Match List I with List II for an electrochemical cell at 298 K ( Given 2.303 RT F = 0.059 V ) : List I (Cell parameters) List II (Equilibrium constant, K_c ) (A) n=1, E^ _ cell =0.118 V (I) 10^2 (B) n=2, E^ _ cell =0.118 V (II) 10^3 (C) n=2, E^ _ cell =0.177 V (III) 10^4 (D) n=3, E^ _ cell =0.059 V (IV) 10^6 Choose the correct answer from the options given below:

Step-by-step solution

The relationship between standard cell potential ( E^ _ cell ) and equilibrium constant ( K_c ) at 298 K is given by: E^ _ cell = 0.059 n K_c Rearranging for K_c gives: K_c = n E^ _ cell 0.059 For (A): K_c = 1 0.118 0.059 = 2 K_c = 10^2 (Matches I) For (B): K_c = 2 0.118 0.059 = 4 K_c = 10^4 (Matches III) For (C): K_c = 2 0.177 0.059 = 6 K_c = 10^6 (Matches IV) For (D): K_c = 3 0.059 0.059 = 3 K_c = 10^3 (Matches II) Therefore, the correct matching is (A)-(I), (B)-(III), (C)-(IV), (D)-(II). Answer: (A)-(I), (B)-(II