R. H. Petrucci and P. C. Moews, JI. Western Reserve University Cleveland,
Ohio
II
H,S Equilibria; the Pretipitation and Solubilities of Metal Sulfides
The role of H ~ Sequilibria in the precipitation and solubilities of metal sulfides is discussed a t considerable length in most qualitative analysis textbooks. I n addition, many articles have been written on these subjects, some of which have appeared in THIS JOURNAL.Various methods of calculating the concentrations of species involved in simultaneous equilibria have been described by Boyd (I), Fritz (t), Davidson and Geller (5), and Nightingale (4). The subject of the solubility of metal sulfides is discussed in several papers including those of Van Rysselberghe and Gropp (5) and Waggoner (6). Our first intention when considering this subject was to clarify certain anomalies which tend to arise in applying the expression, [ [H+]2[S-2J]/[H2S]= KlKz, to alkaline solutions of H2S. In the course of doing so we discovered that the general expression required for this problem applies equally well to all systems involving H2S and sulfide precipitates-acidic, neutral, or alkaline solutions, and saturated or unsaturated solntions of metal sulfides. It is possible to discuss all aspects of Hi3 and metal sulfide systems t,hrough a single mathematical relationship by using the appropriate terms in the expression. The results of these calculations may be of value to chemistry instructors, particularly as assignments to students in honor classes in qua1itat.ive analysis and solution chemistry. The Anomaly
In most qualitative analysis textbooks the student is shown that in a solution of HIS in water one may assume that [H+] = [HS-], and that since [H+][S-2]/[HS-] = Kp = 1 X 10-14, [S-21 = Kp = 1 X 10-14. However, [H+] is no longer equal to [HS-] if either an acid or a base has been added to the H2Ssolution. I n such cases calculation of [S-2] requires the use of both K1 and K2,usually through the expression [H+]2[S-2]/[ H 8 ] = K,&. Since the precipitation of metal sulfides is accomplished in a solution kept saturated in HpS (0.1 M H&, i t has become customary to write [H+]2[S-2] = 0.1 K,K? and to refer to this expression as the "ion product" for H B solutions. Usually a t this point a statement is made that this expression allows one t o calculate [S-2] in a saturated H2S solution if [H+] is known. This statement is certainly valid; but quite often the impression is given that the [H+] of a solution can be maintained constant while a solution is being saturated with HtS, and this may not be the case a t all. A strongly acidic solution can be maintained a t a constant [H+] while being saturated with HnS, but the more basic a solution the more impossible this becomes. The following numerical example illustrates the point.
What is the [S?] in a buffer solution of pH 10, after saturating the solution with HIS? By assuming a constant pH = 10 we would write [S-'1 = 0.1 K1K2/[H+I2. [S-2J = 0.1 X 1.1 X lo-' X 10-'4/10-20; [ E 2 ] = 1.1 X However, if we calculate [HS-I in this same solution: [HS-] = [H+][S-']/Kp; [HS-] = 10-'0 X 1.1 X 10-2/10-'4 = 1.1 X lo2 = 110. Now we must readily admit that [HS-] = 110 is impossible; no buffer solution could be prepared with the 110 mole/liter of base required to yield [HS-] = 110. Obviously in the HIS saturated "buffer" solution the [HS-] < 110, [H+] > 10-'"nd [ P I < 1.1 X A solution cannot be saturated in HpS and also have a pH = 10. If the pH is 10 the solution is not saturated in H2S. If the solution is saturated in HnS the pH must be less than 10. The calculation of [ S P ] in this basic buffer solution is not nearly so simple a problem as it appears at first glance. Exact calculations are worked out in the next section where we find typically that a "buffer" solution originally a t a pH 10 and saturated with HIS would have its [H+] increased to about 10-8 and correspondingly its [SW] would be about lo-', not 1.1 X 10W2. Buffered Alkaline Solution of H2S
