The molar conductivity of $0.02 \mathrm{M} \mathrm{AgI}$ at $298 \mathrm{~K}$ is $142.3 \Omega^{-1}…

The molar conductivity of $0.02 \mathrm{M} \mathrm{AgI}$ at $298 \mathrm{~K}$ is $142.3 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. What is its conductivity?
  1. $1.42 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}$
  2. $2.41 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}$
  3. $2.85 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}$
  4. $7.11 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}$

Solution

$\begin{aligned} \wedge & =\frac{1000 \mathrm{k}}{\mathrm{c}} \\ \mathrm{k} & =\frac{\Lambda \mathrm{c}}{1000} \\ \mathrm{k} & =\frac{142.3 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1} \times 0.02 \mathrm{~mol} \mathrm{~L}^{-1}}{1000 \mathrm{~cm}^3 \mathrm{~L}^{-1}} \\ \therefore \quad \mathrm{k} & =2.85 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}\end{aligned}$

Asked in: MHT CET 2023 (11 May Shift 1)

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