Chemistry - Electrochemistry Question with Solution | TestHub

Let $K$ be conductivity (S), $A$ be area (m²), $C$ be concentration (mol m⁻³), $L$ be length (m).

Given $K\propto \frac{A\cdot C}{L}$.

So, $K=k\frac{A\cdot C}{L}$, where $k$ is the constant of proportionality.

Rearranging for $k$: $k=\frac{K\cdot L}{A\cdot C}$.

Units: $k=\frac{\mathrm{S}\cdot \mathrm{m}}{{\mathrm{m}}^2\cdot (\mathrm{mol}\cdot {\mathrm{m}}^{-3})}=\frac{\mathrm{S}\cdot \mathrm{m}}{{\mathrm{m}}^2\cdot \mathrm{mol}\cdot {\mathrm{m}}^{-3}}=\mathrm{S}\cdot {\mathrm{m}}^{1-2-(-3)}\cdot {\mathrm{mol}}^{-1}=\mathrm{S}\cdot {\mathrm{m}}^2\cdot {\mathrm{mol}}^{-1}$.

The unit of the constant of proportionality is $\mathrm{S}{\mathrm{m}}^2{\mathrm{mol}}^{-1}$.