Question

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

Answer 1

Let us suppose $K_1$ and $K_2$ are the specific conductances of solutions ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ respectively and cell constant is ${}^{\prime }{y}^{\prime }$. We know that,
Specific conductance $=Conductance\times Cellconstant$
For $\left(A\right),K_1=\frac{1}{50}\times y$
For $\left(B\right),K_2=\frac{1}{100}\times y$
When equal volumes of $\left(A\right)$ and $\left(B\right)$ are mixed, the volume becomes double. Then,
Specific conductance of mixture $=\frac{K_1+K_2}{2}$
$\therefore \frac{K_1+K_2}{2}=\frac{1}{2}\times y$
$\frac{1}{2}[\frac{y}{50}+\frac{y}{100}]=\frac{1}{R}\times y$
$\frac{1}{100}+\frac{1}{200}=\frac{1}{R}$
$R=200/3=66.66ohm$.