Calculate the molar conductivity of a solution having a concentration of $0.08 \ M$ and a resistivity of $5 \times 10^{-3} \ \Omega \ cm$.
(N/A) The conductivity $k$ is the reciprocal of resistivity $\rho$:
$k = \frac{1}{\rho} = \frac{1}{5 \times 10^{-3} \ \Omega \ cm} = 200 \ S \ cm^{-1}$
The formula for molar conductivity $\Lambda_{m}$ is:
$\Lambda_{m} = \frac{1000 \times k}{c}$
Substituting the values:
$\Lambda_{m} = \frac{1000 \times 200}{0.08} \ S \ cm^{2} \ mol^{-1}$
$\Lambda_{m} = \frac{200000}{0.08} \ S \ cm^{2} \ mol^{-1}$
$\Lambda_{m} = 2.5 \times 10^{6} \ S \ cm^{2} \ mol^{-1}$
$k = \frac{1}{\rho} = \frac{1}{5 \times 10^{-3} \ \Omega \ cm} = 200 \ S \ cm^{-1}$
The formula for molar conductivity $\Lambda_{m}$ is:
$\Lambda_{m} = \frac{1000 \times k}{c}$
Substituting the values:
$\Lambda_{m} = \frac{1000 \times 200}{0.08} \ S \ cm^{2} \ mol^{-1}$
$\Lambda_{m} = \frac{200000}{0.08} \ S \ cm^{2} \ mol^{-1}$
$\Lambda_{m} = 2.5 \times 10^{6} \ S \ cm^{2} \ mol^{-1}$
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