Finding pH and pOH

Question

The concentration of H₂S in a saturated aqueous solution at room temperature is approximately 0.1 M. Calculate [H3O+],[H3O+], [HS⁻], and [S²⁻] in the solution:

H2S(aq)+H2O(l)⇌H3O+(aq)+HS−(aq)Ka1=8.9×10−8H2S(aq)+H2O(l)⇌H3O+(aq)+HS−(aq)

Ka1=8.9×10−8



HS−(aq)+H2O(l)⇌H3O+(aq)+S2−(aq)Ka2=1.0×10−19HS−(aq)+H2O(l)⇌H3O+(aq)+S2−(aq)

Ka2=1.0×10−19

Answer 1

Figuring out the full concentrations at equilibrium given x₁ and x₂ are the extents of the two reactions respectively. The equilibrium concentrations can be expressed as functions of x₁ and x₂:

[H₂S] = .1 - x₁

[H⁺] = x₁ + x₂ + 10^-7

[HS^-] = x₁-x₂

[S^2-] = x₂

The K expressions are:

K_a1 = (x₁+x₂+10^-7)(x₁+x₂)/(.1-x₁) (It is safe to make the preliminary assumption that x₁ >> x₂+10^-7,(obviously just x₂ as well) and that x₁<<.1) This reduces the problem to

8.9 x 10^-8 = x₁²/.1 or x₁ = 9.4 x 10^-5 M

and K_a2 = x₂(x₁ + x₂ + 10^-7)/(x₁+x₂) which leads to 10^-18 = x₂

(assumption are all well within 2 sig figs.)

All the equilibrium concentrations are easy to calculate from there.