Question

Calculate the pH and [S²⁻ ] in a 0.13 M H₂S solution. Assume K_a1 = 1.0 ✕ 10⁻⁷; K_a2 = 1.0 ✕ 10⁻¹⁹.

Answer 1

In aqueous solution, H₂S is a weak acid. Its dissociation is according to the following equilibrium reactions:

To calculate the pH of a 0.13M solution of H₂S we need calculate first the [H₃O⁺] concentration. The balance equations for diprotic acid, give the following algebraic solution to calculate [H₃O⁺]:

Where:

C_a is the initial concentration of H₂S

K_a1 is the first dissociation constant of the H₂S

K_a2 is the second dissociation constant of the H₂S

Kw is the constant of dissociation of water.

Equation (1) can be simplyfied if we assume some approximations.

In the first approximation, we will not take into account the contribution of water to the hydronium ion concentration because the concentration of H2S is enough to inhibit the dissociation of water, then equation (1) is rewritten as:

In the second approximation, the value of K_a2is too small in front of the [H₃O⁺] and it can be rejected from the numerator and denominator:

Finally, [H₃O⁺] can be simplyfied in numerator and denominator:

Notice that equation (4) is the general equation for solving weak monoprotic acids. The exact solution for this equation is given by solving the quadratic equation:

The solution for [H₃O⁺] is given by:

Substituting known values for K_a1 and C_a , the concentration of [H₃O⁺] in a 0.13M solution of H₂S is:

According to the definition of pH:

The pH of a 0.13 M solution of H₂S is:

The algebraic solution to calculate [S^-2] in this system is given by the equation:

Substituting all the known values in this equation, the concentration of [S^-2] in a 0.13 M solution of H₂S is: