_____________
PRESENTED FOR
_______
THE
""""""'...,...
DEGREE
OF
/Vo. .:~ ~ CJ ·
•
#
#
r
'
•
'
.. .,._
.,._
-
"•
THE
SOLUBILITY OF
IN
A MIXED
CHLORIDE
SOLVENT
METHANOL)
-------
( 20%'
FROM
15°0 TO 45°0
--------
..
••
0
EXPJj)RIMENTAL METHOD
••
••
••
17.
Mat~rials
••
••
17.
Electrodes
••
..
••
••
19.
Cell
••
...
••
20.
Other Apparatus
....
INTRODUCTION
••
TABLES AND GHAPHS
•
••
•
0
25.
••
.
CALCULATION OF RESULTS
"
DISCUSSION
••
SUMMARY
"
HEFERENCES
••
.
23.
•
0
38 ..
..
••
" ..
"
.
49 ..
•
•
51.
44 ..
1
1HE
OF
CHfUSTCHURCH, N.;;>:,
With the development of theories of interionic
attraction and of solvent interaction solubility data have been
used for the estimation of ionic diameters and the degree of
solvation of ions.
The parallelism between the dielectric
constant of a medium and its solvent power on ionic crystals
has been recognised for a long time, and the quantitative expression which links these properties may be derived from
equation.
Bo~'s
This gives the free energy of an ion, carrying
charge Z1
, where
e is the charge of an electron, in a medium
of dielectric constant Dr as
1
E
Dr
where al"is the radius of the ion, which is assumed to be
spherical.
Then the work of transferring the ion from a medium
of dielectric
constant DJ.
to a, medium of di,el,ectric constant.
(~This work of transfer can be equated to a free energy change,
whose value is
2 ..
G
-
per iont where f 1
k T ln
and
f2
are the activity coefficients of the
ion in the two media ..
Imagine a fairly insoluble salt such as silver
chloride dissolved in a medium of dielectric
also in a medium of dielectric constant n2 •
con~tant
If G8
molal free energy of the solid silver chlorid.e, and
-GD
D19
is the
-
G~
and
the sum of the partial molal free energies of the ions in
2
saturated solutions of solvents of dielectric constant n1
D2
and
and
respectively, then
-G~
By assuming that the
satu~ting
salt is a perfect
solute, this expression can be replaced by
-where N1
and N2
and
-
are the mol. fractions in the two solvents ..
In a medium of particular dielectric corll!Jtant there must also be
an additional term per mol. due to electrical forces, since the
ions are assumed to be charged spheres.
So that
and
......
where N is the Avogadro number, and from these equations is
obtained
To correct for the ions not being perfect solutes,
an expression for the activity coefficients must be added to
both sides so
RT ln f 1 ::: RT ln N2
+
Nz!=-~-=-
+
RT ln f2
2al D2
where f is the activity coefficient on the molrll concentration
scale.
On changing to S, the solubility ln molse per li trtt 1
the oquatJ.on becomes
where y is the activity coefficient on the volume concentration
scale.
From this
-...
Nz1 2 e2
---2a1 RT
as ln y
=
cl zl
1
'\
- -Dl/1
.... 1
!J
D2
2
according to the Debye-Huckel theory, where (-Y is the ionar
concentration, and A and B are comstants.
This gives the
relationship between the solubilities :tn two solvents tn terms
of the Debye-Huckel
constants ..
for~ula
for the solvents and of their dielectri<
Actually the effect of the Debye-Htickel eorrections
is rather small, as the two terms$ being about equal :tn magnitude 1
nearly cancel each other.
against.!
Because of this, plotting ln S
would be expected to give a straight line for any
D
one
substan~e
..
However the treatment by which the Bor6lequation
is derived is essentially elementary, and the equat:ton should
only be regarded as an approximation.
In the simple derivation
of the energy of interaction between ion and solvent
BoMn
assumed the dielectric medium to be homogeneous and structureless.
Actually water is molecularly complex, and the single
molecules are highly polar ..
Owing to the intense electric
fteld in the immediate vicinity of the ions, the solvent
molecules are completely oriented, and are powerfully compressed by the field.
When the solvent is a mixture of water
and methanol, then the system becomes still more complex.
The more polarizable molecules will be preferentially oriented
around the charged ions, and by changing the composition of the
bulk of the solvent, and also affecting the dielectric constant
of the medium close to the ions, the adsorption of water has a
tremendous effect on the solubility.
rough agreement, as found by Bjerrum~ 2 5
Consequently only the
is to be expected.
6 ..
METHODS OF MEASUREMENT
~...-----~-------"
The methods of measuring solubility are
numerous and make use of various types of phenomena, the choice
depending on the degree of solubility and the accuracy required.
While analytical methods are quite satisfactory for salts which
are appreciably soluble, they are of limited value when applied
to salts which are only slightly soluble.
Glowezynski
1
has
determined the solubility of silver chloride in water by evaporation and separation of the silver electrolytically from cyanide
solution ..
The silver was dissolved in nitric acid 9 and
titrated with ammonium thiocyanate.
He obtained a value of
1·20 x 10-5 mols .. per litre at 25°0.
Davis; Ricci with Sauter 2
have measured by titration methods the solubilities of barium
iodate, silver acetate and silver sulphate in dioxane - water
mixtures.
These solubilities must be of the lowest order that
such methods can measure with any degree of accuracy.
For
accurate values the solubility of silver .chloride must be determined by using other methods.
Popoff and Neuman3 developed an optical method,
using the
Tyndall effect, to obtain a value of 1•278 x lo- 5
mols. per litre for the solubility of silver chloride in water
Neuman 4 later increased the sensitivity of this
1•
method, when he measured the solubility of silver chloride in
aqueous solutions of some sulphates and nitrates, by increasing
the concentrations of the reacting silver and chloride ions till
a trace of solid silver chloride was detected in a Tyndallometer.
