Chapter 15, Problem 15.133CHP

(a)

Interpretation Introduction

Interpretation:

The concentrations of ${\text{H}}_{\text{3}}{\text{PO}}_{\text{4}}$ , ${\text{H}}_{\text{2}}{\text{PO}}_{\text{4}}{}^{-}$ and ${\text{HPO}}_{\text{4}}{}^{\text{2-}}$ should be calculated, when pH of the final solution is $\text{6}\text{.73}$ when dilution of $\text{0}{\text{.100 mol of H}}_{\text{3}}{\text{PO}}_{\text{4}}$  and $\text{0}\text{.150 mol}$ of $\text{NaOH}$ with dilute $\text{HCl}$.

Concept Introduction:

Equilibrium constant for acid:

The general reaction for the acid dissociation in aqueous solution is,

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

Equilibrium constant for acid is,

${\text{K}}_{\text{a}}\text{=}\frac{{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{][A}}^{\text{-}}\text{]}}{\text{[HA]}}$

Where,

${\text{K}}_{\text{a}}$ is equilibrium constant for acid

$\text{[HA]}$ is concentration of acid

${\text{[H}}_3{\text{O}}^{+}\text{]}$ is concentration of ${\text{H}}_3{\text{O}}^{+}$ ion.

${\text{[A}}^{\text{-}}\text{]}$ is concentration of conjugate base ${\text{A}}^{\text{-}}$

Henderson-Hasselbalch equation:

The pH can be calculated using Henderson-Hasselbalch equation as follows,

$\begin{array}{l}\text{pH}{\text{= pK}}_{\text{a}}\text{ + log}\frac{[\text{conjugate base]}}{[\text{weak acid]}}\\ \text{pH}{\text{= pK}}_{\text{a}}\text{ + log}\frac{[{\text{A}}^{\text{-}}\text{]}}{[\text{HA]}}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The moles of $\text{HCl}$ were inadvertently added to the original solution should be calculated.

Concept Introduction:

Henderson-Hasselbalch equation:

The pH can be calculated using Henderson-Hasselbalch equation as follows,

$\begin{array}{l}\text{pH}{\text{= pK}}_{\text{a}}\text{ + log}\frac{[\text{conjugate base]}}{[\text{weak acid]}}\\ \text{pH}{\text{= pK}}_{\text{a}}\text{ + log}\frac{[{\text{A}}^{\text{-}}\text{]}}{[\text{HA]}}\end{array}$