The resistance of a conductivity cell containing $$0.01$$ MKCl solution at $$298$$ K is $$1750$$ $$\Omega$$. If the conductivity of $$0.01$$ MKCl solution at $$298$$ K is $$0.152 \times 10^{-3}$$ S cm$$^{-1}$$, then the cell constant of the conductivity cell is ______ $$\times 10^{-3}$$ cm$$^{-1}$$

The resistance of the conductivity cell is

$$R = 1750 \; \Omega$$

and the conductivity of 0.01 M KCl solution is

$$\kappa = 0.152 \times 10^{-3} \text{ S cm}^{-1}$$

Since the cell constant is related to conductivity and resistance by

$$\text{Cell constant} = \kappa \times R$$

Substituting the given values yields

$$\text{Cell constant} = 0.152 \times 10^{-3} \times 1750$$

This gives

$$ = 0.266 \text{ cm}^{-1}$$

and equivalently

$$ = 266 \times 10^{-3} \text{ cm}^{-1}$$

Therefore, the cell constant is 266 $$\times 10^{-3} \text{ cm}^{-1}$$.