The method we will use to calculate the concentrations of the various species in buffered alkaline solutions of H2S is one that has been described adequately elsewhere (1-4). We will indicate the number of species in solution and write an equal number of mathematical expressions involving the concentrations of these species. Then these equations will be solved simultaneously. The buffer solution chosen for these calculations is an ammonia-ammonium ion buffer. The anion introduced with the KH4+ is A-. The unknown concentrations and the equations relating these unknowns are listed below. Equations (1)-(4) are equilibrium constant expressions; (5)-(7) are material balance expressions; and (8) is the electroneutrality condition. Concentrations are used in place of activities and only approximate values of equilibrium constants are employed. Species in Solution NH. NH*+, A; H+, OH-, S-: HS-, and HzS. Equations
[NH4+]IOH-I/[NHsI = Ks = 1.8 X 1W6 [H+l[OH-I = K. = 1 X IOP" r H + l l H R - 1 ,, / 1 7,-7 [H+][S-2]/[HSSj= K2 = 1 X 10-l4 [A-I = A (a constant) [NHa]+ [NH,+] = N (total nitrogen-a constant) [HSI + [HS-I + [S-21 = S (total sulfur-a constant) 2[S-21 + [HS-I + [OH-] + A = [NH,+l JH+l L--
,LA..-
+
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The following rearrangements and substitutions can be made, leading to equation (9), which is a single equation in the single unknown H f . Equalities
For [OH-] : For [NH81:
[OH-]
=
[NH,] = N
K,/[Ht1 - [NHet1
IXH,+lK, For [NHatI: [H+I(N - I N H ~ + I ) = Kb
Equation (12) can be solved for different values of N, A, and S. The resulting [H+] can then be used in the expressions derived previously for [S-?I, [HS-1, IHxSl, lNH,+l, INH,], and [OH-]. As an example of the results of such calculations, the concentrations of the various species in solution for N = 2, A = 1, and S varyiug from 0.01 to 1.5 are tabulated in Table 1. Particular attention is called to the entries in Table 1 for S (total sulfur) = 1.01. When the total sulfur concentration in a solution which was originally 1 M NH3 1 M NH4A reaches 1.01 M , the [ H S ] = 0.1 M ; i.e., the solution becomes saturated with HrS. The (the[ H+l [Hf] a t this point is no longer 5.6 X of the original buffer) but is instead 1.2 X Correspondingly the [ S F ] is not 3.6 X (based on a constant [ H + ] during saturation with H?S) but is instead 7.6 X 10-7. It is interesting to note further that the maximum concentration of in the basic solution is not attained in a saturated Hi3 solution (where [H+] is high), nor is it attained for very low total sulfur (where [H+] is low but where [HIS]is also very small). The maximum is attained a t about the half neutralization point of the free iYHain the basic buffer solution. In Figure 1 the change of [S-%]with change in H2S concentration is plotted, and the differences betuveen assuming a constant [H+] = 5.6 X 10-'%and a cont,inuously varying [H+] are illustrated.
+
For [S-'I :
[H+ll[S-'I + LH'I W11 + [S-PI K,zc2 [S-'l
For lH +l
=
ZZ,
[H+12 [H+l Im+ x +I 1 = S
:
The applicability of equation (9) to a variety of common special cases is suggested by the following: 0.1 M H.S ( A = 0, N = 0, S = 0.1). From equation (9) use the terms [HS-] = [H+]. Case 2. 0.1 M HnS,0.3 M HC1 ( A = 0.3, N = 0, S = 0.1). From equation (9) use the terms [HS-] -4 = [H+]. Case 3. 1 M NH. IA = 0. N = 1. S = 0). From eountion 19) , ~ , use the t e r m s - b ~ - ] [NH~'+]. Case 4. lMNH,+ lMNHat(A = 1, N = 2, S = 0). From equation (9) use the terms A = [NHP]. Case I.
=
+
To calculate the concentrations of species present in a "buffer" solution simply substitute various values of S, N, and A into equation (9) and solve for [H+]. This calculation can be greatly simplified by noting that the most significant terms in equation (9) are IHS-1, A, and [NH4+]. Thus the expression can be obtained:
Equation (10) is not difficult to solve. However in many cases, in particular if [H+] > 10-12, the term KIKzis negligible in comparison with Kl[H+] [H+I1, leading to the expression,
+
Figure 1. Variation of %"rningconsbnt [H +] of
Equation (11) can be expanded into the quadratic form,
[S2] with HzS in on alldine solution: n = 0 = data from Table 1. 5.56 X
03-
Precipitation of Metal Sulfides
In an acidic solution where [Hi31 >> [HS-] >> [S-21, the relationship [H+I2[S-?I = 0.1 KIK? can be for which the solutions are
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Table 1.
S
Concentrations of the Species in Solution for N(Total Nitrogen) = 2 M, and A(Anion Concentration) = 1 M
[NHsl
[H +I
[NH
