Influence of Sulfide Ion Hydrolysis on the Solubility-Solubility Product Relationship of Metallic Sulfides PIERRE VAN RYSSELBERGHE and ARMIN H. GROPP University of Oregon, Eugene, Oregon
T
HE .EXACT relationship between the molar .. solub~Wesand the solubility products of the socalled "insoluble sulfides" are complicated by the very extensive hydrolysis of the sulfide ion. Textbooks of analytical chemistry hardly ever touch this important problem and many of them do not even mention it. Students are usually taught to treat the problems on solubilities and solubility products of the sulfides in the same manner as those concerned with the insoluble salts of strong acids and strong bases. Even handbooks give inconsistent data on thij subject. Some important papers on the equilibria in solutions of sulfides have, however, been published by Kolthoff ( I ) , Ravitz (2), and Verhoogen (3), but their contents have not yet found their way into the textbooks and, moreover, a treatment of the subject accessible to students of qualitative analysis, with emphasis on problems of practical interest, has not yet been provided. For instance, the embarrassing situation that predictions as regards the precipitation or nonprecipitation of borderline cases such as that of zinc sulfide are often in patent disagreement with the facts bas, to our knowledge, never received adequate attention in the textbooks. The purpose of the present paper is to give a simple, yet sufficiently exact and complete, treatment of this fundamental topic. Activity corrections will not be made and only round values of the hydrolysis and ionization constants will be used. IONIZATION CONSTANTS OP HYDROGEN SULFIDE IN AQUEOUS SOLUTION, HYDROLYSIS CONSTANTS OP THE SULFIDE AND BISULRIDE ION
The following acid-base reactions take place when H2S dissolves in water [see, for instance, Hammett's (4) excellent textbook] :
At room temperature the ionization constants, KI and Kz, have approximately the following values:
In solutions saturated with HzS the concentration of
the undissociated acid is practically lo-'. a t saturation we have K
=
Therefore
K,KI(H~S) = ( H S O + ) ~ S -= ) 10-~~
The hydrolysis of the sulfide ion takes place as follows: and the hydrolysis constant is
a constant so large that sodium sulfide, for instance, can truly be regarded as a base practically as strong as sodium hydroxide. Mellor (5) in fact states that such sulfides as CaS and Bas in solution have the probable formulas CaHSOH and BaHSOH. The hydrolysis of the bisnlfide ion takes place as follows : HS-
+ H1O = H2S f OH-
and the hydrolysis constant is
SATURATED SOLUTIONS OF THE SULPIDES, WITHOUT ANY ADDED ACIDS,, BASES, OR SALTS
Let us represent sulfides by the general formula Masa. The solubility product P is
If the stoichiometric relations which hold in the absence of hydrolysis are applied here we would have, calling s the molar solubility of the sulfide, ( M + ) = as, (S-) = bs, and P = (as)- (bs)l
Therefore, neglecting hydrolysis, we would have
as is the case with such insoluble salts as AgCl, BaSO,, etc. In the case of the sulfides, however, this relation is not even approximately correct. As solutions of pure sulfides are always basic on account of the marked degree of hydrolysis of the sulfide ion we shall take the OH--ion concentration as the main variable in our treatment. We shall also assume that the hydrolysis of the hydrated
metallic ions, Cu(HzO)rt+ for instance, is always negligible compared to that of the Se-ion. We shall call C the total original "sulfur". concentration. We have, obviously, C = bs = (S-)
lo-' the contribution of the solvent to x = (OH-) is predominant and always equal to lo-'. The correction factor, f,is thus always
+ (HS-) + ( H d )
From the hydrolysis constants above we deduce
Therefore.
