Question

Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for a weak electrolyte, if the symbols carry their usual meaning

• A. \( \Lambda_m^2 C - K_a \Lambda_m + K_a \Lambda_m^{\circ 2} = 0 \)
• B. \( \Lambda_m - \Lambda_m^{\circ} + AC \frac{1}{2} = 0 \)
• C. \( \Lambda_m - \Lambda_m^{\circ} - AC \frac{1}{2} = 0 \)
• D. \( \Lambda_m^2 C + K_a \Lambda_m^{\circ 2} - K_a \Lambda_m^{\circ} = 0 \)

Answer 1

The Correct Option is A

The relationship between molar conductivity $\Lambda_m$, molar conductivity at infinite dilution $\Lambda_m^\circ$, and concentration $C$ for a weak electrolyte can be derived from the dissociation equilibrium. The correct equation involves the dissociation constant $K_a$ and accounts for the variation of $\Lambda_m$ with concentration. For weak electrolytes, the molar conductivity $\Lambda_m$ is related to the degree of dissociation $\alpha$ as:
\[ \alpha = \frac{\Lambda_m}{\Lambda_m^\circ}. \]
The dissociation constant $K_a$ is expressed as:
\[ K_a = \frac{C\alpha^2}{1 - \alpha}. \]
Substituting $\alpha =\frac{\Lambda_m}{\Lambda_m^\circ}$ into the equation:
\[ K_a = \frac{C \left(\frac{\Lambda_m}{\Lambda_m^\circ}\right)^2}{1 - \frac{\Lambda_m}{\Lambda_m^\circ}}. \]
Simplifying and rearranging, the equation becomes:
\[ \Lambda_m^2 C - K_a \Lambda_m^{\circ 2} + K_a \Lambda_m \Lambda_m^\circ = 0. \]
This is the equation that correctly represents the relationship between molar conductivity, concentration, and dissociation constant for a weak electrolyte.
Final Answer: (1)