SOLUBILITY OF SILVER CHLORIDE IN CHLORIDE SOLUTIONS.

1937
[CONTRIBUTION FROM THE CHEMICAL LABORATORY
OF HARVARD
COLLEGE.]
THE SOLUBILITY OF SILVER CHLORIDE IN CHLORIDE SOLUTIONS
AND THE EXISTENCE OF COMPLEX ARGENTICHLORIDE IONS.
BY GEORGBS H A N N O N FORBES.
Received October 9, 19x1.
It has long been known t h a t silver chloride is fairly soluble in concen-
trated solutions of various chlorides. Reinsch’ speaks of its solubility
in concentrated hydrochloric acid. Vogel,2 who appears to have made
the first quantitative study of the reaction, gives solubilities in acid of
specific gravity I . 165 t o which varying proportions of water had been
added, and also speaks of the increase of solubility with the temperature.
Mulder3 studies its solubility qualitatively in other chlorides. These
and other references t o early work on the subject are found in Comey’s
“Dictionary of Solubilities,” pages 372-3, The only attempt to find numer-
ical regularities seems to have been made by Barlow4 who, while seeking
errors in a method for determining sulfur, titrated solutions of sodium
chloride, or of hydrochloric acid, or of both together, with silver nitrate.
He concludes: “The figures show that the solubility of sodium chloride
falls off (at a gradually diminishing rate) with diminishing concentration.”
He investigated only one concentration of hydrochloric acid. The solu-
bilities as observed by Barlow appear roughly proportional to the con-
centration of sodium chloride. Noyes and Bray,5 perhaps with these
figures in mind, stated that a complex anion like AgC1,’ probably exists
in such solutions.
Researches concerning reactions between other pairs of halides are
numerous. Of those most closely related to the present research may
be mentioned that by Hellwigje who prepared in solid form many complex
compounds of silver halides with silver nitrate, also with qlkali halides
including thiocyanates. H e failed to isolate a complex salt between sil-
ver chloride and other chlorides, and did not study the reaction further.
This field was next investigated by B ~ d l a n d e r who
, ~ found evidence of
complex anions of the type AgX,, and by Krym,8 who dealt with the
iodides of sodium and silver. Important work on halides of mercury
and copper will be referred to in the discussion of results below.
The theory of such complex compounds has been discussed a t length
by Abegg.Q
J . prakt. Chem., 13,133.
N . Rep. Pharm., 23, 355.
L O C . cit.
’ THISJOURNAL, 28, 1446 (1906).
* Ibid., 29, 166 (1907).
2 . anorg. Chem., 2 5 , 157 (19~).
Rev., 36, 2878 (1903).
1.Russ. Phys. Chem. Ges., 41, 382 (1909);abstracted in Chem. Zentr., ~ p o g , I I681.
,
OZ. anorg. Chem., 20, 453-499 (1899).
1938 GENERAL, PHYSICAL AND INORGANIC.

