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 `)`.

Answer

`R = 6.67 ohms`

Explanation

Let `K_(1)` and `K_(2)` be the specific conductances of the solutions A and B respectively and the constant of the cell be x.
`:.` For solution A :
sp. Conductance = conductance `xx` cell constant
`K_(1)=(1)/(5-) 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 equations (i),(ii) and (iii), we get `R = 66.67 "ohms"`.