Definitions

# Spontaneous process

A spontaneous process is the time-evolution of a system in which it releases free energy (most often as heat) and moves to a lower, more thermodynamically stable, energy state. The sign convention of changes in free energy follows the general convention for thermodynamic measurements, in which a release of free energy from the system corresponds to a negative change in free energy, but a positive change for the surroundings.

A process that is capable of proceeding in a given direction, as written or described, without needing to be driven by an outside source of energy. The term is used to refer to macro processes in which entropy increases; such as a smell diffusing in a room, ice melting in lukewarm water, salt dissolving in water, and iron rusting.

The laws of thermodynamics govern the direction of a spontaneous process, ensuring that if a sufficiently large number of individual interactions (like atoms colliding) are involved then the direction will always be in the direction of increased entropy (since entropy increase is a statistical phenomenon).

## Overview

For a reaction at constant temperature and pressure, the change ΔG in the Gibbs free energy is:

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

The sign of ΔG depends on the signs of the changes in enthalpyH) and entropyS), as well as on the absolute temperature (T, in degrees Kelvin). Notice that changes in the sign of ΔG cannot occur solely as a result of changes in temperature alone, because the absolute temperature can never be less than zero.

When ΔG is negative, a process or chemical reaction proceeds spontaneously in the forward direction.

When ΔG is positive, the process proceeds spontaneously in reverse.

When ΔG is zero, the process is already in equilibrium, with no net change taking place over time.

We can further distinguish four cases within the above rule just by examining the signs of the two terms on the right side of the equation.

When ΔS is positive and ΔH is negative, a process is spontaneous

When ΔS is positive and ΔH is positive, a process is spontaneous at high temperatures, where exothermicity plays a small role in the balance.

When ΔS is negative and ΔH is negative, a process is spontaneous at low temperatures, where exothermicity is important.

When ΔS is negative and ΔH is positive, a process is not spontaneous at any temperature, but the reverse process is spontaneous.

The second law of thermodynamics states that for any spontaneous process the overall change ΔS in the entropy of the system must be greater than or equal to zero, yet a spontaneous chemical reaction can result in a negative change in entropy. This does not contradict the second law, however, since such a reaction must have a sufficiently large negative change in enthalpy (heat energy) that the increase in temperature of the reaction surroundings (considered to be part of the system in thermodynamic terms) results in a sufficiently large increase in entropy that overall the change in entropy is positive. That is, the ΔS of the surroundings increases enough because of the exothermicity of the reaction that it overcompensates for the negative ΔS of the system, and since the overall ΔS = ΔSsurroundings + ΔSsystem, the overall change in entropy is still positive.

Another way to view the fact that some spontaneous chemical reactions can lead to products with lower entropy is to realize that the second law states that entropy of a closed system must increase (or remain constant). Since a positive enthalpy means that energy is being released to the surroundings, then the 'closed' system includes the chemical reaction plus its surroundings. This means that the heat release of the chemical reaction sufficiently increases the entropy of the surroundings such that the overall entropy of the closed system increases in accordance with the second law of thermodynamics.

Just because a chemist calls a reaction “spontaneous” does not mean the reaction happens with great speed. For example, the decay of diamonds into graphite is a spontaneous process, but this decay is extremely slow and takes millions of years. The rate of a reaction is independent of its spontaneity, and instead depends on the chemical kinetics of the reaction.