If the (E_ cell ^ ) of an equilibrium reaction (A(s)+2 B²⁺(a q) A²⁺(a q)+2 B(s) ) at (298 ~K ) is (0.59 ~V ), the equilibrium constant (K_c ) is

Step-by-step solution

For the reaction, ( gathered A+2 B²⁺(a q) A²⁺(a q)+2 B(s) G^ =-R T K_c=-n F E_ cell ^ (i) gathered ) where, ( aligned G^ & = Gibbs free energy n & = number of electrons involved (=2) F & = Faraday's constant =96500 C charge. E^ & = standard electrode cell potential (=0.59 ~V ) R & = gas constant T & = temperature (=298 ~K ) aligned ) ( ) From Eq. (i), we have ( aligned or K_c & = n F E^ 2.303 R T & = 2 96500 0.59 2303 8.314 298 =-19.96 20 K_c & =1.0 10²⁰ aligned ) Hence, option (c) is the correct answer. Alternativ