adequate vapor

p r e s s u r e measu remen t s between T, and T , no problem was found in con

structing a deviation curve .

In other cases a lack of correspondence between P and the vapor p r e s

sure predicted by the deviation curve at T was revealed by a g ross discon

tinuity in the deviation curve at the cr i t ica l point. Here the p r ime c r i t e r ion

which we used was the necess i ty for a genera l correspondence of the max i

mum and minimum of the deviation curve with those for s imi la r subs tances .

Then, since only two data a r e neces sa ry among i tems 2, 3, and 4, the choice

of ei ther T or P fixed the other . The considerat ions involved in the choices c c

of T and P will be d iscussed below in connection with the specific com-c c ^

pounds involved.

B. SHAPE OF CURVES

For the general ized compar ison of the deviation curves , the t empera

ture range between the boiling point and the cr i t ica l point was normal ized on

a 1/T bas is and expressed as percent , where

%(1/T) = 100 r i / T ^ - l / T y p / T ^ - 1/T^j . (9)

-19 -

The curves a r e presented for each liquid individually in P a r t III of this r e

port but for the purposes of the general ized discuss ion, a r e var iously grouped

in Figures 1-5. It should be noted that in each of F igures 1-5, some curves

shown a r e determined from experimental data of a high degree of prec is ion .

Specifically, the well defined curves a r e those for H^, HD, D^, N , , CO, Ne,

Ar , O^^ CH^, Kr, Xe, N^O, CO^, NH^, SO^, SO3, HF, N^O^, and CCl^.

Curves for which empir ica l considerat ions were involved, to varying deg ree s ,

in fixing their positions were S i F . , CK. C2N2. ^^^2' SnCl . , NO, HCl, HBr,

SF^, H^S, HI, and HCN.

Referr ing to F igures 2-6, it can be seen that the curves fall into two

general c l a s s e s , as further i l lus t ra ted in F igure 7, where various points have

been designated by the l e t t e r s b , j , h, k, and c. The dist inction between

Class I and Class II is not fundamental but resu l t s from the a r b i t r a r y choice

of the normal boiling point as the lower te rminus of the curve . If a lower

t empera tu re were to be taken so as to i nc rease the bj d is tance in curve I, the

Class II curve would be obtained.

C. SLOPE OF CURVE AT NORMAL BOILING POINT

Comparison of eq. 6 with the exact Claus ius-Clapeyron equation

Rd (In P) ^ AH d ( l / T ) ' AZ

shows that

(10)

(4.5758)(AZ)(A) - AH^ ,̂ (11)

where AH, is the heat of vaporization at the boiling point corresponding to a

constant d (log P ) / d ( l / T ) slope, A, between T, and T ; and AZ is the differ

ence between the liquid and vapor compress ib i l i ty . According to Miller (78)

an average AZ for inorganic liquids at the boiling point is 0.97. Substituting

this value for AZ in eq. 5, AH, 's have been calculated and a r e given in Table I,

along with AH, values from NBS Ci rcu la r 500 (83) and P e r r y (91).

E o

LL5

CO

0.6

0 5

04

03

02

01

0

-0.1

-02

1 1

^ - . ^

- ^ ^ \ ^ ^ ^

^^^^^^

^ ^ ^ ^ ^ ^ ^

—

1 1 1

S i F 4 ^ , ^ /

7 ^"°'===::—"^^^ y

/ - ^

/

/ /

/

/

/ ^ ^ S O a

1

—

X -

/ \ y y \

0 GLL-633-439A

20 40 60 % I / T

80

2.4

2.0

1.6

1.2

0.8

0.4

0

-O.A

-o.e

E H—

o • o

rO

o (/)

[

]

100

F i g . 6. D e v i a t i o n c u r v e s for S i F , and SO.,.

2 1 -

% 1/T

Class I curve

% l / T

Class II curve GLL-637-1700

Fig . 7. Classes of deviation cu rves .

- 2 2 -

It can be seen from the above that the difference, AH, - AH, , should k b

indicate whether the slope of the deviation curve at the boiling point will be

positive or negative. Comparison of Column 4 in Table I with the deviation

curves given in P a r t III indicates that this c r i te r ion is quantitatively obeyed

in that, in 27 out of 30 c a s e s , the sign of the slope is cor rec t ly predicted.

The quantitative d ispar i ty of some of the AH differences as compared with the

slopes of the deviation curves leads us to observe , however, that because of

curva ture of the vapor p r e s s u r e t empera tu re function at the boiling point, this

difference may only be quantitatively obeyed for a few degrees above the boil

ing point. In addition, it is probably t rue that in some cases our average value

for AZ is not accura te and that in some cases the value used for AH, may be

inaccura te .

Table I also gives values of 4.5758 B, a psuedo-entropy t e r m , i . e . ,

AS, ,, cal . per degree per mole of vapor . As can be seen from the Table,

values of AS, /, above 21.0 a r e general ly found with associa ted l iquids.

D. RELATION TO LIQUID AND VAPOR DENSITIES ALONG

COEXISTENCE ENVELOPE

The upturn of the deviation curve at b in Class I and at j in Class II curves

is probably mos t closely related to la rge percentage changes which a r e be

ginning to occur in the liquid density along the bubble-point l ine. No c o r r e

lation of this point with coexistence data has been made , but it should be

pointed out as a ma t t e r of exper imental p rocedure that adequate and re l iable

v a p o r - p r e s s u r e data in this region a r e a p r ime requis i te for accura te ly de

fining the deviation curve . As the heat of vaporizat ion and the difference be

tween liquid and vapor volumes become rapidly sma l l e r , the problems of main

taining t empera tu re and p r e s s u r e equil ibrium a r e aggravated. However, the

problems a r e considerably less at this point than at t empera tu re s above point

- 2 3 -

k, and any effort expended in getting accura te measu remen t s in this region

pay dividends toward minimizing the effect of uncer ta int ies encountered in

the kc region. The inflection point at h appears to be due to the inflection

point in the vapor density along the dew-point line as mentioned previously.

It is of in te res t to comment on the evidence for f ine - s t ruc tu re effects

demonstra ted in the p rec i se ly determined c u r v e s . In examining the bjh r e

gion of the curves for accura te ly known subs tances , it is found in all 15 cases

that in this region the curve may be composed of two, th ree , or four near ly

s t ra ight sections joined by relat ively sharp cu rves . These s t ra ight sections

were par t icu lar ly evident for the Class I curves having no negative deviations;

i. e. , H^. N^j CO, Ar , O^i CH. , Kr, Xe, and HF and a r e str ikingly i l lus

t ra ted in the cases of N-, and CH. , for which l a r g e - s c a l e plots a r e provided

below. Although in most cases the data shown could be a lmost as well fitted

with smoother cu rves , and although four points cannot be said to conclusively

establ ish a s t ra ight l ine, it would be equally presumptuous to conclude, a

p r i o r i , that deviation curves must demons t ra te a low-order cu rva tu re , data

points notwithstanding.

E. CORRESPONDENCE OF MAXIMA AND MINIMA

Empir ica l ly , it appears that on the sca les plotted in F igures 2-6 the

peak k of the jhkc loop is located so that the angle formed by the s t ra ight s e c

tion of hk with the ver t ica l is for Class I curves from 60 to 80" and for Class

II curves from 20 to 40°; the angle general ly formed by kc is about half as

great ; and fu r thermore that the d ordinate values for j and k for s imi la r sub

stances do exhibit a general degree of cor respondence as shown in F igures

1-5, Thus the d = 0 requ i rement at P fixes P within relat ively nar row l imi t s .

Because the high d P / d T slope of the deviation curve at the cr i t ica l point is

superimposed on the contribution of the Kirchhoff equation, d P / d T may vary

- 2 4 -

between 1.0 and 2.0 atm-Z^C. For a d P / d T of 1.5 a t m . / d e g . , for example,

a p r e s s u r e difference of 0.01 a tm . is equivalent to a 0.0067''C. t empera tu re

difference. Thus it can be seen that the p r e s s u r e is an especially sensit ive

function of t empera tu re at the c r i t i ca l point. This m e a n s , of course , that

random tempera tu re e r r o r s near the cr i t ica l region r ep re sen t the highest de

gree of p r e s s u r e d ispers ion on the deviation plot. Complementing this , how

ever , is the magnification of the prec is ion with which the p r e s s u r e is fixed

by a well defined deviation curve . If the necess i ty is assumed for the k height

to correspond to a uniform pat tern for s imi la r substances to at leas t within

±0.05 a tm. as d iscussed above, P is fixed cer tainly within these l imits and c

correspondingly T is fixed to within about ±0.03 ' 'C.

F . CORRESPONDENCE OF DATA WITH DEVIATION CURVE

The following section p resen t s general considerat ions involved in s e

lecting the p re fe r red deviat ion-curve location for situations where the vapor

p r e s s u r e data were ambiguous.

In Figure 2, the accura te ly known curves were those of H^, D^, N^,

CO, and COp.

In the case of SF , the only consistent data were those of one investigator

in the kc region. The data in the bjh region were badly sca t te red and one in

ves t iga to r ' s data in the kc region demonst ra ted a l o w - p r e s s u r e "nose" between

k and c. Other examples of this "nose" effect have been found in the course

of this study, and, without exception, they have been found to be spurious

when compared with p rec i se m e a s u r e m e n t s . We have discounted these points ,

the re fore . The curve derived from the average of the sca t te red points in the

bjh region also was suspect in that this curve was not in harmony with the p r e

fe r red hkc data. F u r t h e r m o r e , this curve differed markedly from that of

COp, a compound with a s imi la r coexistence l ine . In this region the re fore .

-25 -

our p re fe r red curve was derived from the normal ized CO^ curve as descr ibed

below. To support this judgment it can be pointed out that N^ and CO, whose

molecular s imi lar i ty a r e well recognized (47), show pract ical ly identical de

viation curves in F igure 2.

In F igure 3 all curves a r e well defined by the data . In F igure 4, the

accura te ly known curves a r e NH^, N^O, and SO^. Three general problems

were encountered in locating the other curves in regions of poorly determined

data . In the case of Br^ and C^N^, where relat ively good data were available

in the bjh region, the problem was to choose a c r i t ica l p r e s s u r e cor respond

ing to the accepted T so that the bjh portion of the curves would form a mu

tually symmet r i ca l pat tern . This was done by adjusting the j and k peaks to

be in mutual correspondence with the other curves shown. In the cases of

HCl and H^S, no data were available in the bjh region, and in the case of CK,

the bj data departed markedly from the genera l s lope. The course adopted

here was to draw the curves to harmonize both with the hjk points and the

other bjh curves shown in F igure 4. In the case of Br_ no data were available

in the kc region, so this curve was drawn to be in mutual harmony with C L .

The third problem in Figure 4 with C L , HBr, and HI was that these data

exhibited excessive sca t te r overa l l . The p re fe r red curves were therefore

drawn so as to bes t approach the points giving curves matching the pa t te rn

established by HCl and H^S. Points deviating from this pat tern by more than

the normal confidence l imits were neglected. It can be seen by examining the

individual curves given below for these substances that a reasonable degree of

agreement with the data has been obtained in the jhk region where the re is l e ss

difficulty in attaining equil ibrium conditions.

In the case of NH^, a choice was made in the kc region between the data

of Beattie (8) and of Keyes (60). The data of Beattie were used because a

-26-

deviation curve following Keyes ' points indicated a c r i t i ca l p r e s s u r e 0.5 a tm.

lower than Bea t t i e ' s . Basing the deviation curve on A and B constants calcu

lated from Keyes ' indicated P would have not only lowered the k point below

that for CpNp but would also have lowered the j point to -0.55 a tm. , or 0.15

a tm. below any other compound shown in F igure 4. It was believed that Keyes

data were in e r r o r here and cr i t ica l values were chosen to correspond with

Beat t ie ' s points so that the deviation curve harmonized as shown in F igure 3.

A s imi la r situation is a lso d iscussed below in Section III. C.7 on CH>.

In F igure 5 the curves were plotted on different p r e s s u r e scales for

convenience in comparing shapes . Fo r Ne, C C l . , and SnCl . , the d ordinate

is 0.1 a tm. /d iv i s ion , for NO and HCN 0.2 a tm. /d iv i s ion , and for HF and N^O.

0.4 a tm, /d iv i s ion . The curves for HF, NpO ., Ne, CCl ., and SnCl. were well

determined by the data . The curve for HCN was found to fit the few observed

data well when matched with that for NpO .. The curve shown for NO was

drawn so as to best fit the few points that seemed to indicate a reasonable

curve and so as to harmonize with the other curves as shown.

F igure 6 p resen t s the deviation curves for SiF . and SO^. These curves

do not conform to those in the previous figures since the d's a r e not zero at

the boiling point and in the case of SO-,, a lso at the cr i t ica l point. By means

of this change, the deviation curves were able to be presented on a scale com

parable to those of F igures 1-4 without excessively large negative values for

the j min imum. It should be noted that the data for SO., in the kc region were

ambiguous but that the kc height shown was drawn to conform to that of SO^,

which appeared to be reasonable .

In the kc region we have noted that the prevail ing d i sagreements with

the mos t accura te data appear to be in the direct ion of lower p r e s s u r e s . This

has been found to be t rue in the cases of Ne, Ar, CH. , HCl, H^S, S F / , NH,,

- 2 7 -

N-O ., and SnCL. In the cases of HBr and HI, where deviation curves were

located so as to correspond to curves for other substances determined by a c

cura te data , data which matched the curve in question in the jhk region were

low in the kc region. We a r e unable to advance any firm reasons for expect

ing exper imental e r r o r s to prevai l in this direction; however, the re la t ive

absence of sca t te r in the other direct ion tends to suggest that this is a sys tem

atic e r r o r . Hence, in the absence of consistently re l iable data in this region,

we have located the curve so as to be symmet r i ca l with s imi la r substances

having approximately the same k coordinates and have avoided points to the

right of k which would flatten the peak and requ i re a d ras t i c inc rease in kc

curva ture and s lope. Substances for which re l iable data were completely un

available in the jhkc region have not been considered in this study. It should

be emphasized that the utility sought for a hypothesis of the genera l behavior

of the deviation curve is that in the face of contradictory data, it m o r e closely

approximates the probable position of the deviation curve than does r e g r e s s i o n

line t rea tment ,

III. DEVIATION CURVES AND TABLES OF INTERPOLATED

VAPOR PRESSURES

A, PROCEDURE

Deviation curves were prepared as descr ibed above and a r e given in this

P a r t in connection with each specific subs tance . The text accompanying each

curve below cites the sources of the data used and d i scusses the considerat ions

involved in locating the p re fe r red position of the curve . Rather than at tempt

to reproduce the l a r g e - s c a l e deviation plots , deviation values read from these

plots have been included in the Tables of Interpolated Vapor P r e s s u r e s . The

f i rs t column of the Tables of Interpolated Vapor P r e s s u r e gives the t e m p e r a

ture in " C , the second column gives the interpolated vapor p r e s s u r e calculated

by the equation

-28 -

P. = Pj^ - d, (12)

and the third and fourth columns give P „ and d, respect ively . The rel iabi l i ty

of the las t figure given for P . is general ly quest ionable. In the cases of hy

drogen, nitrogen, oxygen, methane , and carbon dioxide, reduced size figures

of the original l a r g e - s c a l e plots of d against "C. a re also presented . This

has been done to show for these substances the bas is for our judgment as to

mos t probable position of the deviation curve where the resu l t s of severa l in

ves t iga tors a r e in d i sagreement , and to exemplify the nature of " f ine - s t ruc

t u r e " effects which have been general ly brought out by high-precis ion m e a

s u r e m e n t s . The other subs tances , for which only sma l l - s ca l e graphs a r e

presented , fall into one of two categor ies : ei ther the prec is ion of the data of

severa l invest igators is adequately represen ted by the small scale used, or

the data of a single invest igator is considered to be of super ior rel iabil i ty and

ea r l i e r resu l t s have been rejected on the bases mentioned above. Compar i

sons with these other data have usually been presented by the authors cited.

B. SUMMARIZED CRITICAL PROPERTY AND VAPOR

PRESSURE VALUES

In addition to the individual tables of vapor p r e s s u r e s . Table II is p r e

sented showing the comparison of our p re fe r red cr i t ica l values with those s e

lected by Stull (108) and Kobe and Lynn (63). In genera l , these two authori t ies

values correspond with Picker ing (93) and with other authori t ies in the In ter

national Cri t ical Tables (54).

Our interpolated vapor p r e s s u r e tables giving the vapor p r e s s u r e s for

even t empera tu re values may be compared direct ly with the International Cr i t

ical Tables . For compar ison with Stull 's va lues , we have prepared Table III

giving t empera tu re values for even p r e s s u r e va lues .