By extrapolation he calculated the solubility in pure water at
25°0 to be 1•273 x lo- 5 mols. per litre.
Dave and Krishnaswami
5
Johnson
nephelometrically obtained 1•388 x 10-5 mols. per litre.
and Low6 measured the solubility of silver chloride in nitric
acid solutions at o°C
by both a nephelometric and a potentiome-
tric method, obtaining good agreement between the results.
Conductance methods, first extensively used by
Kohlrausch7, are very suitable for measuring low
solubilities.
International Critical Tables, by a short interpolation from his
data at other temperatures, obtain a value of 1•304 x lo- 5 mols.
per litre for the solubility of silver chloride in water at 25°0@
More precise measurements of low solubilities can
be made by means of electromotive force methods.
Macinnes8
Brown and
used a potentiometric titration method for measuring
the solubility of silver chloride in potassium nitrate solution.
Concentration cells were used, the solution on one side of the
liquid junction was kept
constant~
serving as a
half-referen~e
cellp while potassium chloride solution was added to the other
half.
The liquid junction potential was then allowed
and a correction applied
for the change in volume.
for~
In computing
8 ..
the solubility of silver chloride in pure water, some of Neuman's
data was used, and a value of 1•314 x lo-5 · mols. per litre at
25°0, in good agreement with the figure from conductance measurements ..
Electrometric titration was used by Dunning and Shutt 9
in determining the solubility of silver chloride in aqueous
solutions of glycine and urea ..
The value for the solubility
j_n pure water obtained was 1•68 x lo-5 mols. per litre~
A method using cells with liquid junctions, but
whose liquid junction potentials are eliminated 11 has been
developed recently by Owenlo ..
Since essentially the same
procedure is followed in this work 11 the method is described in
detail ..
The cell may be represented as follows KCl (x) m
KN03 (1-x) m
_
\LAgNOJ (x) m \
KN03 m KNOJ (l-x) m ~ AgCl» Ag
1
The total ionic coricentration in each solution is 2m 11 but a
fraction x
2
of this is composed of chloride ion in the left-hand
compartmentt and silver ion in the right-hand compartment.
The
e .. m.f. of such a cell is given )y
E
=
RT
ln
a'
Ag
Ej
]'
where Ej is the sum of the unknown liquid junction potentials 9
and a'Ag
and a"Ag
represent the activities of tha silver ions
9 ..
in the right-hand and left-hand solutions respectively.
If we
write
k
=
= -RT
F
0•00019844T
log e 10
since the solubility product in the left-hand solution is
K
-
a tt .lAg ..
att
01
then the expression becomes
E
so that
=
E~' - k
a" Cl +
- EJ.
k log a'Ag
log a r .Ag
-r
a 11 Cl
--
-
k log K -t- .ldl
.,1'•'j
The introductions of the concentrations x m, and the individual
ionic activity coefficients leads to
E - 2 k log xm
=
- k log K
k log
f'
Ag
f
11
Ej
01
since the molalities of the silver ion and chloride ion are both
x m..
Variation of x while m is held con.stant must yield on
extrapolation to x ::.o
m] : -
[ E- 2k log.x
x_-)'o
k log K
k log f' Ag f" 01
0
as Ej becomes zero under these conditions, there being the same
solution in each compartment.
For convenience in graphing the
10 ..
experimental results, the term 2 k .A
m
9
where A is the
Debye-Huckel limiting slope 9 given by
for a solvent of dielectric con,stant D at a temperature T 9 is
added to both sides.
Then
[E ... 2 k log xm '"'r2 k
Arm]:::
- k log K+ fk log f'
L
x~o
If this expression is plotted against m
extrapolation tom: o
is equal
to~
t
f"
01
4-2 k
!Aj;J
x·~~jo
the value obtained by
k log K
of the silver and chloride ions at m: o
Ag
~·
as the activities
are unity, and the thi
term on each side also vanishes.
Using this method, Owen10
obtained the value of
1"334 x 10- 5 mols .. per litre for the solubility of silver chloride
in water at 25° ..
The following table shows the amount of
agreement obtained.
Observer.
G1owczynski
Popoff and Neuman
Neuman
Kohlrausch
Brown and Macinnes
Owen
Analytical titration
Tyndall effect
tt
II
Conductance
Potentiometric titration
E.M .. F. measurement.
1·2 x
1•278
1·273
1• 304
1· 314
1•334
lo-5
x lo-5
x lo-5
X 10""5
x 1o-5
X 10-5
lL.
The variation in the physical condition of the
precipitated silver chloride is undoubtedly responsible for most
of the discordance.
Pinkus and Hanrez 24
by a potentiometric
method measured the solubilities of seventeen samples of silver
chloride in 0•1 molar potassium nitrate solution at 25°.
They
got the same value for all solutions except the fine colloidal
suspensions 9
~vhich
gave rather higher resul ts 11 showing that the
particle size of the silver chloride affects the solubility.
11
Davis
measured the solubility of silver chloride
in 10% methanol solution, obtaining the value of •990 x lo- 5
mols .. per litre at 25°0, and the present work continues the investigation to the solubility of silver chloride in 20% methanol
solution.
From a knowledge of the value of log K over a
temperature range there can be derived thermodynamical data for
the reaction
+-
Ag.Cl-7Ag. +Cl
...
From the Van't Hoff isochore
can be obtained the change in the heat content$
0
H » since
so that
The change in the heat capacity at constant
pressure,
Cp 0 ~ can be obtained by differentiating the change
12.
in heat content with respect to temperature 9 in accordance with
Kirchoff's equation
The change in entropy can then be calculated by
using the formula
Latimer and Slansky 21 have obtained the entropy
of solution of HCl, NaCl, KCl and KBr in water-methanol solution
from pure water to pure
met~anol.
