Question

A weak electrolyte having the limiting equivalent conductance of $400\,S \,cm ^{2}$ g.equiv $^{-}$ at $298 \,K$ is $2 \%$ ionized in its $0.1 N$ solution. The resistance of this solution (in ohm) in an electrolytic cell of cell constant $0.4 \,cm ^{-1}$ at this temperature is

• A. 200
• B. 300
• C. 400
• D. 500
• E. 600

Answer 1

Answer: (D)

Since, the weak electrolyte is $2 \%$ ionised,

$C=\alpha \cdot N $

$=\frac{2}{100} \times 0.1 $

$=2 \times 10^{-3} g \text { equiv } L ^{-1}$

Limiting equivalent conductance,

$\Lambda_{e q}=\frac{\kappa \times 1000}{C} $

$400 \,Scm ^{2} g \text { equiv }^{-1}=\frac{\kappa \times 1000}{2 \times 10^{-3}} $

$\kappa=8 \times 10^{-4} \,S \,cm ^{-1} $

Further, $\kappa=\frac{1}{R} \times\left(\frac{l}{a}\right)$

(where, $\frac{l}{a}=$ cell constant )

$8 \times 10^{-4} S cm ^{-1}=\frac{1}{R} \times 0.4 \,cm ^{-1}$

$R=\frac{0.4}{8 \times 10^{-4}} S ^{-1}=\frac{1000}{2} \,\Omega=500 \,\Omega$