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Q)

Resistance of $0.2\; M$ solution of an electrolyte is $50 \Omega$ . The specific conductance of the solution is $1.4 \;m^{-1}$ . The resistance of $0.5\; M$ solution of the same electrolyte is $280\Omega$ .The molar conductivity of $0.5\;M$ solution of the electrolyte in $S m^2mol^{-1}$ is :

$\begin{array}{1 1}(A)\;5\times 10^3\\(B)\;5\times 10^2\\(C)\;5\times 10^{-4}\\(D)\;5\times 10^{-3}\end{array} $

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A)
$\large\frac{k_2}{k_1}=\frac{R_1}{R_2}$
$\Rightarrow k_2=\large\frac{R_1}{R_2}$$\times k_1$
$\Rightarrow \large\frac{50}{280}$$\times 1.4Sm^{-1}$
$\lambda_m=\large\frac{k_2}{C}=\frac{1/4Sm^{-1}}{0.50mol L^{-1}}$
$\Rightarrow \large\frac{1}{4}\times \frac{10^{-3}}{0.50}$
$\Rightarrow 5\times 10^{-4}Sm^2mol^{-1}$
Hence (C) is the correct answer.
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