The entropies were obtained
from the formula
The heats of solution have been measured by
Slansky, and the free energies of solutions were obtained from
solubility and activity coefficient data.
From the entropies
of solution thus found~ and the entropies of the compounds given
22
by·Latimer 9
the sum of the partial molal entropies of the ions
forming each compound were calculated from
0
x-
::: As 0
13.,
-o -+-So
s
H-tCl""'
so -+-so
Na+ Cl-
so+so
cl1\~
so +so
K+
Br-.
Water
13•6
27•6
37•9
43•9
10% Methanol
14·1
27•7
37·6
43•5
20% Methanol
14·4
27•1
36•7
42·9
Partial
so
Relative Ionic
H+
!!!_~!2•
so
Na-1-
so
Water
14·0
24•3
13· 6
19·6
10%' Methanol
13·6
23<>5
14<~1
20•0
20% Methanol
12 .. 7
22·3
14·4
20·6
K+
so
Cl-
so
Br-
The entropy of solvation of the pair of gas ions 9
M~ and
x-
9
is given by the equation
,6so
Solvation
=
s0
t..r'-
~t-s 0
x.-
The entropies of the gas :tons are calculated by
means of the Sackur-Tetrode equa til. on"
--
s
where
k
m
v
h
N
=
R
Boltzmann constant
mass of a single molecule
volume of 1 gm.-mol .. in c. Co
Planck's constant
= Avogadro number
!Ill
--
-
~]
14.,
When this expression is expanded it becomes
s
~
2
:::
=
as
PV
1
1
fl.
2
v +
R ln (mT)
R ln l.g1fk}
h3 N
+- ,2
ln M
;-
5
2
R
R ln T - R ln P - 7" 26 7 ;~ 4,. 96 7 ..
2
2
=
k N T
and evaluating constants.
~
a
This is expressed in calories per grn-mol., and for an ideal gas
at 1 atmosphere
S
0
:::
~
R
ln
5
M
2
R
ln T - 2 • 300 "
2
The entropy correction for volume change ',d.s R ln
_g.!: 46
Sp.Vol.,
for any solution.
Latimer and Buffington
26
suggested that the entropy change
for the process
Ion(gas)
-~~,?·Ion
.
(so.lvrated)
is a function of the ion chargell and th(e radius o.r the ion
cavity in the solution so that ,1\ S
Latimer and Kasper
of the funretion.,
27
=
f (a:)
considered the theoretical evaluation
They assumed that the total entropy of solva-
tion was due to two effects: As 1
pOJ.arisability Of the inedium 9 and
t
the entropy change due to the
82
p
the Change due to the
compression of the solvent» through the electrostatic attraction
of the solvent molecules.
15 ..
After evaluating the expressions they derived for
these quantities, they concluded from a comparison of the
theoretical and experimental values that
that the entropy of solvation was largely due to the compression
of the solvent.
small entropy
So the orientation of dipoles gave only a
cihange.~~
compressed molecules
but the lowering of thermal energy of the
~as
large.
This was the opposite of
th~
magnitude of these effects in the free energy of solvation.
Latimer and Slansky
21
calculated the sum of the ionic
entropies of solvation for certain salts, and found that -As
increases from water to methanol
% methanol
NaCl
KCl
KBr.
0
10
20
20· 5
50
100
58e 5
This may be due to the larger entropy of the methanol
molecules 9 so that there is a greater decrease in entropy when
they are bound by an .ion.
Expressing this physically» this
means that in water hydrogen bonding gives a tetra-coordinated
structure 9 and so the entropy of the water molecules is less than
if the liquid were normal, and the motion of the molecules were
16.
random.
The entropies of solvation of pairs of gas
methanol~
although larger than in water, are less spread
ion~
in
for
the different salts 9 and the effect of the ion size is less in
methanol.
Ma. terials.
Hopkin & Williams• !Analar salt was purified
~.2!~!!Si~_.Qh!.Qri2:~·
by two recrystallisations from distilled water ..
The crystals
were dried in an air oven at 120° for several hours.,
Potassium____
Nitrate.
-----==-"""""
_
British Drug Houses' salt of A. R. purity
was purified in a similar manner, by two recrystallisations and
drying ..
Silver Nitrate.,
---------"""""--
Johnson Matthey and CO's. pure silver nitrate
was twice recrystaJ.lised from distilled water.
dried in an ai.r oven at 100° for several hours.
The salt was
The final pro-
duct had a very faint brownish tinge.,
!All these salts were kept in a dessicator while not being
used, to prevent the absorption of
Meth~!:!.2!•
Kahlbaum's
11
moi~ture ..
Purett methanol was purified by fractional
distillation with an efficient still head 50 ems. high.
The
middle fraction of the distillate was refluxed for several hours
over a water bath with 1% by weight of calcium turnings.,
this was filtered and redistilled ..
Then
The liquid distilled over
at a constant temperature, the first and last portions being discarded ..
This methanol had a B.. P. of 64·5°0.
Weissberger and
The refractive index was
determined by means of an Abbe refractometer» and for the Sodium
D line at 20°0 was 1·3293.
Weissberger and Proskauer give the
refractive index as le3286~ and W.J. Childs 13 gives a value of
1.3292 ..
In making up the 20% methanol - 80% water solvent,
this alcohol was assumed to be pure 9 and distilled water was used ..
The liquids were weighed out on a balance accurate to ·01 gm.
The solvent was made up in approximately four litre lots, and was
stored in a bottle,from which it was drawn off by means of a
siphon.
A calcium chloride
tube~
the only access to the air,
ensured that the proportions remained unaltered by preventing
absorption of water ..
As a check the density of the solvent was
determined with a pyncknometer.
Harned and Thomas 14 give the value of ·9681 at the same tempera~
ture.
