[H^{ +}] × [HS^{ −}] = ‹k› = (0.95E−4)^2 = 0.9E−8. (II)
The concentration of hydrosulphide-ion is, therefore, inversely proportional to the concentration of hydrogen-ion. It is clear that the addition of a strong acid, readily yielding concentrations of hydrogen-ion very much greater than 0.95E−4 (the value of [H^{ +}] in a saturated aqueous solution of hydrogen sulphide) will, as the result of the greatly increased total hydrogen-ion concentration, reduce the concentration of hydrosulphide-ion to correspondingly low values. For instance, the presence of 0.1 molar hydrochloric acid will increase the concentration of hydrogen-ion close to a thousandfold and will reduce the concentration of hydrosulphide-ion to 0.9E−7.
For the secondary ionization (see p. 101) of hydrogen sulphide, HS^{ −} ⇄ H^{ +} + S^{ 2−}, we have
[H^{ +}] × [S^{ 2−}] / [HS^{ −}] = K_{ 2}. (III)
The value of this constant has recently been determined[397] and found to be 1.2E−15. Recalling the fact that the concentrations [H^{ +}] and [HS^{ −}] of hydrogen-ion and hydrosulphide-ion, [p201] respectively, resulting from the primary ionization, are each[398] 0.95E−4, we have for the concentration of the sulphide-ion, in aqueous solution saturated with hydrogen sulphide at atmospheric pressure and 25°, [S^{ 2−}] = 1.2E−15.
Combining equations (II) and (III), we have, further:[399]
[H^{ +}]^2 × [S^{ 2−}] = ‹k› × K_{ 2} = ‹k›_{ 2} = 1.1E−23, (IV)
‹which shows, directly, the relation between the concentration of the sulphide-ion and that of the hydrogen-ion, the relation of primary importance in considering the precipitation of metal sulphides in acid solutions.› The ‹concentration of the sulphide-ion› is, thus, ‹inversely proportional› to the ‹square› of the ‹concentration› of ‹the hydrogen-ion›. A thousandfold increase in the concentration of the latter, which is very nearly the effect produced by the presence of 0.1 molar hydrochloric acid ([H^{ +}] = 0.091), reduces the concentration of sulphide-ion in the saturated aqueous solution a millionfold: If we call [S^{ 2−}]_{ Ac.} the concentration of the sulphide-ion in the acid solution, [S^{ 2−}]_{ Ac.} = (1.1E−23) / (0.091)^2 = 1.3E−21, whereas, in the absence of acid, as found above, [S^{ 2−}] = 1.2E−15.