Question

The molar conductivity of a solution of a weak acid HX (0.01 M) is $10$ times smaller than the molar conductivity of a solution of a weak acid $HY\left(0.10\text{M}\right)$. If ${\lambda }_X^{\circ }={\lambda }_Y^{\circ }$ the difference in their $p{K}_a$ values, $\left(p{K}_a\right(HX)-p{K}_a(HY\left)\right)$ is (consider degree of ionization of both acids to be << 1)

Answer 1

Degree of dissociation $\left(\alpha \right)$
$={\frac{{\lambda }_m}{{\lambda }_m^{\circ }}}_{\text{(limiting molar conductivity)}}^{\text{(molar conductivity at C)}}$
According to question,
Let, the molar conductivity of weak acid $HY$
$={\lambda }_m\left(HY\right)=x$
Then, molar conductivity of weak acid $HX$
$={\lambda }_m\left(HX\right)=\frac{x}{10}$
$\frac{a_1}{a_2}=\frac{\frac{{\lambda }_m\left(HX\right)}{{\lambda }_m^o\left(HX\right)}}{\frac{{\lambda }_m\left(HY\right)}{{\lambda }_m^o\left(HY\right)}}=\frac{1}{10}$