Question

The resistance of a solution ${}^{\prime }{A}^{\prime }$ is $40ohm$ and that of solution ${}^{\prime }{B}^{\prime }$ is $70ohm$, both solutions being taken in the same conductivity cell. If equal volumes of solutions ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ 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 ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ on mixing)

• A. $50.9ohm$
• B. $101.8ohm$
• C. $110ohm$
• D. $50ohm$

Answer 1

The correct option is A $50.9ohm$

Conductance of resultant solution obtained by mixing equal volume of two solution is given by:
$C_M=\frac{1}{2}(C_1+C_2)$
$C_M=\frac{1}{2}(\frac{1}{R_1}+\frac{1}{R_2})$
$\frac{1}{R_M}=\frac{1}{2}\left(\frac{R_1+R_2}{R_1{R}_2}\right)$
$R_M=\frac{R_1{R}_2}{R_1+R_2}\times 2$

So, $R_M=(\frac{2800}{110}\times 2)=50.9ohm$