-29 -

T A B L E II

SUMMARY O F S E L E C T E D DATA C O M P A R E D WITH L I T E R A T U R E

Subs tance

e q - H ^

" " " 2 HD

e q - D ^

n D^

Ne

^ 2 CO

A r

°2 CH4

NO

Kr

Xe

S iF^

N^O

C O ,

HCl

HBr

H , S

HI

Cl^

NH,

S O ,

H F

HCN

N2O4 B r ,

SO 3

CCI4

SnCl ,

b p °C

- 2 5 2 88

- 2 5 2 77

- 2 5 1 02

- 2 4 9 . 5 2

- 2 4 9 49

- 2 4 6 06

- 1 9 5 78

- 191 48

- 1 8 5 91

- 1 8 2 97

- 1 6 1 49

- 1 5 1 74

- 1 5 3 40

- 108 12

- 9 0 2^̂

- 8 8 46

- 5 6 57̂ =

85 03

66 72

-51^^

- 6 0 19

- 3 5 35

- 3 4 05

- 3 3 35

- 2 1 15

- 1 0 02

19 5

25 70

21 0

58 2

44 55

76 7

114 1

c •C

Stull (108) P c

a t m

C r i t i c a l P r o p e r t i e s

Kobe and Lynn (63) This Work

•240 0 12 80

•228 3

147 2

138 7

122 0

118 9

-82 1

-92 9

-63

-14 2

36 5

31 1

51 4

90 0

100 3

151

144

132 4

126 6

157 2

183 5

158

302 2

218 3

283 1

318 7

26 90

33 5

34 6

48 0

49 7

45 8

64 6

54

36 7

71 7

73 0

81 6

84 4

88 9

82

76 1

H I 5

58 2

77 7

50 0

99

121

83 6

45 0

37 9

T c

•c -240 22

-239 9

-237 25

-234 90

-234 81

-228 7

-147 0

•140

•122

•118 4

-82 1

-93

-63 8

16 59

-14 1

36 5

31 0

51 4

90 0

45 55

100 4

150

144

132 3

127

157 5

183 5

158

311

218 2

283 2

318 7

P c atm

12 77

12 80

14 645

16 282

16 432

26 9

33 5

34 5

48 0

50 1

45 8

64

54 3

58 0

36 7

71 7

72 9

81 5

84 0

37 11

88 9

81

76 1

111 3

59

77 8

53 2

100

102

83 8

45 0

36 95

-240 IT^

- 2 3 9 92^

- 2 3 7 25^

- 2 34 90^

- 2 3 4 82^

- 2 2 8 75^

- 1 4 6 93^

-140 23^

- 1 2 2 29^

-118 38^

-82 6 1 ^

- 9 2 9^

- 6 3 77^

16 59^

- 1 4 17*

36 4 3 *

31 04*

51 54*

90 0 *

45 64*

99 9 *

150 7*

144 1^

132 50*

128 3 0 *

157 50*

188*

183 5*

158 2*

3 1 1 *

217 7*

283 15*

318 7*

c a t m

12 76^

12 80a

14 645*

16 28*

16 42*

26 19*

33 54*

34 53*

48 34*

50 14*

45 49^

64 6*

54 31^

57 64*

36 6 6 *

71 60*

72 8 4 *

82 0 7 ^

84 5*̂

37 19*

88 2 6 *

81 9^

76 1*

112 53^

59 98^

77 8 1 *

64 0 7 *

48 89*^

99 6 6 ^

102*

81 4 4 ' '

44 9 7 *

36 9 5 *

' L i t e r a t u r e va lue ci ted in tex t

' 'Value d e t e r m i n e d f rom dev ia t ion c u r v e in th is work

T r i p l e pt above 1 a t m

30

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r^

co

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t\i f^

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fM

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w

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ci ID

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- 3 1 -

An additional, m o r e meaningful compar ison between our deviation curve

and the Stull and ICT values was made by us by comparing the deviations of

these values with our deviation curve . It appears that Cragoe ' s calculated

values in the International Cr i t ica l Tables ag ree fairly well with our values .

Stull 's va lues , however , invariably show la rge negative deviations and no pos i

tive deviat ions. This is to be expected from the nature of the Cox Chart cor

relat ion method used by him which always approaches the cr i t ica l point from

the negative ra ther than the positive deviation side.

While the choice of a location for the deviation curve in the absence of

rel iable data is difficult, especially in cases where apparently re l iable data

a r e in conflict, it is believed that the procedures which have been used have

resul ted in the c loses t possible approach to the t rue vapor p r e s s u r e . This is

based on the demonstra t ion by this study of a high degree of consistency in the

general shape of the deviation curve . F o r severa l different m a t e r i a l s the

curves a r e a lmost identical; for ins tance, the groups N^ and CO; HF and N^O.;

0 ^ , A r , Xe, Kr, and CH, show this t r a i t . The demonstra t ion of conformity of

the deviation curve behavior with the resu l t s of published studies on vapor p res

sure and heats of vaporizat ion also supports this p rocedure . On this bas is the

reasons for rejecting data which a r e in radica l d i sagreement with this behavior

appear justified.

It is worth noting that in addition to NO no rel iable high p r e s s u r e data

a r e available in the l i t e ra tu re for such common substances as C F , , CS-,, COS,

COCl^. SiH^, PH^, ASH3, H2Se, N^H^, BCI3, BF3 , SiCl^, and GeCl^.

It is hoped that this study has sufficiently demonst ra ted the utility of the

deviation curve method as to encourage its future use to demons t ra te the con

sis tency and rel iabil i ty of experimental data .

- 3 2 -

C. INDIVIDUAL SUBSTANCES

1. Hydrogen Isotopes

Deviation curves have been computed for the following hydrogen isotopes

eq-H^, n-Hp, HD, eq-Dp, and n - D , . The curves plotted on a %(1/T) basis

a r e shown in Figure 8. It appears that on this bas is the curves for the ortho

and para forms coincide with each other both for H^ and D , but that cont ra ry

to Fr iedman , White, and Johnston (33) the curves for the H, and D^ isotopes

a r e separa ted from each other by about 5 to 6 % in the b-k region, with HD

falling between Hy and D^. Plotting the curves on a r educed- t empera tu re

basis as was done by F r i edman , White, and Johnston does not appreciably r e

duce this separat ion, since the reduced boiling points do not differ by more

than 1%.

The boiling points quoted in Table II a r e due to the following authors :

n-H2 (118); eq-H^; HD, and eq-D^ (51); and n-D2 (43).

The sources of c r i t i ca l constants used for deriving the Kirchhoff equa

tions were: n-H2 (117); eq-H^ (100); HD and eq-D^ (52); and n-D^ (32).

The v a p o r - p r e s s u r e data from the var ious investigations of the NBS (51,

112, 42) and Grilly (43) show good precis ion and a r e in good agreement .

F r i edman , White, and Johnston 's data on n-D^ (32) a r e in agreement with

Hoge's data and with the deviation curves in F igure 8 above point k. In the

b-k region, F r i edman , White, and Johnston 's resu l t s ag ree after their t em

pe ra tu re s in this region a r e adjusted to agree with Gri l ly ' s boiling point. In

the case of n-H^ nei ther White, F r i edman , and Johnston (116) nor Cath and

Kammerl ingh Onnes (20) agree prec ise ly with Gril ly, as can be seen from

Figure 9. The deviation curve shown in F igure 9 was obtained by projecting

a curve based on Gri l ly ' s resu l t s and coinciding with the deviation curve for

eq-Hp shown in F igure 8.

- 33 -

(33) F r i e d m a n , A. S. , Whi t e , D. , and J o h n s t o n , H. L . , J . C h e m . P h y s .

19, 126 (1951).

(118) Wooley , H. W. , Scot t , R. B . , and B r i c k w e d d e , F . G. , J . R e s . Na t l .

B u r . Std. 4 1 , 379 (1948).

(51) Hoge , H. J . , and A r n o l d , R. D . , J . R e s . Na t l . B u r . Std. 47 , 63 (1951).

(43) G r i l l y , E . R. , J . A m . C h e m . Soc . 73 , 843 (1951).

(117) Whi t e , D. , F r i e d m a n , A . S. , and J o h n s t o n , H. L . , J . A m . C h e m .

Soc . 72, 3565 (1950).

(100) R o d e r , H. M. , D i l l e r , D . E . , W e b e r , L . A . , and Goodwin, R. D . ,

C r y o g e n i c s 3, 16 (1963).

(52) Hoge , H. J . , and L a s s i t e r , J . W. , J . R e s . N a t l . B u r . Std. 4 7 , 75 (1951).

(32) F r i e d m a n , A. S. , Whi te , D. , and J o h n s t o n , H. L . , J . A m . C h e m .

Soc . 73 , 1310 (1951).

(112) W e b e r , L . A . , D i l l e r , D . E . , R o d e r , H. M. , and Goodwin, R. D. ,

C r y o g e n i c s 2^ 236 (1962).

(42) Goodwin, R. D. , D i l l e r , D. E . , R o d e r , H. M. , and W e b e r , L . A . ,

J . R e s . Na t l . B u r . Std. 67A, 173 (1963).

(116) Whi te , D. , F r i e d m a n , A . S. , and J o h n s t o n , H. L . , J . A m . C h e m .

Soc . 72, 3927 (1950).

(20) Ca th , P . G. , and K a m m e r l i n g h O n n e s , H. , Konink l . Ned. Akad .

W e t e n s c h a p . P r o c . S e r . B 26, 490 (1917) L e i d e n C o m m . No. 152a.

U.H-'-h

0.40

0.36

0.32

0.28

^ 0.24 o

Z 0.20

0.16

0.12

0.08

0.04

-

—

—

—

—

—

—

—

i . ^

H2^y^

yyy y7x

1 ^ ^ ^ H D

1 1 1

^ D 2

- - — = 5 : , ^

\ v —

\ ~

\ ""

\ ~

\ ~

\ —

\ —

\ —

1 1 '

0

I

I

10 20 30 40 60 GLL-637-1702A

50

% (l/j)

F i g . 8. D e v i a t i o n c u r v e s for H i s o t o p e s .

70 80 90 100

040

E

• o 020

0

-004

6U-633-44M

n-H2

• Cath and Kammerlingh Onnes

• White

* Wooley

° Gri l ly

_L -253 -252 -240 -239

Fig . 9. Deviation curve for n-H2 vs t °C .

- 3 6 -

T A B L E IV

V A P O R P R E S S U R E O F e q - H ^

log P^ = - 5 8 . 1 5 9 1 / T + 2.86950

^' °*^- P i ' a t m . -p^, a t m . d, a t m

- 2 5 2 . 8 8 2 LOOO LOOO .000

252.50 1.116 1.130 .014

252.0 1.284 1.317 .033

251.5 1.472 1.525 .053

251.0 1.677 1.753 .076

250.5 1.901 2.003

250.0 2.144 2.276

249.5 2.410 2.572

249.0 2.698 2.892

248.5 3.012 3.237

248.0 3.350 3.606 .256

247.5 3.713 4.OOO

247.0 4 .102 4 .420

246.5 4 .518 - 4 .866

246.0 4 .961 5.338

245.5 5.435 5.836

245.0 5.943 6.360

244.5 6.486 6.911

244.0 7.OBO 7.487

243.5 7.670 8.091

243.0 8.303 8.720

242.5 8.998 9.375

242.0 9.722 10.056

241.5 10.489 10.763

241.0 11.299 11.495 .196

'240.5 12.164 12.252 .088

240.174 12.759 12.759

.102

.132

.162

.194

.225

.287

.318

.348

.377

.401

.417

.425

.427

.421

.417

.377 •

.334

.274

- 37 -

T A B L E V

V A P O R P R E S S U R E O F n - H ^

log P^ '-^ - 5 8 . 3 3 6 5 / T + 2.86244

t. °C. P . , a t m . P^, a t m

- 2 5 2 . 7 7 1.000 1.000

252.50 1.080 1.090

252.00 1.241 1.271

251.50 1.421 ^ 1.472

251.00 1.620 1.693

250.50 1.838 1.936

250.00 2.075 2.200

249.50 2.334 2 .488

249.00 2.616 2.798

248.50 2.920 3.132

248.00 3.244 3.491

247.50 3.597 3.874

247.00 3.974 4 .282

246.50 4 .375 4 .715

246.00 4 .803 5.173

245.50 5.260 5.657

245.00 5.749 b . i 6 7

244.50 6.273 6.703

244.00 6.830 7.264

243.50 7.423 7.851

243.00 8.048 8.464

242.50 8.705 9.102

242.00 9.403 9.765

241.50 10.146 10.454

241.00 10.927 11.167

240.50 11.765 11.905

240 00 12.641 12.667

2 3 9 . 9 i b 12.797 12.797

- 3 8 -

T A B L E VI

V A P O R P R E S S U R E O F HD

log P,^ = - 6 7 . 2 8 4 8 / T -f- 3.04002 is.

t, "C. p . , a t m . P , , , a t m . d, a t m , 1 K

-251.017 1.000 1.000 .000

250.5 1.159 1.173 .014

250.0 1.331 ^ 1.360 .029

249.5 1.522 1.567 .045

249.0 1.732 1.794 .062

248.5 1.960 2.044 .084

248.0 2.208 2.31r .108

247.5 2.477 2 . 6 1 i .134

247.0 2.769 2 .931 .162

246.5 3.085 3.275 .190

246.0 3.428 3.646 .218

245.5 3.796 4 .042 .246

245.0 4 .191 4 .465 .274

244.5 4 .613 4 .915 .302

244.0 5.064 5.394 .330

243.5 5.543 5.898 .355

243.0 6.054 6.432 .378

242.5 6.596 6.994 .398

242.0 7.172 7.586 .414

241.5 7.784 8.206 .422

241.0 8.431 8.855 .424

240.5 9.117 9.533 .41b

240.0 9.841 10.240 .399

239.5 10.609 10.977 .368

239.0 11.420 11.742 .322

238.5 12.280 12.536 .256

238.0 13.187 13.360 .173

^37.5 14.152 14.212 .060

237.252 14.645 14.645 .000

-39 -

TABLE VII

VAPOR PRESSURE OF eq-D^

- 7 4 . 8 8 0 1 / T 4- 3.16926

t. "C.

-249 .523

249.5

249.0

248.5

248.0

247.5

247.0

246.5

246.0

245.5

245.0

244.5

244.0

243.5

243.0

242.5

242.0

241.5

241.0

240.5

240.0

239.5

239.0

238.5

238.0

237.5

237.0

^36.5

25b.0

235.5

235.0

234.898

l o g P j ,

P , a t m

1.000

1.005

1.159

1.329

1.518

i .724

1.951

2.198

2.4b8

2.757

3.070

3.406

3.742

4 .159

4 .577

5.023

5.498

6.005

6.545

7.117

7.726

8.370

9.054

9.775

10.536

11.335

12.180

13.074

14.017

15.015

l b .059

16.282

P R

2

2

2

2

3

3.

3,

4

4,

5.

5.

6.

6,

7.

8.

8.

,, a t m

.000

.007

.171

.354

.556

.778

.022

.288

.578

.891

.230

.595

.958

.403

.849

.323

.826

.359

.921

,513

, 1 3 D

790

9.475

10.

10.

1 1 .

12.

13.

14.

15.

16.

191

939

718

528

570

244

150

087

16.282

- 4 0 -

T A B L E VIII

V A P O R P R E S S U R E O F n - D ^

log P^ = - 7 5 . 1 3 5 7 / T + 3 .17564

t, °C. P . , a t m . P..., a t m . d, a t m .

1 xS.

- 2 4 9 . 4 9 1.000 1.000 .000

249.0 1.149 1.160 .011

248.5 1.318 1.341 • . .023

248.0 1.506 1.542 ' .036

247.5 1.713 ' 1.763 .050

247.0 1.938 2.006 .068

246.5 2.185 2 .271 .086

246.0 2.450 2.560 .110 245.5 2.739 2.872 .133

245.0 3.051 3.210 .159

244.5 3.388 3.574 .186

244.0 3.750 3.964 .214

243.5 4 .138 4 .381 .243

243.0 4 .554 4 .826 .272

242.5 5.000 5.300 .300

242.0 5.475 5.802 .327 241.5 5:981 6.334 . : i o j

241.0 6.518 6.896 3 78

240.5 7.089 7.488 .399

240.0 7.695 8.112 .417

239.5 8.338 8.766 428

239.0 9.018 9.451 .433

238.5 9.740 10.168 .428

238.0 10.502 10.916 .414

237.5 11.308 11.696 .388

237.0 12.157 12.508 .351

236.5 13.054 13.352 .298

236.0 13.991 14.228 .237

235.5 . 14.986 15.136 .150

235.0 16.034 16.075 .041

234.82 16.421 16.421 .000

- 4 1 -

2. Neon

The boiling point and cr i t ica l -point data used in computing the deviation

curve for neon were taken from Grilly (44). The v a p o r - p r e s s u r e data used

in computing the deviation curve were kindly supplied to us in a pr ivate com

munication by Dr . Gri l ly. Gr i l ly ' s data agree with the deviation curve to

±0.001 a tm. in the low p r e s s u r e region and ±0.01 a tm. at p r e s s u r e s above

10 a tm. The deviation curve for neon is given in F igure 10.

(44) Gril ly, E. R. , Cryogenics 2, 226 (1962).

0.7

0.6

- 0 . 5

D O . 4

"^ 0.3

0.2

0.1

0

Ne

— • — - •

-246.06 -244

^

^ ^ ^ ^

^ ^ ^ ^ - " ^ ' ' ^ ^

-z^

^ ' s

-2^6

—

—

X -\ -

V J

-232228.75

T e m p ( ° C ) 1 1

0 GLL-637-1703

20 4 0 60 7o l / T

80 100

F i g . 10. Dev ia t i on c u r v e for N e .

-44-

3. Nitrogen

Since 1926 severa l invest igators (12, 27, 30, 74, 94) have measu red

the vapor p r e s s u r e of nitrogen above 1 a tm. , and the d i sagreement between

them shown by Figure 11 is not as ser ious as repor ted by Michels . More

over, F r i edman and White's c r i t ica l point values (31) a r e in good agreement

with his v a p o r - p r e s s u r e data and also with Michels ' r e s u l t s . Therefore , we

have selected a c r i t i ca l t empera tu re of -146.93°C. to fit the c r i t i ca l p r e s

sure of 33.54 a tm. as given by F r i edman and White (31), A boiling point of

-195.78*'C. has been selected as best fitting our deviation curve . This is

in good agreement with the resu l t s of Dodge and Giauque and Clayton (36).

Armst rong (5) has repor ted a value of -195.796°C.

In view of the demonst ra ted over -a l l high prec is ion of Michels ' m e a

su remen t s , and since his points most closely fit the expected course of the

deviation curve , we have used his data to locate our curve . In addition, his

r esu l t s appear to r ep re sen t a good mean value. The prec is ion of F r i e d m a n ' s

points appears to be equally good, with a sys temat ic difference of about

-0.04 a tm. between -180 and -158' 'C. F r i e d m a n ' s point at -147.63 "C. is

apparently in e r r o r , as a r e Dodge's data in the neighborhood of -151°C.

(12) Bloomer , O. T. , and Paren t , J . D. , Inst. Gas. Techn. Tes . Bull.

n , (1952).

(27) Dodge, B. F . , and Davis , H. N. , J . Am. Chem. Soc. 49, 610 (1927).

(30) F r i edman , A. S. , and White, D. , J . Am. Chem. Soc. 72, 3931 (1950).

(74) Michels , A . , Wassenaar , T. , DeGraaf, W. , and P r i n s . , C h r . , Physica

19, 26 (1953).

- 4 3 -

T A B L E IX

VAPOR PRESSURE O F Ne

log P ^ = - 9 8 . 5 6 1 4 / T + 3.63803

t . "C

- 2 4 6 . 0 5 8

2 4 6 . 0

2 4 5 . 5

2 4 5 . 0

2 4 4 . 5

2 4 4 . 0

2 4 3 . 5

2 4 3 . 0

2 4 2 . 5

2 4 2 . 0

2 4 1 . 5

2 4 1 . 0

2 4 0 . 5

2 4 0 . 0

2 3 9 . 5

2 3 9 . 0

2 3 8 . 5

2 3 8 . 0

2 3 7 . 5

2 3 7 . 0

2 3 6 . 5

2 3 6 . 0

2 3 5 . 5

2 3 5 . 0

2 3 4 . 5

2 3 4 . 0

2 3 3 . 5

2 3 3 . 0

2 3 2 . 5

2 3 2 . 0

2 3 1 . 5

2 3 1 . 0

2 5 0 . 5

2 3 0 . 0

2 2 9 . 5

2 2 9 . 0

2 2 8 . 7 5

P , , a t m .