The present research aimed t o determin the solubility of silver chloride

in a large variety of aqueous chloride solutions; to find what complex
ions, if any, were indicated by the data, and to draw conclusions if possi-
ble regarding the relative “activities”’ of the chloride ion in such solutions.
Very concentrated indeterminate solutions of the chlorides were pre-
pared and carefully filtered. The ammonium chloride was barely acid-
ified with hydrochloric acid to avoid hydrolysis. The purity of the ma-
terials is discussed below after recording the effect of impurities inten-
tionally introduced. Silver chloride was precipitated from weighed
portions diluted with much water and weighed on platinum Gooch cruci-
bles with the usual precautions. Dilute solutions of silver nitrate, one
abeut hundredth normal, the other about quarter normal, also one of
silver sulfate for use with hydrochloric acid, about fortieth normal, were
made and analyzed with equaf care.
The determinations were carried out in flat-bottomed glass cylinders of
about 60 cc. capacity, except in the case of the most dilute solutions,
where deep beakers holding 600 cc. were used. These were set on a porce-
lain plate covered with black glazed paper and immersed to a suitable
depth in a thermostat electrically regulated to maintain a temperature
(corrected) of 25.06’ within a few hundredths of a degree. The solu-
tions were examined for opalescence in horizontal light reflected by a n
immersed forty-five degree mirror from an incandescent lamp supported
above the thermostat.
The method was as follows: The dry cylinder was counterpoised,
then carefully weighed with a convenient amount of chloride solution.
Water, or in some cases the solid salt, was added and the additional
weight found as before. A silver solution was next run in from a weight
buret until equilibrium was nearly reached a t some temperature between
24’ and 26’. The vessel was then immersed in the thermostat and ten
minutes allowed for the final adjustment of temperature-ample time,
as proved by special experiments. Hundredth normal silver nitrate
was added drop by drop until the faintest opalescence visible persisted
after careful stirring. Immediately after the final adjustment the cylinder
was wiped and weighed with the stirrer. Then the true density was de-
termined within one part in five thousand by a pycnometer. All effects
of evaporation or change of volume on mixing were thus avoided.
The above end point was proved sufficiently near the true equilibrium
by the following considerations : Concentrated chloride solutions nearly
saturated with silver chloride show a surprizing degree of supersatura-
tion on cooling; this can be promptly relieved by adding, on-the end of
a stirring rod, quantities of precipitated silver chloride so minute as to
produce no visible turbidity in 50 cc. of pure water. I n such concentrated
Lewis, Proc. Am. Acad., 43, 288 (1907).
 SOLUBILITY OF SILVER CHLORIDE IN CHLORIDE SOLUTIONS. I939
chlorides the precipitation of silver chloride is very prompt; larger quan-
tities of i t are required t o produce visible opalescence in these solutions
than in very dilute ones. The precipitate looks coarser from the start,
and becomes rapidly more so, therefore i t should not be allowed to stand
more than a few minutes. Various chloride solutions a t 25' were treated
with successive drops of hundredth normal silver nitrate, seeding after
each drop with minute portions of silver chloride. This seeding never
produced any effect in solutions which had been cleared by stirring,
hence such solutions were not supersaturated. If the last drop of silver
nitrate produced a permanent precipitate, this was dissolved by heat
and the solution quickly cooled t o 25') after which seeding always pro-
duced a precipitate. These experiments eliminated the danger that
solutions which had failed to dissolve all the silver chloride formed in
them were unsaturated, for if this had been the case, no precipitate would
have been produced on seeding a t 25' after cooling. Thus i t was proved
t h a t the solutions a t 25') in which the faintest cloud remained, were
saturated, and that the excess hardly exceeded that derived from the last
drop. Such an excess in 50 cc. was equivalent to 6 x IO-^ mole per liter,
the maximum probable error in the silver concentrations given below.
After much consideration i t was decided to record all concentrations
in gram equivalents per liter. As ample evidence was available that the
chloride ion was the active agent, i t seemed that the cations and the un-
dissociated molecules with their possible hydrate water might well count
as free space. Concentrations could hardly be calculated on such a
basis for lack of any means of determining the volume occupied by the
chlorine ion. Trial calculations showed that the conclusions drawn
from the following figures would be substantially unchanged if concen-
trations were reckoned in equivalents per thousand grams of water.
The table gives the total concentration of dissolved silver, and of the
chloride in each case, the symbols being [Ag] and [MCl] where M is a
gram equivalent of any metal. K, = [Ag]/[MCIJn where m is a small
whole number:
TABLEI.
Sodium Chloride.
IAgl X lo3. [NaCll. k p X le. ksX lo4.
0.086 0.933 0.98 I .os
0.130 I . 190 0.92 0.77
0.184 1.433 0.90 0.63
0.245 I ,617 0.94 0.58
0.348 1.871 0.99 0.53
0.446 2.094 I .04 0.50
0.570 2.272 I.10 0.486
0.684 2.449 I. 14 0.466
0.851 2.658 1.20 0.453
I .040 2.841 I .29 0.453
 GENEMI,, PHYSICAL AND INORGANIC.

