Question

A resistance of a conductivity cell filled with a solution of an electrolyte of concentration $0.1$ M is $100$ ohm. The conductivity of this solution is $1.29$ $S{m}^{-1}$ Resistance of the same cell filled with $0.02$ M of the same solution if the electrolyte is $520$ ohm. The molar conductivity of $0.02$ M solution of electrolyte would 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}$ $S{m}^2$ $mo{l}^{-1}$

Resistant conductivity $R_1=100ohm$

$K=1.29S{m}^{-1}$

cell constant $G^{\ast }=R.K=100\times 1.29$

$=129m^{-1}$

Same cell Resistance $R_2=520\Omega$

So condictivity $=\frac{G^{\ast }}{R}$

$K=\frac{129m^{-1}}{520}$

$=0.2480769S{m}^{-1}$

molar conductivity $=\frac{K}{C}$

$=\frac{0.2480769}{0.02\times {10}^{3}mol/m^3}$

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