Chapter 16, Problem 133AP

Interpretation Introduction

Interpretation:

The value of equilibrium constant for the given reaction is to be determined.

Concept introduction:

Water is a universal solvent and it is a weak electrolyte. It auto-ionizes to produce hydronium as well as hydroxide ions and remains in equilibrium with them according to the reaction:

${\text{H}}_2\text{O}+{\text{H}}_2\text{O}\rightleftharpoons {\text{H}}_3{\text{O}}^{+}+{\text{OH}}^{-}$

At a particular temperature, the equilibrium constant thatrelates the concentration of each of the species present in the above reaction is $K_w$.

The equilibrium expression for $K_w$ is as follows:

$K_w=\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\left[{\text{OH}}^{-}\right]$ …… (1)

The ionization of the weak acid takes place as follows:

${\text{HA}}_{\left(\text{aq}\right)}+{\text{H}}_2{\text{O}}_{\left(\text{l}\right)}\rightleftharpoons {\text{H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\left(\text{aq}\right)}+{\text{A}}^{-}{}_{\left(\text{aq}\right)}$

$K_{\text{a}}$ is a measure of dissociation of an acid and is known as acid-ionization constant, which is specific at a particular temperature.

$K_{\text{a}}=\frac{\left[{\text{H}}_3{\text{O}}^{+}\right]\left[{\text{A}}^{-}\right]}{\left[\text{HA}\right]}$ …… (2)