Chapter 7, Problem 100E

Interpretation Introduction

Interpretation: An expression showing relationship between $p{K}_a$ and $p{K}_b$ for conjugate acid-base pair needs to be derived.

Concept Introduction: An acid is a substance which gives hydrogen ions in the solution and base is a substance which gives hydroxide ions in the solution. The conjugate acid base pair can be represented as follows:

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

Here, HA is an acid as it gives hydrogen ion to ${\text{H}}_{\text{2}}\text{O}$ and ${\text{H}}_{\text{2}}\text{O}$ accepts hydrogen ion thus, it acts as a base. After accepting hydrogen ion, ${\text{H}}_{\text{2}}\text{O}$ forms ${\text{H}}_{\text{3}}\text{O}$ which is conjugate acid and ${\text{A}}^{-}$ is conjugate base as it is formed after release of hydrogen from HA.