1.000

1.017

1.178

1.359

1.559

1.780

2 . 0 2 3

2 . 2 9 0

2 . 5 8 3

2 . 9 0 3

3 . 2 5 1

3 . 6 2 6

4 . 0 2 8

4 . 4 6 3

4 . 9 2 9

5 . 4 3 2

5 . 9 7 1

6 . 5 5 0

7 . 1 6 8

7 . 8 2 7

8 . 5 2 7

9 . 2 7 2

1 0 . 0 6 2

1 0 . 8 9 9

1 1 . 7 8 6

1 2 . 7 2 5

1 3 . 7 1 6

1 4 . 7 6 0

1 5 . 8 5 7

1 7 . 0 0 9

1 8 . 2 2 2

1 9 . 5 0 1

2 0 . 8 5 3

2 2 . 2 8 4

2 3 . 7 9 6

2 5 . 3 7 5

2 6 . 1 9 3

P j ^ , a t m .

1.000

1.018

1.184

1.370

1.577

1.806

' 2 . 0 6 0

2 . 3 3 9

2 . 6 4 4

2 . 9 7 8

3 . 3 4 1

3 . 7 3 6

4 . 162

4 . 6 2 2

5 . 1 1 7

5 . 6 4 8

6 . 2 1 6

6 . 8 2 4

7 . 4 7 0

8-. 158

8 . 8 8 7

9 . 6 6 0

1 0 . 4 7 6

1 1 . 3 3 7

1 2 . 2 4 4

1 3 . 1 9 8

1 4 . 1 9 8

1 5 . 2 4 8

1 6 . 3 4 5

1 7 . 4 9 3

18 .690

1 9 . 9 3 8

2 1 . 2 3 7

2 2 . 5 8 8

2 3 . 9 9 0

2 5 . 4 4 5

2 6 . 1 9 3

d , atnn

. 0 0 0

. 0 0 1

. 0 0 6

. 0 1 1

.0 18

. 0 2 6

. 0 3 7

. 0 4 9

. O o l

. 0 7 5

. 0 9 0

. 1 1 0

. 134

. 1 5 9

. 1 8 8

. 2 1 o

. o 4 5

.274

. 5 0 1

: : 1

3 D C

5 8 8

.4 14

4 5 8

. 4 5 8

4 7 5

4 8 2

. 4 8 8

4 8 8

. 4 8 4

. 4 6 8

. 4 3 7

. 3 8 4

. 3 0 4

. 1 9 4

.0 70

. 0 0 0

-45 -

(94) P o r t e r , F . , and P e r r y , J . H. , J . Am. Chem. Soc. 48, 2059 (1926).


(36) Giauque, W. F . , and Clayton, J . O. , J . Am. Chem. Soc. 55, 4875

(1933).

(5) Arms t rong , G. T. , J . Res . Natl. Bur . Std. 53, 263 (1954).

0.40

E 30.20 TO

0

GLL-633-441A

1

-

—

"

~

-

"C

1 1 1 1 1

N2

* Michels • Porter • Friedman • Dodge ' Giauque 0 Bloomer

« f *

Boiling point

1 1 1 1 1 1

1 1

«

• • — • •

1 1 1

1

•

^^^^

\

\

0

•

^—*

1 1

1 1 1

• •

• * . • • /

• / m D • /

j/^ •

1 i 1 1

1

*

/

•

1

1

• «

y /

1

1

*

^ • • •

1

I I I I •

•

V

\

\»

\ •

\

• \

\ Critical point^..\

1 1 1 1 1 1

—

-

-

-

-

-190 -180 -170 t(°c)

-160 150 144

r

I

F i g . 11 . D e v i a t i o n c u r v e for N2 vs t ^ C .

- 4 7 -

T A B L E X

VAPOR P R E S S U R E O F N^

log P = - 3 0 4 . 9 1 3 / T + 3.94097

t, "C. P . , a t m . PT^J a t m . d, a t m 1 K

195.78 1.000 1.000 .0

194 1.226 1.226 .0

192 1.526 1.526 ' ,0

190 1.879 1.879 .0

188 2 .291 , 2 .291 ' .0

186 2.769 2.769 . . .0

184 3.3 17 3.317 ,, .0

182 3.943 3.943 .0

180 4 .651 4 .652 T O . 0 0 1

178 5.435 5.450 .015

176 6.306 6.344 .038

174 7.276 7.340 , 0 D 4

172 8.352 8.443 .091

170 9.540 9.659 .119

168 10.844 10.994 150

166 12.269 12.454 185

164 13.822 14.043 221

162 15.510 15.766 . 2 5 D

160 ,17.342 17.628 v 286

158 19.326 19.634 .308

156 21 .471 ' 21 .788 .317

154 23.790 24.094 .304

152 26.295 26.555 „ .^oO

150 ' 28.999 29.176 .177

14~9 30.426 30.547 .121

148 ' 31.905 31.959 - 0 . 0 5 4

147 33.432 33.412 . • - 0 . 020

146.93 33.542 33.515 - 0 . 0 2 7

- 4 8 -

4. Carbon Monoxide

The deviation curve for carbon monoxide shown in Figure 12 is based

on the data of Michels et a l . (76). The curve agrees with the data to within

0.001 a tm. The boiling point is taken as -191.48' 'C. as de termined by

Giauque and Clayton (35). The deviation curve appears to be in excellent

agreement with the cr i t ica l data of Mathias and Crommel in (68).

(76) Michels , A, , Wassenaar , T. , and Zwietering, Th. N. Physica 18,

160 (1952).


(1932),

(68) Mathias , E. , and Crommel in , O. A , , Ann. Phys . 5, 137 (1936),

0.4

0.3

E 0.2

So.)

CO

• Michels • Giauque

1 1 -191.481 -185

1 1

1 -180

1

1 1 1 -175 -170 Temp (X )

1 1 1

1 -160

1

^"A-\ -

^

1 1 1 - I 50H40 .23

1

I

20 40 60 80 100

GLL-637-1705 % l/T

Fig . 12. Deviation curve for CO.

-RO

T A B L E XI

V A P O R P R E S S U R E O F CO

log P ^ fe - 3 2 5 . 8 J 3 / T + 3.98938

t . "C. P . , a t m . P , a t m . d, a t m . is.

191.48 1.000 1.000 .0

190 1.183 1.178 - 0 . 0 0 5

188 1.466 1.45b .010

186 1.798 ^ 1.782 .016

184 2.179 2 .161 .018

182 2.620 2.600 .020

180 3.120 3.102 .018

178 3.686 3.674 .012

176 4 .324 4 .322 - 0 . 0 0 2

174 5.042 5.050 +0.008

172 5.845 5.865 .020

170 6.734 6.772 038

168 7.716 7.777 Ool

166 8.797 8.885 .088

P . , a t m

1.000

1.183

1.466

1.798

2.179

2.620

3.120

3.686

4 .324

5.042

5.845

6.734

7.716

8.797

9.982

11.280

12.692

14.228

15.892

17.692

19.634

21 .727

23 .981

26 .413

29.034

30.416

31 .853

33.346

34.529

164 9.982 10.101 .119

162 11.280 11.431 151

160 12.692 , 12.880 .188

158 14.228 14.452 .224

156 15.892 16.152 2 D 0

154 17.692 17.985 .293

152 19.634 19.955 .521

150 21 .727 22.066 339

148 23 .981 24.322 .341

146 26 .413 26.727 314

144 29.034 29.284 .250

143 30.416 30.621 .205

142 31 .853 31.996 .143

141 33.346 33.412 .066

140.23 34.529 34.529 .0

- 5 1 -

5. Argon

The deviation curves shown in Figure 13 a r e based on the measu remen t s

of Michels and Levelt (72) and Michels , Wassenaar and Zwietering (21) and on

measu remen t s by Clark, Din and Robb also repor ted in reference (21). The

boiling point of -185.91'*C. is repor ted by Michels (21) and the c r i t i ca l point

of -122.29'*C. and 48.34 a tm. is repor ted by Michels (72). Michels ' vapor-

p r e s s u r e data (72) from 10 a tm. to the c r i t i ca l point lie between his data (72)

and Clark ' s data (21) with a var iat ion of about 0,01 a tm. We have harmonized

Michels ' l a te r h igh -p re s su re data with his ea r l i e r resu l t s to obtain our p r e

fe r red vapor p r e s s u r e s given in Table XII. Michels ' c r i t i ca l constants a r e in

good agreement with the deviation curve . Crommel in (26) has repor ted the

cr i t ica l point to be -122.44' 'C. and 47.996 a tm.

(72) Michels , A . , and Levelt , J . M. , Physica 24, 659(1958).

(21) Clark , A. M. , Din, F , , Robb, J . , Michels , A . , Wassenaar , T, , and

Zwieter ing, Th. N. , Physica 17, 876 (1951).

(26) Crommel in , C. A, , Koninkl. Ned. Akad. Wetenschap. P r o c . Ser . B

22, 1212 (1913) Leiden Comm. Nos. 115a, 138c, 140a.

0.7

0.6

0.5

0.4

^ 0 . 3

d (a

tr

o

P

_

Ar

-

-

-

-

1 -185.91 -180

1 1

C l a r k ^ ^

^

. . . . ^

1 i l l ! -170 -160

Temp (°C) 1 1 1 1

^^//

'^ M̂ ichels

1 1 1 1 -150 -140

1 1

-X _

\ Y \ v \ -

\ -

(

1 1 -122.29

1 0

GLL-637-1706A 20

1

I

40 60 % l /T

Fig . 13. Deviation curve for Ar .

80 100

- 5 3 -

TABLE XII

VAPOR PRESSURE OF Ar

log P j^ = - 3 4 8 . 4 3 2 / T + 3.99395

t , °C. P . , a t m . P ,^ , a t m . d, a t m . 1 is

- 1 8 5 . 9 1

184

182

180

178

176

174

172

170

168

166

164

162

160

158

156

154

152

150

148

146

144

142

140

138

136

134

132

130

128

126

125

124

123

122.29

1.000

1.218

1.484

1.790

2.144

2 .545

3.000

3.513

4 .087

4 .729

5.444

6.232

7.099

8.049

9.085

10.212

11.438

12.766

14.201

15.749

17.415

19.204

21 .119

23 .169

25 .357

27 .687

30.169

32.818

35 .638

38 .631

41 .821

43 .493

45 .227

47 .020

48 .340

1.000

1.218

1.484

1.792

2 .148

2.555

3.018

3.542

4 .131

4 .789

5.522

6.334

7.230

8.214

9.291

10.464

11.739

13.119

14.609

16.212

17.932

19.773

21 .737

23 .829

26 .052

28 .407

30 .899

33.530

36 .301

39 .215

42 .275

43 .859

45 .481

47 .140

48 .340

.0

.0

.0

.002

.004

.0 10

.018

.029

.044

.060

.078

.102

.131

.165

.206

.252

.301

.353

.408

.463

.517

.569

.618

.660

.695

.720

.730

.712

.663

.584

.454

.366

.254

.120

.0

-54-

6. Oxygen

The work of Hoge (50) is considered to be definitive. We have, however,

p repa red a deviation curve based on an ice point of 273.15°K. as compared

to his ice point of 273.16 "K. Hoge has mathemat ical ly fitted his data very

well by connecting separa te equations for each of five tennperature regions .

Our deviation curve shown in F igure 14 r ep resen t s an accuracy within 0.001

a tm. For a c r i t i ca l d iscuss ion of other measu remen t s on oxygen see Hoge's

paper .

(50) Hoge, H. J . , J . Res . Natl. Bur. Std. 44, 321 (1950).

" I—r T r

0 6 0 -

0 4 0 -

E a.

0 2 0 -

Boiling point

I I I I I L

"I I I 1 I } T

-180 -170 J L J L J L J L

160 -150 -140

t(°c) 130

I

I

_U^J \ I L -120 -122 -120 -118

Fig . 14. Deviation curve for O2 vs f C .

- 5 6 - '

T A B L E XIII

V A P O R P R E S S U R E O F Oi

log Pj^ = - 3 6 7 . 3 9 0 / T -f- 4 .07396

I. "G. p . , a t m . Fi^, a t m . d, a t m .

- 1 8 2 . 9 7 1.000 1.000 .0

182 1.105 1.105 .0

180 1.350 1.349 - 0 . 0 0 1

178 1.633 1.632 - 0 . 0 0 1

176 1.960 1.9faO .0

174 2.334 2.336 -fO.002

172 2.760 ^ 2.766 .006

170 3.241 3.253 .012

168 3.780 3.802 .022

166 4 .384 4 .418 .034

164 5.055 5.106 .051

162 5.800 5.870 .070

160 6.623 6.715 .092

158 7.526 7.646 .120

156 8.514 8.668 .154

154 9.594 9.784 .190

152 10.771 11.001 230

150 12.049 12.322 .273

148 13.431 13.752 . .321

146 14.923 15.295 .372

144 16.528 16.954 ,42b

142 18.255 18.735 .480

140 20 .111 20 .641 .530

138 22 .098 22.676 .578

136 24 .224 24.844 .620

134 26.492 27.147 .655

132 28.911 29.589 .678

130 31.486 32.173 .687

128 34 .228 34.902 .674

126 37.147 37.779 .632

124 40 .255 40 .807 .552

122 43 .562 43 .987 .425

121 45 .300 45 .636 .336

120 47 .091 47 .323 .232

119 48 .951 49 .049 +0.098

118.38 50.140 50.139 - 0 . 0 0 1

- 57 -

7. Methane

The v a p o r - p r e s s u r e data repor ted up to 1955 have been cor re la ted by

Arms t rong , Brickwedde, and Scott (6). Since then Hes te rmans and White

(47) have made additional m e a s u r e m e n t s . Along with Arms t rong , Brickwedde,

and Scott 's smoothed va lues , we have presented in F igure 15 the exper imental

measu remen t s of Keyes, Taylor, and Smith (61), Bloomer and Pa ren t s (12),

and Hes te rmans and White. Bennewitz and Andreev (9) have determined only

the cr i t ica l point. Between -162 and -96*'C. Bloomer and P a r e n t ' s resu l t s

a r e in good agreement with A r m s t r o n g ' s cor re la t ion and with A r m s t r o n g ' s

boiling point value of - l 6 l . 4 9 ' ' C . We have given preference to Bloomer ' s

data in drawing the deviation curve because they follow the common fine-

s t ruc tu re pa t te rn . Hes t e rman ' s and White's values general ly para l le l those

of Bloomer and Pa ren t with a p r e s s u r e difference of -0.04 a tm.

Keyes, Taylor, and Smith's data tend to cor robora te A r m s t r o n g ' s and

Bloomer ' s values at lower t e m p e r a t u r e s , but between -96"'C. and the c r i t i ca l

point, the situation is confused. Here A r m s t r o n g ' s cor re la t ion d iverges con

siderably from the exper imental m e a s u r e m e n t s of Bloomer and of H e s t e r m a n s .

This is due most ly to the fact that Arms t rong has used Keyes ' da ta , which ap

pear to be inaccurate in this region, and possibly part ly to the fact that his

type of equation was not sufficiently flexible to produce the curva ture required

to reach the c r i t i ca l point. Arms t rong has recognized in his paper that his

cor re la t ion in the kc region did not fit the accepted c r i t i ca l value, but Bloomer

and P a r e n t ' s data were not available at the t ime of Arms t rong ' s publication.

Three exper imental measu remen t s of the cr i t ica l t empera tu re a r e in fairly

good agreement , as shown in F igu re 15; those of Keyes, Bloomer , and

Bennewitz. It appears to us that B loomer ' s c r i t i ca l t empera tu re of -82.61 "C.

and the corresponding p r e s s u r e of 45.49 a tm. as indicated by the deviation

- 58 -

curve is a good value for the cr i t ica l point. B loomer ' s c r i t i ca l p r e s s u r e is

45.47 a tm. In the light of Hes t e rmans ' and Bloomer ' s data, Kobe and Lynn's

(63) selected value of -82.1 ' 'C. and 45.8 a t m . , which is based on Keyes ' ca l -

culated p r e s s u r e value, is not well founded and indeed confuses the m a t t e r ,

in spite of a seeming numer ica l s imi la r i ty , since in real i ty , this p r e s s u r e is

0.40 a tm. low at the stated t e m p e r a t u r e .

This point is worth emphasizing s ince , had Hes t e rmans ' and Bloomer ' s

m e a s u r e m e n t s not been avai lable , a deviation curve based on Keyes ' vapor-

p r e s s u r e measu remen t s would be so radically different as to c lass methane

with nitrogen and carbon monoxide instead of with oxygen and the noble gases .

(6) Arms t rong , G. T. Brickwedde, F . G. , and Scott, R. B. , J . Res .

Natl. Bur . Std. 55, 39 (1955).

(47) Hes t e rmans , P . , and White. P . , J . Phys . Chem. 65, 362 (1961).

(61) Keyes, F . G. , Taylor , R. S. , and Smith, L. B. , J . Math. Phys . 1,

211 (1922).

(12) Bloomer , O. T. , and Pa ren t , J . D. , Inst. Gas. Techn. Res . Bull.

17 (1952).

(9) Bennewitz, K. , and Andreev, N. , Z. Physik Chem. , AL42, 37 (1929).

(63) Kobe, K, A . , and Lynn, R. E. , J r . , Chem. Rev. 52, 117(1953).

0 80 —

0 6 0

50 40 —

020 —

-160

GLL-633-^^B

^I30 H20 Temperature (°c)

I

I

Fig . 15. Deviation curve for CH4. vs f C .

-60-

TABLE XIV

VAPOR PRESSURE OF CH4

t, ° c .

- 161.49

160

158

156

154

152

150

148

146

144

142

140

138

136

134

132

130

128

126

124

122

120

118

116

114

112

110

108

106

104

102

100

98_

96

94

92

90

89

88

87

86

85

84

83

82 .61

log P ^ =

P j , a t m .

