Chapter 9, Problem 76P

Interpretation Introduction

Interpretation:

The concentration of ${\text{[OH}}^{-}\text{]}$ and ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ion in the given sample of milk of magnesia with $\text{pH}$ value $10.52$ needs to be determined.

Concept Introduction:

A base is defined as the substance that can give ${\text{[OH}}^{-}\text{]}$ in its solution whereas an acid can give ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ in its solution. General equation for acid and base can be written as:

  ${\text{HA}}_{\text{(l)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ A}}^{\text{-}}{}_{\text{(aq)}}{\text{ + H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}$

  ${\text{BOH}}_{\text{(l)}}\underset{}{\rightleftarrows }{\text{ OH}}^{\text{-}}{}_{\text{(aq)}}{\text{ + B}}^{\text{+}}{}_{\text{(aq)}}$

The ionic product of water can be used to calculate the concentration of ${\text{[OH}}^{-}\text{]}$ and ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$ ions in the given solution.

  ${\text{ K}}_{\text{w}}{\text{ = [OH}}^{\text{-}}{}_{\text{(aq)}}{\text{][H}}_{\text{3}}{\text{O}}^{\text{+}}{}_{\text{(aq)}}\text{] }$

Experimentally proved that at $\text{25}°\text{C}$ , the concentration of ${\text{OH}}^{\text{-}}$ and ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ is same and that is $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-7}}$ . Thus, the value of ${\text{K}}_{\text{w}}$ stands for ion product constant for water with value of $\text{1}\text{.0 }\times {\text{ 10}}^{\text{-14}}\text{ at 25}°\text{C}$.

The acidic and basic nature of the solution can be expressed in terms of pH of the solution. The range of pH lies from 0 to 14. The pH value from 0 to 7 indicates an acidic solution whereas the pH value from 7 to 14 stands for a basic solution. A neutral solution can be expressed as pH 7. It can be calculated with the help of concentration ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ ions and can be formulated as:

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