Question

Resistance of a conductivity cell filled with a solution of an electrolyte of concentration $0.1M$ is $100ohm$. The conductivity of this solution is $1.29S{m}^{-1}$. Resistance of the same cell when filled with $0.2M$ of the same solution is $520ohm$. The molar conductivity of $0.02M$ solution of the electrolyte will be:

• A. $124\times {10}^{-4}S{m}^{2}mo{l}^{-1}$
• B. $1240\times {10}^{-4}S{m}^{2}mo{l}^{-1}$
• C. $1.24\times {10}^{-4}S{m}^{2}mo{l}^{-1}$
• D. $12.4\times {10}^{-4}S{m}^{2}mo{l}^{-1}$

Answer 1

The correct option is A $124\times {10}^{-4}S{m}^{2}mo{l}^{-1}$

$K=\frac{1}{R}\times \frac{1}{A}$

$1.29=\frac{1}{100}\times \frac{l}{A}$

$\frac{l}{A}=129m^{-1}$

${\wedge }_m=K\times \frac{1000}{M}$

$=(\frac{1}{R}\times \frac{l}{A})\times \frac{1000}{M}$

$=(\frac{1}{520}\times 129)\times \frac{1000}{0.02}\times {10}^{-6}$

$=124\times {10}^{-4}S{m}^{2}mo{l}^{-1}$.