Question

At $298\, K$, the limiting molar conductivity of a weak monobasic acid is $4 \times 10^{2} S\, cm ^{2} mol ^{-1} .$ At $298 \,K$, for an aqueous solution of the acid the degree of dissociation is $\alpha$ and the molar conductivity is $y \times 10^{2} \,S \,cm ^{2} mol ^{-1}$. At $298\, K$, upon $20$ times dilution with water, the molar conductivity of the solution becomes $3 y \times 10^{2} S \,cm ^{2} mol ^{-1}$
The value of $y$ is _______.

Answer 1

On dilution conductivity increases three times
Since temperature is constant $K _{ a }$ will be constant
$
\frac{C_{1} a_{1}^{2}}{1-a_{1}}=\frac{C_{2} a_{2}^{2}}{1-a_{2}}
$
$
\begin{array}{l}
\Rightarrow \frac{C \times a^{2}}{1-a}=\frac{\left(\frac{C}{20}(3 a)^{2}\right)}{(1-3 a)} \\
\Rightarrow \frac{1}{1-a}=\frac{9}{20(1-3 a)} \\
\Rightarrow 20-60 a=9-9 a \\
\Rightarrow a=\frac{11}{51}=0.2156 \\
\Rightarrow a=0.22
\end{array}
$
$
a=\frac{y}{4} ; y=4 a=4 \times 0.22=0.88
$
From above question we found the value of $a$.