The Precipitation of Silver Chloride From Aqueous Solutions Part 2

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814 P R E C I P I T A T I O N

O F SILVER

C H L O R I D E

longest of these runs,

so

the whole crystallization probably takes place in accordance with

eqn.

(1).

The constant

s

n this equation can be regarded as representing the area available

for

the deposition, for the amount of AgCl deposited in any run never exceeded

1

x

10-6

mole, and amounted to only 1-3

%

of the total amount of seed present.

The experiments with only

2

ml seed suspension were too slow to follow much beyond

half-completion, and for these runs eqn.

(1)

was tested by calculating the conductivity

value corresponding to 50

%

precipitation, and reading the time of half-completion from

c

x 10 mo l e /

I .

FIG.2.-Initial rates of crystallization, ; subsequent points for expt.

27,

A ;

99,

v ;

101,

;

102,O. (Rates in mole

x

108 1.-1 min-1 ml-1 seed suspension).

the curve. For

a

second-order equation these times should be inversely proportional

to the initial supersaturation, and this was found to be true. The values obtained were

expt.

96 98 100

C-CO (mole/l. x

106) 3-22

2-69 2-07

t+ (min)

52.0 63.0 82.5

C--Co)t*

168 169 171

THE

SOLUBILITY

OF SILVER CHLORIDE

AT

25

C.-The value given in part

1

needs slight

revision in view

of

the above results. Application of eqn.

(1)

to the data given in table 1

of

part 1 shows that for expt. 45 and 76 as much as 7

%

of the precipitable AgCl remained

undeposited when the experiments were stopped. Smaller corrections are required for

the other three points, and the effect of these

is

to reduce the mean value of S (the con-

centration solubility product) from 1.82 to

1-78

x

10-10

(mole/l.)2. Neglecting one

discordant point in table

2,

the mean value of S from this second series is

1.796 x 10-10.

The extrapolated solubility from fig. 2 of the present paper gives S = 1-787

x 10-10,

in agreement with the mean. This is the concentration product in the presence of potassium

nitrate of concentration

(1.60 f 0.1 1)

x

10-5,

and if the ionic strength

Z=(294&0.1)

x

10-5

is inserted in the Debye-Hiickel limiting equation, the value

1,765

x 10-10 is obtained

for the solubility product of silver chloride at zero ionic strength. In the same way,

1-334x 10-5

mole/l. is derived for the solubility of silver chloride in water at 25 . These

values are in remarkably good agreement with those given recently by, respectively,

Guggenheim and Prue,2 and Gledhill and Malan.3

out at initial [Ag+]/[Cl-] ratios of 2

4,

0 5 and

0.25.

Suspension

D

was used in these

experiments. Eqn. 1) cannot apply where the ionic concentrations are unequal;

but

we may rewrite it in the form

EXPERIMENTST NON-EQUIVALENT CONCENTRATIONS.-Additional runs were carried

C/di =z k s h z ,

2)

where A represents the number of moles per litre to be deposited before equilibrium is

reached, and necessarily has the same value for the silver and chloride ions whatever their

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C . W. D A V I E S A N D A L . J O N E S 815

actual concentrations. A test

of

this equation is shown in

fig. 3,

where four runs at

different ionic ratios are compared

;

A, calculated from the relationship

(Cl

) C2

)

=

S

= 1.787

x

10-10,

is plotted against the square root of the velocity. Within the errors of calculation the

points again lie on a straight line, which passes through the origin.

The slopes

shown

in fig.

2

and

3

are not the same, but this does not reflect a variation

in k

;

it is due to the use

of

different seed suspensions in the two series of experiments.

Equal weights of AgCl seed were added in all

cases,

but suspensionD consisted of smaller

seed. The total surface it represented should therefore be greater than that of suspension

C by the approximate factor 4 - 7 / 3 5 the ratio of the linear particle dimensions (assuming

uniform cubes) ; the slopes

of

fig. 2 and 3 are in reasonably good agreement with this,

x lo5

m o l c / l .

FIG.

3.

