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