(N/A) The quantity $\left(\frac{l}{A}\right)$ is called the cell constant,denoted by the symbol $G^*$. Here,$l$ is the distance between the two electrodes of the cell,and $A$ is the area of cross-section of the electrodes. Direct measurement of $l$ and $A$ is often inconvenient and unreliable.
$(A)$ Measurement of cell resistance: The cell constant is usually determined by measuring the resistance of the cell containing a solution whose conductivity is already known. For this purpose,we generally use $KCl$ solutions,whose conductivity is known accurately at various concentrations and temperatures.
$(B)$ Procedure: The conductivity cell is filled with a $KCl$ solution of known concentration and is then connected to a Wheatstone bridge using an $AC$ current source to measure its resistance.
$(C)$ Calculation of cell constant $G^*$: $G^* = \left(\frac{l}{A}\right) = R \cdot \kappa$
Where,$R$ is the measured resistance of the $KCl$ solution,and $\kappa$ is the conductivity of the $KCl$ solution obtained from standard tables.
The table below provides reference values for $KCl$ solutions at $298.15 \ K$:
| Molarity (mol $L^{-1}$) | Molarity (mol $m^{-3}$) | Conductivity $(S \ cm^{-1})$ | Conductivity $(S \ m^{-1})$ | Molar Conductivity $(S \ cm^{2} \ mol^{-1})$ | Molar Conductivity $(S \ m^{2} \ mol^{-1})$ |
|---|
| $1.000$ | $1000$ | $0.1113$ | $11.13$ | $111.3$ | $111.3 \times 10^{-4}$ |
| $0.100$ | $100.0$ | $0.0129$ | $1.29$ | $129.0$ | $129.0 \times 10^{-4}$ |
| $0.010$ | $10.00$ | $0.00141$ | $0.141$ | $141.0$ | $141.0 \times 10^{-4}$ |