______
Solutions •
.....,."""""
Weights calibrated against the laboratory standard
by the usual methods were used for weighing out the salts.
were considered accurate to •0001 gm.
the ratio of salt in each solution
{x
They
As it was important that
1 - x)
should be very
accurately known 9 weighing by difference could not be employed.,
Accordingly the calculated amounts of salt were exactly weighed
and transferred to the stock-bottles 9 great care being taken to
brush out any salt adhering to the walls of the weighing vessel.
The solvent was weighed out accurate to •01 gm., and the •05 m
stock solutions thus made up were diluted successively to the
19 ..
other strengths.
In this way the ratio of the salts in th.e
solutions was constant.
These silver chloride electrodes were of
electrolytic type.
th~
They consisted of •75 sq.cms squares of
platinum gauze welded to platinum wire which made contact with
mercury through glass tubes..
These were plated with silver by
deposition from a cyanide solution
(7 gms. AgNo 3
10 gms KCN in
200 c.c., distilled water) using a silver rod as anode, a current
of 2 milliamps. per electrode being passed for 16 hours.
The
excess potassium cyanide present immediately removed any silver
cyanide tending to form at the anode..
It had been found that
when silver cyanide came into contact with.the electrodes,
J;Ha.tches subsequently appeared on chloridising.,
a solution of potassium silver cyanide
For this reason
(K Ag (CN)2) formed by
crystallisation from a solution containing KCN and AgN0 3 had been
found unsatisfactory, in addition the silver cyanide deposited
round the silver anode caused a drop in current due to polarisation, and so gave a thin silver deposit.,
After
plating,~~
the electrodes were washed in
running tap water for eight hours, and
water.
This was most
sat~:factory,
fi~ally rin~ed
in distilled
boiling diBtilled water could
not be used as it frequently caused cracks in the sealo
20.
Electrodes were then chloridised anodically in
•1 N H 01 solution for 30 minutes with a current density of 6
milliamps. per electrode, the treatment recommended by Allmand
and Hunter. 15
The electrodes were both plated and chloridised
in series as recommended by Owen, 10 to ensure that the
thermodynamic properties of the metallic silver cancelled in the
operation of the cell.
El,ectrodes prepared in this way agreed
to ·1 m.v. except on a few occasions.
All electrodes were left
standing in the chloridising solution for four days as recommenMed
by Smith and Taylor, 16
and before use were washed in running tap
water and then in distilled water.
After use, the electrode~ere cleaned as follows:
silver chloride was removed by means of •880 ammonia solution,
and the silver by standing in warm dilute nitric acid.
cold acid was
used~
and was found to be effective.
Sometimes
After
cleaning, the electrodes were washed in running tap water and
finally stood in distilled water.
Electrodes were used only
once to avoid any possible poisoning.
The cell used was similar to that used by Owen~lO
and is shown in Figure I.
It consisted of three separate com-
partments, joined by two three-way taps F and G.
The end
compartments possessed two side-tubes each, and a barrel into
21 ..
which the silver chloride electrodes were fitted.
After the
electrodes had been fitted into rubber stoppers and rinsed in
cell solutions 11 they were placed in the end arras 11 the joints
being made air tight with collodion..
Rubber plugs with clips
were placed over the outlets of the taps F and G.
All air was
then displaced from the cell by hydrogen, which was passed in
through taps D and E.
The solutions were made up in bottles fitted with
calcium chloride tubes and siphons which could be attached to the
f:i.lling tubes A 11 B11 and
c.
by meam:; of ground glass joints.,
Be-
fore filling the cell, pure electrolytic hydrogen was presaturated
with the solvent, and then passed through each siphon in turn 9 so
that it bubbled through th'e solution and displaced all the air
from above it.
Potassium nitrate solution was first run into
the centre compartment 9 and into the barrels of the taps F and G..
The side arms were next partly filled with their respective solutions, and this was left standing for some minutes.
solutions were flushed
Then the
out through the taps F and G, and the
arms were refilled until the solution was about one inch below the
stoppers~
The outlets of the taps F and G were closed, and
whole cell was placed in the thermostat.
th~
It stood there for fully
twelve hours before measurements were made, an aged cell such as
this came to equilibrium very quickly after a change in temperature to give a value which was reproducible within narrow limits.
'<.
-
A
~
c-.
____ ·~·..)
r.~~··~j~·.~ \ .
(
-
22.
23 ..
If cells were not put aside to age, they took a long time to
reach equilibrium after each change of
temperature~
and the va.lues
obtained would be much greater than those obtained by letting the
cell stand overnight,
A disadvantage of the cell used was the formation
of the three-way taps F and G.
Those used by Owen lO had the
three arms lying in the same plane and spaced at 120° to each
other.
This enabled him to flush out the barrels after each
reading and so obtain clean reproducible boundaries.,
In the
present apparatus, however, the barrels could not be flushed out 9
and consequently mixing occurred» so that sometimes a white
precipitate of silver chloride was thrown down in the centre compartment, and even appeared at times in the compartment containing
the potassium chloride-potassium nitrate solution.
This mixing
would account for small discrepancies noticed at higher temperatures, and also for variations in E.M.F. obtained on lowering
the temperature at the end· of a run.,
Between runs the cell, the mixing bottles and
the siphons were cleaned in a hot chromic acid solution, washed
in tap
w~ter
and distilled water, and then dried in an air oven.
Measurements were made at seven temperatures:
15°c. 20°C, 25°0p 30°c; 35°Cp 40°C, 45°0.
A gas heated
thermostat was used, controlled by a mercury-toluene regulator@
This maintained a steady temperature 9 as recorded on a thermometer
which had been calibrated against the laboratory standard.
To
0
keep the temperature of the thermostat at 15 C it was necessary to
use a lead cooling coil, through which tap water was run.
!
