Thermodynamics in Chemistry: Enthalpy, Entropy, and Free Energy

Thermodynamics sits at the center of nearly every chemical question worth asking — whether a reaction will happen at all, how much energy it releases, and what temperature or pressure conditions tip the balance. This page covers the three core state functions — enthalpy, entropy, and Gibbs free energy — their mathematical relationships, the physical reasoning behind them, and the places where even careful students get turned around. The treatment draws on foundational definitions from NIST and the IUPAC Gold Book.

• Definition and scope
• Core mechanics or structure
• Causal relationships or drivers
• Classification boundaries
• Tradeoffs and tensions
• Common misconceptions
• Checklist or steps
• Reference table or matrix

Definition and scope

Drop a stick of sodium into water and the reaction is instant, violent, and unmistakably spontaneous. Ask why it's spontaneous, and thermodynamics is the only framework that gives a rigorous answer. Chemical thermodynamics governs the energy bookkeeping of matter: how heat flows, how disorder changes, and whether a system at a given temperature and pressure has any chemical "drive" left to spend.

Three state functions do most of the heavy lifting. Enthalpy (H) measures heat exchanged at constant pressure — the condition of essentially every reaction run in an open flask or biological cell. Entropy (S) quantifies the dispersal of energy and matter across accessible microstates, formalized by Ludwig Boltzmann's relation S = k·ln(W), where k is the Boltzmann constant (1.380649 × 10⁻²³ J·K⁻¹, exact by 2019 SI redefinition). Gibbs free energy (G) combines both into a single predictor of spontaneity under constant temperature and pressure conditions.

The scope of thermodynamics in chemistry extends from reaction feasibility and equilibrium constants to electrochemical cell potentials, protein folding, and materials synthesis. It does not address reaction rate — that belongs to kinetics, a distinction explored more broadly on the chemistry conceptual overview.

Core mechanics or structure

Enthalpy is defined as H = U + PV, where U is internal energy, P is pressure, and V is volume. At constant pressure, the enthalpy change ΔH equals the heat exchanged (q_p). Exothermic reactions have negative ΔH; endothermic reactions have positive ΔH. Standard enthalpy values (ΔH°) are tabulated at 298.15 K and 1 bar, per IUPAC recommendations.

Entropy is not disorder in the colloquial sense — it is the logarithm of the number of energetically equivalent microstates available to a system. The Second Law of Thermodynamics states that the total entropy of the universe never decreases in a spontaneous process: ΔS_universe ≥ 0. Entropy increases when gases are produced from solids or liquids, when a substance dissolves, or when temperature rises.

Gibbs free energy at constant T and P is defined as:

G = H − TS

The change in Gibbs free energy for a process is therefore:

ΔG = ΔH − TΔS

A negative ΔG indicates a spontaneous process (thermodynamically favorable). A positive ΔG indicates non-spontaneous. ΔG = 0 marks equilibrium. The relationship between ΔG° and the equilibrium constant K is:

ΔG° = −RT ln K

where R = 8.31446 J·mol⁻¹·K⁻¹ (the molar gas constant, NIST CODATA).

Helmholtz free energy (A) performs an analogous role at constant volume — more relevant to gas-phase reactions modeled computationally than to bench chemistry, where Gibbs dominates.

Causal relationships or drivers

The sign of ΔG is controlled by two competing forces: the enthalpy term (ΔH) and the entropy term (TΔS). Temperature acts as a dial that amplifies or suppresses the entropy contribution. This is not metaphorical — at 1000 K, the TΔS term is roughly 3.4 times larger than at 298 K for the same process.

Enthalpy changes are primarily driven by bond breaking and bond formation. Breaking bonds requires energy input; forming bonds releases energy. The net ΔH of a reaction reflects the difference between bond dissociation energies of reactants and products, calculable via Hess's Law: the total enthalpy change for a reaction is path-independent, depending only on initial and final states.

Entropy changes are driven by changes in the number of gas-phase particles, changes in molecular complexity, solvation effects, and phase transitions. Dissolving NaCl in water increases entropy not just by dispersing the ions but by disrupting the long-range order of the crystal lattice.

