Thermodynamics in Chemistry: Enthalpy, Entropy, and Gibbs Free Energy

Why Do Some Reactions Go and Others Don't?

Iron rusts in air but gold does not. Glucose burns to carbon dioxide and water — never the reverse. Sodium explodes in water while potassium does so even more violently. These observations share a common question: what determines whether a chemical reaction is spontaneous? The answer, worked out by Josiah Willard Gibbs in the 1870s and completed by the development of statistical mechanics, lies not in a single property but in the balance of two competing tendencies — enthalpy (energy) and entropy (disorder) — mediated by temperature. Chemical thermodynamics is the quantitative framework for this balance.

The First Law: Energy Is Conserved

The first law of thermodynamics states that energy cannot be created or destroyed, only converted between forms. For a chemical system, this is expressed as:

ΔU = q + w

where ΔU is the change in internal energy of the system, q is heat transferred to the system (positive when system absorbs heat), and w is work done on the system (positive when surroundings compress the system). In chemistry, most reactions occur at constant pressure in open containers — a condition under which the relevant energy function is enthalpy rather than internal energy:

ΔH = ΔU + PΔV

At constant pressure, ΔH equals the heat transferred. Exothermic reactions (ΔH < 0) release heat; endothermic reactions (ΔH > 0) absorb heat. First law tells us how much energy changes. It says nothing about direction.

Enthalpy: Hess's Law and Standard Formation Enthalpies

Hess's law states that the enthalpy change for an overall reaction equals the sum of enthalpy changes for any series of steps that converts the same reactants to the same products. This additivity — a consequence of enthalpy being a state function — enables calculation of reaction enthalpies that cannot be measured directly.

Standard state is defined as the most stable form of a substance at 298 K and 1 bar. Standard formation enthalpies of elements in their standard state are zero by definition — they provide the reference base from which all other enthalpies are calculated. Hess's law connects what is measurable to what is needed.

Entropy: Beyond "Disorder"

The second law of thermodynamics states that the entropy of an isolated system increases in any spontaneous process. Entropy (S) is often described as "disorder," but this is an oversimplification that misleads. Boltzmann's statistical definition is precise: S = k ln W, where k is Boltzmann's constant and W is the number of microstates — ways of arranging the system's energy among its particles at a given macrostate. Systems spontaneously evolve toward distributions with more microstates — statistically, the most probable states.

• Gases have far more microstates than liquids; liquids more than solids. Gas expansion increases W and therefore S.
• Dissolving a solid in water increases entropy (more microstates for solute ions spread through solvent).
• Reactions that increase the number of gas molecules increase entropy significantly (ΔS > 0).
• Reactions that form ordered structures (crystals, polymers) decrease entropy (ΔS < 0).

Entropy is not disorder. It is the spread of energy across available microstates. The difference matters for precision.

Gibbs Free Energy: The Spontaneity Criterion

Gibbs free energy (G) combines enthalpy and entropy into a single spontaneity criterion applicable at constant temperature and pressure — the conditions of most chemical reactions:

ΔG = ΔH − TΔS

A reaction is spontaneous (thermodynamically favorable) when ΔG < 0. ΔG = 0 indicates equilibrium. ΔG > 0 means the reaction is non-spontaneous in the forward direction (spontaneous in reverse).

The dissolution of ammonium nitrate (NH4NO3) in water is endothermic (ΔH > 0, absorbs heat) yet spontaneous at room temperature because the entropy increase (ΔS > 0) is large enough that ΔG = ΔH − TΔS < 0. This drives the chemistry of cold packs.

Equilibrium and the Gibbs Free Energy Relationship

For a reaction at standard conditions, the equilibrium constant K is related to the standard Gibbs free energy change by:

ΔG° = −RT ln K

where R is the gas constant (8.314 J/mol·K) and T is temperature in Kelvin. This relationship connects two independently measurable quantities — thermodynamic spontaneity and equilibrium position — into a single framework.

• If ΔG° is large and negative (e.g., −40 kJ/mol), K is very large — reaction goes essentially to completion.
• If ΔG° ≈ 0, K ≈ 1 — reactants and products coexist in comparable amounts at equilibrium.
• If ΔG° is large and positive, K is very small — reaction barely proceeds.

The reaction quotient Q compares to K to determine direction of spontaneous change: if Q < K, reaction proceeds forward; if Q > K, backward; if Q = K, equilibrium. Instantaneous ΔG = ΔG° + RT ln Q — the system evolves to minimize G until ΔG = 0.

Le Chatelier's Principle

Le Chatelier's principle states that when a system at equilibrium is perturbed, it shifts to oppose the perturbation and establish a new equilibrium. This qualitative principle follows quantitatively from the Q-versus-K analysis:

• Adding reactant: Q decreases below K; reaction shifts forward to restore equilibrium.
• Removing product: Q decreases below K; reaction shifts forward (basis of continuous industrial processes).
• Increasing pressure (gases): reaction shifts toward the side with fewer moles of gas.
• Increasing temperature in exothermic reaction: K decreases (Haber process: higher T favors NH3 decomposition, reducing yield).

The Haber-Bosch process — industrial nitrogen fixation (N2 + 3H2 ⇌ 2NH3) — is thermodynamically best at low temperature (where K is large) and high pressure (where fewer moles favor products), but kinetics require compromise temperatures of 400–500°C with iron catalysts. Thermodynamics and kinetics pull in opposite directions. The industrial process navigates between them.

The Third Law and Absolute Entropy

The third law of thermodynamics states that the entropy of a perfect crystal at absolute zero (0 K) is zero. This provides an absolute reference point — unlike enthalpy, for which only changes are meaningful, entropy has an absolute value measurable from 0 K by integrating heat capacity data.

Standard molar entropies (S°, J/mol·K at 298 K) reveal intuitive patterns: gases have higher S° than liquids; complex molecules higher than simple ones; heavy atoms higher than light ones (more translational/vibrational microstates). Diamond (S° = 2.4 J/mol·K) has extraordinarily low entropy — its rigid covalent lattice severely constrains atomic motion. Graphite (S° = 5.7 J/mol·K) has more entropy through layer slippage. Third law makes entropy a measurable, universal property. Zero is a real baseline.