The
changes in temperature were made by running in hot water as cold
water ·was run out.
The temperature change was then gradua.l 11
and was carried out in about five minutes.
A Leeds and Northrup Co .. potentiometer was used,
having a range from 0-2·2 volts and reading to •1 m.v.
The
Weston standard cell used to calibrate the instrument was checked
against the laboratory standard, and corrections for temperature
were applied whenever it was used.
A Cambridge Instrument Co .. galvanometer of the
D'Arsonval type was used 9 having a sensitivity of 1800 m.m. scale
divisions per
have this
mi~ro-ampere
s~sitivity
at 1 metre.
It was necessary to
on account of the high resistance of the
25.,
In Table I are recorded the observed electromotive
forces of the cell
AgNO' (x) m
KN03\l-x) m
Ag, AgCl
I
AgC11 Ag.,
at the seven temperatures 15°CJ 20°0 9 25°0 9 30°CJ 35°0 11 40°0 and
45°Co
The values of the expression
[E
- 2
k log x m + 2 kAJID]
calculated from these e"m.f's are given in Table II ..
These
values are plotted against x in Graph I and extrapolated to
x
=o
9
the list of the intercepts being given in Table III"
These values of the intercepts are plotted against m in Graph II »
and the intercepts at m
Table IV ..
= o are
the values of - k log K given in
26.
TABLE
I ..
----~
Observed Electromotive Force
Temperature.
15°c.
20°c.
'30 oc.
35°0.
40°0.
45°0.
•4081
•3873
•3718
•3509
4031
•3820
•3661
• 3448
•3985
• 3769
•3610
•3396
<~~3936
•3841
•3626
•3479
•3264
•3788
•3568
•3421
•3203
•3739
•3517
•3369
•3139
·3685
•3465
•3301
• '3080
.. 3643
•3432
o3289
•3066
•3586
•3369
•3217
•2999
•3535
•3317
<>3159
•2937
"'3479
•3243
•3097
·2871
• 3301
•3092
·2942
•2727
e3238
•3022
•2872
•2656
3182
•2961
•2803
•2584
3119
•2895
•2738
•2518
.!!l--=-.2.:.<2.2·
X
0·6
0•4
0•3
0•2
25°0.
s ..
"4236
•4033
·3886
·3690
•4186
•3976
0 38'30
•3631
e 4134
•3920
•3774
•3563
0
•3716
•3549
•3334
!-::_Q~]·
0·6
0•4
0•3
0"2
·4002
·3801
.3656
"3453
.. 3948
.. 3744
•3597
e 3390
"3890
·3684
·3537
•3325
~-=-Q.:.0 2 •
0"'6
0°4
Qo3
0•2
@3819
3616
'"3474
3270
0
0
"3760
• 54
•3410
·3201
•3700
·3492
3340
·3130
0
~-=-Q.:.Q1·
0•6
Q .. 4
0•3
o•2
.. 3489
e3288
•3144
·2946
•3426
.. 3222
o3080
e2875
•3365
e3159
·3012
•2801
0
0
27.
TABLE
I
(/J
0°!!~~E2~~i~S_!!1u~2f
Temperature.
15°0
20°0
25°0
30°0
A/lu)
35°0
40°0
45°0
•6067
•6070
•6070
•6069
•6055
•6058
"6056
•6057
•6041
•6044
•6039
"6042
•6062
"6061
"6060
"'6057
'"6047
•6045
"6042
"6041
"6034
•6033
•6028
•6029
•6043
"6042
•6043
"6040
•6033
•6032
•6032
•6029
•6019
•6016
"6017
•6014
•6033
•6035
•6035
"60'34
•6022
"6021
·6017
·6018
•6009
•6007
"6006
•6008
~-= O•Ql
X
o•6
0•4
0•3
o•2
[E- 2 k log xm+ 2 k
·6130
·6128
·6126
•6129
•6115
•6114
·6111
•6114
·6097
·6093
o6096
o6092
•6081
·6084
·6083
o6083
~-=-Q!03
0•6
0•4
0"3
0°2
.6118
·6119
o6117
•6116
e~6102
"6103
•6102
"6100
•6084
·6086
•6086
•6083
•6074
"6074
•6073
"6072
m
0•6
0•4
o·3
0•2
o61ll
<>6109
<>6110
•6107
<>6093
<>6092
•6093
•6089
~>6075
•6074
·6071
·6070
=
• 2
<>6059
•6060
•6057
•6056
~-=-Q,:01
0•6
0•4
0<>3
o·2
·6099
·6098
·6097
<>6100
•6082
·6082
·6084
o608'3
•6066
·6067
·6068
·6065
•6049
•6052
•6051
·6048
OF
GP~PH
VALUES
IN
( E - 2 k log xm + 2 k A \fiD
TABGE
)
28.
II.
ag~:dns t
x.
0.?
Volts.
.6130
.m
. tttt1
.;
m
=
o. 03
m = 0.02
.6100
" u
.;;
IDt~
~mllif~~r: . -. .•
Itt'"
u
·HHI
..,.
'
0
. 6060
. 6070
. 6060
. 6050
.6040
(Continued )
GPJiPR
o.o
=
UF'
VALUES
IN
0.2
TAB LE
II.
29.
(Continued)
0.6
V lts.
'"'
.6070
=
m =
o. OS
J
Q.
C) ~=
• r-; o6-Q
Tl:h
=
0.03 .,
0 o 0"2
. 6 04 0
o
6 30
I
~~
.01
H+++-H
HfttH
•.6 ' 60
• 6040
."0 30
~HH
D
IHH
. 6 0 2.0
0
~I
.6030
• 6020
..
•
· ~
.
.6010
.; ...
'
-..
~
I:
:::
. 6000
1
GRAPH
- k log K against
m-
n: p. gq
ffi.TT a
0.02
30.
