A conductivity cell containing $0.001 \mathrm{M} \mathrm{AgNO}_3$ solution develops resistance $6530…

A conductivity cell containing $0.001 \mathrm{M} \mathrm{AgNO}_3$ solution develops resistance $6530 \mathrm{ohm}$ at $25^{\circ} \mathrm{C}$. Calculate the electrical conductivity of solution at same temperature if the cell constant is $0.653 \mathrm{~cm}^{-1}$.
  1. $1.3 \times 10^{-4} \Omega^{-1} \mathrm{~cm}^{-1}$
  2. $1.5 \times 10^{-4} \Omega^{-1} \mathrm{~cm}^{-1}$
  3. $1.7 \times 10^{-4} \Omega^{-1} \mathrm{~cm}^{-1}$
  4. $1.0 \times 10^{-4} \Omega^{-1} \mathrm{~cm}^{-1}$

Solution

$\begin{array}{ll} & \text { Cell constant }=\mathrm{k} \times \mathrm{R} \\ \therefore & 0.653=\mathrm{k} \times 6530 \\ \therefore & \mathrm{k}=\frac{0.653}{6530}=1 \times 10^{-4} \Omega^{-1} \mathrm{~cm}^{-1}\end{array}$

Asked in: MHT CET 2023 (14 May Shift 2)

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