1.000

1.129

1.322

1.541

1.786

2 .054

2 .353

2 .686

3.054

3 .459

3.904

4 . 3 9 1

4 . 9 1 5

5.474

6 .079

6 .734

7 .445

8 .210

9.032

9 .906

10.838

11 .836

12.898

14 .029

15 .229

16 .501

17 .847

19 .268

2 0 . 7 6 0

2 2 . 3 3 4

2 3 . 9 9 4

2 5 . 7 4 4

2 7 . 5 8 8

2 9 . 5 2 7

3 1 . 5 9 1

3 3 . 7 2 3

3 5 . 9 9 2

3 7 . 1 7 1

3 8 . 3 8 2

3 9 . 6 2 9

4 0 . 9 0 4

4 2 . 2 1 3

4 3 . 5 5 7

4 4 . 9 3 8

4 5 . 4 9 0

- 4 4 7 . 2 5 9 / T + 4 . 0 0 5 5 4

P j ^ , a t m .

1.000

1.129

1.322

1.54 1

1.786

2 .059

2.>364

2 .702

3 .076

3 .487

3 .938

4 . 4 3 1

4 . 9 6 8

5 .552

6 .185

6 .868

7 .606

8 . 3 9 8

9 .248

10 .158

11.130

12.166

13 .267

14 .437

15 .676

16 .987

18.371

19 .831

2 1 . 3 6 7

22 .982

2 4 . 6 7 6

26 .452

2 8 . 3 1 2

3 0 . 2 5 5

3 2 . 2 8 3

3 4 . 3 9 9 36 .602

3 7 . 7 3 7

38 .894

4 0 . 0 7 4

4 1 . 2 7 6

4 2 . 5 0 1

4 3 . 7 4 9

4 5 . 0 2 0

4 5 . 5 2 2

d , at2-i-i.

.0

.0

.0

.0

.0

.005

.011

.016

.022

. 028

.034

.040

.053

.078

.106

.134

.161

. 188

.216

.252

.2 92

.330

.3 69

.408

.447

.486

.524

.563

. 6 0 7

.648

.682

.708

.724

. 728

.692

.676

.610

.566

.512

.445

.372

.288

.192

.082

.032

- 6 1 -

8. Nitric Oxide

No h i g h - p r e s s u r e m e a s u r e m e n t s have been made on ni t r ic oxide since

Adwentowski's (2) work in 1909. This is su rp r i s ing , since analysis of his r e

sults indicates that this work fails ser ious ly to mee t modern s tandards of p r e

cision for purity of sample , measu remen t of t empera tu re and p r e s s u r e , and

at tainment of p r e s s u r e and t empera tu re equi l ibr ium. Our deviation curve

shown in Figure 16 is based on Johnston and Giauque's (56) determinat ion of

the boiling point and Adwentowski 's value for the cr i t ica l point. Adwentowski'

data can in no sense be said to de te rmine the deviation curve since alnnost

60% of them do not exhibit any expected consis tent behavior. Never the less ,

a deviation curve consistent with his c r i t i ca l point can be reasonably drawn

through some of his data , this has been done in F igure 16. No conclusions

can be drawn as to the accuaracy of our proposed v a p o r - p r e s s u r e values or

Adwentowski's repor ted cr i t ica l point, and certainly the need for a r e d e t e r

mination of this vapor p r e s s u r e is dictated.

(2) Adwentowski, K. , Intern. Bull. Acad. Sci. Cracovie LLllOg, 742.

(56) Johnston, H. L. , and Giauque, W. F . , J . Am. Chem. Soc. 5j., 3194

(1929).

3-1 3

1.0

0 .8

0 .6

0 . 4

0 .2

0 .2

0 .4

0 .6

—

-

-

—

-

-

-1

151

N O

. 7 4

1

1 1 -140

1 1

• A d w e n t o w s k i

• Gia uque

1

1

_ _ ^

1 -130

T e m p

X

(

L

y X

1

°C)

•

y /

1 -120

1

^

J ^

•

1 1 -110

1 1

— ^ ^ ^

^ V

\

\

]

1 1 -100 - 9 2 . 9

1 1 0 10

GLL-637-1709

20 30 40 60 50

% l / T

F i g . 16. D e v i a t i o n c u r v e fo r NO.

70 80 90 100

I

- 6 3 -

T A B L E XV

V A P O R P R E S S U R E O F NO

leg ^ „ ^ . e ? 3 . 2 7 3 / T + S.S4545

t ,

151.

150

145

140

135

130

125

120

115

110

105

100

95

9 2 .

"C.

74

9

P . , a t m .

1.00

1.23

2.09

3.33

5.00

7.18

10.04

13.81

18.84

25 .41

33.86

44 .53

57.97

64.60

P „ , a t m .

1.00

1.20

1.96

^ 3.08

4.70

6.95

10.02

14.10

19.42

26.23

34.79

45.40

58.37

64.60

d, at:

.0

- 0 . 0 3

. 1 3

. 2 5

. 30

. 2 3

- 0 . 0 2

+0.29

. 5 8

. 8 2

. 9 3

. 8 7

. 40

0

•

- 6 4 -

9. Krypton

The v a p o r - p r e s s u r e deviation curve for krypton shown in F igure 17 is

based on the work of Michels , Wassenaar , and Zwietering (75). The data

ag ree with the deviation curve to within 0.001 a tm. The cr i t ica l t empe ra

ture of Meihuizen and Crommel in (69) of -63.77' 'C. is taken, and the cr i t ica l

p r e s s u r e corresponding to this t empera tu re is 54.31 a tm. This is in good

agreement with Meihuizen's value of 54.270 a tm. The boiling point is due to

Michels (75).

(75) Michels , A . , Wassenaar , T. , and Zwietering, Th. N. , Physica 18

63 (1952).

(69) Meihuizen, J . J . , and Crommel in , C. A. Physica 4, 1 (1937).

0.9

0.8

0.7

0.6

0.5

0.4

I 0.3 o

" " 0.2 •o

0.1

0

Kr

• — • -

-153.401

GLL-637-1710

- • ^

I - 1 4 0

20

I

(Jl

J--130

Temp («C) -no - 9 0

' . ' -63.77

40 60 80 100 % l/T

Fig . 17. Deviation curve for Kr.

-66-

T A B L E XVI

VAPOR PRESSURE O F Kr

log 1 ' , , - - . iM ' i . , ' . iM/ ' i ' I d .O ' ian i

U 'C.

- IS i . - lO

I S i

ISO

148

146

144

142

140

138

136

134

132

130

128

126

124

122

120

I I H

116 114

112

1 10

108

106

104

102

100

98

96

94

92

90

88

86

84

82

80

78

76

74

72

70

68

67

66

65

64

63. 77

P-, a t m .

1.000 1. i 14

1.2 94

1.4 96

1.720

1.969

2.245

2.549

2.883

3.249

3.649

4.084

4.554

5.062

5.611

6.203 6.838

7.521

8.247 9.024

9.857

10.745

11.690

12.695

13.754

14.876

16.062

17.319

18.639

20 .028

21 .485

23 .017

24 .625

26.313

28 .080

29.934

31 .877

33.915

36.047

38.274

40 .603 43 .034

45 .577

48 .226

49 .599

51.015

52.473

53.960

54.306

PpQ, a t m .

1.000

1.114

1.294

1.496

1.72 1

1.972

2.250

2.557

2.895

3.266

3.672

4 .115

4 .596

5.118

5.682

6 .291 6.946

7.651

8.405 9.212

10.073

10.989 11.964

12.999

14.095

15.254

16.478

17.769

19.127

20 .556

22.055

23.627

25.273

26.995

28.793

30.669

32.624

34.660

36 .777

38.976

41 .259 43 .626

46 .078

48 .616

49 .917

51.240

52.585

53.952

54.270

cl. ;itn\

.0

.0

.0

.0

.001

.003

.005

.008

.012

.017

.023

.031

.042

.056

.071

.088

.108

.130

.158

. 188

.216

.244

.2 74

.304

.341

.376

.416

.450

.488

.528

.5 70

.610

.648

.682

.713

.735

.747

.745

.730

.702

.656

.592

.501

.390

.318

.225

f 0 . 1 1 2

- 0 . 0 0 8

- 0 . 0 3 6

-67 -

10. Xenon

The deviation curve for xenon shown in F ig . 18 is based on the data

of Michels and Wassenaar (73). The data ag ree with the curve within 0.001

a tm. Pa t t e r son , Cr ipps , and Whytlaw-Gray (89), and Weinberger and

Schneider (113) have both found the cr i t ica l t empe ra tu r e to be 16.59"'C.

The corresponding vapor p r e s s u r e from our cruve is 57.64 a tm. Habgood and

Schneider (45) have reported the c r i t i ca l p r e s s u r e to be 57.636 a tm. The boil

ing point is due to Michels (73).

(73) Michels , A . , and Wassenaar , T. , Physica ^ , 253 (1950).

(89) Pa t t e r son , H. S. , Cr ipps , R. S. , and Whytlaw-Gray, R. , P r o c . Roy.

Soc. (London) A86, 579 (1912).

(113) Weinberger , M. A . , and Schneider, W. G. , Can. J . Chem. 30, 422

(1952).

(45) Habgood, H. W. , and Schneider, W. G. , Can. J . Chem. 32, 98 (1954).

0.9

0.8

0.7

0.6

0.5

04

I 0.3 o

0.1

0

Xe

-105.121-iooT

" • 9r

I

00 I

:i ^̂ 8D^ X

Temp (*'C) -40

J L -20

I . I 0 116.59

20 40 1 60 80 100

GLL-637-1711 % I /T

Fig . 18. Deviation curve for Xe.

- 6 9 -

I. 'C

108.12

108

106

104

102

100

98

96

94

92

90

88

86

84

82

80

78

76

74

72

70

68

66

64

62

60

58

56

54

52

50

48

46

44

42

40

T A B L E XVII

V A P O R P R E S S U R E O F Xe

log Pj^ = - 6 7 4 . 9 7 4 / T + 4 .09000

P i , a t m . P j^ , a t m . d, a t m .

1.000 1.000 .0

1.007 1.007 .0

1.128 1.127 - 0 . 0 0 1

1.260 1.258 .002

1.403 1.400 .003

1.559 1.555 .004

1.728 ' 1.723 .005

1.910 1.905 .005

2.106 • 2 .101 .005

2.317 2.312 .005

2.541 2.539 - 0 . 0 0 2

2.783 2.783 .000

3.041 3.044 +0.003

3.316 3.323 .007

3.609 3.621 .012

3.922 3.940 .0 18

4.254 4 .278 .024

4.608 4 .638 .030

4.984 5.020 .036

5.381 5.425 .044

5.801 5.854 .053

6.243 6.307 .Ob4

6.710 6.786 .076

7.203 7.291 .088

7.720 7.822 .102

8.265 8.382 .117

8.836 8.970 .134

9.435 9.587 .152

10.062 10.234 .172

10.720 10.912 .192

11.407 11.621 ^ .214

12.125 12.363 .238

12.874 13.137 .263

13.658 13.946 .288

14.475 14.789 .314

15.323 15.667 .344

- 70 -

TABLE XVII (Continued) P , atm.

1 16.205

17.1 19

18 0 74

19.067

20.099

21.170

22.282

23.434

24.D2O

25.861

27.140

28.464

29.836

31.255

32.722

54.236

35.801

37.416 39.082

40.802

42.584

44.425

45.367

46.326

47.299

48.288

49.295

5C.325

51.372

52.450

53.546

54.660

55.793

56.950

57.639

P , atm.

16.58J

17.'̂ ^ 1

18.519

19.544

20.608

21.711

2^.854

24.038

25.2o2

26.528

27.836

29.186

30.580

32.017

33.498

35.024

36.595

38.212 39.875

41.584

43.340 Hi

45.143

46.062

46.994

47.937

48.892

49.859

50.839

51.830

52.834

53.850

54.878

55.919

56.972

57.599

d, atn

3 76

1 1..

44 S

4"? .5 0'"̂

o4

57„

D04

>36

^ D07

o96

.7^2

.744

.762

.77o

.788

.794

.796

.793

782

.756

.7 18

.o95

.OD8

028

.o04

.5b4

5 i4

.458

384

304

.2i8

.126

+0.022

-0.040

- 7 1 -

11. Silicon Tetrafluoride

The deviation curve in F igure 19 for silicon te t raf luoride is based on

the data of Patnode and Papish (88), and Booth and Swinehart (13). The t r ip le

point and cr i t ica l p roper t ies a r e due to these au thors . Patnode and Pap ish ' s

points appear to be fairly consistent although not of the highest prec is ion .

Only about half of Booth and Swinehart 's data approach the expected deviation

curve , and, in addition, no data a r e available for the center portion of the

curve between -75 and -40 ' 'C. The rel iabi l i ty of the vapor -p res su re values

above -75 ' 'C. i s , therefore , probably not be t ter than ±0.05 a tm.

(88) Patnode, W. I. , and Papish , J . , J . Phys . Chem. 34, 1494 (1930).

(13) Booth, H. S. , and Swinehart, C. F . , J . Am. Chem. Soc • 57, 1337

(1935).

0.7

0

GLL-63T-1712

20

- J rsj I

- 6 0 TempC^C)

H4.I7

40 6 0 80 100 % l /T

Fig . 19. Deviation curve for S iF^ .

- 7 3 -

TABLE XVIII

VAPOR PRESSURE OF SiF^

l og P ^ = - 8 8 8 . 7 4 3 / T + 4 .99589

t, ° c .

90.2

90

85

80

75

70

65

60

55

50

45

40

35

30

25

20

15

14.17

P., atm.

1.756

1.781

2.500

3.351

4.35

5.52

6.86

8.40

10.14

12.12

14.35

16.87

19.72

22.94

26.60

30.80

35.72

36.66

P„, atm. is.

2.076

2.098

2.720

3.479

4.396

5.490

6.783

8.299

10.059

12.089

14.411

17.051

20.032

23.380

27.116

31.267

35.854

36.660

d, atm

+0.320

.317

.220

.128

+ 0.047

-0.027

.080

.100

.082

-0.028

+ 0.062

179

.3 10

.442

5 12

.4b5

il'O

0

•

" 7 4 -

12. Nitrous Oxide

The v a p o r - p r e s s u r e data of Hoge (49) and Couch and Kobe (24) have

been used to der ive the deviation curve shown in Figure 20. Our deviation

curve was drawn to a prec is ion of 0.001 a tm. and appears to agree quite well

with the data except for Couch's point at 35.5' 'C. , which is high. The boi l

ing point and cr i t ica l point values quoted a r e the above au thors ' exper imental

va lues .

(49) Hoge, H. J . , J . Res . Natl. Bur. Std. 34, 281 (1945).

(24) Couch, E. J . , and Kobe, K. A . , J . Chem. Eng. Data 6, 229 (1961).

0.3

0.2

0.1

0<

io.i 3 0.2

" ^ 0 . 3

-

-

-

-

1 -88.46|-80

1

N2 0

• Hoge

• Couch

^ " ^ ^ ^ " " " ^ - ^ ^ . ^

1 1 1 1 1 -60 -40

Temprc) 1 1 1 1 1

y

1 -20

1

^

/

/

/

1 0

1

/ \

/ \

J —

1 1 1 1 3443

1 20

GLL-637-1713

I -vl

I

40 60 80 100 % I / T

Fig . 20. Deviation curve for N2O.

= 76-

T A B L E XIX

VAPOR P R E S S U R E O F N2O

log P j . = - 8 4 9 . 1 2 2 / T + 4 .59767

t, "C.

- 8 8 . 4 6 5

88

86

84

82

80

78

76

74

72

70

68

66 64

62

60

58

56

54

52

50

48

46

44

42

40

38

36

34

32

30

28

2o

24

22

20

P^, a t m .

1.000

1.028

1.156

1.297

1.452

1.620

1.804

2.003

2.217

2.451

2.702

2.971

3.260

3.571

3.903

4 .258

4 .637

5.042

5.472

5.929

6.414

6.928

7.470

8.045

8.651

9.291

9.965

10.675

11.421

12.207

13.031'

13.894

14.800

15.746

16.738

17.774

P ^ . a t

1.000

1.027

1.150

1.284

1.431

. 1.590

1.764

1.953

2.157

2.379

2.618

2.875

3.152

3.450

3.769

4 .111

4 .477

4 .868

5.285

5.729

6.202

6.704

7.236

7.801

8.399

9.031

9.698

10.403

11.145

11.927

12.750

13.614

14.522

15.474

16.472

17.516

-77 -

TABLE XIX (Continued)

18. 857

19.986

21.163

22.388

23.663

24.995

26.378

27.815

29.309

30.861

32.474

34.147

35.883

37.682

39.545 41.474

43.474

45.550

47.704 49.934

52.242

54.629

57.101

59.661

62.311

63.671

65.064

66.483

67.936

69.418

70.931

71.596

18.610

19.752

20.946

22.192

23.491

24.846

26.25b

27.723

29.249

30.835

32.482

34.191

35.963

37.800

39.703 41.674

43.712

45.820

47.999 50.249

52.572

54.969

57.441

59.989

62.614

63.956

65.318

66.699

68.100

69.522

70.964

71.596

-0.247

.234

.217

.196

.172

.149

.122

.092

.060

-0.026

+ 0.008

.044

.080

.118

.158

.200

.238

.270

.295

.315

.330

.340

340

.328

.303

.285

254

.216

.lb4

.104

.033

.0

-78-

13. Carbon Dioxide

The most re l iable and consistent measu remen t s of CO^ a r e those of

Michels , Wassenaar , Zwietering, and Smi t s (77) and Meyers and Van Dusen

(70).

The t r iple-point value of -56.573 "C. and 5.116 a tm. is due to Michels .

Meye r s ' value of -56.60°C. and 5.112 a tm. differs from Michels ' p r e s s u r e of

5.110 a tm. at -56.60°C. by +0.002 a tm. Between the t r ip le point and +3°C. ,

Michels ' and Meye r s ' data a r e in good agreement . F r o m this point to the

cr i t ica l point, the data of Michels , B la i s se , and Michels (71), de termined in

1936, a r e in radica l d i sagreement both with Meye r s ' resu l t s and with their

la te r work cited above. Unfortunately, Michels ' la ter paper does not resolve

this contradict ion. The m e a s u r e m e n t s of Roebuck, Mur re l l , and Miller (101)

in the range from -20°C. to the c r i t i ca l , while not to as high a degree of a c

curacy as the work of Meyer s , well support his data, as compared to those of

Michels , B la i s se , and Michels . Because , as is shown in Table XX, Wentorf 's

(114) measu remen t of the cr i t ica l point excellently confirms Michels ' va lues ,

we have adjusted the deviation curve between 20 "C. and the c r i t i ca l point to

conform to this value ra ther than Meyer s ' value.

