Question

For a strong electrolyte, a plot of molar conductivity against $(\text{concentration})^{1/2}$ is a straight line, with a negative slope, the correct unit for the slope is:

• A. S cm$^2$ mol$^{-3/2}$ L$^{1/2}$
• B. S cm$^2$ mol$^{-1}$ L$^{1/2}$
• C. S cm$^2$ mol$^{-3/2}$ L
• D. S cm$^2$ mol$^{-3/2}$ L$^{-1/2}$

Answer 1

Answer: (A)

S cm$^2$ mol$^{-3/2}$ L$^{1/2}$

Answer 2

For a strong electrolyte, the molar conductivity $\Lambda_m$ can be expressed as:
$\Lambda_m = \Lambda_m^0 - A\sqrt{C}$
where $\Lambda_m^0$ is the molar conductivity at infinite dilution, $A$ is a constant, and $C$ is the concentration.
The term $A\sqrt{C}$ has units of $\text{S cm}^2 \text{mol}^{-1}$, so the units of $A$ must be $\text{S cm}^2 \text{mol}^{-3/2} \text{L}^{1/2}$ to ensure dimensional consistency when multiplied with $\sqrt{C}$ (units of $\text{mol}^{1/2} \text{L}^{-1/2}$).