A KCl solution of conductivity $0.14 \mathrm{~S} \mathrm{~m}^{-1}$ shows a resistance of $4.19 \Omeg

Question

A KCl solution of conductivity $0.14 \mathrm{~S} \mathrm{~m}^{-1}$ shows a resistance of $4.19 \Omega$ in a conductivity cell. If the same cell is filled with an HCl solution, the resistance drops to $1.03 \Omega$. The conductivity of the HCl solution is ______ $	imes 10^{-2} \mathrm{~S} \mathrm{~m}^{-1}$. (Round off to the Nearest Integer)\

Professor PC Thomas Classes · Answer

(57) : For KCl solution,\ $R=ho\left(\frac{l}{A}ight)$\ $4.19=\frac{1}{0.14}\left(\frac{l}{A}ight) \Rightarrow\left(\frac{l}{A}ight)=0.587 \mathrm{~m}^{-1}$\ Since $\left(\frac{l}{A}ight)$ is constant for same cell for HCl solution,\ $1.03=\frac{1}{\kappa}(0.587) \Rightarrow \kappa=57 	imes 10^{-2} \mathrm{~S} \mathrm{~m}^{-1}$