The values in Table XX were obtained from the l a r g e - s c a l e plot of the

region between 20.0 and 31.1°C. drawn in F igure 21. It can be seen from

Figure 21 that Michels ' repor ted p r e s s u r e of 72.85 a tm. at 31.04°C. is higher

than that obtained from a smooth curve through his points at 29.929, 30.409,

and 31.0 13 "C. F r o m this curve , we obtained a p r e s s u r e of 72.842 a tm. as

compared to Wentorf's reported value of 72.839 a tm. Meyers ' value of 72.800

a tm. is also seen from the plot to be about 0.005 a tm. below the mean of his

values through the c r i t i ca l region. Additional cr i t ica l data (106, 67, 3) a r e

also given in Table XX. Figure 22 is a plot of the deviation curve on a %(1/T)

b a s i s .

- 7 9 -

(77) Michels , A . , Wassenaar , T. , Zwietering, Th. N. , and Smits , P . ,

Physica 16, 501 (1950).

(70) Meye r s , C. H. , and Van Dusen, M. S. , J . Res . Natl. Bur. Std. 10,

381 (1933).

(71) Michels , A . , B la i s se , B. , and Michels , C , P r o c . Roy. Soc. (London)

A160, 358 (1937).

(101) Roebuck, J . R. , Mur re l l , T. A . , and Mi l le r , E. E . , J . Am. Chem.

Soc. 64, 400 (1942).

(114) Wentorf, R. H. , J r . , J . Chem. Phys . 24, 607 (1956]^.

(106) Schmidt, E . , and Thomas, W. , F o r s c h . Gebeite . Ingeniurw 20jB, 161

(1954).

(67) Lorentzen, H. C , Acta Chem. Scand. 7, 1335 (1953).

(3) Ambrose , D. , Trans Faraday Soc. 52, 772 (1956).

TABLE XX

CRITICAL PROPERTIES OF CO2 AS MEASURED BY

VARIOUS INVESTIGATORS

Observer

Meyers

Michels

Wentorf

Schmidt and Thomas

Lorentzen

Ambrose

Reported

Tc

31.00

31.04

31.04

31.01

31.04

31.01

P c

72.80

72.85

72.839

72.50

F r o m

Tc

31.00 31.04

31.04

F r o m deviation curve plot

72.805 72.872

72.842

0 40

0 30

^ 2 0

E 3 T3

0 10

0

1

•

-

•

~_

~

-

-

1 20

CO 2 • Miche ls

• Meyers

• Roe buck

» Cr i t ica l point

1 I 1 22

'

•

! 24

1 *

•

• t •

1 1

X

1 26

1

^ v •

\ ^ ^y

\ • \

1 28

1 1

-

-

~

_

\ •

1 \

• \

\vVentorf • '^Michels

• Meyers \f

•

1 1 30

GLL-633-445A Temperature (°c)

F ig . 21 . Deviation curve for CO2 vs t °C . from 20 °C. to the cr i t ica l point.

00 o

s . 4 - 1

0.5

0.

0.3

0.2

0.1

0

•0.1

•0.2

• 0 . 3 -

C O .

-bb.bU|-50

0 GLL-637-1714

10

^ M i c h e l s

• M e y e r s

•Roebuck

- 4 0 ^ — r i ^ T e m p ( ° C )

10 10

± 20 30 40 50

% l / T 60 70 80

00

31.04

90 100

F i g . 22 . D e v i a t i o n c u r v e for CO2 vs % ( 1 / T ) .

- 8 2 -

T A B L E XXI

VAPOR P R E S S U R E O F CO^

itif. 1 -̂., - .Hbi.i^i/r I 4.ili'i(t

l . ° C

S6. S73

S4

S.!

SO

' !8

•4 6

•44

•42 40

38

36

34

32

30

28

26

24

22

20

18

16

14

12

10

8

6

4

- 2

0

+ 2

4

6

8

10

12 14

16 13

20

22

24

26

27

28

29

30

31 31.04

P j , a i m .

S.116

S.71 1

6.210

6.740

7.302

7.901

8 .536

9.209 9.918

10.668

1 1.457

12.290

13.166

14.089

15.059

16.078

17.146

18.265

19.436

20 .662

21 .944

23 .283

24 .679

26 .135

27 .655

29 .239

30 .890

32 .606

34.392

36 .249

38 .179

40 .184

42 .265

4 4 . 4 2 7

4 6 . 6 7 1

48 .999

51 .414 53 .920

56 .521

59 .221

62 .024

64 .936

66 .439 67 .972

69 .537

71 .138

72 .773 72 .840

P j ^ , a t m .

5.118

5.70 3

6 .193

6.715

7.270

7.861

8 .488

9^ 1 5 3 9 .857

10.602

11.389

12.220

13.096

14.019

14.990

16.012

17.085

18 .211

19.391

20 .628

21 .923

23 .277

24 .692

26 .169

2 7 . 7 1 1

29 .318

30 .993

32 .736

34 .550

36 .435

38 .395

4 0 . 4 2 9

4 2 . 5 3 9

4 4 . 7 2 8

4 6 . 9 9 6 4 9 . 3 4 5

51 .777

54 .292

56 .893

59 .581

62 .357

65 .222

66 .689

68 .179

69 .692

71 .228

72 .787 72 .850

d , a t m

40 .002

- 0 . 0 0 8

.017

.025

.032

.040

.048

.056

.061

.066

.068

.0 70

.070

.070

.069

.066

.061

0 54

045

034

.02 1

- 0 . 0 0 6

+ 0.013

.034

.056

.079

.103

.130

.158

.186

.216

.245

.274

.301

.325

.346

.363

.372

.372

.360

.333

.286

.250

,207

.155 " .0 90

.014

.010

- 8 3 -

^^' Hydrogen Chloride

The data of Thomas (109a) and of Cardoso and Germann (19), between

-30 and 50 "C. appear to be in d i sagreement by a constant sys temat ic e r r o r

as seen in Figure 23. The deviation curve has been located to correspond

to Thomas ' data because his work is more recent and appears to give the most

consistent agreement with the other hydrogen halide curves shown in Figure

3. Thomas has measured a cr i t ica l t empera tu re of 51.54 "C. and calculated

a c r i t i c a l - p r e s s u r e of 81.97 a tm. from his v a p o r - p r e s s u r e equation. We

have found a c r i t i ca l p r e s s u r e value of 82.07 to be in be t te r ag reement with

out deviation curve . This difference is at tr ibuted to the inability of Thomas '

equation to follow the curvature of the v a p o r - p r e s s u r e curve near the cr i t ica l

point. Cardoso and Germann (18) reported cr i t ica l point values of 51.4°C.

and 81.55 a tm. Kopper (64) has measu red a value of 51.0 °C. for the c r i t i ca l

t empe ra tu r e . Giauque and Wiebe's (39) measu remen t s have been used to lo

cate the deviation curve in the vicinity of the boiling point.

(109a) Thomas, W. , P rog . Intern. Res . Thermodynamic Transpor t P r o p e r

ties ASME Second Symposium, 1962.

(19) Cardoso, E . , and Germann, A. F . O. , J . Chim. Phys . U, 632(1913).

(18) Cardoso, E. , and Germann, A. F . O. , J . Chim. Phys . 10, 517 (1912).

(64) Kopper, H. , Z. Physik. Chem. A175, 469 (1936).

(39) Giauque, W. F . , and Wiebe, R. , J . Am. Chem. Soc. 50, 101 (1928).

0.8

0.6

0.4

0.2

0.2

1

HCl

CARDOSO THOMAS GIAUQUE

1 TEMPERATURE r O J \ \ L.

•85.03! -70 -50 -30 J L

20 GLL-63T-1715A

40 60 % I/T

80

00

I I \ \ i _ a 30 51.54

100

Fig . 23. Deviation curve for HCl.

- 8 5 -

T A B L E XXII

V A P O R P R E S S U R E O F HCl

log P :- -856.120/T + 4.55093

P . . a tm . P ^ , a tm. d, atm

1.00

LOO

1.32

1.72

2.20

2.78

3.47

4 .29

5.25

6.37

7.65

9.12

10.79

12.68

14.79

17.15

19.74

22.62

25.80

2 9 . 3 1

33.18

37.42

42 .05

47 .09

52.57

58.50

64 .91

71 .91

79.56

82.07

1.000

1.002

1.314

1.700

2 .171

2 .741

3.423

4 . 2 3 1

5 .181

6.288

7.568

9.038

10.714

12.616

14.759

17.162

19.842

22 .816

26.102

29.718

33.680

38.005

42 .708

47 .807

53.315

59.248

65.619

72.443

79.732

82.073

.000

.000

- 0 . 0 0 8

.018

.025

.038

.050

.060

.070

.078

.080

.080

.075

.060

- 0 . 0 3 2

+0.015

.100

.200

.305

.405

.500

.590

.660

.714

.744

.747

.710

.530

.170

.0

-86 -

15. Hydrogen Bromide

The only data available for HBr a r e those of Drozdowski and P ie t rzak

(28), whose m e a s u r e m e n t s on HCl a r e in very poor agreement with our curve

for HCl. Never the less , the points shown for HBr appear to agree fairly well

with the projected curve shown in Figure 24 and Giauque and Weibe's boiling

point value (40). The cr i t ica l t empera tu re determined by Kopper (64) is

89.9' 'C. , by Moles (81) 89.8°C, and by Drozdowski and P ie t rzak 90.0' 'C. We

have used 90.0' 'C. and found the corresponding p r e s s u r e to be 84.5 a t m . ,

which is in good agreement with Drozdowski 's value of 84.44 a tm.

(28) Drozdowski, E. , and P ie t rzak , J . , Bull. Intern. Acad. Sci. Cracovie

A 1 9 n , 219.

(40) Giauque, W. F . , and Wiebe, R. , J . Am. Chem. Soc. 50, 2193 (1928).

(64) Kopper, H. , Z. Physik. Chem. A. 175, 469 (1936).

(81) Moles , E. , J . Chim. Phys . 17, 415 (1919).

-66.72 -50

1

00

I

-30 -10 10 TEMPERATURE (*»C)

0 10 20 G]aL-63T-lTl6A

30 4 0 50 % l/T

60 70 80 90 100

Fig . 24. Deviation curve for HBr.

- 8 8 -

TABLE XXIII

VAPOR PRESSURE OF HBr

log P j^ = - 9 2 1 . 6 8 7 / T + 4 .46489

t , ° C . P^ . a t m . P ^ , a t m . d, a t m .

66 .72

65

60

55

50

45

40

35

30

25

20

15

10

- 5

0

+ 5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90.0

1.000

1.09

1.39

1.76

2.20

2.72

3.32

4 .03

4 .85

5.78

6.84

8.02

9.35

10.81

12.44

14.23

16.20

18.36

20 .73

23 .33

26 .18

29 .27

32 .64

36.30

40 .25

4 4 . 5 1

49 .10

54.02

59.28

64 .91

70.94

77.43

84.50

1.000

1.089

1.383

1.737

2.160

2 .661

3.249

3.933

4 .724

5.632

6.668

7.844

9.170

10.658

12.320

14.166

16.210

18.461

20 .932

23 .634

26 .578

29 .775

33 .236

36.972

40 .992

45 .306

49 .924

54.855

60 .108

65 .691

71.612

77.880

84.500

.0

.0

- 0 . 0 1 0

.020

.035

.055

.075

.100

.125

.150

.170

.180

.180

.155

.120

- 0 . 0 6 0

+0.010

.105

.200

.300

.400

.502

.600

.675

.740

.796

.823

.840

.828

.785

.670

.450

.0

- 8 9 -

16. Sulfur Hexafluoride

The deviation curve for SF/ shown in F igure 25 is based on the t r ip le

point of 2.20 a tm. at -51 °C. determined by Mi l le r , Verdell i , and Gall (79)

and a c r i t ica l point of 37.193 a tm. at 45.642 "C. de termined by Wentorf (114).

Unfortunately, t he re a r e no data of comparable rel iabi l i ty between these two

t e m p e r a t u r e s . The average of Mi l l e r ' s liquid v a p o r - p r e s s u r e m e a s u r e m e n t s

from -50 to 0°C. does not show the expected negative region for the deviation

curve and does not match Clegg, Rowlinson, and Sutton's (23) 0 and 10 °C.

points . Because of the s imi lar i ty of its coexistence line with that of S F , ,

it was expected that the normal ized CO-, curve might well r ep re sen t the S F ,

data; and, as shown in Figure 25, it indeed fits Clegg's data fairly well. On

this bas is we have used this curve for SF/ in the -51 to 30 "C. region as shown

in Figure 1 above. Otto and Thomas ' (87) data a r e suspect between 0 and

20 "C. because they do not predict a negative deviation region below O^C. a n d a r

evidently in e r r o r above 30 "C. , where the exhibit a "nose" effect in d i s a g r e e

ment with Clegg's data . Near the cr i t ica l point the measu remen t s of both

Otto and Clegg agree with Wentorf 's c r i t ica l point.

(79) Mil ler , H. C , Verdell i , L. S. , and Gall, J , F . , Ind. Eng. Chem. 43

1126 (1951).

(114) Wentorf, R. H. , J r . J . Chem. Phys . 24, 607 (1956).

(23) Clegg, H. P . , Rowlinson, J . S. , and Sutton, J . R. , T r a n s . Faraday

Soc. 5J, 1325 (1955).

(87) Otto, J . , and Thomas, W. , Z. Physik. Chem. (Frankfurt) 23, 84 (I960).

90-

O

o

o

CO

o

o

ID

O

in

o

5t

o 1-\ 55

v£) h

C

fi

u

0 OJ

> u

11

0 .f-( •i->

a > (U

p

in

ro

O

_ O

10

0 ^ 0

ro

0 C

J

0 ~

0 -

0 0 1

(UJ4D

)P

CM

0 1

ro

0 1

^ 0 1

10 0 1

H

- 9 1 -

T A B L E XXIV

VAPOR P R E S S U R E O F S F

log P = - 8 9 9 . 3 3 5 / T + 4 .39153

t , "C.

- 5 1

50

45

40

35

30

25

20

15

10

- 5

0

+ 5

10

15

20

25

30

35

40

45

45.64

P . , a t m .

2.20

2.30

2.84

3.46

4 .18

5.00

5.93

6.97

8.15

9.46

10.92

12.53

14.32

16.28

18.43

20.80

23.40

26.26

29.39

32.82

36.64

37.19

P j ^ , a t m .

2 .204

2.298

2.816

3 .421

4 .123

4.930

5.853

6.902

8.086

9.418

10.906

12.562

14.396

16.419

18.641

21.072

23.722

26 .601

29.719

33.085

36.708

37.191

d, a t m

.000

- 0 . 0 0 4

.022

.038

.053

.066

.073

.072

.062

.042

-0 .010

+0.032

.080

.138

.208

.273

.324

.343

.330

.265

.070

.0

-92 -

17. Hydrogen Sulfide

The h igh -p re s su re data for H-,S in the l i t e ra tu re do not extend below

O'C. The measu remen t s of Reamer , Sage, and Lacey (95) and Kay and

Rambosek (58) ag ree to bet ter than 0.1 a tm. below 70 "C. , as shown in F igure

26. Above 70 "C. R e a m e r ' s points r ep re sen t vapor p r e s s u r e s which a r e lower

by 0.2 to 0.3 a tm. Most of Cardoso ' s (15) measu remen t s a r e sys temat ical ly

lower by 0.5 a tm. than those of Reamer and of Kay. F igure 23 shows a s i m i

lar difference between Cardoso ' s and Thomas ' data for HCl. We have based

our deviation curve on Kay and Rambosek 's data because they a r e m o r e com

plete than R e a m e r ' s in the jhk region and because R e a m e r ' s measu remen t s

in the kc region appear to exhibit a "nose" effect. R e a m e r ' s points shown

in F igure 26 a r e comprised of three published experimental points and three

o thers kindly supplied to us by him. We have not used any of R e a m e r ' s pub

lished smoothed points since he has stated that they a r e of poorer prec is ion .

It is r emarkab le that our vapor p r e s s u r e values shown in Table XXV agree

within 0.1 a tm. with Cragoe ' s (54) smoothed points published in 1928.

Giauque and Blue (34) and Clark, Cockett, and Eisner (22) repor t boil

ing points of -60.33 and -60.19' 'C. , respect ive ly . Kopper (64) has determined

a cr i t ica l t empera tu re of 100.1°C. and Cardoso repor t s a cr i t ica l point of

100.4''C. and 88.90 a tm. Kay and Rambosek 's cr i t ica l point of 99.92°C. and

88.26 a tm. ag rees well with our deviation curve .

(95) Reamer , H. H. , Sage, B. H. , and Lacey, W. N. , Ind. Eng. Chem.

42, 140 (1950).

(58) Kay, W. B. , and Rambosek, G. M. , Ind. Eng. Chem. 22J (1953).

(15) Cardoso , E. , Gazz. Chim. Ital. 51, 1 (192 1).

- 93 -

(54) "International Cri t ical T a b l e s , " Vol. Ill, McGraw-Hil l Book Company,

Inc . , New York, 1928, pp. 201-249.

(34) Giauque, W. F . , and Blue, R. W. , J . Am. Chem. Soc. 58, 831 (1936).

(22) Clark, A. M. , Cockett, A. H. , and E i sne r , H. S. , P r o c . Roy. Soc.

(London) A209, 408 (1951).

(64) Kopper, H. , Z. Physik. Chem. AJ175, 469 (1936).

1.0

0 8

0.6

0.4

0.2

0

0 2

- HgS

—

1 -60.19!

A CARDOSO • REAMER • KAY

^ ^ ^

1 1 1 1 -^O -20

> ^ •

1 0

A

1 20

A

A A

I

/

7

1 1

40

A - A A

A A

/ \

/ • \

1

1 1 i 1

60 80 99.9 1

0 GLL-63T-1718B

20 40 60

TEMPERATURE CO % l/T

Fig . 26. Deviation curve for H2S.

80 100

55

50

45

40

35

30

25

20

15

10

-5

0

+ 5

10

15

20

25

30

40

50

55

60

65

70

75

80

85

90

95

-95-

TABLE XXV

VAPOR PRESSURE OF H^S

t ' °C. P., atm. P^, atm. d, atm.

