Chapter 9, Problem 9.25P

Interpretation Introduction

Interpretation:

The limiting value for $\text{α}$ for the given ${\text{K}}_{\text{b}}$ has to be calculated and the expression $\text{α=}\frac{{\text{10}}^{\text{7}}{\text{K}}_{\text{b}}}{\left({\text{1+10}}^{\text{7}}{\text{K}}_{\text{b}}\right)}$ has to be proved.

Concept Introduction:

Consider a reaction of weak base,

${\text{B+H}}_{\text{2}}\text{O}\stackrel{{\text{K}}_{\text{b}}}{\rightleftharpoons }{\text{BH}}^{\text{+}}{\text{+OH}}^{\text{-}}$

The value of ${\text{K}}_{\text{b}}$ can be calculated as,

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

Where ${\text{K}}_{\text{b}}$ is called as base dissociation constant.

$\begin{array}{l}\text{α=}\frac{\left[{\text{BH}}^{\text{+}}\right]}{\left[\text{B}\right]\left[{\text{BH}}^{\text{+}}\right]}\\ \\ \text{α=}\frac{\text{x}}{\text{F}}\end{array}$

Where $\text{α}$ is called as Fraction of association of base