Question

For the two aqueous solutions of an acid $HA(K_{a_1})$ and another acid $HB(K_{a_2})$, the lowering of vapour pressure is $\Delta P_1$ and $\Delta P_2$ respectively. Assuming the same concentration for both acids, choose the correct relation in the options if $\Delta P_1 > \Delta P_2$.

• A. $pK_{a_1} > pK_{a_2}$
• B. $pK_{a_1} < pK_{a_2}$
• C. $pK_{a_1} = pK_{a_2}$
• D. $K_{a_2} > K_{a_1}$

Answer 1

Answer: (B)

$pK_{a_1} < pK_{a_2}$

Answer 2

$\Delta P_1 > \Delta P_2 \implies i_1 > i_2$ (due to same concentration).

$i = 1+\alpha$ for a weak acid $\implies \alpha_1 > \alpha_2$.

For a weak acid, $K_a = \frac{C\alpha^2}{1-\alpha}$. Given same $C$, $\alpha_1 > \alpha_2 \implies K_{a_1} > K_{a_2}$.

$pK_a = -\log_{10} K_a$. If $K_{a_1} > K_{a_2}$, then $pK_{a_1} < pK_{a_2}$.