•60 .19 1.00 1.000 .0

60 1.01 1.009 - 0 . 0 0 1

l o g P j , - -

p . , a t m . 1

1.00

1.01

1.38

1.64

2.04

2.53

3.10

3.76

4 .52

5.38

6.38

7.50

8.77

10.19

11.77

13.52

15.45

17.57

19.89

22 .44

2 5 . 2 1

28 .22

31 .49

3 5 . 0 1

38.83

4 2 . 9 4

47 .35

52 .07

57.13

62 .55

68 .34

74.56

81 .22

88 .26

965 .518 + 4 .53380

P „ , a t m

1.000

1.009

1.282

1.611

2 .004

2.470

3.017

3.655

4 .395

5.245

6 .218

7.324

7.573

9 .978

11.550

13.301

15 242

17.386

19.744

22 .328

25 .149

28 .220

3 1 . 5 5 1

35.153

39 .038

4 3 . 2 1 7

47 .698

52 .494

57.613

63 .064

68 .858

7 5 . 0 0 1

81 .504

88 .260

.010

.025

.040

.060

.080

.100

.120

.140

.160

.180

.200

.210

.220

.220

.210

.185

.150

.110

35 2 5 . 2 1 25 .149 - 0 . 0 6 0

.000

45 31 .49 3 1 . 5 5 1 +0 .065

.140

.2 10

.280

.350

.420

.480

.510

.510

.440

.280

99.92 88 .26 88 .260 .000

-96 -

18. Hydrogen Iodide

As is the case of HBr, the only data for HI have been determined by

Drozdowski and P ie t rzak (28). The deviation curve shown in F igure 27 is

drawn to fit Giauque and Wiebe's boiling point (41) and matches the deviation

curve pat terns shown in Figure 3. Drozdowski 's points in the k region of

the curve a r e much too low to fit the curve and have been d i scarded . The

c r i t i ca l t empera tu re used, 1 5 0 . T ' C , is that of Kopper (64). The correspond

ing p r e s s u r e is 81.9 a tm. Drozdowski and P i e t r zak ' s cr i t ica l values a r e

150.0 "C. and 80.8 a tm.

(28) Drozdowski, E. , and P ie t rzak , J . , Bull . Intern. Acad. Sci. Cracovie

A 1 9 n , 219.

(41) Giauque, W. F . , and Wiebe, R. . J . Am. Chem. Soc. 5J, 1441 (1929).

(64) Kopper. H. , Z. Physik. Chem. A175, 469 (1936).

-35.35 -20 0 20 40 60 TEMPERATURE (•C)

I \ I

150.7

10 GLL-637-1719A

20 30 40 50 % l /T

60 70 80 90 100

Fig . 27. Deviation curve for HI.

- 98 -

TABLE XXVI

VAPOR PRESSURE OF HI

log P ^ = - 1 0 3 6 . 5 1 / T + 4.35875

t, "C.

-35 .35

35

30

25

20

15

10

- 5

0

+ 5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

105

110

115

120

125

130

135

140

145

150

150.7

l o g JT-j, - - l U J U

P . , a t m . 1

1.00

1.02

1.26

1.54

1.87

2.26

2.70

3.19

3.76

4.41

5.12

5.93

6.82

7.81

8.90

10.09

11.40

12.83

14.38

16.06

17.86

19.80

21.88

24.10

26.48

29.01

31.72

34.61

37.69

40.96

44.45

48.15

52.09

56.25

60.64

6 5 . 2 8

70.19

75.46

81.09

81.90

. J 1 / J. T T . J_ '*J 1 ~>

P „ , a t m .

1.000

1.015

1.247

1.520

1.838

2.206

2.630

3.114

3.665

4.288

4.990

5.776

6.652

7.626

8.702

9.887

11.189

12.613

14.165

15.852

17.681

19.656

21.785

24.074

26.528

29.152

31.954

34.937

38.107

41.470

45.031

48.793

52.761

56.941

61.335

65.949

70.785

75.847

81.139

81.898

d, a t m

.0

.0

-0 .0 10

.020

.035

.050

.065

.080

.100

.120

.135

.150

.165

.180

.195

.205

.215

.220

.220

.205

.180

.140

.090

-0 .025

+0.050

.140

.230

.330

.420

.510

.581

.640

.670

.690

.691

.665

.595

.385

.045

.0

-99-

19. Chlorine

Knietsch (62) and Pellaton (90) have both measured the vapor p r e s s u r e

of CK between the boiling point and the c r i t i ca l point. Knietsch's resu l t s a r e

considered to be general ly unrel iable since below O^C. they show a high p r e s

sure "nose" and above 40 °C. they diverge steeply in the high p r e s s u r e d i

rect ion. Pel la ton 's values a r e f ragmentary and not too consistent between 80

and 100 "C. However, in general they fit the projected curve fairly well.

Giauque and Powel l ' s value (37) has been used for the boiling point. The

deviation curve for Cl^ is shown in F ig . 28.

(62) Knietsch, Ann. Chem. 259. 100 (1890).

(90) Pel laton, M. , J . Chim. Phys . 13, 426 (1915).

(37) Giauque, W, F . , and Powell , T. M. , J . Am. Chem. Soc. 6J., 1970

(1939).

10

0-

•

• (

• v

• N

CM

O

1 1

r-̂^*^

•

\^

X

o

CO

1-UJ

z ^ •

1

s^

o

H

< _I

_l

LU

Q.

• 1

• •

•

\

•J i •

^1 •P

Jl

/ •

/• /

•

/ H

/•

—

—

^^

—

—

—

^_

—

_ — o

o

(Oo) 08 09 °^ 3 —

1-<

ott:

CV

IUJ

CL

-

0 0 TEM

1 1

CM

1

lO

o •

lO

1

o

o

o 0

)

o 00

o o CD

o lO

t—I

u u

o >

u

u

0 • rH

•4->

> O

>$

P

o

s

00

•i-i

<: o

C5

<J> 00

N

• •

•

oo

o

CD

lO

^ to

CM

—

O

d

o

d

d

d

d

(UJ

|D)p

CM

P

6

- 1 0 1 -

TABLE XXVII

VAPOR PRESSURE OF CI2

log P^ = - 1 0 5 3 . 4 5 / T + 4 .40590

t , " C .

- 3 4 . 0 5

30

25

20

15

10

- 5

0

+ 5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

105

110

115

120

125

130

135

140

144.12

P . , a t m .

1.00

1.19

1.47

1.79

2.15

2 .58

3.07

3.62

4 .25

4 .95

5.74

6.61

7.59

8.66

9.85

11.15

12.57

14.11

15.78

17.58

19.53

21 .62

23 .86

26 .28

28 .86

31 .63

34 .59

37 .76

4 1 . 1 4

44 .74

48 .56

52.62

56.92

61 .49

66 .34

71.52

76.10

P , a t m .

1.000

1.184

1.448

1.756

2 .114

2 .527

3 .001

3.542

4 .155

4 .846

5.623

6.492

7 .458

8.529

9 .711

11.012

12.437

13.994

15.690

17.531

19.524

21 .675

2 3 . 9 9 1

2 6 . 4 7 8

29 .143

3 1 . 9 9 1

35 .029

38 .262

4 1 . 6 9 7

4 5 . 3 3 7

4 9 . 1 8 9

53 .258

57 .549

62 .066

66 .813

71 .796

76 .081

d, a t m .

0 .000

- 0 . 0 1 0

.019

.029

.040

.053

.067

.080

.095

.106

.115

.120

.128

.132

.135

.137

.130

.119

.092

.052

- 0 . 0 0 3

+0.060

.130

.203

.285

.362

.435

.500

.555

.600

.630

.640

.630

.576

.470

+0.280

- 0 . 0 1 9

-102-

20. Ammonia

The deviation curve for ammonia shown in Figure 29 is constructed

from the data of Cragoe, Meyer s , and Taylor (25) and Beattie and Lawrence

(8). The data of Cragoe a r e in excellent agreement with those of Beattie up

to 40 °C. At 70 "C. , which is the highest t empera tu re measured by Cragoe,

his resu l t s a r e about 0.03 a tm. lower than those of Beat t ie . The resu l t s of

Keyes and Brownlee (60) a r e also shown in Figure 29. Keyes and Brownlee 's

resu l t s at low t empera tu res a r e about 0.10 a tm. higher than those of Beattie

and Lawrence , while converging with those of Beattie at higher t e m p e r a t u r e s .

Above llO^C. , however, Keyes ' values drop considerably below those of

Beat t ie . Section III. F d i scusses the considerat ions involved in further detai l .

Our deviation curve agrees with Beat t ie ' s data to within 0.001 a tm. , except

at high t e m p e r a t u r e s , where Beattie did not r epor t his p r e s s u r e s to the third

decimal place. Kopper 's (64) value of 132.5 "C. for the cr i t ica l t empera tu re

was used, and the cr i t ica l p r e s s u r e corresponding to this t empera tu re is

112.53 a tm. These cr i t ica l constants a r e much more consistent with Beat t ie ' s

v a p o r - p r e s s u r e data than those given in the l i t e ra tu re by other authori t ies

whose cr i t ica l p r e s s u r e is about 1 a tm. lower. Arms t rong also a r r ived at the

same conclusion in his unpublished repor t (4) in which a c r i t ica l point of

132.4"'C. and 112.4 a tm. was selected.

(25) Cragoe, C. S. , Meyers , C, H, , and Taylor, C. S. , Natl. Bur . Std.

Sci. and Tech. Pape r s 16, 1 (1920) and J . Am. Chem. Soc. 42, 206 (1920).

(8) Beat t ie , J . A . , and Lawrence , C. K., J . Am. Chem. Soc. 52, 6 (1930).

(60) Keyes, F . G. , and Brownlee, R. B. , J . Am. Chem. Soc. 40, 25 (1918).

(64) Kopper, H. , Z. Physik. Chem. ATTS; 469 (1936).

(4) Arms t rong , G. T. , Natl. Bur. Std. Rept. 2626 (1953).

0.6

0.5

0.4

0.3

0.2

0.1

? 0. • • -

3 -0.1

•° -0.2

-0.3

-0 .4

—

—

—

—

—

—

—

—

—

-33.351 1

-20

1

NH

^•"" - -^^

1

1

3

• ^

1 0

1

• Cragoe

• Keyes

A Bea t t i e

• ^ * ^ A ^

•

1 1 1

•

1 20 40

Temp rc) 1 1 1

• •

1 1 60

1

X

1

J

; /

/

/ r

1 80

1

)

/ I 1 / 1

1 1 100

1

• _

'̂ V V V \

\ A

—

—

1 132.50

o 00 I

0 GLL-637-1721

20 40 6 0 80 100 % 1 / T

Fig . 29. Deviation curve for NH3.

104-

T A B L E XXVIII

VAPOR P R E S S U R E OK NH3

log P^ = - 1 2 0 3 . 0 5 / T + 5 .01689

Pj^, a t m . Pj< ,̂ atmi. d, a t i n .

1.000 1.000 .0

1.070 1.067 - 0 . 0 0 3

1.180 1.172 .008

1.301 1.287 .014

1.430 1.410 .020

1.569 1.543 .026

1.717 1,685 .032

1.878 1.839 .039

2 .050 2 .004 .046

2 .234 2 .180 .054

2 .432 2 .369 .063

2 .643 2 .571 .072

2 .869 2 .787 .082

3 .110 3 .017 .093

3 .367 3 .263 .104

3.640 3 .524 .116

3.930 3.802 .128

4 . 2 3 8 4 . 0 9 8 .140

4 . 5 6 3 4 . 4 1 1 .152

4 . 9 0 8 4 . 7 4 4 .164

5 .273 5.096 .177

5 .659 5 .468 .191

6 .068 5 .862 .206

6 .499 6 .279 .220

6.952 6 .718 .234

7 .429 7 .182 .247

7 .931 7 .670 .261

8 .459 8 .185 .274

9 .013 8 .726 .287

9 .594 9 .295 .299

10.204 9 .893 .311

10.842 10.520 .322

11.512 11 .179 .333

12.213 11.869 .344

12 .945 12.591 .354

13.711 13.348 .363

14.510 14.139 .371

15.344 14.966 .378

16 .215 15.831 .384

17.122 16.733 .389

18.066 17.674 .392

19.052 18.656 .396

2 0 . 0 7 5 19.679 .396 2 1 . 1 3 7 2 0 . 7 4 5 .392

2 2 . 2 4 1 21 .854 .387

2 3 . 3 8 9 2 3 . 0 0 8 .381

- 1 0 5 -

T A B L E XXVIII (Cont inued)

t,> ° c .

S8

60

62 64

66

68

70

72

74

76

78

80

82

84

86

88

. ̂ ° 92

94

96

98

100

102

104

106

108

110

112

114

116

118

120

122

124

125

126

127

128

129

130

131

132

132.50

P J I a t m .

24.580

25.817

27.100

28.430

29.809

31.236

32.714

34.244

35.826

37.459

39.148

40.894

42.699

44.563

46.488

48.474

50.523

52.637

54.819

57.070

59.390

61.780

64 .241

66.776

69.385

72.070

74.830

77.676

80.612

83.643

86.762

89.978

93.293

96.705

98.450

100.221

102.020

103.848

105.715

107.622

109.567

111.535

112.526

Pj.^) a t m .

24.207 25.454

26.749 28.093

29.488

30.934

32.433

33.986

J5.595

37.259

38.982

40.763

42.604

44 .506

46.470

48 .498

50.591

52.749

54.975

57.269

59.632

62.066

64 .571

67.150

69.802

72.530

75.335

78.217

81.178

84.219

87.340

90.544

93.832

97.203

98 .921

100.661

102.422

104.205

106.009

107.836

109.685

111.557

112.501

d 1 a t m

-0 .373

.363

.351

.337

.321

.302

.281

.258

.231

.200

.166

.131

.095

.057

- 0 . 0 1 8

+0.024

.068

.112

.156

.. .199

.242

.286

-'.3 30

.374

.417

.460

.505

.541

.566

.576

.578

.566

.539

.498

.471

.440

.402

.357

.294

.214

.118

+0.022

- 0 . 0 2 5

-106-

21. Cyanogen

Measurements of vapor p r e s s u r e of C2N2 have been repor ted by P e r r y

and Bardwell (92) and by Terwen (109). The resu l t s of both invest igators a r e

in good agreement , and our curve shown in F igure 30 indicates a good fit in

the jhkc region. Terwen 's value of the cr i t ica l t empera tu re I26.55°C. does

not fit well with the deviation curve and Cardoso and Baume's (16) value of

I28.3"'C. is p re fe r r ed . The corresponding cr i t ica l p r e s s u r e is 59.98 a tm.

compared to 58.20 a tm. and 59.75 a tm. reported by Terwen and Cardoso and

Baume, respect ively . Ruehrwein and Giauque's (99) value of the boiling point

is in good agreement with the deviation curve .

(92) P e r r y , J . H. , and Bardwell , D. C. , J .Am. Chem. Soc. 47, 2629 (1925).

(109) Terwen, J , W. , Z. Physik. Chem. 91, 469 (1916).

(16) Cardoso , E. , and Baume, G. , J . Chim. Phys . 10, 509(1912).

(99) Ruehrwein, R. A. , and Giauque, W. F . , J . Am. Chem. Soc. 61,

2940 (1939).

0.5

0.4

0.3

0.2

0.1

0

-0

C2N2

-21.15

GLL-637-1722

A Per ry

• Te rwen

j _ j _

20 40 60 Temp (°C)

I I \

80 J L

100 128.30

o I

20 40 60 % l / T

80 100

Fig . 30. Deviation curve for C^N-.

- 108-

T A B L E XXIX

V A P O R P R E S S U R E O F C2N

log P = - 1 2 0 3 . 5 7 / T + 4 .77607

t, 'C.

21.15

20

18

16 14

12

10

8

6

4 -2

0

+ 2

4 6

8 10 12

14

16 18

20 22 24 26 28 30

32

34

36 38 40 42

44

46 48 50 52

P p a t m .

1.000

1.052

1.151

1.258

1.373

1.494

: .6Z4

1.763

1.911

2.066 2,234

2.413

2.603

2.803 3.014

3,237 3.473 3.723

3.986 4 .263

4.554

4.860 5.182 5.518 5.872 6.244 6.631

7.038

7.463

7.906 8.370 8.853 9.358

9.883 10.432

11.002 11.595 12.211

P j^ , a t m .

1.000

1.051

1.145

1.246 1.354

1.470

1.594

1.725

1.866

2.015 2.174

2.343

2.523

2.713 2.914

3.127 3.353 3 .591

3.843 4 .108

4 .388

4 .682 4 .992 5.317 5.659 6.019 6.395

6.790

7.204

7,637 8.090 8,563 9,058

9.574 10.113

10.675 11.261 11.871

d, a t m

.0

- 0 . 0 0 1

.006

.012

.019

.024

.020

.038

.045

.051

.060

.070

.080

.090

.100

.110

.120

. L 1 ^

143 155

. loo

.178 19c 20 i

.215

.225

.236

.248

.259

.269

.280

.290

.300

.309

.319

.327

.334

.340

- 109-

TABLE XXIX (Continued) P - , a t m .

1 2 . 8 5 2

1 3 . 5 1 8 1 4 . 2 1 0 1 4 . 9 2 8

15 .674

1 6 . 4 4 7

1 7 . 2 4 7

1 8 . 0 7 6

1 8 . 9 3 2 1 9 . 8 2 0

2 0 . 7 3 4

2 1 . 6 7 9

2 2 . 6 5 3 2 3 . 6 5 8

2 4 . 6 9 3

2 5 . 7 6 1

2 6 . 8 6 0

2 7 . 9 9 3

2 9 . 1 6 1 3 0 . 3 6 8

3 1 . 6 0 6

3 2 . 8 8 0

3 4 . 1 8 9

3 5 . 5 3 6

3 6 . 9 2

3 8 . 3 5

3 9 . 8 2

4 1 . 3 3

4 2 . 8 8

4 4 . 4 8

4 6 . 1 3

4 7 . 8 3

4 9 . 5 9 5 1 . 4 2

5 3 . 3 3

5 5 . 3 3

5 6 . 3 6

5 7 . 4 3

5 8 . 5 2

5 9 . 6 4

5 9 . 9 8

P j ^ , a t m . d ,

1 2 . 5 0 6 - 0

1 3 . 1 6 6 1 3 . 8 5 3 1 4 . 5 6 7

1 5 . 3 0 8

1 6 . 0 7 8

1 6 . 8 7 7

1 7 . 7 0 5

. 1 8 . 5 6 3 1 9 . 4 5 3

2 0 . 3 7 4

2 1.327

2 2 . 3 1 3 2 3 . 3 3 3

2 4 . 3 8 7

2 5 . 4 7 7

2 6 . 6 0 2

2 7 . 7 6 3

2 8 , 9 6 1 3 0 . 1 9 8 3 1 . 4 7 2

3 2 . 7 8 6

3 4 . 1 3 9

3 5 . 5 3 3 - 0 .

