Chapter 14, Problem 14.115CHP

Interpretation Introduction

Interpretation:

$\text{pH}$ of $\text{0}\text{.040M}$ Pyruvic acid $\left({\text{C}}_3{\text{H}}_4{\text{O}}_3\right)$ is $1.96$.  ${\text{K}}_{\text{a}}$ and ${\text{pK}}_{\text{a}}$ for Pyruvic acid has to be calculated.

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,

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

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.

The value of ${\text{K}}_{\text{w}}$ is calculated by the formula,

${\text{K}}_{\text{w}}{\text{=K}}_{\text{a}}{\text{×K}}_{\text{b}}$

$p{K}_a:$

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

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