TABLEI (continued).
Sodium Chloride.
[Agl X los. [NaCl]. kzXlo4. ksX104.
I94
1* 3.000 1.33 0.442
1.583 3.270 I .48 0.453
1.897 3.471 1.57 0.454
2.462 3.747 1.75 0.468
2.879 3.977 1.82 0.458
3.335 4.170 I .g2 0.460
3.810 4.363 2 -05 0.458
4.298 4 * 535 2.09 0.461
6.039 5.039 2.38 0.472
Calcium Chloride.
[Ad X 10'. [CaCWZ] . ks X 10'. k r X 10'.
0.289 1.748 0.95 0.54
0.501 2.201 I .03 0.47
0.900 2.741 1.20 0.44
1.463 3.264 1.37 0.42
2.182 3.737 I .5B 0.418
2.802 4.033 I .72 0.427
4. I75 4.538 2.03 0 * 447
5.823 5 $005 2.32 0.464
Ammonium Chloride.
[Ad X lo*. [NHdCl]. kz X lo4. ka X 10'. kr X lo".
0.042 0.513 1.59 2.46
0.113 0.926 1.33 1.43
0.172 I. 141 1.32 I . 16 ...
0.365 1.574 1.47 0.94 ...
0.842 2.143 1.80 0.86 ...
1.425
2.160
2.566
2.918
2.16
2.54
0.84
0.87
...
2 * 795 3.162 .... 0.88 0.280
4.029 3.510 .,.. 0.93 0.265
9.353 4.363 .... 1.13 0.258
14.92 4.902 .... 1.27 0.258
24.04 5.503 .... 1.44 0.262
30.I 7 5.764 .... 1.57 0.273
Strontium Chloride.
[Ad X los. [SnCld21. kz X 104. ks X 10'. k4 X l e .
0.033 0.550 I . IO 2 .oo ...
0.092 0.989 0.94 0.95 ...
0.I73 1 a359 0.94 0.69 ...
0.236 1.572 0.95 0.61 ...
0.284 I. 698 0.98 0.58 ...
0.348 I .818 I .05 0.58
0.510 2.140 1.11 0.52
0.747 2.476 1.22 0.49
I .252 2.992 I .40 0.47
2.018 3.494 I .65 0.47 ...
3 * 594 4.152 2 .OS 0.50 0.121
8.174 5.216 3 .oo 0.58 0.110
12.04 5.775 3.61 0.62 0.108
 SOLUBILITY OF SILVER CHLORIDE I N CHLORIDE SOLUTIONS. 1941
TABLEI (cohtinued).
Potassium Chloride.
[Ag X lo3]. [KC11 . k2 X 104. ka X 104. kr X le.
0.141 1.111 1.11 I.02 ...
0.235 I .425 I. 16 0.81 ...
0.391 1.713 1.33 0.78 ...
0.616 2.022 I .SI 0.74 ...
I .050 2.396 I .84 0.763 ...
1.390 2.628 .... 0.766 0.291
1 .a45 2.850 .... 0.797 0.280
2.435 3.081 .... 0.83 0.270
3.602 3.424 .... 0.90 0.262
5.725 3.843 .... I .OI 0.262
Hydrochloric Acid.
[Ag x loa]. [HCI] . k 2 X le. ka X lo4.
0.032 0.649 0.76 1.18
0.126 I .300 0.75 0.57
0.266 1.911 0.73 0.38
0.374 2 . I49 0.81 0.38
0.610 2.569 0.86 0.325
0.814 2,975 0.92 0.309
1.358 3.576 I .06 0.297
2. I47 4.182 1.23 0.294
3.168 4.735 I .41 0.298
5.126 5.508 I .69 0.307
Barium Chloride
[Agl X 10'. BaCld2. k2 X 10'. ka X 10'.
0.186 I .248 1.20 0.96
0.339 1.610 1.31 0.81
1.274 2.676 1.78 0.67
2.366 3.260 2.20 0.67

Since silver chloride is virtually insoluble in concentrated mercuric

chloride solution, the chloride ion, and not the undissociated molecules,
must be responsible for its solubility in the cases studied above. I n the
rather feebly dissociated zinc chloride its solubility is small, 0.000364
mole per liter of 4.777 normal solution as compared with 0.0135 mole
in ammonium chloride equally concentrated. Richards and Archibald'
found mercurous chloride unchanged by concentrated cadmium chloride.
solutions, although highly dissociated chlorides decomposed i t into mer-
curic chloride and mercury. They similarly attributed the lack of action
to the low concentration of the chloride ion.
Bodlander and Storbeck2 proved very conclusively that the complex
anion CuBr,' is present in a solution of cuprous bromide in potassium
bromide. Richards and Archibald2 concluded t h a t the ion HgC1,N was
Proc. Am Acad., 37, 347 (1902).
2. anorg. Chew!., 31,I (1902).
I942 GENERAL, PHYSICAL AND INORGANIC.

