Chemistry Labs

International Chemistry Olympiad · 2020

Problems

  1. Problem 6In a hypothetical universe, an unknown amount of diborane reacts: BX2HX6(g)+6 HX2O(l)→2 HX3BOX3(s)+6 HX2(g)\ce{B2H6(g) + 6H2O(l) -> 2H3BO3(s) + 6H2(g)}. The obtained HX3BOX3(s)\ce{H3BO3(s)} is completely sublimed at 300 K; the necessary energy is supplied as work from one cycle of an ideal heat engine in which one mole of monatomic perfect gas undergoes: A→B isothermal reversible expansion absorbing qH=250q_H = 250 J at TH=1000T_H = 1000 K; B→D reversible adiabatic expansion; D→C isothermal reversible compression at TC=300T_C = 300 K releasing qCq_C; C→A reversible adiabatic compression, with qH/qC=TH/TCq_H/q_C = T_H/T_C. Reaction enthalpies at 300 K (kJ mol−1^{-1}): (1) BX2HX6(g)+6 ClX2→2 BClX3(g)+6 HCl(g)\ce{B2H6(g) + 6Cl2 -> 2BCl3(g) + 6HCl(g)} ΔrH(1)=−1326\Delta_r H(1) = -1326; (2) BClX3(g)+3 HX2O(l)→HX3BOX3(g)+3 HCl(g)\ce{BCl3(g) + 3H2O(l) -> H3BO3(g) + 3HCl(g)} ΔrH(2)=−112.5\Delta_r H(2) = -112.5; (3) BX2HX6(g)+6 HX2O(l)→2 HX3BOX3(s)+6 HX2(g)\ce{B2H6(g) + 6H2O(l) -> 2H3BO3(s) + 6H2(g)} ΔrH(3)=−493.4\Delta_r H(3) = -493.4; (4) 12 HX2(g)+12 ClX2(g)→HCl(g)\ce{1/2 H2(g) + 1/2 Cl2(g) -> HCl(g)} ΔrH(4)=−92.3\Delta_r H(4) = -92.3. (a) Calculate the molar enthalpy of sublimation of HX3BOX3\ce{H3BO3} at 300 K. (b) Calculate ΔrU\Delta_r U of reactions (2) and (4). (c) Calculate ∣w∣|w|, ∣qC∣|q_C| and the efficiency of the engine. (d) Calculate the amount of HX2(g)\ce{H2(g)} produced per engine cycle.Solutions: 1