The first disinfectant used by Joseph Lister was called carbolic acid. This substance now is known as phenol, C6H5OH (pKa = 9.90). What is the pH of a 0.10 M solution of phenol?

5.5

Explanation:

Phenol is a weak acid that dissociates according to the following reaction.

C₆H₅OH (aq) ⇄ C₆H₅O⁻ (aq) + H⁺ (aq)

The pKa is 9.90. The acid dissociation constant (Ka) is:

pKa = - log Ka

Ka = antilog - pKa = antilog - 9.90

Ka = 1.26 * 10⁻¹⁰

Given the concentration of the acid, Ca = 0.10 M, and the Ka, We can find [H⁺] using the following expression.

[H⁺] = √ (Ka * Ca)

[H⁺] = √ (1.26 * 10⁻¹⁰ * 0.10)

[H⁺] = 3.5 * 10⁻⁶ M

The pH is:

pH = - log [H⁺]

pH = - log 3.5 * 10⁻⁶

pH = 5.5