II.
m.
o. 06
o.o~
·t·
'r
+rt:
,.;h'
'
i+t
ft]
:._!+;l"'FI±
1-+i:.n
;:;
ii
,....._
: '-++
K=J
. 6030
'""+
I :~ :;J.U
H:!tt
•fT·
·~ lt'~it
~-
,... 141!
.6020
fl•IJEffi
Pi'
· +~
. 6010
It
::i
34o
!ABLE III ..
-
!~~~!~~~~!_f£2~_firs~-~~~!~E21~~i2~-~2-!-=-2·
Temperature.,
15°0
20°0
25°0
. 30°0
35°0
40°0
45°0
•6082
•6068
•6055
•6041
.. 6080
•6067
10
6052
•6036
•6024
@6071
•6057
•6041
•6028
°6014
m = 0•0
•6128
•6112
•6094
~-=-Q.!Q]
•6114
.. 6098
m
•6106
e6089
m
=
=QeOl
35 ..
!!BL~_il,.
... k log K..
-log K(obs) ..
10•65
10•44
10•25
10•04
9·86
9•68
9•49
10•65
10•44
10•24
10"04
9·86
9·68
9·50
•6091
o6074
6057
•6041
o6025
•6010
.. 5996
15°0
20°0
25°0
30°0
3500
40°0
45°0
- log K{ calc .. ) m0 x 10 5
0
0 0xlO
•460
•475
•599
•752
•953
1"180
1•452
1•778
"725
•917
1•133
1•390
1•716
Eo
Eo
~579
!AB~!L....Y•
k
15oo
20°0
2500
30°0
35°0
40°0
45°0
!!J?LE
S).
15°0
2500
35°0
45°0
10
•615
o990
1° 539
2•315
•9681
•9663
•9644
o9622
•9598
<>9572
•9544
72o84
71"02
69•20
67•48
65o75
64·13
62·60
•o5717
•05816
•05915
0
06015
•06114
•06213
•o6312
X
do
D
5
AgCl
•2141
•2116
•2088
"2057
•2025
•1991
<>1955
Ag
•8232
•8190
•8145
•8098
•8050
•8001
•7951
Yl·
82
X
10
·460
·725
1•133
1"716
-
1
Dl
5
01288
"01350
•01416
@01486
0
1
-D2
·ol371
•01445
.01521
•01600
a x. 10 8
1*05
1•12
1•22
1•'37
5
L\ Ho
15°0
20°0
25°0
30°0
35°0
40°0
4500
16p390
161)310
16g230
16;t130
16,040
15,950
14jl040
14,000
131)960
13 9 920
13,880
13,850
1311820
15~860
LlH
15°0
25°0
35°C
LlG
0
L\so
16p022
15.!1'653
151)\ 313
9e19
7•90
6o77
!hl?1~L
16,180
15,980
15t770
L\s 0
8•15
7•88
7•61
7•31
6·99
6•71
6•41
Cpo
-34•7
-35o5
-36·3
g ..
-20•0'
-20•5
-21<>4
D.opo
-16•8
-17•1
"-17•3
-17•7
-18•0
-18•3
-18·6
J7o
Water - Methanol Solutionso
----~-----~~--~~--~-------
Weight of
CH30H%
JAgCl
KCl
NaCl
HCl
0
.. 23 .. 1
-22•9
-31•7
-36•4
10
-23•3
-2
4
-32•1
-36•0
20
-23<>6
-24•3
-32"'4
-35•7
From the observed electromotive forces E, values of the
expression
[E - 2 k log xm
+- 2
J
k A Jiil
were calculated, the quantities k and A being given by means of
the formulae
and
k
=
RT
-F
!A
-
<>506
The values of
.
solut~on,
D,
log 10
e
-
0•00019844 T
______ii_T
~78•54
X ______
298•1)~
the dielectric constant of
ok erlo.,
.. f 17
were taken f rom the results of A
20%
methanol
the values
at intermediate temperatures being obtained by interpolation.
The values calculated for each temperature are given in Table
v.
By using the method of Owen}0 the intercepts from the
second extrapolation give - k log
K~
and values of - log K
calculated from these data are given in Table IV..
following method was employed to find m0
per kilogram of solvent, and c 0
li.tre ..
!)
,
the solubility in mols.
the solubility in mols. per
The thermodynamic solubility produet
K
:::
as
a
:::
aAg~t~
acl-
mAg·I"
mel-
mf·
Then the
JAgt
rl-
39 ..
= log
and - log
f
m0 2
= A~
from the Debye-Huckel
theory of dilute solutions.
So
log
mo
-
1
~
log K
A
log K
A
1
since
Co
::::
2
--
mo do
For a first approximation, assume that
=
Then log
m0
So a value of m0
:;:;
=
1
log Ko
2
may be derived.
Substituting this
value in the right-hand side of the equation gives a new value of
m0
»
which is again substituted, the process being continued
until a constant value of m0 is obtained.
approximation~
m0 •
In this case two
were found to be sufficient to give constancy to
The results obtained are listed in Table
IV~
together
with the values of C0 obtained by multiplying by the density d
40 ..
The densities used for this purpose were taken from the dat~ of
14
Harned and Thomas · 9 and are listed in Table V. It was necessary
to extrapolate to find the density at 45°0.
By combining the values of - k log K with the standard
potential of the silver chloride electrode
0
E AgCl
9
the standard
electrode potential of metallic silver can be c.alculated by the
use of the relationship
0
E Ag
=
k log K
+
0
E AgCl
0
Data for E AgCl
in 20% methanol solution were taken
from the results of Harned and Thomas14 9 and are listed in Table
Again it was necessary to extrapolate for the value at 45°0.
values of E
in Table
0
Ag
v.
The
which were derived from the equation are also given
v.
The variation of - k log K with temperature can be ex-
pressed in an equation found by applying the method of least
squares.
