Chapter 16, Problem 146AP

Interpretation Introduction

Interpretation:

The expression for the pH of a strong acid solution by taking into account the contribution of water is to be derived. Also, the pH of the solution for the given concentration of strong acid is to be determined.

Concept introduction:

pH is the measure of acidity of a solution, which depends on the concentration of hydronium ions and the temperature of the solution.

The formula to calculate the pH of the solution from the concentration of hydronium ions is as follows:

$\text{pH}=-\log \left[{\text{H}}_3{\text{O}}^{+}\right]$ …… (1)

The auto-ionization of water is as follows:

${\text{2H}}_{\text{2}}\text{O}\rightleftharpoons {\text{H}}_{\text{3}}{\text{O}}^{\text{+}}+{\text{OH}}^{\text{-}}$

The above equation can be formulated as follows:

$K_{\text{W}}={\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][OH}}^{\text{-}}\text{]}=1.0\times {10}^{-14}$ …… (2)

The ionization of a strong acid takes place as:

$\text{HA}\to {\text{H}}^{+}+{\text{A}}^{-}$

The concentration of ${\text{H}}^{+}$ is equal to the concentration of the acid ionized and the concentration of the conjugate base, ${\text{A}}^{-}$.

The pH of the solution as:

$\text{pH}=-\log \left(\frac{\left[{\text{A}}^{-}\right]\pm \sqrt{{\left[{\text{A}}^{-}\right]}^2+4{\text{K}}_{\text{w}}}}{2}\right)$