1

Isothermal vapour + liquid equilibrium measurements and correlation

for the pentafluoroethane + cyclopropane and the cyclopropane +

1,1,1,2-tetrafluoroethane binary systems

Laura Fedele1, Sergio Bobbo1,2, Roberto Camporese1, Mauro Scattolini1

1 Institute of Building Technologies – Division of Padova, National Research Council,

35127 Padova, Italy.

2 To whom correspondence should be addressed (tel. +39 049 8295831, fax +39 049

8295728 and e-mail: laura.fedele@itc.cnr.it)

2

Abstract

Isothermal vapour + liquid equilibria (VLE) data were measured for the

pentafluoroethane (R125) + cyclopropane (RC270) and the RC270 + 1,1,1,2-

tetrafluoroethane (R134a) binary systems at 253.15, 273.15 and 293 15 K, using a static

analytical method. The phase compositions at equilibrium were measured by gas

chromatography. The experimental estimated accuracies are ±0.02 K for temperature,

±1 kPa for pressure, and ±0.003 in mole fraction for both liquid and vapour phase

composition. Both systems show strong positive deviations from the Raoult’s law with

the formation of an azeotrope. The experimental data were regressed using the Peng-

Robinson-Stryjek-Vera equation of state, with different mixing rules, i.e. the Van der

Waals with one or two interaction parameters, the Huron-Vidal and the Wong-Sandler

mixing rules. A comparison with the data available in the literature was performed.

KEYWORDS: (vapour + liquid) equilibria, cyclopropane (RC270), pentafluoroethane

(R125), 1,1,1,2-tetrafluoroethane (R134a).

3

1. Introduction

Mixtures formed by hydrocarbons (HCs) and hydrofluorocarbons (HFCs) are

possible compromise alternative refrigerants, since the hydrocarbons lower the GWP of

HFCs and hydrofluorocarbons reduce the flammability of HCs. Vapor-liquid (VLE)

measurements are essential for a proper representation of the thermodynamic properties

of mixtures. Moreover, they give interesting information on the interaction forces

between the two families of fluids.

Following our previous measurements for mixtures formed by propane, iso-butane

and n-butane with some HFCs (e.g. [1], [2] and [3]), here isothermal VLE for systems

formed by R125, R134a and RC270 are presented. For comparison, only one datum is

available in the literature for the binary mixture RC270 + R134a whereas no data were

found for the R125 + RC270 system.

2. Experimental section

Materials

R125 (pentafluoroethane, C2HF5) was provided by Solvay, with a declared purity >

99.9%, while R134a (1,1,1,2-tetrafluoroethane, C2H2F4) and RC270 (cyclopropane,

C3H6) were supplied by Ausimont.

In order to eliminate the non-condensable gases, each sample underwent several

cycles of freezing with liquid nitrogen, evacuation, thawing and ultrasound. The

samples were then used with no further purification.

Apparatus

The experimental setup used in the present work was already described more in

detail in [1]. The equilibrium was reached into a stainless steel cell of about 50 cm3

Comment: Controllare la purezza di tutti I composti.

4

endowed with glass windows for the visual observation of the mixture and equipped

with a magnetic pump to force the vapour through the liquid. The composition of the

phases was measured by a gas chromatograph (Hewlett-Packard 6890) connected on-

line to the equilibrium cell, after a careful calibration of the FID detector by means of

gravimetrically prepared mixtures. The uncertainty in the composition measurement is

estimated to be within ±0.003 in mole fraction for both the liquid and the vapour phase.

The temperature was measured by means of a 100 Ω platinum resistance thermometer,

connected to a multimeter (Hewlett-Packard 3458) and continuously recorded during

the measurements. The temperature stability was of ±1 mK, while its uncertainty is

estimated to be ±0.02 K. The pressure was measured by means of a Ruska 6000

pressure gauge, with a full scale of 3500 kPa and an uncertainty of ± 1 kPa.

