Chapter 15.2, Problem 2PE

Interpretation Introduction

Interpretation:

The concentration of ${\text{OH}}^{\text{-}}$ ion in the given solution of $\text{HCl}$ has to be calculated.

Concept Introduction:

Determining the expression for the Ion product constant of water:

Water is a poor electrolyte. So it ionizes to a very small extent and it is known as autoionization of water. It can be represented as follows:

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

The rate constant for this equilibrium reaction is

${\text{K}}_{\text{c}}=\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\left[{\text{OH}}^{\text{-}}\right]$

To indicate that the rate constant is being the rate constant for the autoionization of water, ${\text{K}}_{\text{c}}$ can be replaced as ${\text{K}}_{\text{w}}$.

So, ${\text{K}}_{\text{w}}=\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\left[{\text{OH}}^{\text{-}}\right]$

${\text{K}}_{\text{w}}$ is known as the ion product constant of water.

Since ${\text{H}}_{\text{3}}{\text{O}}^{\text{+}}$ and ${\text{H}}^{\text{+}}$ are interchangeably representing the hydrated proton, hence ${\text{K}}_{\text{w}}$ can also be expressed as

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

At ${\text{25}}^{\text{o}}\text{C}$,

${\text{K}}_{\text{w}}=\left[{\text{H}}^{\text{+}}\right]\left[{\text{OH}}^{\text{-}}\right]=\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]\left[{\text{OH}}^{\text{-}}\right]=1.0\times {10}^{-14}$