The resistance of a 0.2text M electrolyte solution is 50text Omega with a specific conductance of 1.4text S m ^ -1 . If a 0.5text M solution of the same electrolyte shows a resistance of 280text Omega, find the molar conductivity of this second solution in text S m ^ 2 text mol ^ -1 .

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EEJ MAIN Chemistry QUESTION #7108

Question 1

The resistance of a $0.2\text{ M}$ electrolyte solution is $50\text{ }\Omega$ with a specific conductance of $1.4\text{ S m}^{-1}$. If a $0.5\text{ M}$ solution of the same electrolyte shows a resistance of $280\text{ }\Omega$, find the molar conductivity of this second solution in $\text{S m}^{2}\text{ mol}^{-1}$.

$5 \times 10^{3}$
$5 \times 10^{2}$
$5 \times 10^{-4}$✔️
$5 \times 10^{-3}$

Correct Answer Explanation

First, find cell constant ($G^*$): $G^* = \kappa \times R = 1.4 \times 50 = 70\text{ m}^{-1}$.
Then find conductivity ($\kappa$) for $0.5\text{ M}$: $\kappa = G^*/R = 70/280 = 0.25\text{ S m}^{-1}$.
Molar conductivity $\Lambda_m = \frac{\kappa}{1000 \times M} = \frac{0.25}{1000 \times 0.5} = 5 \times 10^{-4}\text{ S m}^{2}\text{ mol}^{-1}$.

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