Chapter 18, Problem 18.82P

Interpretation Introduction

Interpretation:

The $\text{pH}$ of Acetylsalicylic acid (${\text{HC}}_{\text{9}}{\text{H}}_{\text{7}}{\text{O}}_{\text{4}}$, aspirin) has to be calculated for $\text{0}{\text{.018 M HC}}_{\text{9}}{\text{H}}_{\text{7}}{\text{O}}_{\text{4}}{\text{ (K}}_{\text{a}}\text{ = 3}\text{.6}\times {10}^{-4})$.

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.