formed accqrding to the reaction Hg,Cl, +

2C1' HgCl," Hg.+
The results presented above are now completely explained by assuming
the existence of complex anions of the type (AgCl),Cl"', where x is proba-
bly one by analogy with the very similar cuprous bromide. If AgCl +
mC1' J_ AgCl$+,, then according to the so-called law of mass action,
if this may be assumed to hold in spite of the high concentration, [Ag] =
k[Cl']" in a solution saturated with silver chloride. If next the further
assumption is made, as no better could be devized, that the activity of
the chloride ion is nearly proportional to the total chloride concentration
throughout moderate ranges of the latter, the figures in Table I may be
explained. The values of k,, in the third column, are constant from
I . 5n down to the smallest concentrations studied; that is, solubility is
closely proportional to the squaw of the chloride concentration. Sup-
port is thus lent to the hypothesis that the ion AgC1,N exists in such solu-
tions. No evidence of the ion AgCl,' is to be f0und.l I n the fourth col-
umn the values of k , are very constant from 2 . 5 n upward, t h a t is, solu-
bility is closely proportional to the cubes of the concentrations, hence
the ion AgCl," is suggested, except in the cases of potassiym and ammo-
nium chlorides, where this ion appears to be present from I . 5n to 3 . on,
above even which a third ion, AgCl,N", is suspected from the data.
That m is really integral throughout considerable ranges of concentra-
tion, and does not increase continuously except in those solutions where
no single complex predominates, is also shown by plotting the common
logarithms of the chloride concentrations as abscissas against the common
logarithms of the silver concentrations as ordinates. The equation of
any graph is found by taking the logarithm of each side of the equation
[Ag] = km [MCl]" for the corresponding salt. The result is : log [Ag] =
log Km + m log [MCl], which is the equation of a straight line if m is
a constant. Now all the graphs are seen to consist of straight parallel
lines connected by shorter curved portions, which shows t h a t m is con-
stant and also the same for different salts throughout given ranges of
concentration. The values of *
log [Agl which must be numerically
A log [MCl]'
equal to m, are seen to be almost exactly equal to 2, 3 or 4,according to
the concentration region in which the straight lines lie. Thus i t is shown
graphically that complex ions of silver chloride molecules with two, three
or perhaps even four chlorine ions exist in well defined concentration in-
tervals.
Is i t possible to connect the solubility of silver chloride more closely
with the true concentration of the chloride ion? Not only is the latter
uncertain, but also the degree of association of the complex anions with
The increase in k, at the smallest concentrations is to be attributed largely
t o the excess of silver chloride used t o produce opalescence.
 SOLUBILITY OF SILVER CHLORIDE I N CHLORIDE SOLUTIONS. 1943

cations is entirely unknown. The work of Le Blanc and Noyes' on the

conductance and catalytic power of hydrochloric acid containing mer-
curic chloride, and the experiments of Richards and Archibald2 on the

- 1.9
- 2.0
-2.1
-2.2
-2.3
-2.4
-2.5
h
o) -2.6
;. -2.7
$O -2.a
-2.9
5 -3.0
v1 -3.1
-3,Z
.-a
Y
-3.3

---2g -3.4
-3.5
-3.6
-3.7
32 -38
4 -3.9
-A.O
- 4 1
4 2
-1.3
-4.4
-4,5

conductance of sodium chloride containing mercuric chloride led them

to conclude that any well dissociated chloride, MC1, and the complex
compound M,HgCl, are about equally dissociated up to normal concen-
tration of the former. Thus the total mercury could be written as
+
C C( I-a) / cr or C / a , where C represented the concentration of the ionized
portion. Then by the law of mass adtion C / a = k x F / a , where x is the
specific conductance of chloride and m the number of chloride ions entering
the complex. To find whether a corresponding relation existed in the case
of silver chloride, sodium nitrate was added to sodium chloride solution
before running in silver solution. If in tbe case of the silver complex we
can write C/ a = K x m / a , any repression of ionization should lower the total
solubility, since the complex ion must decrease as the mth power of the
Le Blanc and Noyes, 2. physik. Chem., 6, 389, e t seq. (1890).
' Proc. Am. Acad., 37, 347 ( 1 9 0 2 ) .
I944 GENERAL, PHI’SICAL AND INORGANIC.

