10.Entropy and Gibbs Free Energy

Name	Symbol	Unit
Entropy	$S$	$\frac{J}{K}$
Gibbs free energy	$G$	$\frac{J}{K}$

Equation	Explain
$\Delta S = \frac{q}{T}$
$\Delta S^\circ=\sum\limits_{\text{products, P}}c_PS^\circ_P[\text{P}]-\sum\limits_{\text{reactants, R}}c_RS^\circ_R[\text{R}]$	$\Delta S^\circ$: standard entropy of reaction $c_P \text{ and } c_R$: stoichiometric coefficient of P and R
$\Delta S-\frac{\Delta H}{T} > 0$	the criteria for a spontaneous reaction at constant temperature and pressure
$G=H-TS$	at constant temperature and pressure
$\Delta S_{vap}=\frac{\Delta H_{vap}}{T}$
$\Delta H = \Delta H^\circ$
$\Delta G =\Delta H^\circ - T\Delta S^\circ$	temperature dependence of $\Delta G$ (all standard condiiton except temperature)
$\Delta G = \Delta G^\circ +RT\ln Q$	$\Delta G$ in non-standard conditions $Q$: reaction quotient in equilibrium
$\Delta G=RT\ln(\frac{Q}{K})$
$\Delta G <0$	at constant temperature and pressure, for spontaneous reaction
$\Delta H < T\Delta S$	at constant temperature and pressure
$T_{cross}=\frac{\Delta H}{\Delta S}$	Exothermic processes with negative entropy change are spontaneous only below $T_{cross}$ Endothermic processes with positive entropy change are spontaneous only above $T_{cross}$
$\Delta G^\circ=\sum\limits_{\text{products, P}}c_P \Delta G^\circ_f[\text{P}]-\sum\limits_{\text{reactants, R}}c_R \Delta G^\circ_f[\text{R}]$	$\Delta G^\circ$: standard gibbs free energy of reaction

To determine the entropy of a molecule

1. Entropy of: solid < liquid < aq << gas
2. More complex molecules have larger standard molar entropy
3. Two substances in the same phase, consisting of small molecules of the same complexity. The substance with the larger molar mass has the greater molar entropy

To determine the $\Delta S$ of a reaction

1. If $\Delta n_{gas} \ne0$
2. $\Delta S$ has the same sign as $\Delta n_{gas}$ and large in magnitude
3. Else if $\Delta n_{aq} \ne 0$
4. $\Delta S$ has the same sign as $\Delta n_{aq}$ and intermediate in magnitude
5. Else if $\Delta n_{liq} \ne 0$
6. $\Delta S$ has the same sign as $\Delta n_{liq}$ and intermediate in magnitude
7. Else
8. $\Delta S$ is small

A non-spontaneous reaction can be coupled to a spontaneous reaction, such that the combined process is spontaneous

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Last update: December 6, 2021
Created: November 29, 2021