Whether a reaction proceeds spontaneously is not determined by ΔH alone. Entropy S (disorder) and Gibbs free energy G are key factors.
Basic Knowledge
Entropy is a state function defined as the disorder of a system or the logarithm of the number of microscopic states (S=kBln W). It is greater for gases than liquids and greater for liquids than solids, and it increases with rising temperature, an increase in the number of gas molecules, and dissolution.
Gibbs free energy G = H - TS. At constant temperature and pressure, a reaction proceeds spontaneously when ΔG < 0.
ΔG = ΔH - TΔS. If a reaction is exothermic (ΔH<0) and entropy increases (ΔS>0), ΔG is always negative and the reaction is spontaneous. If it is exothermic but ΔS<0, it is spontaneous at low temperatures. If it is endothermic but ΔS>0, it is spontaneous at high temperatures. If ΔS is small and has the unfavorable direction, the reaction is nonspontaneous regardless of whether it is exothermic or endothermic.
Entropy S（disorder of a system. S=kBln W）
Second law of thermodynamics（ΔS≥0 for an isolated system）
Gibbs free energy G（G=H-TS）
ΔG=ΔH-TΔS（criterion for spontaneity at constant temperature and pressure）
Equilibrium condition（ΔG=0）
Standard state（25℃, 1 atm, ΔG° in the standard state）
Further Study (Principles and Applications)
Ice melts above 0℃ because melting gives ΔS>0 and TΔS exceeds ΔH. At 0℃, ΔG=0 (equilibrium). A refrigerator becomes colder than the outside because electrical work transports entropy in the reverse direction; this does not violate the second law.
Living processes may appear to decrease entropy locally by creating order, but they increase the entropy of the surroundings as waste heat, so they satisfy the second law overall.
- Entropy = disorder
- Gas > liquid > solid
- A spontaneous reaction has ΔG<0
- ΔG=ΔH-TΔS
- ΔH<0 and ΔS>0 is always spontaneous
- ΔH>0 and ΔS>0 is spontaneous at high temperatures
- ΔG=0 indicates equilibrium
Points of Caution (Common Confusions and Frequent Mistakes)
① ΔS is measured in J/K, not energy itself, while ΔH is measured in kJ. Match the units before calculating. ② Spontaneity means “direction,” not “rate.” A spontaneous reaction may still be slow and can be accelerated by a catalyst. ③ The second law applies to an isolated system or the universe as a whole. Because living systems are open systems, local decreases in S are possible. ④ ΔG=0 means equilibrium.
Practice
- Is the ΔS of water evaporation (liquid→gas) positive, negative, or zero? State the reason.
- Water evaporation has ΔH=+44 kJ/mol and ΔS=+118 J/(K·mol). Find the minimum temperature at which it becomes spontaneous under standard atmospheric pressure.
- For ΔG=ΔH-TΔS, at what temperatures is a reaction with ΔH<0 and ΔS<0 spontaneous?