The resistance offered by 0.1 M solution of acetic acid when placed in a conductivity cell of length 1.0 cm and area of cross section 3.0cm2 is found to be 7×103Ω. The molar conductivity of the solution is

# The resistance offered by 0.1 M solution of acetic acid when placed in a conductivity cell of length 1.0 cm and area of cross section $3.0{\mathrm{cm}}^{2}$ is found to be $7×{10}^{3}\mathrm{\Omega }$. The molar conductivity of the solution is

1. A

$4.76×{10}^{-3}\mathrm{S}{\mathrm{cm}}^{2}{\mathrm{mol}}^{-1}$

2. B

$4.76×{10}^{-4}\mathrm{S}{\mathrm{cm}}^{2}{\mathrm{mol}}^{-1}$

3. C

$0.476\mathrm{S}{\mathrm{cm}}^{2}{\mathrm{mol}}^{-1}$

4. D

$4.76\mathrm{S}{\mathrm{cm}}^{2}{\mathrm{mol}}^{-1}$

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### Solution:

$\kappa =\frac{1}{R}\left(\frac{l}{A}\right)=\left(\frac{1}{7×{10}^{3}\mathrm{\Omega }}\right)\left(\frac{1.0\mathrm{cm}}{3.0{\mathrm{cm}}^{2}}\right)=4.76×{10}^{-5}\mathrm{S}{\mathrm{cm}}^{-1}$

$\mathrm{\Lambda }=\frac{\kappa }{c}=\frac{4.76×{10}^{-5}\mathrm{S}{\mathrm{cm}}^{-1}}{0.1\mathrm{mol}{\mathrm{dm}}^{-3}}=4.76×{10}^{-4}\mathrm{S}{\mathrm{dm}}^{3}{\mathrm{cm}}^{-1}{\mathrm{mol}}^{-1}=4.76×{10}^{-4}\mathrm{S}\left(10\mathrm{cm}{\right)}^{3}{\mathrm{cm}}^{-1}{\mathrm{mol}}^{-1}=0.476\mathrm{S}{\mathrm{cm}}^{2}{\mathrm{mol}}^{-1}$

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