Chapter 17, Problem 17.30QP

Interpretation Introduction

Interpretation:

From the given acid dissociation constant, the colour at given $\text{pH}$ value has to be identified.

Concept introduction:

$\text{pH}$: 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.

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

$K_a$: Acid ionization constant ${\text{K}}_{\text{a}}$ represents how strong the acid is in a solution.

Equilibrium constant ${\text{K}}_{\text{eq}}$ represents extend of dissociation of acid in aqueous solution.

  For a dissociation of acid $\left(HA\right)$ in aqueous solution,

  $HA+H_{2}O\underset{}{\overset{}{\rightleftharpoons }}{H}_3{O}^{+}+A^{-}$

  $k_{eq}=\frac{\left[H_3{O}^{+}\right]\left[A^{-}\right]}{\left[HA\right]\left[H_{2}O\right]}$

Where,

  ${\text{K}}_{\text{eq}}\to \text{Equilibrium constant}$

  ${\text{[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}\to \text{concentration of hydrogen ion}$

  ${\text{[A}}^{\text{-}}\text{]}\to \text{concentration of acid anion}$

  $\text{[HA]}\to \text{concentration of the acid}$

Relationship between ${\text{K}}_{\text{eq}}$ and ${\text{K}}_{\text{a}}$,

  ${\text{K}}_{\text{a}}\text{=}{\text{K}}_{\text{eq}}\left[{\text{H}}_{\text{2}}\text{O}\right]$

  where, $\left[{\text{H}}_{\text{2}}\text{O}\right]$ is the molar concentration of water

  ${\text{K}}_{\text{a}}$ is acid ionization constant.

$p{K}_a$ represents the chance of losing proton from a compound and it is denoted as $-\log \left[K_a\right]$.

  $\begin{array}{cc}\text{pH}& \text{Colour}\\ \text{Less than 3}& \text{Red}\\ \text{3}\text{to}\text{6}& \text{Orange or Yellow}\\ \text{7}& \text{Green}\\ \text{8}\text{to}\text{11}& \text{Blue}\\ \text{Greater}\text{than}\text{11}& \text{Violet or indigo}\end{array}$