Expt. 103, [Ag]/[CI]= 2 ;

expt. 105, [Ag]/[Cl]= 4

;

expt. 104, [Ag]/[Cl]= 0 5;

D expt. 106, [Ag]/[Cl]= 0.25 ;

(rates in mole

x

108

1.-1

min-1 ml-1 seed suspension).

as

are also further unreported measurements using suspension E. Within the possible

error, therefore, k has the same value in eqn.

1)

and (2). The actual surface area can

be roughly calculated, using the data of table

1

and the value 5.6 for the density of silver

chloride thus for suspension

C

the approximate value 2.2 cm2

ml 1

suspension is ob-

tained. Givings his value in eqn. (2), the velocity constant k has the approximate value

15 per cm2 with A in moles per litre and time in sec.

AGEINGF

SEED

CRYSTALS T

NON-EQUIVALENT

CONCENTRATIONS.-Aumber of further

runs were made in which the seed, before use, was equilibrated with saturated solutions

in

which the ionic ratio was varied up to a value of 10/1. After this treatment the seed

behaved precisely as before, and the runs fitted eqn. (2) without modification.

DISCUSSION

At its simplest, the crystallization of

a

sparingly soluble salt from solution

would seem to involve the following three mechanisms i) the diffusion

of

solute

to the surface, (ii) the deposition of

ions on

the crystal face, (iii) the opposing

process of solution.

According to eqn. 2) the r ate throughout the crystallization

process

is governed

by the concentration that each ion will eventually reach at equilibrium A repre-

sents the difference between this value and the momentary ion concentration.


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816

P R E C I P I T A T I O N O F S IL V E R C H L O R I D E

This at first suggested that the rate-determining process in our experiments was

one of diffusion processes (ii) and (iii) were sufficientlyrapid tomaintainaneffective

concentration corresponding to saturation of each ion at the surface, and the rate

of growth was governed by a concentration gradient A16 through a diffusion layer

of thickness 8. This diffusion hypothesis, however, would lead to a first-order

equation, and

is

therefore unacceptable

;

for silver chloride ion-pairs wodd diffuse

to the surface under a common concentration gradient, and their rate of arrival

would be given by the classical Nernst equation, = DsA/S, where

D

is the dif-

fusion coefficient of silver chloride. Much evidence that the solution in contact

with a growing crystal is supersaturated5 also tells against diffusion being the

governing factor in most crystallization processes, and the independence of the

rate on conditions of stirring points in the same direction.

Since mechanism (i) is not rate-determining, we turn to (ii) and (iii). The

saturation of a solution is frequently cited as an exampIe

of

kinetic equilibrium,

leading to the following formulation (for equal concentrations of silver and

chloride ions)

rate

of

crystallization of AgCl = kls C2,

rate of solution of AgCl

=

k2s.

In a saturated solution these rates are equal, and

so

k2

=

kl

C .

In a super-

saturated solution, assuming that diffusion exerts no influence, the net rate

of

deposition will thus be given by

This is contrary to our findings.

In any case this analysis into two independent

opposing processes does not givea correct picture of conditions in a heterogeneous

system, where we are not considering the statistical result of a number of isolated

chemical actions, but the net change at a fixed reaction site.

Special conditions prevail at the interface where the reaction is occurring, and

we may therefore postulate an adsorption layer, and formulate the kinetics in

terms of a stationary concentration of silver and chloride ions in the adsorbed

phase. We find that this will lead to the observed results on the following two

assumptions

1) A crystal in contact with an aqueous solution always tends to be covered

with a monolayer of hydrated ions. Secondary adsorption

on

this monolayer is

negligible. Crystallization, i.e. incorporation of further units into the crystal

lattice, can only occur if the resulting configuration satisfies this condition.

(2) Crystallization of silver chloride occurs through the simultaneous dehydra-

tion of pairs of silver and chloride ions.

