Chapter 5, Problem 5.43P

Interpretation Introduction

Interpretation:

The $p{K}_a$ value for given acid has to be calculated using $pH$ measured at half way point in the titration. The $pH$ for solution at given concentration 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.

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

If the value of $\text{pH}$ is less than $7$, then the solution is acidic whereas if the value of $\text{pH}$ is greater than $7$, then the solution is basic.

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

  $p{K}_a=-\log K_a$

The strength of acid decreases as the value of $p{K}_a$ increases.

Henderson-Hasselbalch equation:

$\text{pKa}\text{=}\text{pH}\text{+}\text{log}\frac{\left[\text{HA}\right]}{\left[{\text{A}}^{\text{-}}\right]}$

Henderson-Hasselbalch equation explains the relationship between $pH$ of solution and $p{K}_a$ of acid. For a dissociation of acid $\left(HA\right)$ in aqueous solution,

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

  $p{K}_a=pH+\log \frac{\left[HA\right]}{\left[A^{-}\right]}$