Chem33-1, C-hour Problem Set 7

1.The overall reaction and the value for the equilibrium constant for a hydrogen-oxygen fuel cell at 298K are 2 H2 (g) + O2 (g) → 2H2O(l) K=1.28x1083 a)b)c)Calculate the standard cell potential E0 as well as ΔG0 at 298 K for this fuel cell reaction. Predict the signs of ΔH0 and ΔS0 for the reaction. As temperature increases, does the maximum amount of work from the fuel cell increase, decrease, or stay the same? Explain. ANSWER: In the chemical reaction Oxygen is reduced from an oxidation number 0 to -2. Since 2 mols of Oxygen (atoms) appear in the chemical equation, the total number of electrons exchanged in the reaction is n = 4. a) E 0 = 0.0591 log(K ) = 0.0591 log ( 1.28 x 10 83 ) = 1.23 V n 4 ΔG 0 = − nFE 0 = − ( 4mol e − ) ⎛ ⎜ 96.485 C − ⎟ ⎞ ( 1.23 J ) = −4.75x 10 5 = −475kJ ⎝ mol e ⎠ C b) Since the mols of gas decrease as the reaction proceeds, ΔS0 will be negative. Since ΔG0 is also negative, ΔH 0 must be negative as well. c) ΔG0 = wmax = ΔH0 - TΔS0 with a negative ΔS0 implies that with increasing temperature ΔG0 becomes more positive (= close to zero). Therefore, wmax decreases with increasing temperature.