What is the conductivity of $0.02 \mathrm{M} \mathrm{KCl}$ solution if cell constant is $1.29…

What is the conductivity of $0.02 \mathrm{M} \mathrm{KCl}$ solution if cell constant is $1.29 \mathrm{~cm}^{-1}$ with resistance $645 \Omega$ ?
  1. $5.0 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}$
  2. $2.0 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}$
  3. $8.3 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}$
  4. $2.5 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}$

Solution

$\begin{aligned} & \mathrm{K}=\frac{1}{\mathrm{R}} \cdot \frac{\ell}{\mathrm{A}} \quad\left(\text { Cell constant }=\frac{\ell}{\mathrm{A}}\right) \\ & \mathrm{K}=\frac{1}{645} \times 1.29 \\ & =0.002 \\ & =2 \times 10^{-3} \Omega^{-1} \mathrm{~cm}^{-1}\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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