Chapter U4.19, Problem 2E

Interpretation Introduction

Interpretation: The relationship between the H+ and OH- concentrations in a solution needs to be explained.

Concept Introduction: An aqueous solution produces both H+ and OH- ions. Depending on the higher concentration of the H+ or the OH- ion concentration, the solution is termed as an acid or a base.

Answer to Problem 2E

The H+ and the OH- concentrations in an aqueous solution are related by the ionic product of water, K_w as

${\text{K}}_{\text{W}}=\left[{\text{H}}^{+}\right]{\left[{\text{OH}}^{-}\right]}^2{\text{M}}^2$

Where the square brackets, [..] denote molar concentrations.

Explanation of Solution

Water is itself an electrolyte (when acidified) and ionizes as below.

${\text{H}}_2\text{O}\left(\text{l}\right)\to {\text{H}}^{+}\left(\text{aq}\right)+{\text{OH}}^{-}\left(\text{aq}\right)$

The equilibrium constant for the above reaction is the ionic product of water, K_w and is given as

$\begin{array}{c}{\text{K}}_{\text{W}}=\left[{\text{H}}^{+}\right]\left[{\text{OH}}^{-}\right]\\ =1.0\times {10}^{-14}{\text{ M}}^2\end{array}$

at $\text{25}°\text{C}$ .

For an acidic solution, [H⁺] is high and thus, [OH^-] is low as per the above expression. The reverse is true for a basic solution.

Conclusion

The H+ and OH- concentrations are related by the ionic product of water as

${\text{K}}_{\text{W}}=\left[{\text{H}}^{+}\right]{\left[{\text{OH}}^{-}\right]}^2{\text{M}}^2$