Question

The resistance of $0.01N$ solution of an electrolyte is $210\Omega $ at $298K$ with a cell constant of$0.88c{m^{ - 1}}$ . Calculate the conductivity and equivalent conductivity of the solution.

Answer 1

Hint: Conductivity or specific conductivity of any solution is the measure of its ability to conduct electric current. Equivalent conductivity is the conductivity (or equivalent conductance is conductance) of the solution containing one gram equivalent of the given electrolyte contained in a container having two electrodes with very large surface area placed $1cm$ apart.
Formula used:
For the calculation of conductivity
$K = C \times \dfrac{l}{a}$
Here, K is specific conductivity, C is conductance, l is distance between the electrodes and a is the area of the electrodes.
For the calculation of equivalent conductivity
${\Lambda _{eq}} = \dfrac{{K \times 1000}}{N}$
Here, ${\Lambda _{eq}}$ is equivalent conductivity, K is specific conductivity, N is normality of the solution.

Complete step by step answer:
Given quantities are
Normality of the solution, $N = 0.01N$
Resistance of the solution, $R = 210\Omega $
Temperature, $T = 298K$
Cell constant, $\dfrac{l}{a} = 0.88c{m^{ - 1}}$
Calculation of conductivity, conductance of any solution is inversely proportional to resistance.
Conductance, $C = \dfrac{1}{R}$
Putting the values, we get $C = \dfrac{1}{{210}}{\Omega ^{ - 1}}$
Conductivity, $K = C \times \dfrac{l}{a} = \dfrac{1}{{210}} \times 0.88 = 4.19 \times {10^{ - 3}}{\Omega ^{ - 1}}c{m^{ - 1}} = 4.19 \times {10^{ - 3}}Sc{m^{ - 1}}$
Calculation of equivalent conductivity, putting the values in the formula we get
Equivalent conductivity, ${\Lambda _{eq}} = \dfrac{{K \times 1000}}{N} = \dfrac{{4.19 \times {{10}^{ - 3}} \times 1000}}{{0.01}} = 419Sc{m^2}e{q^{ - 1}}$
Thus, conductivity is $4.19 \times {10^{ - 3}}Sc{m^{ - 1}}$ and equivalent conductivity is $419Sc{m^2}e{q^{ - 1}}$ for the given solution.
Additional information: There are two types of cells: electrolytic and electrochemical cells. Electrolytic cells convert electric energy to chemical energy and electrochemical cells convert chemical energy to electric energy. The solutions capable of conducting electricity are called electrolytes. In solutions the electrolytes dissociate into ions which are responsible for their conduction properties. These ions move through the solutions towards opposite electrodes and conduct electricity in cells.

Note:
The unit of resistance is $\Omega $ and conductance is ${\Omega ^{ - 1}}$ or S (Siemens), this should not be confused. Cell constant is the distance between the electrodes divided by their area. The terms conductance and conductivity should not be confused as specific conductivity is generally referred to as conductivity.