3. Results and discussion

Experimental data

The VLE (T-P-x-y) data for the R125 + RC270 and the RC270 + R134a systems

were measured at 253.15, 273.15 and 293 15 K. The experimental data are presented in

Table 1 and Figure 1 for the R125 + RC270 system and in Table 2 and Figure 2 for the

RC270 + R134a system, respectively. Within this temperature range the two systems

present an homogeneous liquid phase, even if they are azeotropic with a strong positive

deviation from the Raoult’s law. For the two mixtures the compositions of the

azeotropes at each temperature were evaluated by zeroing an analytical equation

expressing the difference between the dew point and the bubble point composition (y-x)

as a function of the bubble point composition (x). The azeotropic compositions of both

the systems are presented in Table 3.

5

Data reduction

The experimental VLE data were regressed by means of the Peng-Robinson (PR)

equation of state (EoS) [2] in the modified form proposed by R. Stryjek and J. H. Vera

in [3] and four different mixing rules, using the software available in [4]. The Peng-

Robinson-Stryjek-Vera (PRSV) EoS was employed in the form

( )( ) ( )bvbbvv

Tabv

RTP−⋅−+⋅

−−

= (1)

where P is the pressure (kPa), R the ideal gas constant [8314.5 (cm3·kPa)/(gmole·K)], T

the temperature (K), v the molar volume (cm3/ gmole) and a and b the equation of state

constants.

In the PRSV EoS the b constant takes the usual form

c

c

PRTb 077796.0= (2)

where the subscript c stands for critical property, while a is

( ) ( )TPTRTac

c α⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

22

457235.0 (3)

with

( )2

11⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

cTTT κα (4)

and

( ) ( )rr TT −⋅+⋅+= 7.01 5.010 κκκ (5)

320 0196554.017131848.04897153.1378893.0 ϖϖϖκ ⋅+⋅−⋅+= (6)

The subscript r refers to the reduced temperature cr TTT = , while ω is the Pitzer’s

acentric factor defined as

6

( )⎥⎦

⎤⎢⎣

⎡ =−−=

c

rsat

PTP 7.0log1 10ϖ (7)

In equation (5) κ1 is specific for each pure compound and is calculated fitting the

saturation pressure of the pure compound in relation to the temperature data. The

saturation pressure and temperature data were calculated with [5], as the critical

pressure and temperature. The κ1 values for the three components are shown in Table 4.

This equation of state was used together with different mixing rules.

First of all the classical Van der Waals mixing rule (VdW1) with one adjustable (kij)

parameter for the a calculation and a linear form for the b parameter was applied, i.e.

∑

∑∑=

=

iii

i jijji

bxb

axxa (8)

with

( )ijjjiiij kaaa −= 1 (9)

Each isotherm was correlated as a separate set. The obtained kij parameters are

summarized in Table 5 and 6 for the R125 + RC270 and the RC270 + R134a systems,

respectively, together with the results of the correlation.

Then a modified version of the Van der Waals mixing rule (VdW2) was applied,

consisting in a composition dependent form for the a parameter. In equation (9)

jjiiijij xlxlk += (10)

The results of this regression are also shown in Table 5 and 6 for the R125 + RC270

and the RC270 + R134a systems, respectively.

Therefore the VLE data were correlated implementing the Huron-Vidal (HV) [6] and

Wong-Sandler (WS) [7] mixing rules into the PRSV EoS.

Comment: Controllare se scrivere lij e lji o se usare un altro parametro.

7

The HV mixing rule takes the form

⎥⎦

⎤⎢⎣

⎡−= ∞∑ C

gbaxba

E

i ii

iii (11)

∑=i

iiibxb (12)

where Eg∞ is the excess Gibbs energy at infinite pressures and C = 0.632252.

