Question

Which of the following reactions would you predict to be spontaneous at all temperatures (assuming ΔH°­rxn does not change significantly with temperature)?

H2S(g) + 2O2(g) → H2SO4(l) ΔH°­rxn = –793 kJ/mol

2Ag(s) + 3N2(g) → 2AgN3(s) ΔH°­rxn = +1240 kJ/mol

C6H6(l) + 3H2(g) → C6H12(l) ΔH°­rxn = –207 kJ/mol

Na2CO3(s) + 2HCl(aq) → 2NaCl(aq) + H2O(l) + CO2(g) ΔH°­rxn = –834 kJ/mol

CaCO3(s) → CaO(s) + O2(g) ΔH°­rxn = +179 kJ/mol

Answer 1

Gibbs free energy G related to enthalpy and entropy by following equation

∆G = ∆H - T (∆S)

Where T is temperature

Na₂CO₃(s) + 2HCl (aq) → 2NaCl (aq) + H₂O(l) + CO₂(g) ΔH°­rxn = –834 kJ/mol

∆S will be positive, because there are no gases in reactants but 1mole of gas in the products. ∆H is negative (–834 kJ/mol ), so ∆G will be negative at all temperatures. Thus, the reaction is spontaneous at all temperatures.

The other two reactions in which ΔH°­rxn is negative

H₂S(g) + 2O₂(g) → H₂SO₄(l) ΔH°­rxn = –793 kJ/mol

∆S will be negative, because 3 moles gases in reactants but no moles of gases in the product and ∆H is negative. ∆G will be negative at low temperatures and positive at high temperatures. Thus, the reaction is spontaneous only at low temperature.

C₆H₆(l) + 3H₂(g) → C₆H₁₂(l) ΔH°­rxn = –207 kJ/mol

∆S will be negative, because 3 moles gases in reactants but no moles of gases in the product and ∆H is negative. ∆G will be negative at low temperatures and positive at high temperatures. Thus, the reaction is spontaneous only at low temperature

The other two reactions in which ΔH°­rxn is positive

2Ag(s) + 3N₂(g) → 2AgN₃(s) ΔH°­rxn = +1240 kJ/mol

∆S will be negative, because 3 moles gases in reactants but no moles of gases in the product and ∆H is positive. . ∆G will be positive at all temperatures. Thus, the reaction is never spontaneous.

CaCO₃(s) → CaO(s) + O₂(g) ΔH°­rxn = +179 kJ/mol

∆S will be positive, because there are no gases in reactants but 1mole of gas in the products. ∆H is positive. At low temperatures T∆S is small and the reaction will be nonspontaneous while at high temperature T∆S is large and the entropy dominates and the reaction becomes spontaneous.