Question

Consider a weak monobasic acid $HA$ having a concentration C with degree of dissociation, $\alpha <<1.$. The pH of this weak acid in terms of acid dissociation constant $K_a$ and concentration $C$ is :

• A. $-lo{g}_{10}\left(\sqrt{\frac{K_a}{C}}\right)$
• B. $-lo{g}_{10}\sqrt{K_a.C}$
• C. $pH=-lo{g}_{10}\sqrt{K_a.C^2}$
• D. $pH=-lo{g}_{10}\sqrt{K_a^2.C}$

Answer 1

The correct option is B $-lo{g}_{10}\sqrt{K_a.C}$

For weak acid $HA$ with concentration $‘C^{\prime }$, ionization constant $K_a$ and degree of dissociation $(\alpha <<1)$
In aqueous solution,
$HA\left(aq\right)\rightleftharpoons H^{+}\left(aq\right)+A^{-}\left(aq\right)$
At $t=0$ $C$ $0$ $0$
$Equilibrium$ $C-C\alpha$ $C\alpha$ $C\alpha$
$K_a=\frac{C{\alpha }^2}{1-\alpha }$
As $\alpha <<1,(1-\alpha )\approx 1$

$K_a=C{\alpha }^2$

As $H^{+}$ concentration is $C\alpha$
By multiplying $C$ on both sides, we get:
$K_a\times C=C{\alpha }^2\times C=K_a\times C=(C\alpha {)}^2{K}_a\times C=[H^{+}{]}^2$
$\left[H^{+}\right]=\sqrt{K_a.C}$
$pH=-lo{g}_{10}\sqrt{K_a.C}$