Metal sulfides in acidic H2S solutions
H2S is a weak diprotic acid. Because the second ionization is very weak,
free \(\mathrm{S^{2-}}\) is strongly suppressed in water, especially in acidic
solution. Sulfide precipitations are therefore carried out in acidic H2S
media.
Overall equilibrium and effective constant
For a metal sulfide \(\mathrm{MS}(s)\):
\[
\mathrm{MS}(s) + 2\,\mathrm{H_3O^+}
\rightleftharpoons
\mathrm{M^{2+}} + \mathrm{H_2S} + 2\,\mathrm{H_2O}
\]
The effective equilibrium constant in acidic solution is
\[
K_{\mathrm{spa}} =
\frac{[\mathrm{M^{2+}}][\mathrm{H_2S}]}{[\mathrm{H_3O^+}]^2}.
\]
It is related to the usual constants by
\[
K_{\mathrm{spa}} = \frac{K_{sp}}{K_{a1}K_w}.
\]
Reaction quotient and precipitation criterion
For given concentrations:
\[
Q_{\mathrm{spa}} =
\frac{[\mathrm{M^{2+}}][\mathrm{H_2S}]}{[\mathrm{H_3O^+}]^2},
\qquad [\mathrm{H_3O^+}] = 10^{-\mathrm{pH}}.
\]
- \(Q_{\mathrm{spa}} < K_{\mathrm{spa}}\): undersaturated, no MS(s) precipitates.
- \(Q_{\mathrm{spa}} \approx K_{\mathrm{spa}}\): saturated, MS(s) at equilibrium.
- \(Q_{\mathrm{spa}} > K_{\mathrm{spa}}\): MS(s) precipitates until \(Q_{\mathrm{spa}} = K_{\mathrm{spa}}\).
How the calculator uses this
-
Mode 1: from \(K_{sp}\), \(K_{a1}\) and \(K_w\) it computes
\(K_{\mathrm{spa}} = K_{sp}/(K_{a1}K_w)\).
-
Mode 2: from \([\mathrm{M^{2+}}]\), \([\mathrm{H_2S}]\) and pH it evaluates
\(Q_{\mathrm{spa}}\) and compares it with \(K_{\mathrm{spa}}\) to decide if MS(s)
precipitates under those conditions.
Comparing \(Q_{\mathrm{spa}}\) and \(K_{\mathrm{spa}}\) for different metals in the
same H2S / acid medium explains selective precipitation of one metal
sulfide while others remain dissolved.