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

The Correct Option is A

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 \(\text{mol}^{1/2} \text{L}^{-1/2}\)).