Enthalpy, Entropy, and Gibbs Free Energy: A Complete Guide to Chemical Thermodynamics

Thermodynamics and kinetics answer two different questions about a chemical reaction. Kinetics asks: how fast does this reaction occur? Thermodynamics asks: does this reaction favor products or reactants at equilibrium — and will it happen spontaneously? A reaction can be thermodynamically favorable (products are more stable than reactants) but kinetically slow (there is a high activation energy barrier). Diamond converting to graphite is thermodynamically favorable at room temperature — graphite is the more stable form of carbon — but the rate is so slow that your diamond ring is safe for the foreseeable future. Conversely, a reaction can be kinetically fast but thermodynamically unfavorable, in which case it only proceeds if energy is continuously supplied. Understanding thermodynamics means you can look at a reaction and determine whether it will spontaneously produce products under given conditions, without knowing anything about how fast it happens. The three quantities that make this possible are enthalpy (ΔH), entropy (ΔS), and Gibbs free energy (ΔG).

Enthalpy is the heat absorbed or released by a reaction at constant pressure — which is the condition for virtually every reaction you encounter in an open beaker, a biological system, or the atmosphere. The symbol is ΔH, where Δ means change. If ΔH is negative, the reaction releases heat to the surroundings — it is exothermic. The products have less energy than the reactants, and the excess energy is given off as heat. Burning methane (CH₄ + 2O₂ → CO₂ + 2H₂O, ΔH = -890 kJ/mol) is highly exothermic — you feel the heat when you light a gas stove. If ΔH is positive, the reaction absorbs heat from the surroundings — it is endothermic. The products have more energy than the reactants, and the reaction requires energy input. Dissolving ammonium nitrate in water (used in instant cold packs) is endothermic — the solution gets cold because the dissolution absorbs heat from the water. To calculate ΔH for a reaction, you use standard enthalpies of formation (ΔH°f): ΔH°rxn = Σ[ΔH°f(products)] - Σ[ΔH°f(reactants)]. This is Hess's Law applied through formation enthalpies. Every element in its standard state (O₂ gas, Fe solid, C graphite, etc.) has ΔH°f = 0 by definition — they are the reference point. You look up the ΔH°f for every compound in the reaction, multiply by stoichiometric coefficients, and subtract reactants from products.

Entropy measures the number of ways energy can be distributed among the particles in a system — often informally described as 'disorder,' though 'energy dispersal' is more accurate. The second law of thermodynamics states that the total entropy of the universe always increases for a spontaneous process. This is the fundamental arrow of nature — it is why ice melts at room temperature, why gases expand to fill their container, and why you have never seen a broken egg reassemble itself. ΔS is positive when entropy increases (more dispersal, more accessible microstates). ΔS is negative when entropy decreases (less dispersal, more order). Several rules help you predict the sign of ΔS for a reaction: (1) Entropy increases when a solid becomes a liquid becomes a gas — gases have far more microstates than liquids or solids. (2) Entropy increases when the number of moles of gas increases — 2 mol of gas has more entropy than 1 mol. (3) Entropy increases when a substance is dissolved in a solvent — the particles go from an ordered crystal to a dispersed solution. (4) Entropy increases with temperature — higher temperature means more kinetic energy distributed among more microstates. To calculate ΔS° for a reaction: ΔS°rxn = Σ[S°(products)] - Σ[S°(reactants)]. Note that unlike enthalpy, absolute entropy values (S°, not ΔS°f) are used, and elements in their standard states do NOT have S° = 0. Every substance has a positive standard entropy. This is because the third law of thermodynamics defines S = 0 only at absolute zero (0 K) for a perfect crystal.

Gibbs free energy combines enthalpy and entropy into a single quantity that determines whether a reaction is spontaneous at a given temperature: ΔG = ΔH - TΔS. If ΔG is negative, the reaction is spontaneous (thermodynamically favorable) in the forward direction. If ΔG is positive, the reaction is non-spontaneous in the forward direction (but spontaneous in reverse). If ΔG = 0, the system is at equilibrium. This equation is the most powerful single equation in chemical thermodynamics. It tells you that spontaneity depends on the balance between two competing drives: the enthalpic drive (systems tend toward lower energy, favoring exothermic reactions with negative ΔH) and the entropic drive (systems tend toward greater disorder, favoring reactions with positive ΔS). The temperature acts as a weight on the entropy term — at high temperatures, entropy becomes more important; at low temperatures, enthalpy dominates. This temperature dependence creates four cases that every chemistry student should internalize.

