Question 23.4: Predict under what conditions the following processes will b......
Predict under what conditions the following processes will be spontaneous:
(a) Br_{2}(l ) → Br_{2}(g)
(b) CH_{4}(g) + 2\ O_{2}(g) → CO_{2}(g) + 2\ H_{2}O(l )
(c) Ar(g,\ 1L) → Ar(g,\ 2L) (free expansion at constant T)
(d) 3\ O_{2}(g) → 2\ O_{3}(g) (endothermic)
(a) The vaporization of bromine requires an input of energy as heat, so that \Delta H_{vap} > 0. However, Br_{2}(g) has a greater positional disorder than Br_{2}(l), so \Delta S_{vap} > 0. Thus, the reaction will be spontaneous when T\Delta S_{vap} > \Delta H_{vap} because the value of \Delta G_{vap} will be less than zero.
(b) This is a combustion reaction and is highly exothermic. Therefore, the magnitude of the \Delta H_{rxn} < 0 term is much greater than that of the -T\Delta S_{rxn} term in Equation 23.13 and the reaction is spontaneous under most conditions.
\Delta G_{rxn} = \Delta H_{rxn} – T\Delta S_{rxn} (23.13)
(c) For the free expansion of argon gas at constant temperature, \Delta H_{rxn} ≈ 0. However, \Delta S_{rxn} > 0 because the entropy of a gas increases with increasing volume. Thus, the reaction is always spontaneous.
(d) This reaction is endothermic, so \Delta H_{rxn} > 0. Furthermore, two moles of a gas have a lower entropy than three moles of a gas, so that \Delta S_{rxn} \lt 0. Thus, the reaction is not spontaneous.