Question

The resistance a solution A is 50 ohm and that of solution B is 100 ohm, 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 α of A and B on mixing)

• A. R = 96.67 ohm.
• B. R = 76.67 ohm.
• C. R = 86.67 ohm.
• D. R = 66.67 ohm.

Answer 1

The correct option is D R = 66.67 ohm.

How to approach this problem?
First get conductivity for both the solutions in terms of cell constant.
For solution A,
Conductivity $\left(k_A\right)$ = G(Conductance) $\times$ G* (cell constant)
$=\frac{1}{50}G\ast$
For solution B,
$Conductivity\left(k_B\right)=\frac{1}{100}\times G\ast \cdots \left(ii\right)(\because G\ast issameforAandB)$
Now,
When equal volumes of A and B are mixed, volume is the same and is DOUBLE of the initial volume in both the solutions. Hence, their individual contribution towards the conductivity of the mixture will be $\frac{k_A}{2}and\frac{k_B}{2}$, respectively, and conductivity of the mixture will be $\left(\frac{k_A+k_B}{2}\right)$
or the mixture: $\left(\frac{k_A+k_B}{2}\right)=\frac{1}{R}\times G\ast \cdots \left(iii\right)$
From Eqs. (i), (ii) and (iii), we get
R = 66.67 ohm.