Chapter 9, Problem 9.33P

Interpretation Introduction

Interpretation:

The Henderson –Hasselbalch equation is always true and those values of $\left[{\text{A}}^{\text{-}}\right]$ and $\left[\text{HA}\right]$ that are not correct to use in the equation has to be explained.

Concept Introduction:

Henderson-Hasselbalch equation:

Henderson-Hasselbalch equation is rearranged form of acid dissociation expression.

For acid:

Consider an acidic reaction:

$\text{HA}\stackrel{{\text{K}}_{\text{a}}}{\rightleftharpoons }{\text{H}}^{\text{+}}{\text{+A}}^{\text{-}}$

The Henderson-Hasselbalch equation for an acidic reaction can be given as,

${\text{pH=pK}}_{\text{a}}\text{+log}\frac{\left[{\text{A}}^{\text{-}}\right]}{\left[\text{HA}\right]}$

For base:

Consider a basic reaction:

${\text{BH}}^{\text{+}}\stackrel{{\text{K}}_{\text{a}}{\text{=K}}_{\text{w}}{\text{/K}}_{\text{b}}}{\rightleftharpoons }{\text{B+H}}^{\text{+}}$

The Henderson- Hasselbalch equation for a basic reaction can be given as,

${\text{pH=pK}}_{\text{a}}\text{+log}\frac{\left[\text{B}\right]}{\left[{\text{BH}}^{\text{+}}\right]}$

Where, ${\text{pK}}_{\text{a}}$= acid dissociation constant for weak acid ${\text{BH}}^{\text{+}}$