3 6 . 9 6 9 , - 0

3 8 . 4 4 6 3 9 . 9 6 5

4 1 . 5 2 8

4 5 . 1 3 4

4 4 . 7 8 5

4 6 . 4 8 1

4 8 . 2 2 3

5 0 . 0 1 1

5 1 . 8 4 6 5 3 . 7 3 0

5 5 . 6 6 1

5 6 . 6 4 5

5 7 . 6 4 2

5 8 . 6 5 1

5 9 . 6 7 2

5 9 . 9 8 1

atnr

. 3 4 6

, 3 ^ 2 . 3 5 7

^361

. 3 6 6

. 3 6 9

. 370

. 3 7 1

. 3 6 9

. 3 6 7

. 3 6 0

. 3 5 2

. 3 4 0

. 3 2 5

306

2 8 4

2 58

230 2 CO

I 70

134

0 94

0 50

oo:-0 4 o

0 99 •50

20>

2 54

2 04

J 52

3 92

4 2 0

4 2 6

2 9 6 3 30

2 8 1

2 1 6

132

0 3 3

0 0 1

-110-

22. Sulfur Dioxide

Although a grea t many m e a s u r e m e n t s of the vapor p r e s s u r e of SO-,

have been made, the data a r e in poor agreement above 30 "C. Between the

boiling point and 30°C. , Hirth, as quoted in reference (57) (which contains

data obtained independently by Hirth, Kang, and Hellwig) and Riedel (98) a r e

in excellent agreement . Riedel 's boiling point value of - lO .Ol 'C . has been

used by us . Between 30 and 95 °C. Hir th ' s and Kang's data quoted in r e f e r

ence (57) a r e in radical d i sagreement with each other . Unfortunately their

paper does not resolve this question, and no other data of comparable p r e

cision a r e available for confirmation of the t rue p r e s s u r e s . Toriumi and

Hara ' s (HO) measu remen t s shown in F igure 31 general ly support Hir th ' s r e

su l t s . The data of Regnault (96) and Cardoso and Fiorentino (17) not shown

in F igure 31, a r e quite sca t te red in this region. This mean of Regnault 's

data appears to support Hirth, while the data of Cardoso and Fiorent ino a r e

c lose r to those of Kang and Hellwig quoted in reference (57). Pending defini

tive m e a s u r e m e n t s , we have chosen Hir th ' s data for the location of the devi

ation curve in the 30-95"'C. range, since his measu remen t s a r e in good a g r e e

ment with p rec i se measu remen t s above and below these t e m p e r a t u r e s , and a

deviation curve through his data harmonizes best with other curves in F igure

3. F r o m 95 to 135°C. Kang's points have been used to locate the deviation

curve . F rom 135 °C. to the cr i t ica l point Kang's data a r e inconsistent and

indicate an inflection point in the kc region which is considered to be spur ious .

Our deviation curve has been drawn in the kc region to harmonize with Kang's

data in the jh region and with other deviation curves in Figure 3.

- 1 1 1 -

(57) Kang, T. L. , Hir th, L. J . , Kobe, K. A . , and McKetta, J . J . , J . Chem.

Eng. Data 6, 220 (1961).

(98) Riedel, L. , Bull. Intern, Inst, Refrig, 20, No. 4, Annex No. 5, Bl

(1939).

(110) Tor iumi , T. , and Hara , R. , J . Soc. Chem. Ind. (Japan) 47, 502 (1944).

(96) Regnault, H, V. , Mem. De P a r i s 26, (1862).

(17) Cardoso, E. , and Fiorent ino, U. , J . Chim. Phys . 23, 841 (1926).

T3

0 10

GLL-637-1723

100

I

F i g . 3 1 . D e v i a t i o n c u r v e for SO2-

-113-

TABLE XXX

VAPOR PRESSURE OF SO2

log P „ = -1279 .15 /T + 4.86128

t , • € .

10 .01

10 .00

8

6

4

- 2

0

+ 2

4

6

8

10

12

14

16

18

20

22

24

26

2 8

30

32

34

36

38

40

42

44

4 6

4 8

50

52

54

56

58

60

62

64

66

68

70

72

P . , a t m . 1

1.000

1.001

1.092

1.190

1.296

1.410

1.532

1.661

1.799

1.946

2.102

2.267

2.444

2.631

2.828

3.037

3.258

3.492

3.738

3.997

4.269

4.557

4.858

5.174

5.507

5.854

6.219

6.600

6.998

7.415

7.851

8.305

8.780

9.272

9.786

10.318

10.873

11.447

12.045

12.667

13.311

13.980

14.676

1.000

1.001

1.089

1.183

1.284

1.392

1.508

1.631

1.762

1.901

2.049

2.206

2.374

2.551

2.738

2.936

3.146

3.368

3.602

3.849

4.108

4.383

4 .671

4.974

5.293

5.626

5.977

6.345

6.730

7.133

7.555

7.996

8.458

8.939

9.442

9.966

10.513

11.082

11.675

12.293

12.935

13.602

14.296

.0

.0

-0 .003

.007

.012

.018

.024

.030

.037

.045

.053

.061

.070

.080

.090

.101

.112

.124

.136

.148

.161

.174

.187

.200

.2 14

.228

.242

.255

.268

.282

.296

.309

.322

.333

.344

.352

.360

.365

.370

.374

.376

.378

.380

- 1 1 4 -

T A B L E XXX (Cont inued)

i> -c 74

76 78 80 82 84 86 88 90 92 94 96

98 100 102 104 106

108

110

112

114

116

118 120

122 124 126 128

130 132 134 136 138

140

142 144 146

148

150

151

152

154 156 157 157.50

P|) atm,

15.397

16.145 16.920

17.725 18.556 19.417 20.308

21.228 22.178 23.160 24.172 25.217

26.293 27.405 28.544

29.729 30.949

32.206

33.502

34.838

• 36.215

37.633

39.095 40.598

42.144 43.734 45.366

47.043

48.765 50.533 52.356 54.227 56.151

58.126

60.154 62.236 64.374

66.569 68.822

69.968

71.132

73.504 75.939 77.181 77.810

Pl<Jy atlDi

15.016

15.764 16.540

17.345

18.179 19.043 19.938

20.864

2̂ 1.822

22.814

23.839

24.898

25.991 27.121 28.282

29.489 30.729

32.008

33.325

34.682

36.080

37.518

38.999 40.522

42.088

43.698

45.352

47.051

48.797 50.589 52.428 54.315 56.251

58.236

60.270

62.356

64.492

66.681

68.922

70.062

71.216

73.564

75.966

77.188

77.804

d. fttn

-0.381

.381

.380

.380

.377

.3 74

.370

.364

.356

.346

.333

.319

.302

.284

.262

.240

.220

.198

.177

.156

.135

.115

.096

.076

.056

.036

-0.014

+0.008

.032

.056

.072

.088

.100

.110

.116

.120

.118

.112

.100

.094

.084

.060

.027

+0.007

-0.006

-115-

23, Hydrogen Fluor ide

The data of J a r r y and Davis (55) and Franck and Spalthoff (29) a r e in

good agreement and appear to have good prec i s ion . F ranck and Spalthoff

a r e to be commended for the care taken in adequately defining the kc region

of the curve . We note, however, in comparing in F igure 4 the deviation

curve for HF with that obtained for N^O ., that the HF curve lies somewhat

to the right of the N2O . curve in the kc region. In drawing the N^O , curve ,

we have p re fe r red the data of Schlinger and Sage over that of Sheffer and

Treub, whose points seem to exhibit a typical l o w - p r e s s u r e defect in this

region. It is poss ible , then, that F ranck and Spalthoff s data may be slightly

low in this region a l so . Kelley's (59) boiling point of 19,5 "C. appears to

ag ree with the above data .

(55) J a r r y , R. L. , and Davis, W. , J r . , J . Phys . Chem, 57, 600 (1953)

and Am. Doc. 4069.

(29) F ranck , E . V . , and Spalthoff, W. , Z . E lek t rochem. 6j., 348 (1957).

(59) Kelley, K. K. , U. S. Bur. Mines Bull, 383 (1935),

6

GLL-637-1725 % l / T

F ig . 32. Deviation curve for HF,

100

I

- 1 1 7 -

T A B L E XXXI

V A P O R P R E S S U R E O F H F

log P j , = - 1 4 4 6 , 9 7 / T + 4 .94437

t , " C .

19 .5

20

25

30

35

40

4 5

50

55 60

65

70

75 80 85

90 95

100

105

110

115

120

125

130

135

140 145

150

155

160

165

170

172

174

176

178

ISO

182

184

186 188 .0

p., a t m .

i.OOO

J . 0 1 8

1,208

1.433

1.097

1.998

2 . 2 6 6 2 . 7 2 9

3 . 1 9 9 2 . 6 7 2

4 . 2 3 7

4 . 8 6 1 5 .540

6 . 2 9 9 7 . 1 5 8 8 ,12

9 . 1 9

1 0 . 3 6

1 1 . 6 8

1 3 . 0 7

14 .64

1 6 . 3 8

1 8 . 3 1

2 0 . 4 3

2 2 . 7 2

2 5 . 2 3

2 7 . 9 5

3 0 . 8 8

3 4 . 0 7

3 7 . 5 0

4 1 . 2 2

4 5 . 2 3

4 7 . 1 0

4 8 , 9 9 5 0 . 9 2

5 2 . 9 2

5 4 . 9 7

5 7 . 1 0

5 9 , 3 2

6 1 , 6 4

6 4 , 0 6

P T ^ , a t m i .

1.000

1.020

1.234

1.483

1.773

2 . 107

. 2 . 4 9 0

2 , 9 2 9

3 . 4 2 7

3 . 9 9 1 1.627

5 . 3 4 1 6 . 1 4 0

7 . 0 3 1 8 . 0 2 1

9 .12

1 0 . 3 3

1 1 . 6 6

13 .12

1 4 . 7 2

1 6 . 4 6

1 8 . 5 6

2 0 . 4 2

2 2 . 6 6

2 5 . 0 7 2 7 . 6 7

3 0 . 4 8

3 3 . 4 8

3 6 . 7 1

4 0 . 1 6

4 3 . 8 4

4 7 . 7 2

4 9 . 4 1

5 1 . 1 0

5 2 . 8 2

5 4 . 5 8

5 6 . 3 9 5 8 . 2 4

6 0 . 1 4

6 2 , 0 8

6 4 , 0 6

d , a t m

0

. 002

. 0 2 6

. 0 5 0

. 0 7 6

. 1 0 9

. 1 2 4

.2 00

. 2 2 8

.3 19

. 3 9 0

. 480

. 6 0 0

. 7 3 2

. 8 6 3 1.00

i 14

1.30

1.44

1 D l

1.81

L9tf

2 . 1 .

2 . 2 3 2 . 3 5

2 . 4 4

2 . 5 2 2 , 6 0

2 o4

^ , 6 6

2 . 6 2

2 . 4 9

2 .3x

2 . 1 i

1.90

1,66

1,42

1.14

, 8 2

. 4 4

.0

-118-

24. Hydrogen Cyanide

Giauque and Ruhrwein 's (38) boiling point is in good agreement with the

p r e s s u r e measu remen t s of Hara and Sinozaki (46) and Bredig and Teichman

(14). Above 50 "C. the data of Bredig and Teichman shown in F igure 33 a r e

s p a r s e but show a reasonably accura te fit to a curve based on our N-,0_>

curve . Bredig and Teichman's cr i t ica l p r e s s u r e (53.2 atm.) is in very poor

agreement with their c r i t ica l t empe ra tu r e and we have selected a c r i t i ca l

p r e s s u r e of 48.89 a tm.

(38) Giauque, W. F . , and Ruhrwein, R. A. > J. Am. Chem. Soc. 6J, 2626

(1939).

(46) Hara, R. , and Sinozaki, H. , Tech. Repts . Tohoku Imp. Univ. 4, 145

(1924).

(14) Bredig, G. , and Teichman, L. , Z. Elekt rochem. M, 449 (1925).

1.2

1.0

0 .8

0 .6

0 .4

0 ,2

rii

—

—

-

-

-

2 5 . 7 |

HON

1 40

1 1

i 1 60

1

AHara

• B r e d i g

1

1

• >*

^y^ " ^

1 1 1 80 100 T e m p ( ° C )

1 1

y ^

1

/

^ •

1 1 120

1

^

1 140

1

- < A

1 1 160

1

\

\

\

\

\

1 1 183.5

0 10 GLL-637-1726

20 30 W 40 50 % l / T

F i g . 33 . Dev ia t ion c u r v e for HON.

70 80

I

90 100

- 1 2 0 -

T A B L E XXXII

V A P O R P R E S S U R E O F HCN

log P j , = - 1 4 5 9 . 4 2 / T + 4 .88345

t, "C.

25.7

30

35

40

4 5

50

55

60

65

70

75 80

85

90

95

100

105

110 115

120

125

130

135

140

145

150

155

160

165

170

174

176

177

178

179

180

181

182

183

183.5

p . , a t m .

1.000

1.17

1.40 1.66

1.97 2.31

2.70 3.13

3.61

4.14 4.72 5.36

6.08

6.89

7.79 8.78

9.89 11. t l 12.45

13.92 15.53

17.29 19.21 21.29

23 .55 26.01

28.66 31.54 34.65

38.02

40 .95

42 .51 43 .32 44 .14

44 .98

45 .82

46 .69 47.50 48 .45

48 .89

P j^ , a t m .

1.000

1.17

1.40 1.67

1.98 2.33

2.73 3.18

3.69

4 .27 4 .92 5.63

6.43 7.32

8.30 9.38

10.57 11.87 13.29

14.84 16.51

18.34 20 .31 22.44

24 .73 27.20

29.84 32.67 35.69

38.92

41 .65

43 .07 43 .79 44 .52

45 .26

46.00 46 .76

47 .53 48 .31

48.70

d, a tm .

-0

.0

.0

. 0 1

. 0 1

. 0 2

. 0 3

. 0 5

. 0 8

. 1 3

. 2 0

. 2 7

. 3 5

. 4 3

. 5 1

.bO

. 6 8

. 7 b

. 84

,9c

98

!.0 5 1. [V

1. i5

1 18 1.19

i , i 8 1.13 1 04

. 90

. 70

. 5 6

.47 •

.38 •

. 2 8

. 1 8

. 0 7

+ 0.03 - 0 . 1 4

- 0 . 1 9

- 1 2 1 -

25. Nitrogen Tetroxide

V a p o r - p r e s s u r e measu remen t s have been made by Baume and Robert

(7) up to 38' 'C. and 2 a tm. ; by Mit tasch, Kuss , and Schlueter (80) up to 60°C.

and 5 a tm.; by Schlinger and Sage (105) up to 149 "C. and 79 atm.; and by

Scheffer and Tr&ub (103) up to the cr i t ica l t empera tu re of 158.2''C. Bennewitz

and Windisch (10) repor t a cr i t ica l t empera tu re value of 158.4''C. The c r i t i

cal p r e s s u r e of N^O . has never been experimental ly de te rmined .

Cr i t ica l values of 158.0 "C. and 99 a tm. , which a r e at t r ibuted by Kobe

and Lynn (63) to Baume and Robert , appear in real i ty to be due to Cragoe ' s

calculated values given in the International Cri t ical Tables (54). The resu l t s

of all invest igators a r e in good agreement up to 130 °C. , as shown in F igure

34. Above this t empera tu re some of Sheffer and Treub ' s data exhibit a low-

p r e s s u r e "nose, " and since Schlinger and Sage's data show the mos t cons is t

ent prec is ion , we have chosen to extrapolate their data to the observed c r i t i

cal t empera tu re where we find fair agreement with Sheffer and Treub. The

c r i t i ca l p r e s s u r e determined by the deviation curve is 99.66 a tm . Kelley's

(59) boiling point of 21.0*0. appears to ag ree well with these data.

(7) Baume, G. , and Robert , M. , Compt. Rend. 168, 1199 (1919).

(80) Mit tasch, A., Kuss, E . , and Schlueter , H. , Z. Anorg. AUgem. Chem.

^ , 1 (1926).

(105) Schlinger, W. G. , and Sage, B. H., Ind. Eng. Chem. 42, 2158 (1950).

(103) Schef fe r ,F . E. C , and Treub, J . P . . Z. Physik. Chem. 8^, 308(1913).

(10) Bennewitz, K. , and Windisch, J . J . , Z. Physik. Chem. A166, 401 (1933).

(63) Kobe, K. A . , and Lynn, R. E. , J r . , Chem. Rev. 52, 117 (1953).

(54) "International Cri t ical T a b l e s , " Vol. Ill, McGraw-Hil l Book Company,

I n c . , New York, 1928, pp. 201-249.

(59) Kelley, K. K. , U. S. Bur . Mines Bull. 383 (1935).

2.

2 . 4 -

2.0

N2O4

21.0

0 10 GLL-637-1727

40

• Sch l inge r

•She f fe r

^ M i t t a s c h

I 60 80

T e m p (°cO 100

J u 120

± ± 20 30 40 50

% 1/T

60 70 80

± 140 158.2

90 100

tSJ

I

F i g . 34. D e v i a t i o n c u r v e for N ^ O ^ .

- 1 2 3 -

T A B L E XXXIII

VAPOR P R E S S U R E O F N^O^

t , ° C .

21

22

24

26

28

30

32

54

:-6

38

40

4 2

4 4

4 6

4 8

50

52

54

56

58

60

62 64

66

6 8

70

72

74

76

78

80

82

84

8b

8 8

90

92

l og P^ =

P j , a t m .

1 .000

1.046

! . 1 4 4

1.251

1.368

1.494

; . 6 3 0

i . 7 7 o

1.954

2 . 1 0 6

2 . 2 9 0

2 . 4 8 9

2 . 7 0 4

2 . 9 3 3

3 . 1 7 9

3 . 4 4 4

3 . 7 2 7

4 . 0 2 7

4 . 3 4 7

4 . 6 8 9

5 . 0 5 4

5 . 4 4 3 5 . 8 5 8

6 . 3 0 0

6 . 7 7 2

7 . 2 7 4

7 . 8 1 0

8 . 3 7 8

8 . 9 8 2

9 . 6 2 2

1 0 . 2 9 9

1 1 . 0 2 0

1 1 . 7 8 2

1 2 . 5 9 3

i 3 ; 4 4 8

1 4 . 3 5 6

1 5 . 3 1 4

- 1 8 4 8 . 2 0 / T + 6 . 2 8 3 2 0

P j ^ , a t m .

