Consider the following two half-cell reactions along with the standard reduction potential given: CO_2 + 6H^+ + 6e^- CH_3 OH + H_2 O E°_ red = 0.02 V 1 2 O_2 + 2H^+ + 2e^- H_2 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 condi

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Consider the following two half-cell reactions along with the standard reduction potential given: CO_2 + 6H^+ + 6e^- CH_3 OH + H_2 O E°_ red = 0.02 V 1 2 O_2 + 2H^+ + 2e^- H_2 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 using 1 mol of CH_3 OH is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas, V = _____ m^3. (nearest integer) Given: F = 96500 C mol^ -1

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Correct answer: A. A

The half-cell reactions for the fuel cell are: Anode (Oxidation): CH_3OH + H_2O CO_2 + 6H^+ + 6e^- E^ _ ox = -0.02 V Cathode (Reduction): 3 2 O_2 + 6H^+ + 6e^- 3H_2O E^ _ red = 1.23 V The overall cell reaction is: CH_3OH + 3 2 O_2 CO_2 + 2H_2O 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 CH_3OH 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^ _ cell = 6 96500 1.21 = 700590 J Since the fuel cell operates at 80\% efficiency, the actual work derived is: W_ actual = 0.80 700590 = 560472 J This work is used to compress an ideal gas isothermally against a constant external pressure of 1 kPa (1000 Pa). The work done on the gas during compression is positive: W = -P_ ext V Substituting the values: 560472 = -1000 V V = -560.472 m^3 Rounding to the nearest integer, the change in volume is -560 m^3. Answer: -560

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