Spontaneity and Free Energy Applications

Gibbs Free Energy Review

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

| $\Delta H$ | $\Delta S$ | $\Delta G$ | Spontaneity | |------------|------------|------------|-------------| | $-$ | $+$ | Always $-$ | Always spontaneous | | $+$ | $-$ | Always $+$ | Never spontaneous | | $-$ | $-$ | Depends on T | Spontaneous at low T | | $+$ | $+$ | Depends on T | Spontaneous at high T |

Standard Free Energy

$\Delta G° = \sum \Delta G°_f(\text{products}) - \sum \Delta G°_f(\text{reactants})$

Relationship to Equilibrium

$\Delta G° = -RT\ln K$

| $\Delta G°$ | $K$ | Meaning | |-------------|-----|---------| | $\Delta G° < 0$ | $K > 1$ | Products favored | | $\Delta G° = 0$ | $K = 1$ | Neither favored | | $\Delta G° > 0$ | $K < 1$ | Reactants favored |

Non-Standard Conditions

$\Delta G = \Delta G° + RT\ln Q$

At equilibrium: $Q = K$, so $\Delta G = 0$.

Coupled Reactions

An unfavorable reaction ($\Delta G > 0$) can be driven by coupling with a favorable one ($\Delta G < 0$), as long as the total $\Delta G < 0$.

Example: ATP hydrolysis ($\Delta G° = -30.5$ kJ/mol) drives many biological processes.

Electrochemistry Connection

$\Delta G° = -nFE°$

• $n$ = moles of electrons transferred
• $F$ = Faraday's constant ($96,485$ C/mol)
• $E°$ = standard cell potential

A positive $E°$ means negative $\Delta G°$ (spontaneous).

Temperature Dependence

$T_{\text{crossover}} = \frac{\Delta H}{\Delta S}$

The temperature at which $\Delta G = 0$ (equilibrium transition).

AP Chemistry Tip: The connection between $\Delta G°$, $K$, and $E°$ is a favorite exam topic. Know how to convert between them.