A spontaneous process is one where the total entropy of the universe increases, which translates to a negative change in Gibbs free energy (ΔG < 0) for the system at constant temperature and pressure. That single condition is the definitive test. If ΔG is negative, the process is spontaneous. If ΔG is positive, it is not. If ΔG equals zero, the system is at equilibrium.
The Core Requirement: Negative Gibbs Free Energy
Gibbs free energy (G) combines two competing factors into one number: the energy released or absorbed by a process (enthalpy, H) and the disorder created or destroyed (entropy, S). The relationship is expressed as:
ΔG = ΔH − TΔS
Here, T is temperature in Kelvin, ΔH is the change in enthalpy, and ΔS is the change in entropy. When this calculation produces a negative number, the process is spontaneous. A positive result means the process is non-spontaneous as written, though it would be spontaneous in the reverse direction. And when ΔG equals exactly zero, the system has reached equilibrium, with no net change in either direction.
Why Entropy of the Universe Is the Deeper Rule
The second law of thermodynamics states that any spontaneous process increases the total entropy of the universe. This is the fundamental requirement, and Gibbs free energy is really just a convenient way to check it without having to calculate changes in the surroundings separately. When ΔG is negative for a system at constant temperature and pressure, the entropy of the universe is increasing (ΔS_univ > 0). The math works out so that the two criteria always agree.
This means a process can decrease the entropy of the system itself and still be spontaneous, as long as the surroundings gain even more entropy to compensate. Ice forming in a freezer reduces the disorder of water molecules, but the heat released into the surroundings more than makes up for it. The universe, taken as a whole, becomes more disordered.
How Enthalpy and Entropy Work Together
Whether a reaction is spontaneous depends on the interplay between its enthalpy and entropy terms. There are four possible combinations:
- Negative ΔH, positive ΔS: The process releases energy and increases disorder. ΔG is always negative, so the process is always spontaneous regardless of temperature.
- Positive ΔH, negative ΔS: The process absorbs energy and decreases disorder. ΔG is always positive, so the process is never spontaneous at any temperature.
- Negative ΔH, negative ΔS: The process releases energy but decreases disorder. Spontaneity depends on temperature. At low temperatures, the enthalpy term dominates and the process is spontaneous. At high temperatures, the entropy penalty grows large enough to make ΔG positive.
- Positive ΔH, positive ΔS: The process absorbs energy but increases disorder. At low temperatures, it is non-spontaneous because the energy cost outweighs the entropy gain. At high temperatures, the TΔS term becomes large enough to drive ΔG negative, making it spontaneous.
Temperature is the one variable that can tip the balance when enthalpy and entropy pull in opposite directions. Since T is always positive on the Kelvin scale, raising the temperature amplifies the entropy term (TΔS), which can flip a reaction from non-spontaneous to spontaneous or vice versa.
Spontaneous Does Not Mean Fast
One of the most common misunderstandings is equating “spontaneous” with “instant” or “rapid.” In thermodynamics, spontaneous only means that product formation is favored energetically. It says nothing about speed. A sheet of paper sitting on your desk will not suddenly burst into flames, even though combustion of paper is a spontaneous reaction. What is missing is the activation energy, the initial push needed to get the reaction started. Once you supply that energy (a match, for instance), the reaction proceeds on its own until completion.
Diamond converting to graphite is spontaneous under normal conditions, yet it takes geological timescales. The rate of a reaction is governed by kinetics, specifically the size of the energy barrier reactants must overcome. Spontaneity is governed by thermodynamics, specifically the difference in free energy between products and reactants. A process can be thermodynamically favored and kinetically slow at the same time.
Standard-State vs. Actual Conditions
Chemistry courses often introduce ΔG° (standard-state Gibbs free energy), which is calculated with all reactants and products at standard conditions, typically 1 atmosphere of pressure and 1 molar concentration at a specified temperature. This value is useful for comparing reactions, but it does not always tell you whether a reaction is spontaneous in a real system where concentrations vary.
The actual Gibbs free energy at any moment is given by:
ΔG = ΔG° + RT ln Q
Here, R is the gas constant, T is temperature, and Q is the reaction quotient, a measure of the current ratio of products to reactants. When Q equals 1 (all species at standard concentrations), ΔG equals ΔG°. As the reaction progresses and Q changes, ΔG shifts. The sign of ΔG at any given moment tells you which direction the reaction needs to move to reach equilibrium, and its magnitude tells you how far from equilibrium the system is.
At equilibrium, Q equals the equilibrium constant K, and ΔG equals zero. The reaction has no net driving force in either direction.
Exergonic and Endergonic Reactions
In biochemistry especially, spontaneous reactions are called exergonic (ΔG < 0), meaning they release free energy that can do useful work. Non-spontaneous reactions are called endergonic (ΔG > 0), meaning they require an input of free energy. Your body breaks down sugars in an exergonic process and uses that released energy to power endergonic processes like building proteins and other complex molecules. The endergonic reactions do not violate the rules of spontaneity. They proceed because they are coupled to exergonic reactions that provide enough energy to make the overall ΔG of the combined process negative.