16.1 Spontaneity

Spontaneity and Gibbs Free Energy

Spontaneity in chemistry describes whether a process can occur on its own, without continuous outside energy input. Understanding spontaneity helps you predict which reactions and physical changes will happen naturally and which ones won't. The main tool for this is Gibbs free energy, which combines enthalpy, temperature, and entropy into a single value that tells you if a process is spontaneous.

Spontaneous vs. Nonspontaneous Processes

A spontaneous process occurs naturally without needing continuous external energy. "Spontaneous" doesn't mean fast; it just means the process is thermodynamically favorable. Iron rusting takes years, but it's still spontaneous.

• Spontaneous examples: ice melting at room temperature, gas expanding to fill a container, iron rusting in the presence of oxygen and water
• Nonspontaneous examples: water freezing at room temperature, gas being compressed into a smaller volume, converting rust back into pure iron

Nonspontaneous processes require a continuous input of energy to occur. They're the reverse of spontaneous ones.

Dispersion in Spontaneous Processes

Entropy ($S$) measures the disorder or randomness of a system. Spontaneous processes tend to increase the total entropy of the universe ($\Delta S_{universe} > 0$), which includes both the system and its surroundings. This is a core idea behind the second law of thermodynamics.

Spontaneous processes disperse both matter and energy:

• Matter dispersal: Gas molecules spread out to fill a container. A solute dissolves and distributes throughout a solvent.
• Energy dispersal: Heat flows from a hot object to a cold one, never the reverse on its own. A concentrated solution becomes more dilute as energy and particles spread.

Gibbs Free Energy for Spontaneity

Gibbs free energy ($G$) lets you predict spontaneity at constant temperature and pressure. It's defined as:

$G = H - TS$

• $H$ = enthalpy (heat content of the system)
• $T$ = absolute temperature (must be in Kelvin)
• $S$ = entropy

For a process, you care about the change in Gibbs free energy:

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

Here's how to interpret the result:

1. $\Delta G < 0$: the process is spontaneous (thermodynamically favorable)
2. $\Delta G > 0$: the process is nonspontaneous (requires energy input)
3. $\Delta G = 0$: the system is at equilibrium (no net change occurring)

Three factors influence the sign of $\Delta G$:

• Enthalpy ($\Delta H$): Exothermic processes ($\Delta H < 0$) release heat, which pushes $\Delta G$ negative.
• Entropy ($\Delta S$): Processes that increase disorder ($\Delta S > 0$) also push $\Delta G$ negative.
• Temperature ($T$): Higher temperatures amplify the $T\Delta S$ term. This means temperature can determine whether an entropy-driven process (positive $\Delta S$) is spontaneous or not. For example, ice melting has positive $\Delta H$ and positive $\Delta S$, so it only becomes spontaneous above 0°C, where the $T\Delta S$ term outweighs $\Delta H$.

Thermodynamics and Spontaneity

Thermodynamics is the study of energy transfer and transformations. Several key ideas connect to spontaneity:

• The second law of thermodynamics states that the total entropy of the universe always increases for any spontaneous process. This is why spontaneous processes go in the direction they do.
• Free energy represents the maximum amount of useful work a system can perform. When $\Delta G$ is negative, the process can do work on its surroundings.
• A reversible process is an idealized process that can go forward or backward without any net change in the system or surroundings. Real processes are always at least slightly irreversible, meaning some energy is lost (usually as heat), and total entropy increases.