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
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)
