Question

Which of the following statement is correct regarding an eqiumolar solution of a weak acid $C{H}_{3}COOH$ and a weak base $N{H}_{4}OH$ at ${25}^{\circ }C$ ?

• A. Higher the concentration of $C{H}_{3}COOH$, lesser is the $pH$ value.
• B. Higher the concentration of $N{H}_{4}OH$, higher is the $pH$ value.
• C. $pH$ does not depend on the concentration of $C{H}_{3}COON{H}_4$.
• D. None of the above

Answer 1

The correct option is C $pH$ does not depend on the concentration of $C{H}_{3}COON{H}_4$.

Theory:
For a salt of weak acid and weak base:
$\left[H^{+}\right]=\sqrt{\frac{K_w{K}_a}{K_b}}$
$log\left[H^{+}\right]=\frac{1}{2}log{K}_w+\frac{1}{2}log{K}_a-\frac{1}{2}log{K}_b$
$-log\left[H^{+}\right]=-\frac{1}{2}log{K}_w-\frac{1}{2}log{K}_a+\frac{1}{2}log{K}_b$
$pH=\frac{1}{2}(p{K}_w+p{K}_a-p{K}_b)$ valid only if h<0.1 or 10%
$pH=7+\frac{1}{2}(p{K}_a-p{K}_b)$ at ${25}^{o}C$
Since, expression for $\left[H^{+}\right]$ or pH does not contain any concentration term. Thus $pH$ is independent of the concentration value.