Question

Resistance of a cconductivity cell filled with a solution of an electrolyte of concentration $0.1M$ is $100\Omega$. The conductivity of this solution is $1.29S{m}^{-1}$. Resistance of the same cell when filled with $0.02M$ of the same solution is $520\Omega$. 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

Answer: (A)

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

Cell constant= Conductivity $\times$ Resistance

$=1.29\times 100$

$=129m^{-1}=1.29c{m}^{-1}$ .

Now for 0.02M solution,

$K=\frac{1}{R}\times$ Cell constant

$=\frac{1.29c{m}^{-1}}{520ohm}=0.248\times {10}^{-2}Sc{m}^{-1}$

${\lambda }_m=\frac{K\times 1000}{M}=\frac{0.248\times {10}^{-2}\times 1000}{0.02}=124Sc{m}^{2}mo{l}^{-1}$

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

Option A is correct.