Chapter 19.3, Problem 30LC

Interpretation Introduction

Interpretation: The ${\text{K}}_{\text{a}}$ of a weak acid or the ${\text{K}}_{\text{b}}$ of a weak base is to be determined.

Concept introduction: The ratio of the concentration of the ionized form of an acid to the concentration of the unionized form of the acid is known as the dissociation constant or ionization constant. Weak acids or weak bases are slightly ionized or dissociate in an aqueous solution.

Answer to Problem 30LC

The measured concentration of all the substances present at equilibrium is substituted into the equilibrium expression for ${\text{K}}_{\text{b}}$ or ${\text{K}}_{\text{a}}$ determines the ${\text{K}}_{\text{b}}$ of a weak base and ${\text{K}}_{\text{a}}$ of a weak acid.

Explanation of Solution

The strength of an acid in solution is measured by the acid dissociation constant. It is denoted as ${\text{K}}_{\text{a}}$. The dissociation of hypothetical weak acid HA is written as follows:

  $HA\rightleftharpoons H^{+}+A^{-}$

The dissociation constant ${\text{K}}_{\text{a}}$ of the acid HA is written as,

  ${\text{K}}_{\text{a}}=\frac{\left[H^{+}\right]\left[A^{-}\right]}{\left[HA\right]}$

Here, $\left[H^{+}\right]$ is the molar concentration of hydronium ion at equilibrium

  $\left[A^{-}\right]$ is the molar concentration of the conjugate base at equilibrium

  $\left[HA\right]$ is the molar concentration of weak acid at equilibrium

Therefore, to find ${\text{K}}_{\text{a}}$ substitute the values for the equilibrium concentration into the equilibrium expression and solve the value for ${\text{K}}_{\text{a}}$ .

The strength of the weak base in the solution is measured by the base dissociation constant. It is denoted as ${\text{K}}_{\text{b}}$. The dissociation of the hypothetical weak base is written as follows:

  $B+H_{2}O\rightleftharpoons B{H}^{+}+O{H}^{-}$

The dissociation constant ${\text{K}}_{\text{b}}$ of the weak base is written as,

  ${\text{K}}_{\text{b}}=\frac{\left[B{H}^{+}\right]\left[O{H}^{-}\right]}{\left[B\right]}$

Thus, to find ${\text{K}}_{\text{b}}$ substitute the values for the equilibrium concentration into the equilibrium expression and solve the value for ${\text{K}}_{\text{b}}$ .