The equilibrium constant K connects thermodynamics directly to measurable concentrations. A ΔG° of −5.7 kJ·mol⁻¹ at 298 K corresponds to K ≈ 10, while a ΔG° of −57 kJ·mol⁻¹ gives K ≈ 10¹⁰ — a factor-of-a-billion difference in favorability from a factor-of-10 difference in free energy. That logarithmic relationship is worth sitting with.

Classification boundaries

Thermodynamics classifies processes along two independent axes: the sign of ΔH and the sign of ΔS. This produces four distinct behavioral categories with different temperature dependencies for spontaneity.

It also distinguishes between standard state (ΔG°, 298.15 K, 1 bar, 1 mol/L solutes) and non-standard conditions (ΔG), connected through:

ΔG = ΔG° + RT ln Q

where Q is the reaction quotient. A reaction can have a positive ΔG° and still proceed spontaneously if Q is much smaller than K — a fact directly relevant to metabolic biochemistry, where cells maintain reactant concentrations far from equilibrium.

The boundaries between thermodynamics and kinetics are firm: thermodynamics predicts whether a reaction can proceed; kinetics determines whether it does at any observable rate. Diamond converting to graphite has a negative ΔG at standard conditions (graphite is the stable allotrope) but an activation energy so prohibitively large that the conversion is geologically slow. The thermodynamics says "favorable." The kinetics says "not in your lifetime." Both are correct simultaneously. A broader look at how chemistry is structured — including where thermodynamics fits within the discipline — is available on the chemistry index.

Tradeoffs and tensions

The ΔH vs. TΔS competition creates genuine thermodynamic tension in real systems. Many biochemical reactions are endothermic (positive ΔH) but proceed because TΔS is large and positive — the dissolution of hydrophobic molecules in aqueous environments being a canonical example. Protein folding runs the opposite direction: it is driven largely by enthalpy (hydrogen bonding, van der Waals interactions) at the cost of entropy, since folding restricts conformational freedom.

A persistent pedagogical tension involves the meaning of "spontaneous." Thermodynamic spontaneity carries no implication about speed — it is a statement about free energy difference, not activation energy. Combustion of cellulose is spontaneous at room temperature; it still requires ignition.

There is also genuine scientific debate about how to apply classical thermodynamics to small systems — protein complexes, single molecules, nanoparticles — where the statistical mechanics of Boltzmann begins to show edge effects as particle counts drop below ~10³. The fluctuation theorem and Jarzynski equality represent 21st-century extensions that handle these cases, though they remain outside introductory chemistry curricula.

Common misconceptions

"Endothermic reactions can't be spontaneous." This is false. The dissolution of ammonium nitrate in water (ΔH ≈ +25.7 kJ/mol) is spontaneous at room temperature because ΔS is large and positive, making TΔS dominant at 298 K.

"Entropy always increases in a chemical reaction." The Second Law applies to the universe, not to the system alone. A reaction can decrease system entropy (protein folding, freezing water) if it releases sufficient heat to increase surroundings entropy by a larger amount.

"ΔG° tells you what happens at reaction conditions." Standard state (1 mol/L, 1 bar, 298.15 K) is rarely the actual condition. The full ΔG = ΔG° + RT ln Q expression must be used for real concentrations.

"A large negative ΔG means a fast reaction." Reaction rate is governed by activation energy (kinetics), not by ΔG. Two reactions can have identical ΔG values and differ in rate by 12 orders of magnitude.

"Heat and enthalpy are the same thing." Enthalpy equals heat only at constant pressure. At constant volume, internal energy ΔU = q_v. The distinction matters in bomb calorimetry, where reactions occur at constant volume and measure ΔU directly.

Checklist or steps

The following sequence describes how the thermodynamic favorability of a reaction is established from tabulated data:

1. Locate standard enthalpy of formation (ΔH°_f) values for each species from NIST WebBook or equivalent tabulations.

Reference table or matrix

Values calculated from ΔG° = −RT ln K with R = 8.31446 J·mol⁻¹·K⁻¹ (NIST CODATA), T = 298.15 K.