and the solubility product becomes
The solubility, s, is obtained from P by the formula
and setting (OH-) = x, the solubility product P becomes
We see that, because of hydrolysis, the usual value of the solubility product has to be multiplied by the correction factor, r
1
With, for instance, as = bs = 10-lo, a = b = 1, we find that P = X while without taking hydrolysis into account, we would find P = Case 3: When the solvent and the sulfide contribute similar amounts to the OH-- ion concentration, i. e., both of the order of lo-', we have to solve the following two simultaneous equations: 1. The relation between the S--ion concentration, which we shall now call y, and the alkalinity already used above:
l b
2. An additional stoichiometric relation between y and x , namely, the condition of electroneutrality:
It will now be convenient, and a t the same time practical, to divide the insoluble sulfides into three classes :
- ( M + ) + (H,Oi) 2b
=
(HS-)+ (OH-)
+ 26-)
1. Those whose solubility, s, is much greater than 10-' 2. Those whose solubility is much smaller than 10-7. 3. Those whose solubility is in the vicinity of lo-'.
Case 1: When s is much greater than lo-', the contribution of the solvent to x = (OH-) is negligible compared with that due to the hydrolysis of the sulfide ion. We have, in this case, (HS-) = (OH-) = bs, since the hydrolysis of HS- is negligible. Suppose we take bs = 10W4. The hydrolysis constants xive
With (HS-) = x = lo-* we find (S-) = and (HzS) = lo-'. In general we have (S-) = bzsa/lO and the solubility product becomes
a = b = 1, we find If, for instance, as = bs = P = 10-13, while without taking hydrolysis into account we would find P = The solubility, s, is obtained from the formula
Case 2: When the solubility is much smaller than
from which we deduce 25s
+ lo-" (2)
Y =
'0+2
Equating the values of y deduced from (1) and (2) we get
which can readily be transformed into the following equation in which the unknown u is ' / x :
In the u2 term, 10-l4 is negligible in presence of loa. Remembering that s is in the neighborhood of lo-', and considering the case of the symmetrical sulfides MS for which b = 1, the above equation gives, as expected, u = ' / z X lo7 or x = 2 X lo-'. The correction factor, f,is here
and for the MS sullides the solubility product becomes
In the general case we take x = (b find that
+ 1) lo-'
and we
and hence
from which we deduce
If we take, for instance, the case of thallium sulfide, TlzS, whose solubility product is 6.39 X we find, according to the above formula, s = 1.06 X lo-', while the incorrect P = (as)'(bs)O formula would give s = 2.51 X 10P8. If we consider this case as belonging to class 1 (s>10-') we find that s = 3.46 x 10-5.
For ps > 7 we have pP = 29s
+ 8 + lop 2
=
2ps
+ 8.3
These two straight lines are plotted in Figure 1. If we extend them both to ps = 7 we find, with case 1, p P = 22, and, with case 2, pP = 22.3. The exact relationship, however, is, as can be deduced from the treatment of case 3, pP = 21.8, which value lies almost exactly on the straight line drawn between the exact pP for ps = 6 and 8 ( p P = 19 for ps = 6, pP = 24.3 for ps = 8). In Table l we give the thermodynamically determined values of the solubility products of some of the common sulfides, taken from the work of Ravitz (2), the values of s as given by Ravitz, and the calculated values of s obtained from our formulas. SOLUB~LITYPRODUCTS AND
Svlfldc
P
TABLE 1 SOLVBILCTIBS OF SOY* MBTALWC SULRD&S s (Rouilz)
I
(Cab.)
CdS
cus
cu,s
PbS HGS*
AGIS TLIS ZNS X
T h e caw of HgS is still in doubt, since the values for P range from 1.0 lo-.? to 3 X lo-".
PRECIPITATION OF' SULFIDES IN SOLUTIONS OF ADJUSTED
pH I n any solution saturated with respect to both H2S and a sulfide Mesa, and kept a t constant pH we have the simultaneous conditions (M+).(S-)a = P and (HsOf)'(S-) = lo-"
FIGURE
I.-PP-Ps
RELATIONSHIP OI. SULPIDES OF THE MS TYPE
It is interesting to represent the above results by a graph. Denoting by ps and p P the negative logarithms of s and P we have for ps 10-', s
