For a generic electrochemical cell reaction involving the transfer of two electrons, the equilibrium constant ( K_ c ) is 10¹⁴ at 298 K . The standard cell potential ( E^ _ cell ) for this reaction is: [ Given: 2.303RT F = 0.059 V at 298 K ]

Step-by-step solution

The relationship between standard cell potential ( E^ _ cell ) and equilibrium constant ( K_ c ) is given by the Nernst equation at equilibrium: E^ _ cell = 2.303RT nF K_ c Given that 2.303RT F = 0.059 V , the equation simplifies to: E^ _ cell = 0.059 n K_ c For the given reaction, the number of electrons transferred is n = 2 , and K_ c = 10¹⁴ . Substituting these values: E^ _ cell = 0.059 2 (10¹⁴) E^ _ cell = 0.059 2 14 E^ _ cell = 0.059 7 = 0.413 V Answer: 0.413 V