Chapter 8, Problem 8.59QP

Interpretation Introduction

Interpretation:

Between hydrogen chloride and acetic acid solutions a solution with greater $\text{pH}$ has to be identified and explained.

Concept Introduction:

pH:  The $\text{pH}$ of a solution is defined as the negative logarithm of the molar concentration of the hydronium ion.

    $\text{pH}\text{=}\text{-log}{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$

Explanation of Solution

Given,

    $\begin{array}{l}\text{[HCl]}\text{=}1.0\text{ ×}{\text{10}}^{\text{-1}}\text{M}\\ {\text{[CH}}_{\text{3}}\text{COOH]}\text{=}1.0\text{ ×}{\text{10}}^{\text{-1}}\text{M}\end{array}$

Hydrogen chloride is a strong acid which undergoes complete dissociation and produce hydronium ion.  The $\text{pH}$ of hydrogen chloride solution is calculated as,

    $\begin{array}{l}{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}\text{=}\text{1}\text{.0}\text{×}{\text{10}}^{\text{-1}}\text{M}\\ \\ \text{pH}\text{=}\text{-log}{\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}\text{=}\text{-log}\text{(1}\text{.0}\text{×}{\text{10}}^{\text{-1}}\text{M)}\\ \\ \text{=}1\\ \\ \text{pH}\text{=}1\end{array}$

From the ICE table, the concentration of protons in acetic acid solution is calculated as,

    $\begin{array}{l}{\text{CH}}_{\text{3}}{\text{COOH}}_{\left(\text{aq}\right)}\stackrel{}{\rightleftarrows }{\text{ CH}}_{\text{3}}{\text{COO}}_{\left(\text{aq}\right)}^{\text{-}}{\text{+H}}_{\left(\text{aq}\right)}^{\text{+}}\\ \\ \text{Initial(M)}\text{0}\text{.1 }\text{0}\text{0}\\ \text{Change(M)}\text{-x}\text{+x}\text{+x}\\ \text{Equili}\text{.(M)}\text{0}\text{.1-x}\text{x}\text{x}\\ \\ {\text{K}}_{\text{a}}\text{=}\frac{{\text{x}}^{\text{2}}}{\text{0}\text{.1-x}}\text{=1}\text{.75}{\text{×10}}^{\text{-5}}\text{(x}\text{is}\text{very}\text{small}\text{neglect}\text{it)}\\ \\ {\text{x}}^{\text{2}}\text{=}\text{1}\text{.75}{\text{×10}}^{\text{-6}}\\ \\ \text{x}\text{=}\sqrt[]{\text{1}\text{.75}{\text{×10}}^{\text{-6}}}\text{=}\text{1}\text{.32}{\text{×10}}^{\text{-3}}\\ \\ {\text{[H}}^{\text{+}}\text{]}\text{=}\text{1}\text{.32}{\text{×10}}^{\text{-3}}\text{M}\end{array}$

The pH of acetic acid solution is calculated as,

    $\begin{array}{l}{\text{[H}}^{\text{+}}\text{]}\text{=}\text{1}\text{.145}{\text{×10}}^{\text{-3}}\text{M}\\ \\ \text{pH=-log}\left(\text{1}\text{.32}{\text{×10}}^{\text{-3}}\right)\text{=2}\text{.88}\\ \\ \text{pH}\text{=}\text{2}\text{.88}\end{array}$

Acetic acid is a weak acid which does not ionize completely.  And hydrochloric acid is a strong acid and dissociates completely.  Therefore, pH of acetic acid is greater than hydrochloric acid.