chloride ion, while the associated part increases only as the first power
of the same. Consider now Table 11; the k’ values are interpolated for
equal concentrations of pure chloride :
TABLE11.
[ A d X lo3. [NaCIl. [NaNOJ. kz X le. ka X 10’. &z‘ X lo4. &a‘ X le.
2.457 3.743 0.00 1.75 0.469 .... ...
2.493 3.592 0.84 1.93 0.538 1.65 0.461
2.538 3.462 1.50 2.12 0.611 1.57 0.454
The addition of sodium ion increases the constants, and hence the solu-
bility also. Neglecting the change in the medium produced by so much
sodium nitrate, i t would appear that the concentration of a t least the tri-
valent anion AgC1,”’ is lowered relatively much more than that of the
chloride ion by adding sodium ion, for the increase in [M,AgCl,] far more
than compensates for the loss in [AgCl,”’]. Therefore the hypothesis
of equal dissociation of MCl and M,AgCl, was abandoned, and in despair
of evaluating the many unknown variables, the activity of the chloride
ion was taken as roughly proportional to total chloride concentration
for moderate increments of the latter.
Richards and Archibald‘ suggested that the extent of action of chlorides
on mercurous chloride might possibly be used to detennin the concentra-
tion of the chloride ion. If the extent of action in the case of each such
complex is an explicit function of the activity of the chloride ion, a mere
comparison of constants ought to show whether complex formation is a
measure of the relative activities in various solutions. I n normal solu-
tions, where the same type of complex ion is formed from both mer-
curic and silver chlorides, K , may be calculated from the data of Rich-
[Hg] dissolved
ards and Archibald, k, = -___
[MC1I2 *
HC1. NaC1. CaClz. BaC12.
k, X IO* for HgC1,. . . . . . . . . . . . . . 2.4 2 .O 1.7 2.2
k, X IO( for AgC1,. .............. 0.75 0.97 0.9 1.2

The ratio between the hydrochloric acid constants differs so widely

from the other ratios that the difference cannot be attributed to errors
in experiment or extrapolation. Redistillation of the acid failed to
increase the values of its constcints. It must therefore be concluded
that complex formation by mercurous and silver chlorides is not propor-
tional to the activity of the chloride ion unless perhaps a single salt is
considered a t a time. Possibly the undissociated portions of the chlor-
ides, while incapable of direct combination with silver chloride, support
or hinder the action of the chloride ion in varying degrees.
One equilibrium was determined in the presence of a known amount
of sodium bromide:
Proc. Am. Acad., 37, 359 (1902).
 SOLUBILITY O F SILVER CHLORIDE I N CHLORIDE SOLUTIONS. 1945
[Ag] X 10s. [CaClz/Z]. [NaBr]. kz X 101. ka X 104. ka‘ X 101. k3‘ X 10‘.
5.62 5.074 0.0018 2.18 0,430 2.37 0.467
These figures, together with those on sodium nitrate, show pretty con-
clusively that the purest commercial preparations, such as were used in
this research, could hardly have contained impurities of serious conse-
quence t o the results. Bromide and iodide were the only anions capa-
ble of forming highly insoluble silver compounds which were likely to be
present. No test for these could be obtained, and yet a fifth of the above
concentration of bromide can be detected under the same conditions
with, carbon disulfide and chlorine water. Of other salts i t appeared
likely, in view of the results with sodium nitrate, that even a whole per
cent. would have had a negligible effect.
The temperature coefficient of the solubility was investigated in thrice
normal potassium and calcium chlorides, salts widely different in most
respects, a t I . o o , 2 5 . o o and 35 . o o . Silver nitrate was first introduced
at I . o o until equilibrium was attaihed; then the solution was warmed
to 25. o o and more silver nitrate added; then a further addition was made
a t 35.0’. The normality of the chloride was changed by each addition
of silver solution, so that in order to compare solubilities a t the same
concentration but at different temperatures extrapolation was neces-
sary. Table I shows that for these concentrations [Ag]/[KC1I4 = k ,
and [Ag]/ [CaC1,/2I3 = k, a t 25.0’. Assuming these equations to hold
a t I . o o and 35.0°, take the logarithm of each side and differentiate.
A log [Ag] = 4 4 log [KCl] and 4 log Ag = 3 4 log [CaC1,/2]. The
solubilities in 3.083% KC1 and in 3.320%CaC1, may now be calculated
a t I . o o and 35.0’. The “primes” indicate values obtained with the
help of this artifice.
log[Agl ’i2- log[Agl’tl
t. [ A d X 10’. [KCII. [Ad’ X 10’. [KCI]’. log[Ag]’tz.-l0g[Ag’I2~.
12- tl
1.0’ 1.734 3.325 1.283 3.083
0,2747 0.0113
25.0’ 2.415 3.083 2.415 3.083
0.1356 0.0136
35.0’ 2.786 2.955 3.300 3.083