This equation was
- k log K =
•6041
- 317
foun~
to be
(t- 30) lo-6 cl 127 (t- 30) 2 10-8
Reducing this to the absolute scale• this becomes
log K
= 5•466
"006373 T --- {1)
The values of log K at each temperature calculated by meansi of this
41.
equation are listed in Table IV.
Differentiating the above equation with respect to
temperature:t
But
__
K.
d -'!""_,__ _
log
dT
=
§:_12eL!f
.=;
__4112•9
__
•006 373
T2
....,..
f!H
0
2:353-Firr2
dT
----(2)
=
so that
By substituting appropriate values of T in this expression, the
change in heat capacity is found for each temperature.
so derived are listed in Table VII.
From the change in heat capacity, the standard entropy
change,~S
0
,
can be calculated.
The equation connecting the
.two is
But
T L\S
where
:::
.6H
L1 G is
and ~G
-
~G
the change of free energy
RT ln K ::: 2•303 RT log K.
Values of~S 0 andLla are li~ted in Table VII.
Differe~tiating
is obtained.,
equation (2)
Differentiating equatjlon (1) there is obtained
42 ..
:::
Equating the two 9 since
0
dLl H
---"""""'dT
:::
-
then _1!QE~----2
2· 303 RT
Rearranging this gives
The list of values of~Cp 0 calculated by means of this
expression is given in Table VII@
For calculating the entropy of solvation 9 the partial
molal entrppy of the pair of ions, Ag -t- and 01- » was found first"
c•·
-so , + +-so
,,JJ_nee
Ag
01-
-
it was only necessary to find the value of S 0 AgCl
Latlmer..
g i ven b y
Then
L1so
Solvation
The last two terms were found from the
:::
3
R ln M + ~
2
2
Sack~r-Tetrode
equatlon
43o
The values of~S 0 Solvation at 25°0 of silver chloride in
various methanol solutions are given in Table X, use being ·made
of the figures of Owen and Brinkley, 19 and of Davis. 11 For
comparison the entropies of other salts in the same solutions are
given, the values being those or Latimer and Slansky. 21
44 ..
The method may be summarised as a study of series of
cells containing solutions of varying concentrations of the
dissimilar ions giving rise to the junction potentials 9 but maintained at constant ionic strength by the presence of an additional
electrolyte, which takes no part in the .electrode reactions.
Extrapolation to zero concentrations of the dissimilar ions
eliminates the junction potentials, and subsequent extrapolation
to zero ionic strength eliminates the effect of the inert electrolyte.
Justification for the extra-thermodynamic hypothesis
involved in the extrapolation must be on empirical grounds 9 and
the simplicity of linear extrapolations renders its verification
possible.
Owen, 10
who first us,ed this method I) found his extra-
polations were linear within estimated uncertainties.
FUrther
work on buffered cells by Owen and Brinkley19 supported the valid11
ity of the hypothesis, and the results of Davis
were in excellent
agreement.
The results of the present investigation are equally
in agreement with the linear extrapolation, for although a few
points do not lie on the lines, as can be seen in Graph I, the
variation may be attributed to experimental error, which must be
greater than in the experiments of Owen and of Owen and Brinkley ..
The radii of the circles in Graph I are plotted as •2 M.V. 9 and the
intercepts obtained by extrapolation to x
= o are
plotted in
Graph II with circles of radius •1 m.v.
It can be seen that
individual errors in Graph I are modified in plotting, and have
not a great effect on the values of the intercepts.
For this
reason their influence on the final extrapolation in Graph II to
m
=o
is very small, and they do not interfere with the excellent
linearity obtained.
No measurements of the solubility of silver
chloride in 20% methanol solution are given in the literature 9 so
no direct comparison of the results of this work is possible, but
the solubility found may be compared with those found by Owen and
Davis.
Koch 23
givesthe solubility of silver chloride in absolute
methyl alcohol as 3·9 x lo-7 mols. per litre at 25oc, so that the
salt is practically insoluble in pure methanol.
Davis found a
decrease in solubility in passing from pure water to 10% methanol
solution~
as was to be expected, and this trend is continued in the
present work» as shown by the following results.
mo
X
105 (Owen)
mo
X
10 5 (Davis)
m0 x 10 5 (Present
work) ..
•475
15°0
«>841
•604
25°0
1•338
•970
•752
35°0
2mQ48
1•502
1•180
45°0
3•026
2o250
lm778
The values for the standard el.ectrode potelfiltial of
silver in the three solutions show a similar trend..
They were
obtained by combining the data for E0 A
of Harned and
01
18
1
g
Ehlers
and Harned and Thomas 4 with the values of k log K derived from the experiments.,
Eo
Ag (Owen and Brinkley)
Eo
Ag (Davis)
Eo
Ag
(Present
work).
15°0
•8o9o
"8179
•8232
25°0
"7992
"8087
•8145
35°C
•7892
•7989
•8050
45°0
•7791
"'7886
•7951
By combinlng th'e solubill ty data .for silver chloridl3
i11 10%' and 20% methanol solutionsv a value for a» the raean ionic
radius, can be derived ..
Th0 fm:-rau:ta used for calculating this quantity is
ln S1 -
~l~l~L- •
1 cl·o ~ !)1,·-
and was derived in the introduct:i.on.
As the activity coefficients
tend to unity at infinite dilution in both media.\! the l>ebye ...
n1ickel corrections cancel 9 and the expression becomes
47.
In Table VI the necessary data is collected,
s1
being Davis' figures for the solubility of silver chloride in
10%' methanol solution» and 82 are the values obtained in this
work J'or 20% methanol solution a
!.
and
~1
!
are the reciprocals
D2
of the dielectric constants of the two solvents, the values being
taken from the paper of .Rkerlof or interpolate'd from them for
The other va.lues for insertion in the
intermediate temperatures ..
equation are universal constants
N = 6oQ6
e
= 4<~>774
z
=1
1
10 2 3
X
x 1o-10
as the valency of silver and chlorine
is unity.
