The resistance of a solution `'X'` is `50 Omega` and that of solution `'Y'` is `100 Omega`, both solution beinf taken in the same conductivity cell. If equal volumes of solution `X` and `Y` are mixed, what will be the resistance of the mixture using the same cell?

Options

A. `66.67 Omega`
B. `76.66 Omega`
C. `85.58 Omega`
D. `58.85 Omega`

Answer

A

Explanation

Assume that there is no increase in the degree of dissciation pf `X` and `Y` on mixing.
Let `kappa_(1)` and `kappa_(2)` be the conductivity of the solutions `X` and `Y` respectively and the cell constant be `Z`.
`kappa_(1) = (1)/(50) xx Z`, …..(i)
for solutions `Y`:
`kappa_(2) = (1)/(100) xx Z`, ........(ii)
when equal volumes of `X` and `Y` are mixed, both the solutions get double diluted, hence their individual contribution towards the conductivity of the mixture will be `kappa_(1)//2` and `kappa_(2)//2` respectively. Consequently the conductivity of the mixture will be `(1)/(2) kappa_(1) = (1)/(50) xx Z,`.
Assuming that `R` is the resistance of mixture, we have (for the mixture):
Conductivity = conductance `xx` Cell const.
`(1) /(2) (kappa_(1)+kappa_(2)) = (1)/(R) xx Z`.......(III)
From equations (i) and (ii), we get
`(1)/(2)((1)/(50)xx Z+(1)/(100)xxZ) = (1)/(R) xx Z`
Or `R = 66.67 Omega`