Question

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

Answer 1

Answer: 0.88

On dilution conductivity increases three times
Since temperature is constant $K_a$ will be constant
$<br/>\frac{C_1{a}_1^2}{1-a_1}=\frac{C_2{a}_2^2}{1-a_2}<br/>$
$<br/>\begin{array}{l}<br/>\Rightarrow \frac{C\times a^2}{1-a}=\frac{\left(\frac{C}{20}(3a{)}^2\right)}{(1-3a)}\\ <br/>\Rightarrow \frac{1}{1-a}=\frac{9}{20(1-3a)}\\ <br/>\Rightarrow 20-60a=9-9a\\ <br/>\Rightarrow a=\frac{11}{51}=0.2156\\ <br/>\Rightarrow a=0.22<br/>\end{array}<br/>$
$<br/>a=\frac{y}{4};y=4a=4\times 0.22=0.88<br/>$
From above question we found the value of $a$.