Question

Problem: (a) Calculate the pH of a 0.20 M solution of benzoic acid at 25°C.

Short answer

The pH of the benzoic acid solution is 2.44.

Step-by-step solution

Given data

The molarity of the benzoic acid is 0.20M.

The temperature is ${\text{25}}^{\text{o}}\text{C}$.

Chemical reaction

The chemical reaction when the benzoic acid is dissolved in water that results in the formation of the benzoic acid solution is written as follows:

${\mathrm{C}}_6{\mathrm{H}}_5\mathrm{COOH}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{COO}}^{-}+{\mathrm{H}}_3{\mathrm{O}}^{+}$

The ${\text{K}}_{\text{a}}$value of the benzoic acid is $6.5\times {10}^{-5}$

calculating the pH

The pH of the benzoic acid (weak acid) is calculated using the formula as follows:

$\begin{array}{rcl}\mathrm{pH}& =& -\log \sqrt{\left[{\mathrm{C}}_6{\mathrm{H}}_5\mathrm{COOH}\right]\times {\mathrm{K}}_{\mathrm{a}}}\\ & & =\text{- log}\sqrt{{\text{0.20×6.5×10}}^{\text{- 5}}}\\ & & \text{=}\text{- log}\left(\text{0.0036}\right)\\ & & \text{=}\text{2.44}\end{array}$

Therefore, the pH of the benzoic acid solution is 2.44.