Chapter 18.4, Problem 18.7AFP

Interpretation Introduction

Interpretation:

$K_a$ of ${\text{NH}}_{\text{4}}^{\text{+}}$ has to be calculated when $\text{0}\text{.2 M}{\text{NH}}_{\text{4}}\text{Cl}$ solution of has $\text{pH}$ is 5.

Concept Introduction:

An equilibrium constant $\left(K\right)$ is the ratio of concentration of products and reactants raised to appropriate stoichiometric coefficient at equlibrium.

For the general acid HA,

  $\text{HA}\left(\text{aq}\right)+{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)\rightleftharpoons {\text{H}}_{\text{3}}{\text{O}}^{+}\left(\text{aq}\right)+{\text{A}}^{-}\left(\text{aq}\right)$

The relative strength of an acid and base in water can be also expressed quantitatively with an equilibrium constant as follows:

  $K_a=\frac{\left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]\left[{\text{A}}^{-}\right]}{\left[\text{HA}\right]}$                                                                                                 $\left(1\right)$

An equilibrium constant $\left(K\right)$ with subscript $a$ indicate that it is an equilibrium constant of an acid in water.

The formula is given below for calculating concentration of ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$,

${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{] = 10}}^{\text{-pH}}$