The WS mixing rule is

Ca

ba

xbaE

i

ii ⎥

⎦

⎤⎢⎣

⎡+= ∞∑ (13)

∑

∑∑

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

⎟⎠⎞

⎜⎝⎛ −

=∞

RTba

xRTa

RTabxx

b

i

ii

Eij

ji

1 (14)

where Ea∞ is the excess Helmholtz energy at infinite pressure, C is the constant defined

above, and

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟

⎠⎞

⎜⎝⎛ −

−=⎟

⎠⎞

⎜⎝⎛ −

RTa

bRTa

bk

RTab j

ji

iij

ij 21

(15)

In both these mixing rules, the NRTL equation [8] was used for the excess Gibbs

energy representation at infinite pressures, using α = 0.3.

The results of these correlation are collected in Table 5 and 6 for the R125 + RC270

and the RC270 + R134a systems, respectively.

All the models are well representing both the systems. From the results, it seems the

PRSV-WS-NRTL model gives the best correlations amongst all. In Figure 3 and 4 the

deviations from this model are shown in terms of vapour phase composition and

saturated pressure, respectively.

Comparison with literature data

Comment: Controllare che sia giusta la costante.

8

No VLE data are available in the literature for these two systems, except for one

point, referred to the liquid phase, for the RC270 + R134a system [9]. This point is

shown for comparison in Figure 2, suggesting that the saturated pressure of this point is

slightly higher (around 10 kPa) than that obtained for the present experimental VLE

data.

4. Conclusions

VLE data for the mixtures R125 + RC270 and RC270 + R134a were measured at 3

temperatures between 253.15 and 293.15 K. The data show a strong positive

homogenous azeotrope for both systems. The VLE data of the systems are well

represented by the PRSV EoS with the VDW1, the VDW2, the HV and the WS mixing

rules.

List of symbols

a = parameter in the PRSV EoS

a = Helmholtz energy

b = parameter in the PRSV EoS

C = constant in the HV and WS mixing rules

g = Gibbs energy

kij = interaction parameter in the VdW and in the WS mixing rules

lij = interaction parameter in the VdW2 mixing rule

Np = number of experimental points

P = pressure (kPa)

R = ideal gas constant

Comment: Controllare.

9

T = temperature (K)

v = molar volume (cm3/gmole)

x = liquid mole fraction

y = vapour mole fraction

α = NRTL equation parameter

∆g12, ∆g21 = NRTL equation parameters

κ, κ0, κ1 = parameters of the PRSV EoS

ω = acentric Pitzer’s factor

Subscripts

1 = low-boiling mixture component

2 = high-boiling mixture component

azeo = azeotropic property

c = critical property

exp = experimental

i, j = one mixture component

r = reduced property

sat = saturation property

Superscripts

E = Excess property

Acknowledgements

Alessandro Falcone is gratefully acknowledged for his cooperation in the

experiments.

10

References

[1] S. Bobbo, R. Stryjek, N. Elvassore , A. Bertucco, Fluid Phase Equil. 150-151 (1998)

343-352.

[2] D. Y. Peng, D. B. Robinson, Ind. Eng. Chem. Fund. 15 (1976) 59-64.

[3] R. Stryjek, J. H. Vera, Can. J. Chem. Eng. 64 (1986) 323-333.

[4] H. Orbey, S. I. Sandler, Modeling Vapor-Liquid Equilibria – Cubic Equations of

State and Their Mixing Rules, Cambridge University Press, 1998.

[5] E. W. Lemmon, M. O. McLinden, M. L. Huber, NIST Reference Fluid

Thermodynamic and Transport Properties (REFPROP), Version 7.0, Physical and

Chemical Properties Division, National Institute of Standards and Technology:

Gaithersburg, MD, 2002.

[6] M. J. Huron and J. Vidal, Fluid Phase Equil. 3 (1979) 255-272.

[7] S. H. Wong, S. I. Sandler, AIChE J. 38 (1992) 671-680.

[8] H. Renon, J. M. Prausnitz, AIChE J. 14 (1968) 135-14.

[9] D. R. Defibaugh, G. Morrison, Int. J. Refrig. 18 (1995) 518-523.

11

Table 1. Experimental vapour-liquid equilibrium data for the R125 + RC270 system.

