Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for…

Strategy: Use Ostwald's Dilution Law combined with the definition of \degree of dissociation ($\alpha = \Lambda_m / \Lambda_m^\circ$) to derive an relationship between concentration ($C$) and molar conductivity.

Step 1: Start with $K_a$ $K_a = \frac{C\alpha^2}{1-\alpha}$

Step 2: Substitute $\alpha$ $K_a = \frac{C(\Lambda_m / \Lambda_m^0)^2}{1 - (\Lambda_m / \Lambda_m^0)} = \frac{C\Lambda_m^2}{\Lambda_m^0 (\Lambda_m^0 - \Lambda_m)}$

Step 3: Rearrange into the target form $K_a \Lambda_m^0 (\Lambda_m^0 - \Lambda_m) = C\Lambda_m^2$ $K_a (\Lambda_m^0)^2 - K_a \Lambda_m \Lambda_m^0 = C\Lambda_m^2$ $C\Lambda_m^2 + K_a \Lambda_m \Lambda_m^0 - K_a (\Lambda_m^0)^2 = 0$

Note based on the signs in the options: $C\Lambda_m^2 + K_a (\Lambda_m^0)^2 - K_a \Lambda_m \Lambda_m^0 = 0$ Matches Option (c).

$\boxed{\text{Answer: (c)}}$