Chapter 5, Problem 5.18P

Interpretation Introduction

Interpretation:

The equilibrium constant expression for given reaction has to be estimated and also the extent of dissociation is small and $\alpha$ is inversely proportional to the square root of the total pressure, $\alpha \propto p^{\text{-1/2}}$ has to be showed.

Concept Introduction:

Ionic-product constant for water: It is the hydronium ion concentration times the $O{H}^{-}$ concentration present in the solution.

$\begin{array}{l}{H}_2{O}_{\left(l\right)}+H_2{O}_{\left(l\right)}{H}_3{O}^{+}{}_{\left(aq\right)}+O{H}^{-}{}_{\left(aq\right)}\\ K=\frac{\left[H_3{O}^{+}\right]\left[O{H}^{-}\right]}{\left[H_{2}O\right]\left[H_{2}O\right]}\\ \left[H_3{O}^{+}\right]=\left[O{H}^{-}\right]=1.00\times {10}^{-7}M\\ \therefore K_W=K\left[H_{2}O\right]\left[H_{2}O\right]=\left[H_3{O}^{+}\right]\left[O{H}^{-}\right]\\ K_W=1.00\times {10}^{-14}M\end{array}$

The $K_w$ will apply to all aqueous solution.

For acidic solution $\left[H_3{O}^{+}\right]$ is large that is $\left[H_3{O}^{+}\right]>{10}^{-7}Mand\left[O{H}^{-}\right]<{10}^{-7}M$

For basic solution $\left[O{H}^{-}\right]$ is large that is $\left[H_3{O}^{+}\right]<{10}^{-7}Mand\left[O{H}^{-}\right]>{10}^{-7}M$

$\text{pH}$: The concentration of hydrogen ion is measured using $\text{pH}$ scale.  The $\text{pH}$ of a solution is a figure that expresses the acidity or the alkalinity of a given solution.

It is defined as the negative base-10 logarithm of the hydrogen or hydronium ion concentration.

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