Consider the following two half-cell reactions along with the standard reduction potential given: CO₂ + 6H^+ + 6e^- CH₃ OH + H₂ O E°_ red = 0.02 V 1 2 O₂ + 2H^+ + 2e^- H₂ O E°_ red = 1.23 V A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80 % efficiency. If the work derived from the cell usi

Step-by-step solution

The half-cell reactions for the fuel cell are: Anode (Oxidation): CH₃OH + H₂O CO₂ + 6H^+ + 6e^- E^ _ ox = -0.02 V Cathode (Reduction): 3 2 O₂ + 6H^+ + 6e^- 3H₂O E^ _ red = 1.23 V The overall cell reaction is: CH₃OH + 3 2 O₂ CO₂ + 2H₂O The standard cell potential is: E^ _ cell = E^ _ cathode - E^ _ anode = 1.23 - 0.02 = 1.21 V The number of electrons transferred per mole of CH₃OH is n = 6 . The maximum electrical work that can be obtained from the cell is given by the decrease in Gibbs free energy: W_ max = nFE^ _ c