# How can I calculate the dissociation constant?

May 7, 2014

You need some information to calculate a dissociation constant. Here's how to calculate the dissociation constant of a weak acid from the molarity and the pH.

Example

A 0.031 mol/L solution of an unknown monoprotic acid has a pH of 4.69. What is the acid dissociation constant for this acid?

Solution

1. Write the equation for the dissociation of a generic monoprotic acid:

HA + H₂O ⇌ H₃O⁺ + A⁻

2. Write the dissociation constant expression.

K_a = (["H₃O⁺"]["A⁻"])/["[HA]"]

3. Determine the equilibrium concentrations.

pH = -log[H₃O⁺] = 4.69

[H₃O⁺] = ${10}^{-} 4.69$ mol/L = 2.04 × 10⁻⁵ mol/L

From the equation, [A⁻] = [H₃O⁺] = 2.04 × 10⁻⁵ mol/L

[HA] = (0.031 - 2.04 × 10⁻⁵) mol/L = 0.031 mol/L

4. Substitute these values in the expression and that is it!

K_a = (["H₃O⁺"]["A⁻"])/["[HA]"] = (2.04 × 10⁻⁵ × 2.04 × 10⁻⁵)/0.031 = 1.34 × 10⁻⁸