Chapter 9, Problem 9.17P

Interpretation Introduction

Interpretation:

Among the buffers that have highest buffer capacity at $\text{pH}$ equals to 9 has to be determined.

Concept Introduction:

Buffers are those that resist $\text{pH}$ change on addition of acid or base and even if it is diluted. It is formed by combination of weak acid and strong base or vice versa. Buffer capacity is defined as the quantity of acid or base added to volume of buffer  to bring change in $\text{pH}$.

The equation for buffer is described by Henderson-Hasselbach equation and it is a rearranged form of equilibrium constant, $K_{\text{a}}$. It relates $\text{pH}$ of buffer solution and $\text{p}{K}_{\text{a}}$ value. It also helps to find equilibrium $\text{pH}$ in acid-base reactions. Consider an equation of dissociation of an acid as follows:

  $\text{HA}\rightleftharpoons {\text{H}}^{+}+{\text{A}}^{-}$

Formula to calculate $\text{pH}$ is as follows:

  $\text{pH}=\text{p}{K}_{\text{a}}+\log \left(\frac{\left[{\text{A}}^{-}\right]}{\left[\text{HA}\right]}\right)$

Here,

$\text{p}{K}_{\text{a}}$ is acid dissociation constant of weak acid $\text{HA}$.

$\left[{\text{A}}^{-}\right]$ is concentration of conjugate base ${\text{A}}^{-}$

$\left[\text{HA}\right]$ is concentration of acid $\text{HA}$.

The maximum value of buffer capacity is attained when $\text{pH}$ becomes equal to $p{K}_{\text{a}}$ and this can happen only if ratio of $\left(\frac{\left[{\text{A}}^{-}\right]}{\left[\text{HA}\right]}\right)$ is one. At this condition there is no change in $\text{pH}$ of solution.