Chapter 14, Problem 14.126CHP

Interpretation Introduction

Interpretation:

The following statement has to be proved.

Beginning with the equilibrium equation for the dissociation of a weak acid HA, show that “the percent dissociation varies directly as the square root of ${\text{K}}_{\text{a}}$and inversely as the square root of the initial concentration of HA when the concentration of HA that dissociates is negligible compared with its initial concentration”

Concept Introduction:

Consider a weak-acid equilibrium reaction,

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

The acid dissociation constant ${\text{K}}_{\text{a}}$ can be given as,

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

$p{K}_a:$

${\text{pK}}_{\text{a}}{\text{ = -logK}}_{\text{a}}$

Where, ${\text{pK}}_{\text{a}}$ decreases as ${\text{K}}_{\text{a}}$ increases.

Percent dissociation:

It is defined as concentration of dissociated acid divided by the concentration of the acid times $100\%$.

$\text{Percent}\text{dissociation =}\frac{{\left[\text{HF}\right]}_{\text{dissociated}}}{{\left[\text{HA}\right]}_{\text{initial}}}\times 100\%$