'rhe values of a obta.ined by means of this expression
are given in Table VI.
'rhe theoretical mean ionic radius may be
calculated using the relation
-
2
1
where r 1 and r 2 are the individual radii of the two ions.
da.ta due to Pauling 20
chloride ion are 1•26 ~
to a value of 1<>49
i ,
ance has been made for
the ionic radii of
and 1 .. 81
i
th(~
Uslng
sil·<rer ion and
respectively..
th~
This leads
which must be a minimum value, as no allowsolvat~on.
The experimental results are
much lower than this figure:P agreeing with the results obtained by
48 ..
Dunning and Shutt 0
9
whose calculation also led to a low
Plotting logS
against!
value~
for the solubility of
D
silver chloride in water 9 10%' methanol and 20% methanol gives
three points 9 which certainly lie on a straight line» but there
is not enough data for an adequate test of the BoMftequation 9 and
inclusion of the figure for absolute methanol of Koch 23 shows
that the plot is not a straight line 11 but deviates rather rapidly<>
A greater range of methanol-water solutions will need to be investigated before a more extens:i.ve test of the theory can be
made~
The values for the entropy of solvation of' silver
chloride are interesting» as they can be compared wtth other salts
in the same solvents ..
The values for all the salts increase with
increasing concentration of methanol, as do those for hydrogen
chloride, after reaching a minimum at about a 20% concentration of
methanol ..
Silver chloride follows the same trend, moreover the
values for silver chloride are about the same magnitude as those
of potassium chloride.
Pauling gives the radii of the potassium
ion and the silver ion as 1•33
i
and 1•26
i
respectively, so
that the close agreement in the entropy of solvation is to be expected 1 particularly as Latimer and Slansky postulate only a small
effect for the difference in size of the positive ion.
The change in t'\Op 0 between the work of Owen and
Brinkley and that of Davis 9 with only a small consequent lowering
in the present work is notable, but no explanation seems to be
availa.bleo
49.
1.
Measurements of the electromotive force of cells with
liquid junctions of the type
Ag, AgCl
KCl (x)m
KN0 3 (1-x)m
l
KN0 3 (m)
0
have been made at 15 0 9 20
0
c,
0
IAgNO(
~KN0
25 C9 30
0
3
(x) m
1-x)m
c.
35
0
c~
AgCl, JAg.
40°0, and
45°0 11 using 20% methanol-water solution as solvent.,
2.
From these results the solubility product and solubility of
silver chloride have been evaluated at each temperature by
means of an extrapolation method for eliminating the liquid
junction potentials.
3.
The standard electrode potential of silver in this solvent
has been calculated for each temperature, and these values,
together with solubility data 11 have been compared with the
corresponding values in water and 10% meths,nol solution.
4.
The solubility data in 10% and 20% methanol solutions have
been used in
Bo~1s
equation as a test, by the calculation of
a, the mean ionic radius.
5.
Derived thermodynamical quantities have been calculated for
the reaction AgCl
Ag+"' + Cl- , and compared with corresponding
values in water and 10% methanol solution.
CllRISTCHlJHCH, N.L:.
5o.
6a
The entropy of solvation of silver chloride in waterg
10% and 20% methanol solutions has been calculated, and com...
pared with the entropies of other salts in the same solutions.
51.
1.
GloVH}Zynski
Kolloid. Beihefte (1914) 6 9 147.
2.
Davis)) Ricci with
Sauter
J.A.c.s. (1939) 61,3274.
3.
Popoff and Neuman
J. Phy. Cham. (1930) 34»1853.
4.
Neuman
J.A.c.s. (1932)
5.
Dave and Krishnaswami.
J. Ind.Inst.dhem. (1933)
6.
Johnson and Low
J .. A.c.s. (1933)
7.
Koh1rausch
z.
8.
Brown amil Macinnes
J.A.c.s. (1935)
9.
Dunning and Shutt
Trans. Farad.Soc .. (1938)
10.
owen
J.A .. c.s .. (1938)
11.
Davis
Thesis~
ssberger and Proskauer
12.
54,2195.
Pt.14,153.
55,2262.
Physik. Ohem., (1908)
64!1129
57,459.
34 9 1192 ..
60,2229.
University of New
Zealand~>
"Organic So1ventsn (19'35) ..
13..
Childs
"Physical Constants" (1939).
14 <>
Harned and Thomas
J .A.c .. s. (1935)
15..
A1lmand and Hunter
Trans. Farad. Soc. (1928)
16.
Smith and Taylor·
u.s. Bureau of Standards.
57,1666o
Journal of Research (1938)
0
.
17.
.~:\kerlof
J .. A.o.s. (1932)
54,4125.
18.
Harned and Ehlers
J.A.o.s. (1933)
55,2179.
19o
Owen and Brinkley
J .. A.o .. s .. (1938)
60' 2233.
20.
Pauling
J.A.c.s. (1927)
49g765o
21.
Latimer and Slansky
J .. A.c.s .. (1940)
62g2019.
24ll 300 ..
20,837
22 ..
. 23 ..
25.
Latimer
"Oxidation Potentials"
Koch
J.Chem.Soc. (1930)
Pinkus and Hanrez
Bull.Soc.,Chem'.Belg.(l938) 47 11 532 ..
Bjerrum
9hemistry at 1931 meeting of Brit-
(1938} ..
133 9 1551.
ish Association for the Advancement of Science ..
26 ..
Latimer and Buffington
J.A.c . s . (1926)
48,2297 ..
1"'
)7
e.,'
Latimer and Kasper
J .A.c.s. (1929)
51 9 2293 ..
@
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