Entropy, Free Energy and Thermodynamic Favorability

Measure of disorder/dispersal of energy. Units: J/(mol·K)

$S_{gas} \gg S_{liquid} > S_{solid}$

$\Delta S$ increases when:

• Solid → liquid → gas
• More moles of gas produced
• Dissolution
• Higher temperature

$\Delta S^\circ_{rxn} = \sum S^\circ(\text{products}) - \sum S^\circ(\text{reactants})$

$\Delta G = \Delta H - T\Delta S$

Temperature Dependence

At crossover: $T = \Delta H / \Delta S$ (convert units!)

$\Delta G^\circ = -RT\ln K$

• $\Delta G^\circ < 0 \Rightarrow K > 1$ (products favored)
• $\Delta G^\circ > 0 \Rightarrow K < 1$ (reactants favored)

Non-standard conditions: $\Delta G = \Delta G^\circ + RT\ln Q$

A non-spontaneous reaction can be driven by coupling with a spontaneous one (add $\Delta G$ values). Example: ATP hydrolysis driving biological processes.

• $\Delta S_{rxn} = \sum S(\text{prod}) - \sum S(\text{react})$
• $\Delta G = \Delta H - T\Delta S$; spontaneous when $\Delta G < 0$
• $\Delta G^\circ = -RT\ln K$
• Non-standard: $\Delta G = \Delta G^\circ + RT\ln Q$
• Coupled reactions: sum $\Delta G$ to drive unfavorable processes