The resistance of a solution `A` is `50 ohm` and that of solution `B` is `100ohm,` both solutions are taken in the same conductivity cell. If equal volumes of solution`A` and `B` are mixed, what is the resistance of the mixture using the same cell ? `(` Assume there is no change or increase in the `prop` of `A` and `B` on mixing `)`.

Explanation

Let `K_(1)` and `K_(2)` be the specific conductance of the solution A and B respectively and the cell constant of the cell be `X`.
For solution A: Sp. Conductance = Conductance `xx` Cell constant
`k_(1) = (1)/(50) xx X` ....(i)
For solution B: Sp. conductance, `k_(2) = (1)/(100) xx X` ...(ii)
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))`
`:.` For the mixture : `(1)/(2) (k_(1)+k_(2)) = (1)/(R) xx X` ...(iii)
`(R` is the resistance of mixture)
From equation (i),(ii) and (ii), `R = 66.67 ohm`.