Case 1: ΔH < 0 and ΔS > 0. Both enthalpy and entropy favor the reaction. ΔG is always negative regardless of temperature. The reaction is spontaneous at all temperatures. Example: combustion reactions (exothermic and produce more moles of gas). Case 2: ΔH > 0 and ΔS < 0. Both enthalpy and entropy oppose the reaction. ΔG is always positive. The reaction is non-spontaneous at all temperatures. Example: the reverse of combustion — you cannot un-burn methane spontaneously. Case 3: ΔH < 0 and ΔS < 0. Enthalpy favors the reaction but entropy opposes it. ΔG = ΔH - TΔS. At low temperatures, the ΔH term dominates and ΔG is negative (spontaneous). At high temperatures, the -TΔS term (which is positive because ΔS is negative) overwhelms ΔH and ΔG becomes positive (non-spontaneous). Example: freezing water — exothermic (releases heat) and decreases entropy (liquid → solid). Spontaneous below 0°C, non-spontaneous above 0°C. Case 4: ΔH > 0 and ΔS > 0. Entropy favors the reaction but enthalpy opposes it. At low temperatures, ΔG is positive (non-spontaneous). At high temperatures, -TΔS (which is negative because ΔS is positive) overwhelms the positive ΔH and ΔG becomes negative (spontaneous). Example: melting ice — endothermic but increases entropy. Non-spontaneous below 0°C, spontaneous above 0°C. For Cases 3 and 4, there is a specific crossover temperature where ΔG = 0 (equilibrium): T = ΔH/ΔS. Above or below this temperature, the reaction switches between spontaneous and non-spontaneous.

Method 1 — From ΔH° and ΔS°: Calculate ΔH°rxn and ΔS°rxn separately from formation/standard values, then plug into ΔG° = ΔH° - TΔS°. This is the method that gives you the most insight because you see the individual contributions of enthalpy and entropy. Remember to convert units: ΔH is typically in kJ and ΔS in J/K, so convert ΔS to kJ/K before combining (divide by 1000). Forgetting this unit conversion is one of the most common exam mistakes. Method 2 — From standard Gibbs energies of formation: ΔG°rxn = Σ[ΔG°f(products)] - Σ[ΔG°f(reactants)]. This is the fastest method when you have ΔG°f values available. Like ΔH°f, the ΔG°f of any element in its standard state is zero. Method 3 — From the equilibrium constant: ΔG° = -RT ln K, where K is the equilibrium constant at temperature T. This connects thermodynamics to equilibrium: a large K (products heavily favored) gives a large negative ΔG° (strongly spontaneous). A small K (reactants favored) gives a positive ΔG° (non-spontaneous in the forward direction). When K = 1, ΔG° = 0, meaning products and reactants are equally favored under standard conditions. This relationship is one of the deepest connections in chemistry — it unifies the concepts of energy, spontaneity, and chemical equilibrium into a single mathematical framework.

There is an important distinction between ΔG° (standard Gibbs energy change) and ΔG (actual Gibbs energy change under any conditions). ΔG° is calculated with all reactants and products at standard conditions (1 atm for gases, 1 M for solutions, pure solids and liquids at 25°C unless otherwise stated). It tells you the direction of spontaneity when everything starts at standard conditions. ΔG tells you the direction of spontaneity under the actual conditions of the reaction, which may be far from standard. The relationship is: ΔG = ΔG° + RT ln Q, where Q is the reaction quotient (the same expression as K, but using the current concentrations/pressures, which may not be equilibrium values). At equilibrium, Q = K and ΔG = 0, which gives: 0 = ΔG° + RT ln K, or ΔG° = -RT ln K (the equation from above). The practical significance: even if ΔG° is positive (non-spontaneous under standard conditions), a reaction can still proceed forward if the actual conditions are sufficiently different from standard — specifically, if Q < K, the reaction will shift forward to approach equilibrium regardless of the sign of ΔG°. This is why reactions with positive ΔG° can still occur in nature — they are driven forward by non-standard concentrations.

Mistake 1: Confusing spontaneous with fast. ΔG tells you direction, not speed. A reaction with ΔG = -500 kJ/mol might be extremely slow if the activation energy is high. Thermodynamics says the reaction is favorable; kinetics determines whether it happens on a human timescale. Mistake 2: Forgetting to convert ΔS units. ΔH is typically in kJ; ΔS is typically in J/K. If you plug them into ΔG = ΔH - TΔS without converting, your answer will be off by a factor of 1000. Always convert ΔS to kJ/K (divide by 1000) before combining. Mistake 3: Using Celsius for T. The temperature in ΔG = ΔH - TΔS and ΔG° = -RT ln K must be in Kelvin. Using Celsius gives a meaningless result. Mistake 4: Assuming ΔG° tells you everything. ΔG° applies to standard conditions only. The actual spontaneity under non-standard conditions depends on ΔG = ΔG° + RT ln Q. A reaction with positive ΔG° can still proceed if Q is small enough (concentrations are far from equilibrium). Mistake 5: Thinking that endothermic reactions cannot be spontaneous. Positive ΔH works against spontaneity, but if ΔS is sufficiently positive and T is sufficiently high, the -TΔS term can overcome the positive ΔH, making ΔG negative. Melting ice above 0°C is endothermic and spontaneous. ChemistryIQ can walk you through thermodynamics problems step by step — photograph your homework and get guided solutions that show the sign analysis, unit conversions, and calculation at each stage.