1.000

1.050

1.157

1.274

1.400

1 . 5 3 D

^ . . 6 8 5

1 .845

2 . 0 1 8

2 . 2 0 4

2 . 4 0 6

2 . 6 2 2

2 . 8 5 5

3 . 1 0 6

3 . 3 7 5

3 . 6 6 3

3 . 9 7 2

4 . 5 0 3 4 . 6 5 7

5 . 0 3 6

5 . 4 3 9 5 . 8 7 0

6 . 3 2 9

6 . 8 1 8

7 . 3 3 9 7 . 8 9 2

8 , 4 8 1

9 . 1 0 5

9 . 7 6 7

1 0 . 4 6 9

1 1 . 2 1 3

1 2 . 0 0 0

1 2 . 8 3 3

1 3 . 7 1 4

1 4 . 6 4 4

1 5 . 6 2 6

1 6 . 6 6 2

d , a t m .

. 0 0 0

004

0 1 3

0 23

, 032

0 4 2

0 5 5

. 0 6 9

. 0 8 4

. 0 9 8

. 1 1 6

. 1 3 3

. 1 5 1

. 1 7 3

t9D

. 2 . 9

24 5

2 7-j

3 .0

.34 7

3^^5 42 7

^ 4 7 1

, 5 ' 8

^o7

D S

, b 7 ;

7-7

.7>?5

. 8 4 7

-914

. 9 8 0

1.051

l . i 2 1

1.19b

1.270

1 3 4 8

- 1 2 4 -

TABLE XXXIII (Continued)

t, °c . 94

96

98

100

102

104

106

108

110 112

114

116

118

120

122

124

126

128

130

132

134

136 138

140

142

144

146

148

150

151

152

153

154

155

156

157

158 158.2

P . , a t m .

16.328

17.402

18.533

19.728

20.988

22.317

23.714

25.185 2 6 . 7 4 1 28.382

30.111

31.933

33.846

35.856 37.961

40 .169

42 .491

44 .941 47 .511 50.21 53.05 56.02 59.14

62.41 65.83

6 9 . 4 i 73.16 77.08

81.16

83.27 85.41

87.60 89.83

92.10

94.42 96.78 99.18 99.66

P j^ , a t m .

17.754

18.904

20.116

21 .391 22.732

24 .141

25.b22

27.176 ^ 28 .807

30 .518

32.310

34 .188

36 .154

38.212 40 .364

42 .613

44 .964

47 .418 49 .981 52.654 55.442 58 .348 61,377

64.530

67.813

71.229 74.783 78.476

82 .316

84 .291 86 .303

88 .356 90.445

92.574

94.743 96.952 99.203 99 .658

d, a t m .

1.426

1.502

1.583

1.663

1.744

1 824

1.908

1.991 2.066 2.136

2 .199 2 .255

2 .308

2.356 2.403

2.444

2.4 73

2 477 2,470 2 443 2 3 9: 2,3 24 2 239

2. 124 i .987

1.822 L b 2 l 1.400

1.158

1.025

.891

.757

.615

.4b9

.324

.176 + 0.027 - 0 . 0 0 2

-125-

26. Bromine

The only h igh -p re s su re measu remen t s on bromine have been made by

Scheffer and Voogd (104). Their resu l t s a r e in ag reement with our deviation

curve shown in F igure 35; however, no data were taken above 200 "C. Be

yond this point, the curve is projected so as to correspond with other curves

shown in F igure 4. Scheffer and Voogd did de te rmine the cr i t ica l t empe ra

ture to be 3 11 °C. and calculated a corresponding cr i t ica l p r e s s u r e of 102 a tm.

This value is in good agreement with our deviation curve and is definitely to

be p re fe r red over StuU's value of 121 a tm. (108) calculated from Nadejine's

(82) c r i t ica l t empera tu re of 302 °C. StuU's boiling point (108) has been used.

(104) Scheffer, F . E . C , and Voogd, M., Rec. T rav . Chim. 45, 214 (1926).

(108) Stull, D. R. , Ind. Eng. Chem. 39, 517 1684 (1947).

(82) Nadejine, Bull. Acad. Imp. Sci. St. Pe t e r sbu rg 30, 327 (1886).

d(a

tm)

era

O

3 n c <

0)

i-h 0 td

tv

P I ON

O

J -<

1 I H

-J

ro

CO

>

ro

O

OJ O 8-

^ C

Ji

:- o

en o el-

cx>

o to

o

o

o

I I

I p

po

o

pp

op

oo

pp

OJ

ro

—

o

—

ro

OJ

i^

b

i en

->

i bo

CO

CJ

I

P

ro

GO

O o

o

-• m

h

s "0 go

h

-• c ^ m

""^

L

0 r

^0

0 •^

o

[—

ro

ro

O

ro

o>

o —1

—1 1

1

- _ •

•

~ •

—

—

1 f

1 1

1 1

1 1

1 1

1 r I OD

1 i^

" m

( 1 1 1 J *

1 1 1 *

1 *

/ [ Y N

. •

• ^

s^

• •

^v

^^

^\

^ ^

S^ \

^^

.^

1

•92

1

127-

t, °C. P . , a t m . P , atnn. d, a t m .

1 r\

58.2 1.00 1.000 .0

60 1.06 1.059 -0 .002

70 1.45 1.444 .012

80 1.96 1.934 .022

90 2.58 2.549 .034

100 3.36 3.311 .049

110 4.30 4 .241 .062

120 5.44 5.365 .080

130 6.81 6.708 .102

140 8.42 8.297 .120

150 10.30 10.160 .135

160 12.47 12.326 .145

170 15.97 14.823 .150

180 17.83 17.682 .145

190 21.06 20 .931 .125

200 24 .67 24.602 - 0 . 0 7 0

210 28.72 28 .724 .000

220 33.22 33.32 +0.10

230 38.22 38.44 .22

240 43.75 44 .09 .34

250 49 .87 50.31 .44

260 56.61 57.12 .51

270 63.98 64.54 .56

280 72.04 72.62 .58

290 80.80 81.36 .56

300 90.38 90.80 .42

305 95.50 95.79 .29

311.0 102.00 102.00 .00

-128-

27. Sulfur Trioxide

The deviation curve for SO^ was calculated from original data kindly

supplied by Dr . P . F . Tiley (1). We have computed a boiling point of 44.55*0.

from our deviation curve . Hyne and Tiley (53) have repor ted a boiling point

of 44.45 ± 0,15*C. Tiley (1) has determined the cr i t ica l point to be 217.7*0

± 0.2 *C. and calculated the cr i t ica l p r e s s u r e to be 80.8 a tm. We have ca l

culated a P of 81.44 a tm. from our deviation curve , est imating a kc peak

height equivalent to that for SO^ in absence of p rec i se data in this region.

The resu l t s of Smits and Schoenmaker (107) and Berthoud (11) a r e in good

agreement at the boiling point and Berthoud's data a r e in fair agreement near

the c r i t i ca l point. Berthoud's c r i t i ca l point is 218.2*0. and 83.8 a tm.

(I) Abercomby, D. C , and Tiley, P . F . , J . Chem. Soc. (London) lg.63, 4902.

(53) Hyne, R. A . , Tiley, P . F . , J . Chem. Soc. (London) 1961, 2348.

(107) Smits , A . , and Schoenmaker, P . , J . Chem. Soc. (London) 19^26, 1108.

(II) Berthoud, A. , Helv. Chim. Acta 5̂ , 513 (1922).

GLL-637-1729

40 60 7o( l / T )

100

tv sO I

Fig . 36. Deviation curve for SO3.

- I S O -

T A B L E XXXV

VAPOR P R E S S U R E O F SO3

1 6 2 3 . 8 7 / T + 5.22851

t, °C. 44 ,55

4 5

50

55

60

65

70

75

80

85

90

95

100

105

110

115

120

125

130

135

140

145

150

155

160

165

170 175

180 185

190 195 200

205

210 212

214 216

217 217.7

log

Pi" 1

1

1

1 •>

2

2

3 4

5

5

6

7

9

10

11

13

14,

16,

^ ^ K ^ a t m .

. 00

.02

.30

. 6 3

. 0 1

, 46

. 9 8

. 5 8

. 26

. 04

.90

. 8 6

. 9 1

. 0 7

. 3 3

.72

.22

.86

,67

18.61 20.

22 ,

2 5 .

2 7 .

3 0 .

3 3 .

3 6 .

4 0 .

4 3 .

4 7 .

5 2 .

56 .

6 1 .

6 6 .

7 1 .

7 4 .

7 6 .

7 9 .

8 0 .

8 1 .

,70

.91

.29

84

,62

61

83

29

97

90

10

58

35

44

89 22

64

18

50

4 4

K' 1 1

1

1

2

2

3

3 4

4

5

6

7

8

9 11

12,

14,

15.

17,

19.

2 2 ,

a t m . .31 . 33

.60

. 9 1

. 26

,b7

. 14

. 6 7

,27

. 9 5

. 7 1

. 5 7

. 53

.60

. 78

. 0 9

.53

.12

,87

.78

,86

,13

24.60

2 7 .

3 0 .

3 3 .

3 6 .

4 0 .

4 4 .

4 8 .

5 2 .

5 7 .

6 2 .

,27

,17

29 65

27

16 32

77 52

58

67.98

7 3 .

7 6 .

7 8 .

8 1 .

8 2 .

8 3 .

7 1

10

54

04

32

22

d , + 0

-fO

- 0

- 0

+ 0

a t m .31

.31

.30

28

25

21

. l b

.09

.01

.09

.19

.29

.38

.47

.55

.63

,b9

74

,80

83

84

.78

o9

57 .45

,18

. 0 ^

.19 ,42

.67

.94

,23

.54

,82

,88

.90

,86

,82

,78

- 1 3 1 -

28. Carbon Tet rachlor ide

The data of Young (119) and Wer the imer (115) shown in F igure 37 a r e

in good agreement and give a well defined deviation curve . Young's c r i t i ca l

point value of 283.15*0. and 44.97 a tm. is well confirmed by the deviation

curve . Hildenbrand and McDonald's (48) boiling point of 76.73*0. is used.

(119) Young, 5 . , J . Chem. Soc. 59, 911 (1891).

(115) Wer the imer , E. , Ber . Deut. Physik. Ges . 21, 435 (1919).

(48) Hildenbrand, D. L. , and McDonald, R. A. , J . Phys . Chem. 63, 1521

(1959).

s TJ

0 . 4

0 . 3

0 .2

0.1

0

-0 .1

-0.2

C C l

76.7 100

0 10 GLL-637-1730

•Young

• W e r t h e i m e r

I 120 140 160

T e m p (°C)

180 ± _L

200 240

20 30 40 50 60 % l / T

70 80

260 283.2

90

OJ tv

100

F i g . 37. D e v i a t i o n c u r v e for C C l ^ .

- 133-

T A B L E XXXVI

VAPOR P R E S S U R E O F CCl

log Pj^ = -1558 .62 /T + 4.45472

t, ' C . P . , a tm . 1

76.73 1.00

80 1.10

85 1.28

90 1.47

95 1.68

100 1.92

105 2.19

110 2.48

115 2.80

120 3.15

125 3.53

130 3.94

135 4.40

140 4.89

145 5.42

150 5.99

155 6.61

160 7.27

165 7.98

170 8.74

175 9.54

180 10.39

185 11.30

190 12.27

195 13.30

200 14.40

205 15.56

210 16.79

215 18.09

220 19.46

225 20.91

230 22.44

235 24.07

240 25.78

245 27.59

250 29.49

255 31.49

260 33.59

265 35.81

270 38.14

275 40.59

280 43.15

283.15 44.97

' K ' ^'™-1.000

1.10

1.267

1.455

1.664

1.896

2.153

2.437

2.749

3.092

3.468

3.878

4.325

4.810

5.337

5.907

6.522

7.184

7.897

8.661

9.480

10.356

11.291

12.287

13.348

14.474

15.669

16.934

18.273

19.687

21.179

22.751

24.405

26.143

27.969

29.883

31.888

33.986

36.180

38.470

40.860

43.351

44.974

d, a tm

.0

-0 .003

.009

.015

.021

.027

.033

.040

.047

.054

.060

.066

.072

.077

.082

.085

.087

.086

.084

.076

.060

.038

-0.012

+ 0.017

.047

.077

.110

.145

.182

.223

.268

.306

.336

.362

.380

.393

.400

.393

.368

.330

.270

.202

.0

-134-

29. Tin Tet rachlor ide

Young (119) and Wer th imer (115) have measured the vapor p r e s s u r e of

SnCl . , and their data a r e in agreement on a boiling point of 114.1*C. Above

280*0. Young's data that a r e not shown in F igure 38 a r e evidently inaccura te

and we have used Wer the imer ' s data to the cr i t ica l point. The cr i t ica l -poin t

values of 318.7*0. and 36.95 a tm. a r e repor ted by Wer the imer but appear to

be based on Young's calculated T of 318.7*C. , corresponding to his observed

cr i t ica l p r e s s u r e of 36.95 a tm. (120).

(119) Young, S. , J . Chem. Soc. 59, 911 (1891).

(115) Wer the imer , E. , Ber . Deut. Physik. Ges. 2^, 435 (1919).

(120) Young, S. , Sci. P r o c . Roy. Dublin Soc. 12, 374 (1909).

a 4-"

T3

0 10 GLL-637-1731

100

Fig . 38. Deviation curve for SnCl^.

- 1 3 6 -

T A B L E X X X V I I

V A P O R P R E S S U R E O F S n C l ^

log P = - 1 ? 5 6 . 0 5 / T + 4.53467

t, °c . 1 14.1

lis 120

125

130

135

140

145

150

155

160

165

170

175

180

185

190

195

200

205

210

215

220

225

230

235

240

245

250

255

2 60

265

270

275

280

285

2 90

295

300

i05

310

315

318.7

P̂ , atm.

1.00

1.02 1.18

1.35

1.54

1.74

1.97

2.21

2.48

2.78

3.10

3.45

3.83

4.24

4.68

5.16

5.67 6.21

6.80

7.42

8.08

8.79

9.55

10.35

11.20

12.10

13.04

14.05

15.12

16.24

17.42

18.66

19.98

21.37

22.82

24.36

24.97

27.67

29.45

31.32

33.28

35.34

36.95

Pj^, atm.

1.000

1.024 1.170

1.331 1.510

1.707

^ 1.924

2.163

2.425

2.711

3.024

3.364

3.733

4.133

4.565

5.032

5.535

6.076

6.657

7.279

7.945

8.656

9.414

10.222

11.080

11.992

12.959

13.983

15.066

16.209

17.415

18.687

20.026

21.433

22.910

24.461

26.086

27.787

29.567

31.427

33.370

35.396

36.950

d, atmi

.000

-0.001

.008

.017

.025

.033

.042

.050

.060

.069

.079

.089

.100

.109

.118

.126

.133

.138

.140

.141

.140

.138

.134

.126

.1 15

.103

.087

.069

.04 9

.027

-0.003 4 0.0̂ 22

.045

.067

.085

.100

.112

.118

.118

.109

.088

.052

.0

-137-

30. Water

The deviation curve for H^O taken from the tables of Osborne, Stimson,

and Ginnings (86), is presented in Figure 39 for the purpose of comparison

with the other curves in this r epor t . The fact that water is highly associa ted

is responsible for the disproport ionate length of the bj section of the curve .

It should be noted, however, that the sum of the j and k peaks of 1.22 a tm. is

only slightly higher than that of HCl, H^S, HBr, and HI and less than that for

HF, N^O^, and SO^.

(86) Osborne , N. S. , Stimson, H. F . , and Ginnings, D. C. , J . Res . Natl.

Bur . Std. 23, 261 (1939).

1.2

1.0

0.8

0.6

0-4

0.2

S 0 a '^ -0.2

-0.1

—

-

—

-

-

-

-

-

ioo |

H^O

1

I

1 140

1

1

«

J 1 1 180 220

Temp (°C)

1 1 1

1 1 260

1

y V 1 1

300

1

/ ' \

/ \

/

/

1 1 1 34q374;l^

1 0 10

GLL-637-1732

20 30 40 50

% l / T

60 70 80

00 00

90 100

Fig . 39. Deviation curve for H^O.

-139-

IV. ACKNOWLEDGMENTS

We wish to thank Joseph L. Brady and M r s , Mary Lou Higuera of the

Computation Division of the Lawrence Radiation Laboratory (Livermore) for

their help in p rogramming and running the calculations for this work; and

Donald G. Miller of the Chemist ry Depar tment for his helpful c r i t i c i sm .

- 140-

V. REFERENCES

(1) Abercomby, D. C. , and Tiley, P . F . , J . Chem. Soc. (London) 1963,

4902.

(2) Adwentowski, K. , Intern. Bull. Acad. Sci. Cracovie II 1909. 742.

(3) Ambrose , D. , T rans . Faraday Soc. 52, 772 (1956).

(4) Arms t rong , G. T. , Natl. Bur. Std. Rept. 2626 (1953).

(5) Arms t rong , G. T. , J . Res . Natl. Bur. Std. 53, 263 (1954).

(6) Arms t rong , G. T. , Brickwedde, F . G. , and Scott, R. B. , J . Res .

Natl. Bur . Std. 55, 39 (1955).

(7) Baume. G. , and Robert , M. , Compt. Rend. 168 ,̂ 1199 (1919).

(8) Beat t ie , J . A. , and Lawrence, 0 . K. , J . Am. Chern. Soc. 52, 6 (1930).

(9) Bennewitz, K. , and Andreev, N. , Z. Physik. Chem. A142, 37 (1929).

(10) Bennewitz, K. , and Windish, J . J . , Z. Physik. Chem. Al66 , 401(1933).

(11) Berthoud, A. , Helv. Chim. Acta 5, 513 (1922).

(12) Bloomer , O. T. , and Pa ren t , J . D. , Inst. Gas Techn. Res . Bull. 17

(1952).

(13) Booth, H. S. , and Swinehart, C. F . , J . Am. Chem. Soc. 57, 1337(1935).

(14) Bredig, G. , and Teichman, L. , E lek t rochem. M. 449 (1925).

(15) Cardoso, E. , Gazz. Chim. Ital . 5^, 1 (1921).

(16) Cardoso , E. , and Baume, G, , J . Chim. Phys . 10, 509 (1912).

(17) Cardoso , E. , and Fiorent ino, U. , J . Chim. Phys . 23, 841 (1926).

(18) Cardoso , E. , and Germann, A, F . O. , J . Chim. Phys . 10, 517 (1912).

(19) Cardoso , E. . and Germann. A. F . O. , J . Chim. Phys . H , 632 (1913).

(20) Oath, P . G. , and Kammerl ingh Onnes, H. , Koninkl. Ned. Akad.

Wetenschap. P roc . Ser. B. 26, 490 (1917) Leiden Comm. No. 152a.

(21) Clark, A. M. , Din, F . , Robb, J . , Michels , A . , Wassenaar , T. , and

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- 1 4 1 -

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