For the cell reaction, 2 Al _ ( s ) +3 Cu ⁺² _ ( aq ) 2 Al ⁺³ _ ( aq ) +3 Cu _ ( s ) If G ^ =-1158 ~kJ , What is E _ cell ^ ?

Step-by-step solution

The standard cell potential E^ _ cell relates to the standard Gibbs free energy change G^ through the fundamental equation G^ = -nFE^ _ cell where n represents the number of electrons transferred and F = 96485 C/mol is Faraday's constant. Given G^ = -1158 10^3 J , we first determine n from the balanced redox reaction 2 Al _ (s) + 3 Cu ²⁺_ (aq) 2 Al ³⁺_ (aq) + 3 Cu _ (s) . The oxidation half-reaction 2 Al 2 Al ³⁺ + 6 e ^- shows n = 6 moles of electrons transferred. Solving for E^ _ cell gives E^ _ cell = - G^ nF = 1