1. [Ag] X los. [CaClz/2]. [ A d ’ X lo3. [CaCldZ]’. A log [Ag]”. Alog [Ag]’/Al.

1.0’ 0.964 3.512 0.814 3.320
0,2694 0.0112
25.0’ 1.514 3.320 1.514 3.320
0.1156 0.0116
35.0’ 1.806 3.221 1.976 3.320

The increase in solubility with temperature is roughly logarithmic,

about three per cent. change for one degree, hence the variations of a few
hundredths of a degree were permissible in the determinations. The
activity of the chloride ion seems to vary with temperature to about the
I946 GENERAL, PHYSICAL AND INORGANIC.

same extent in both salts, the differences being perhaps due to unequal
changes in dissociation with temperature.
The data obtained in the research incidentally make i t possible to cal-
culate what excess of chloride will make silver chloride most insoluble-
a n imporant question in analytical work. As the solubility product of
silver chloride a t 25' is nearly 2 X I O - ~ O , ~ the concentration of silver
in solution due to incomplete repression of ionization is given by the
equation [Ag], = 2 X IO-'O/[MCI], assuming complete dissociation of MCI.
The concentration of silver in solution due to complex ion formation
is given by the equation.[Ag], = IO-' [MCl],, where IO-^ is the average
value of k, a t low concentrations. Total dissolved silver is the sum of
the above: [Ag] = 2 X IO-~~/[MCI] IO-^ [MCI],. + Differentiating,
+
d[Ag]/d[MCl] = -2 X I O - ~ ~ / [ M C I ] 2~ x IO-^ [MCI]. If the left hand
side of the equation becomes zero, z x IO-'O/[MC~]~ = 2 X IO-^ [MCl]
whence [MCl] = IO-^. Hence silver chloride ought to be most insoluble
in hundredth normal chloride solutions.
One determination was also made of the solubility of silver chloride
in concentrated silver nitrate.2 This salt was recrystallized from fifty
per cent. nitric acid, whirled on a centriiugal, fused in a platinum dish,
and dissolved t o form a solution about twice normal. A cloud was pro-
duced in 40 cc. by 0 . og cc. of 0.014 N KCI, that is, by a concentration of
3 X IO-^ gram equivalent or 0.001gram of chlorine per liter, less than
one-tenth the solubility of silver chloride in a twice normal chloride
solution.
Summary.
The solubility of silver chloride in concentrated solutions of various
chlorides was determined mainly a t 25 '.
The solubility is nearly doubled in going from o o to 25', the rate of in-
crease above and below 25 ' being nearly logarithmic.
The solubility is sharply proportional to integral powers of the chloride
concentra'tion throughout considerable ranges, a fact explained by as-
suming the existence of the complex anions AgCl,", AgC1," and possibly
AgC1,N". No evidence of the ion AgCl,' is found.
The extent of complex formation by mercurous and silver chlorides
cannot be used as a measure of the activity of the chloride ion in concen-
trated solutions.
Silver chloride should be most insoluble, a t 25', in hundredth normal
chloride solutions.
CAMBRIDGE, Mass.

Data from Goodwin, 2.physik. Chem., 13, 645 (1894).

* Hellwig, 2.amorg. Chem., 25, 177 (I~oo),states that 100 cc. of thrice normal sil-
ver nitrate dissolved o .OS gram of silver chloride, a quantity which fell off very rapidly
with dilution.