For the galvanic cell involving the reaction Ni(s) + Cu ²⁺( aq ) Ni ²⁺( aq ) + Cu(s) the standard cell potential ( E^ _ cell ) is 0.59 V at 298 K . Calculate the logarithm of the equilibrium constant ( K_c ) for the cell reaction. (Given: 2.303 RT F = 0.059 V at 298 K )

Step-by-step solution

The relationship between standard cell potential and equilibrium constant is given by the Nernst equation at equilibrium: E^ _ cell = 2.303 RT nF K_c For the given reaction, Ni is oxidized to Ni ²⁺ and Cu ²⁺ is reduced to Cu . The number of electrons transferred, n = 2 . Substituting the given values into the equation: 0.59 = 0.059 2 K_c K_c = 0.59 2 0.059 K_c = 10 2 = 20 Using n=1 leads to the incorrect value of 10 , and confusing the sign with the G^ formula leads to -20 . Answer: 20