5. Thermodynamics
Thermochemistry measured heat; thermodynamics decides whether a process can happen at all. Three quantities — enthalpy, entropy, and free energy — answer that question.
Entropy and the Second Law
Entropy $S$ measures disorder. The second law: the entropy of the universe always increases for a spontaneous process. Gases have far higher entropy than liquids or solids, and dissolving usually increases entropy.
Gibbs Free Energy
$$\Delta G = \Delta H - T\Delta S$$$\Delta G < 0$: spontaneous. $\Delta G > 0$: non-spontaneous. $\Delta G = 0$: equilibrium. A reaction with $\Delta H < 0$ and $\Delta S > 0$ is spontaneous at all temperatures; $\Delta H > 0$ and $\Delta S < 0$ is never spontaneous.
Example: Water freezing: $\Delta H = -6.01$ kJ/mol, $\Delta S = -22.0$ J/mol·K. At −10 °C (263 K):
$$\Delta G = -6010 - (263)(-22.0) = -6010 + 5786 = -224\ \text{J/mol}$$
Negative — freezing is spontaneous below 0 °C, as expected.
Free Energy and the Equilibrium Constant
$$\Delta G^\circ = -RT \ln K$$
Example: For the ammonia synthesis equilibrium with $K = 2.96$ at 298 K:
$$\Delta G^\circ = -(8.314)(298)\ln(2.96) = -2.69\ \text{kJ/mol}$$
$K > 1$ means $\Delta G^\circ < 0$ — products are favoured under standard conditions.
Practice Problems
- For the Haber process, ΔH = −92 kJ/mol and ΔS = −199 J/mol·K. Find ΔG at 298 K. Is it spontaneous?
- A reaction has ΔH = +180 kJ/mol and ΔS = +300 J/mol·K. Above what temperature does it become spontaneous?
- If K > 1, what is the sign of ΔG°?
- Does entropy increase or decrease when a solid sublimes to a gas?
Answers: 1. ΔG = −32.7 kJ/mol — spontaneous 2. T > 600 K 3. Negative 4. Increases