In terms of this picture, an unsaturated solution is one in which hydrated ions

leave the surface faster than they are replaced from the solution, causing further

hydration at the surface. When the surface reaches equilibrium the rate of

adsorption of ions from the solution becomes just sufficient to maintain the

monolayer of hydrated ions intact, and it must be assumed (to avoid squared terms

in the rate equation) that every

ion

striking the surface from a saturated solution

enters this mobile adsorbed monolayer. For a saturated solution we can there-

fore write: rate of adsorption of Ag ions

=

kls[Ago+], and similarly for the

chloride ions. From

a

supersaturated solution the ions reaching unit surface

do not all enter the adsorbed monolayer, and the remainder, kl([Ag+J Ago+]),

are available for deposition; i.e. they either suffer elastic collisions at the surface

of the monolayer or, in the event of the simultaneous arrival of a silver ion and a

chloride ion at a site of growth the underlying ion pair can become dehydrated,

and we obtain

which

is

eqn. 1).

dC/dt = Icls(C2

Co2).

dC/dt

k3([Ag+] Co)([Cl-] CO ,


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C . W . D A V I E S A N D A .

L .

J O N E S

817

In the foregoing we have assumed that the adsorbed monolayer contains

equal numbers of silver and chloride ions,

so

that there is no differenceof electrical

potential between crystal and solution.

This will not generally be true. Even if

the concentrations of silver and chloride ions in a saturated solution are equal

there will be a difference between the numbers of silver and chloride ions adsorbed

owing to the difference in the adsorption energies

of

the ions. This difference

will

be

too small to affect the validity

of

the equation just developed. It is im-

portant, however, to consider cases in which the concentrationsof silver and chloride

ions in the solution are unequal. Suppose a seed crystal is immersed in a solution

in which [Ag+]/[Cl-]= r , where r

>

1 . At first more silver than chloride ions

will be adsorbed, and a potential difference will be established between adsorbed

layer and solution. The equilibrium value of will be such that silver and chloride

ions enter the adsorbed layer in equal numbers. An electrical double layer now

surrounds the crystal, and the former equations must be replaced by

availability of Ag ions at the surface= kls[Ag+] exp - ( R T )

availability of Cl ions at the surface

=

kls[Cl-] exp

( /RT).

Since these are equal, exp ( / R T )= [Ag+l*/[Cl-]*= 4.

The number of ions of each type entering the monolayer in unit time is as before

CO nd the rate

of

crystallization becomes

dC/dt = ks([Ag+Jr-* Co)([cl-]~*

CO

kls([Agf]*[Cl-]*

C O ) ~ .

3)

If

ro is the

final

ionic ratio after equilibrium has been reached, the equilibrium

concentrations of silver and chloride ions are respectively Coro* and Cora- for

[Ag+][CI-]

=

C02 and [Ag+]/[Cl-]= ro. Eqn. 2) can therefore be written

and it differs from the equation just derived in containing the equilibrium ionic

ratio instead of the actual ionic ratio.

A comparison of the two equations shows that they are not compatible; if

k in eqn.

(2)

is constant, kl

of

eqn. 3) will vary by up to about 3

%

during the

course of a run, and vice versa. This is within our experimental error, however,

and experimentally it is impossible to prefer one equation to the other;

fig.

3

shows the good agreement with eqn. 2), and eqn. 3) is illustrated in part 3

(following paper). When runs at differing ionic ratios are compared, k (eqn. 2))

remainsconstant;

k l ,

on theother hand, depends on the ionic ratio, and has its

maximum value when this is unity. Eqn. 2) is therefore the simplest representa-

tion of the facts within the restricted range of concentration and ionic ratio that

we were able to investigate; but from the mechanism of crystallization outlined

above a variation in kl will be expected, and will reflect the restriction, through

adsorption, of the number of sites available for growth.

Further data in conformity

with this idea are given in part

3.

dC/dt = ks([Ag+] Coroi)([Cl-] Cora-*),

We

thank the D.S.I .R. for a grant to

A.

L.

J.

1946-49) during the tenure of

which this work was carried out.

1 Davies and Jones, Faruduy

SOC.Discussions,

1949,

5,

103.

2

Guggenheim and Prue,

Trans. Furuday

SOC.,

954, 50,236.

3 Gledhill and Malan,

Trans. Fizroduy

Soc.

1952,48,258.

4

Landolt-Bornstein,

Tabellen,

5te.

Aufl.,

I, 307.

5 Miers, Proc. Roy. SOC.A ,

1930, 71, 439;

see Bunn,

Faruday

SOC.

Disczrssions,

1949, 5, 132.

Wells,

Ann. Rep orts, 1946,

43 7 3 .


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The Precipitation of Silver Chloride From Aqueous Solutions Part 2

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