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Given: delta_f(G) for Cr2O3(s) = -527 kJ/mol, delta_f(G) for Al2O3(s) = -827 kJ/mol; delta_f(H) for Cr2O3(s) = -1100 kJ, delta_f(H) for Al2O3(s) = -1600 kJ. Which of the following statements is/are correct? (A) Cr2O3(s) is reduced by Al(s) under standard conditions. (B) Al2O3(s) is reduced by Cr(s) under standard conditions. (C) delta_r(H) for the reduction of Cr2O3 by Al is -500 kJ. (D) The reduction of Cr2O3 by Al is spontaneous at all temperatures.

1. (A) Cr2O3(s) is reduced by Al(s) under standard conditions.
2. (B) Al2O3(s) is reduced by Cr(s) under standard conditions.
3. (C) delta_r(H) for the reduction of Cr2O3 by Al is -500 kJ.
4. (D) The reduction of Cr2O3 by Al is spontaneous at all temperatures.

Correct answer: (A) Cr2O3(s) is reduced by Al(s) under standard conditions.

Solution

Reaction: Cr2O3(s) + 2Al(s) -> Al2O3(s) + 2Cr(s). delta_r(G) = -827-(-527) = -300 kJ (<0): spontaneous (A is correct, B is incorrect). delta_r(H) = -1600-(-1100) = -500 kJ (C is correct). For (D): delta_r(S) = delta_r(H) - delta_r(G) [at 298K not directly but using delta_G = delta_H - T*delta_S]: delta_S = (delta_H - delta_G)/T = (-500-(-300))*1000/298 = -200000/298 < 0. Since delta_H < 0 and delta_S < 0, reaction is spontaneous only below T = delta_H/delta_S = 500/0.671 ≈ 745 K — not all temperatures. D is incorrect.

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