The resistance of a solution A is 50 Ω and that of solution B is 100 Ω, both solutions being taken i

Question

The resistance of a solution A is 50 Ω and that of solution B is 100 Ω, both solutions being taken in the same conductivity cell. If equal volumes of solution A and B are mixed, what will be the resistance of the mixture using the same cell? Assume that there is no increase in the degree of dissociation of A and B on mixing.

Accepted Answer

$\kappa_{A} = \frac{1}{50} 	imes G^{*}	ext{ and }\kappa_{B} = \frac{1}{100} 	imes G^{*}$Now, $G_{mix} = \frac{1}{G^{*}}\left( \frac{\kappa_{A}}{2} + \frac{\kappa_{B}}{2} ight) = \frac{3}{200}	ext{ oh}	ext{m}^{- 1}$$	herefore R = \frac{1}{G} = \frac{200}{3}	ext{ ohm}$

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