T = 253.15 K T = 273.15 K T = 293.15 K

x1, exp y1, exp Pexp / kPa x1, exp y1, exp Pexp / kPa x1, exp y1, exp Pexp / kPa 0.000 0.000 171.3 0.000 0.000 344.1 0.000 0.000 631.7 0.033 0.210 212.1 0.039 0.208 426.7 0.030 0.146 731.6 0.104 0.395 264.2 0.159 0.431 553.1 0.118 0.343 907.9 0.173 0.484 295.1 0.274 0.515 613.4 0.209 0.442 1018.9 0.208 0.507 306.2 0.384 0.572 651.7 0.350 0.534 1126.2 0.250 0.532 315.8 0.499 0.626 680.0 0.463 0.594 1183.7 0.350 0.578 333.3 0.680 0.712 704.2 0.614 0.673 1236.4 0.397 0.597 339.7 0.758 0.762 707.8 0.695 0.722 1252.4 0.558 0.659 355.4 0.868 0.848 701.7 0.761 0.768 1260.2 0.761 0.757 362.8 0.897 0.873 697.8 0.766 0.771 1259.0 0.839 0.816 361.2 0.932 0.913 690.6 0.836 0.826 1256.8 0.939 0.913 350.9 0.951 0.938 685.1 0.911 0.896 1242.4 1.000 1.000 337.3 1.000 1.000 672.1 0.964 0.954 1224.4

1.000 1.000 1204.7

12

Table 2. Experimental vapour-liquid equilibrium data for the RC270 + R134a system.

T = 253.15 K T = 273.15 K T = 293.15 K

x1, exp y1, exp Pexp / kPa x1, exp y1, exp Pexp / kPa x1, exp y1, exp Pexp / kPa 0.000 0.000 133.5 0.000 0.000 291.8 0.000 0.000 572.1 0.115 0.308 178.5 0.058 0.154 335.9 0.067 0.152 645.8 0.189 0.406 196.9 0.183 0.358 394.7 0.172 0.307 730.5 0.299 0.488 209.2 0.307 0.460 426.1 0.207 0.340 744.4 0.388 0.533 216.2 0.457 0.535 445.8 0.306 0.421 784.0 0.504 0.579 220.7 0.518 0.570 447.9 0.463 0.516 815.6 0.617 0.616 221.4 0.601 0.597 450.5 0.565 0.568 821.1 0.674 0.638 221.4 0.613 0.604 450.2 0.596 0.584 820.8 0.730 0.660 219.4 0.685 0.635 446.6 0.691 0.633 814.4 0.870 0.745 210.3 0.910 0.805 406.0 0.763 0.676 800.7 0.971 0.904 185.6 0.978 0.934 366.0 0.828 0.726 779.0 1.000 1.000 171.2 1.000 1.000 354.7 0.929 0.844 716.6

0.966 0.910 680.6 1.000 1.000 632.2

13

Table 3. Composition and pressure of the azeotrope for the R125 + RC270 and RC270

+ R134a systems.

R125 + RC270 RC270 + R134a

T / K xazeo P / kPa T / K xazeo P / kPa 253.15 0.755 363 253.15 0.620 221273.15 0.779 708 273.15 0.599 450 293.15 0.792 1260 293.15 0.573 821

14

Table 4. κ1 parameter regressed for the pure components in the PRSV EoS.

R125 RC270 R134a

κ1 .0274 -.0020 .0295

Comment: Controllare il parametro.

15

Table 5. Results of VLE data reduction for the R125 + RC270 system by means of the

PRSV EoS with the VdW1, the VdW2, the HV and the WS mixing rules.

