A $\mathrm{KC}$ 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 $\mathrm{HCl}$ solution, the resistance drops to $1.03 \Omega$. The conductivity of the $\mathrm{HC} 1$ solution is____________ $\times 10^{-2} \mathrm{~S} \mathrm{~m}^{-1}$. (Round off to the Nearest Integer).
(57)
$\kappa=\frac{1}{R} \cdot G^{*}$
For same conductivity cell, $\mathrm{G}^{*}$ is constant and hence $\kappa \cdot R$. constant.
$\therefore 0.14 \times 4.19=\kappa \times 1.03$
or, $\kappa=\frac{0.14 \times 4.19}{1.03}$
$=0.5695 \mathrm{Sm}^{-1}$
$=56.95 \times 10^{-2} \mathrm{Sm}^{-1} \approx 57 \times 10^{-2} \mathrm{Sm}^{-1}$
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