Fuel cells are purported to be the future of “green vehicles”. They use hydrogen

Question

Fuel cells are purported to be the future of “green vehicles”. They use hydrogen gas for the fuel and oxygen from the atmosphere to make water and an electric current. What is the change in Gibb’s free energy (in MJ) for the conversion of 45.0 moles of hydrogen gas and excess oxygen gas to water vapor in a fuel cell? The cathode reaction in a fuel cell is O2 + 2H2O + 4e- = 4OH- . The anode reaction in the fuel cell is 2H2 + 4OH- = 4H2O + 4e-. The units are MJ (megajoules) and include a minus sign if needed.

Explanation / Answer

delta G = -nFEcell

cathode:     O2 + 2H2O + 4e- = 4OH-                     E = 0.4 V

anode:       2H2 + 4OH- = 4H2O + 4e-                     E = 0.828 V

overall:       O2 + 2H2   = 2H2O                             E = 1.23 V

   for one mol of hydrogen gas, two electrons were involved. so for 45 moles, 90 electrons

delta G = -nFEcell

              = -(90 mol e) (96,484 C/mol e)(1.23 V)

              = -10680778.8 J

               = -10.6807788 MJ

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