T / K 253.15 273.15 293.15PRSV-VdW1

kij 0.0976 0.1025 0.1033AAD(∆y) 0.0025 0.0030 0.0017 AAD(∆P%) 0.46 0.41 0.28

PRSV-VdW2

lij 0.1043 0.1034 0.1046lji 0.0934 0.0995 0.1000 AAD(∆y) 0.0040 0.0033 0.0024 AAD(∆P%) 0.40 0.37 0.30

PRSV-HV ∆g12 (J/mol) 1236.484 1097.235 819.448∆g21 (J/mol) 2817.029 2942.614 3181.652 AAD(∆y) 0.0026 0.0032 0.0017 AAD(∆P%) 0.31 0.36 0.26

PRSV-WS kij 0.1187 0.0778 0.1001∆g12 (J/mol) 1406.416 1273.258 992.858 ∆g21 (J/mol) 2534.398 3137.634 3175.364 AAD(∆y) 0.0041 0.0024 0.0020 AAD(∆P%) 0.38 0.33 0.25

( ) ∑= ⎟

⎟⎠

⎞⎜⎜⎝

⎛=

pN

1i iexpp PP

N100%PAAD

∆∆ ( ) ( )∑

=

∆=∆pN

ii

p

yN

yAAD1

1

Comment: Controllare come chiamare questi parametri.

16

Table 6. Results of VLE data reduction for the RC270 + R125 system by means of the

PRSV EoS with the VdW1, the VdW2, the HV and the WS mixing rules.

T / K 253.15 273.15 293.15PRSV-VdW1

kij 0.1150 0.1178 0.1194AAD(∆y) 0.0047 0.0043 0.0027 AAD(∆P%) 0.53 0.45 0.23

PRSV-VdW2 lij 0.1086 0.1159 0.1188lji 0.1234 0.1196 0.1203 AAD(∆y) 0.0077 0.0047 0.0028 AAD(∆P%) 0.43 0.46 0.23

PRSV-HV ∆g12 (J/mol) 2828.647 3333.700 3209.391∆g21 (J/mol) 1652.352 1136.803 1093.051 AAD(∆y) 0.0065 0.0043 0.0026 AAD(∆P%) 0.40 0.43 0.20

PRSV-WS kij -0.0946 -0.0686 -0.0496∆g12 (J/mol) 4276.453 4389.891 4245.039 ∆g21 (J/mol) 2608.009 2288.953 2221.978 AAD(∆y) 0.0030 0.0059 0.0037 AAD(∆P%) 0.27 0.36 0.18

( ) ∑= ⎟

⎟⎠

⎞⎜⎜⎝

⎛=

pN

1i iexpp PP

N100%PAAD

∆∆ ( ) ( )∑

=

∆=∆pN

ii

p

yN

yAAD1

1

Comment: Controllare come chiamare questi parametri.

17

Figure captions

Figure 1. Experimental VLE data for the R125 (1) + RC270 (2) system at T = 253.15 K

(), 273.15 (◊), and 293.15 K ().

Figure 2. Experimental VLE data for the RC270 (1) + R134a (2) system at T = 253.15

K (), 273.15 (◊), and 293.15 K (). Data point from [9] at T = 273.15 K (♦).

Figure 3. Deviations of the vapour phase composition for the R125 (1) + RC270 (2) ()

and the RC270 (1) + R134a (2) () systems from the PRSV-WS-NRTL model.

Figure 4. Deviations of the saturated pressure for the R125 (1) + RC270 (2) () and the

RC270 (1) + R134a (2) () systems from the PRSV-WS-NRTL model. (x) Deviation

between the data point from [9] and the PRSV-WS-NRTL model.

18

Figure 1

100

300

500

700

900

1100

1300

1500

0.0 0.2 0.4 0.6 0.8 1.0

x 1 , y 1

P /

kPa

19

Figure 2

100

200

300

400

500

600

700

800

900

0.0 0.2 0.4 0.6 0.8 1.0

x 1 , y 1

P /

kPa

20

Figure 3

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.0 0.2 0.4 0.6 0.8 1.0x 1

ycal

c-y e

xp

21

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0x 1

100*

(Pca

lc-P

exp)/P

exp

Figure 4

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0x 1

100*

(Pca

lc-P

exp)

/Pex

p