Question

Resistance of a solution (A) is $50\text{ohm}$ and that of a solution (B) is $100\text{ohm}$, both solution being taken in the same conductivity cell. If equal volume of solution (A) and (B) are mixed, what will be the resistance of the mixture, using the same cell?
Assume thta there is no increase in the degree of dissociation of (A) and (B) on mixing.

• A. $75.0\text{ohm}$
• B. $50.0\text{ohm}$
• C. $33.33\text{ohm}$
• D. $66.66\text{ohm}$

Answer 1

The correct option is D $66.66\text{ohm}$

Let us suppose ${\kappa }_1$ and ${\kappa }_2$ are specific conductances of solutions 'A' and 'B' respectively and cell constant is ${}^{\prime }{y}^{\prime }$. We know that,
$\text{Specific conductance = Conductance}\times (\text{Cell constant}$
For (A), ${\kappa }_1=\frac{1}{50}\times y$
For (B), ${\kappa }_2=\frac{1}{100}\times y$

When equal volume of (A) and (B) are mixed, the volume becomes double. Then,
$\text{Specific conductance of mixture}=\frac{{\kappa }_1+{\kappa }_1}{2}$
$\therefore \frac{{\kappa }_1+{\kappa }_1}{2}=\frac{1}{R}\times y$
$\Rightarrow \frac{1}{2}[\frac{y}{50}+\frac{y}{100}]=\frac{1}{R}\times y$

$\Rightarrow \frac{1}{100}+\frac{1}{200}=\frac{1}{R}$

$\Rightarrow R=200/3=66.66\text{ohm}$