The resistance of a solution A is 50 ohms and that of solution B is 100 ohms 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.)

The resistance of a solution A is 50 ohms and that of solution B is 10

1.	The resistance of a solution A is 50 ohms and that of solution B is 100 ohms 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.)
Answer» Solution :Let `K_(1)` and `K_(2)` be the specific conductance of the solutions A and B respectively and the constant of the cell be x. `therefore` for solution A : sp. conductance = conductance `xx` cell constant `K_(1) = (1)/(50) xx x` ….(1) For SOLUTON B : sp. conductance `K_(2) = (1)/(100) xx x` .......(2) When equal VOLUMES of A and B are mixed, both the solutions get doubly diluted , hence their individual contribution TOWARDS the sp. conductance of the mixture will be `(K_(1))/(2)` and `(K_(2))/(2)` respectively and the sp. conductance of the mixture will be `(1)/(2)(K_(1) + K_(2))`. `therefore` for the mixture: `(1)/(2)(K_(1) + K_(2)) = (1)/(R) xx x`. ......(3) R is the resistance of mixture) From eqns. (1), (2) and (3), we get R = 66.67 ohms.