Thermochemistry Guide: Enthalpy, Entropy, and Gibbs Free Energy
Chemical reactions absorb or release energy. The explosive decomposition of nitroglycerin releases enormous energy in microseconds. The photosynthesis of glucose absorbs sunlight energy over hours. Every reaction has an energy signature, and understanding these energy changes allows chemists to predict whether reactions will occur, how much heat they will produce, and how to optimize conditions.
Thermochemistry quantifies these energy changes. It explains why some reactions happen spontaneously, why others require energy input, and how the laws of thermodynamics govern all chemical change.
Energy and Its Forms
Energy exists in multiple forms: thermal, chemical, electrical, nuclear, and mechanical. Chemical energy is the energy stored in chemical bonds. When bonds form, energy is released. When bonds break, energy is absorbed.
The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another. In any chemical reaction, the total energy of the universe is conserved. The energy lost by the system equals the energy gained by the surroundings.
Enthalpy and Enthalpy Change
Enthalpy (H) is the heat content of a system at constant pressure. The enthalpy change (ΔH) for a reaction is the heat absorbed or released at constant pressure. Exothermic reactions release heat and have negative ΔH. Endothermic reactions absorb heat and have positive ΔH.
The combustion of methane: CH4 + 2 O2 → CO2 + 2 H2O, ΔH = -890 kJ/mol. This means burning one mole of methane releases 890 kJ of heat — enough to boil about three liters of water from room temperature.
Standard Enthalpy of Formation
The standard enthalpy of formation (ΔH°f) is the enthalpy change when one mole of a compound forms from its elements in their standard states. By convention, elements in their standard states have ΔH°f = 0. This provides a reference for calculating reaction enthalpies.
Table salt (NaCl) has ΔH°f = -411 kJ/mol. Carbon dioxide has ΔH°f = -393.5 kJ/mol. Most compounds have negative formation enthalpies, reflecting that compounds are generally more stable than their elemental components.
Calorimetry
Calorimetry measures heat changes in chemical reactions. A calorimeter is an insulated container that measures temperature change. The heat released or absorbed equals the product of the heat capacity, mass, and temperature change: q = mcΔT.
Constant Pressure Calorimetry
A coffee cup calorimeter operates at constant pressure (open to the atmosphere). It directly measures ΔH for reactions in solution. Dissolving ammonium nitrate in water absorbs heat: q = mcΔT gives the heat absorbed.
Bomb Calorimetry
Bomb calorimeters operate at constant volume, measuring ΔE (internal energy change). The reaction occurs in a sealed steel container (the bomb) surrounded by a water bath. Combustion reactions are measured in bomb calorimeters. The heat released equals Ccal × ΔT, where Ccal is the calorimeter’s heat capacity.
Hess’s Law
Hess’s law states that the enthalpy change for a reaction is the same whether the reaction occurs in one step or multiple steps. Enthalpy is a state function — it depends only on initial and final states, not the path taken.
This allows calculating ΔH for reactions that are difficult to measure directly. To find ΔH for C + 1/2 O2 → CO (partial combustion, which always produces some CO2), combine: C + O2 → CO2 (ΔH = -393.5 kJ) and CO2 → CO + 1/2 O2 (ΔH = +283.0 kJ). Adding gives ΔH = -110.5 kJ for CO formation.
Hess’s law connects to stoichiometry — reaction quantities scale with coefficients, allowing enthalpy calculations for any amount of reactant.
Standard Enthalpies of Reaction
Using standard enthalpies of formation, the standard enthalpy of any reaction can be calculated: ΔH°rxn = Σ(n × ΔH°f products) - Σ(n × ΔH°f reactants). This powerful equation allows predicting reaction enthalpies without experiments.
For the combustion of propane: C3H8 + 5 O2 → 3 CO2 + 4 H2O. Using ΔH°f values: ΔH°rxn = [3(-393.5) + 4(-241.8)] - [(-103.85) + 5(0)] = -2219.9 kJ/mol. The negative value confirms the reaction is highly exothermic.
Entropy and the Second Law
Entropy (S) measures disorder or randomness. The second law of thermodynamics states that the total entropy of the universe always increases for a spontaneous process. This explains why some exothermic reactions do not occur and some endothermic reactions occur spontaneously.
Melting ice is endothermic (requires heat) but occurs spontaneously above 0°C because the entropy increase of water molecules becoming disordered compensates for the energy cost. Gas formation from solid reactants produces large entropy increases that can drive endothermic reactions.
Entropy changes can be calculated from standard entropy values: ΔS°rxn = Σ(n × S° products) - Σ(n × S° reactants). Entropy typically increases when gases are produced, when the number of particles increases, and when solids dissolve.
Gibbs Free Energy
Gibbs free energy (G) combines enthalpy and entropy to predict spontaneity: ΔG = ΔH - TΔS. A negative ΔG indicates a spontaneous reaction (products more stable than reactants). A positive ΔG indicates a non-spontaneous reaction. At equilibrium, ΔG = 0.
The temperature dependence of spontaneity is captured in this equation. For reactions with ΔH negative and ΔS positive, ΔG is always negative — spontaneous at all temperatures. For ΔH positive and ΔS negative, ΔG is always positive — never spontaneous. For other combinations, spontaneity depends on temperature.
The Haber process for ammonia synthesis: N2 + 3 H2 → 2 NH3. This reaction has ΔH negative (exothermic) and ΔS negative (4 molecules become 2). At low temperatures, ΔG is negative (spontaneous). At high temperatures, ΔG becomes positive — the reaction is no longer spontaneous.
Free Energy and Equilibrium
The standard free energy change relates to the equilibrium constant: ΔG° = -RT ln K. This powerful equation connects thermodynamics to chemical equilibrium. A large positive ΔG° means K « 1 (reactants favored). A large negative ΔG° means K » 1 (products favored). At ΔG° = 0, K = 1.
Bond Enthalpies and Reaction Energetics
Average bond enthalpies provide a quick method for estimating reaction enthalpies without extensive thermodynamic data. Breaking bonds requires energy (endothermic), and forming bonds releases energy (exothermic). The approximate reaction enthalpy is the sum of bond enthalpies broken minus the sum of bond enthalpies formed.
The combustion of methane: break 4 C-H bonds (4 × 413 kJ/mol) and 2 O=O bonds (2 × 498 kJ/mol). Total in: 2648 kJ/mol. Form 2 C=O (2 × 799 kJ/mol) and 4 O-H bonds (4 × 467 kJ/mol). Total out: 3466 kJ/mol. Estimated ΔH: 2648 - 3466 = -818 kJ/mol, reasonably close to the experimental value of -890 kJ/mol.
Limitations of Bond Enthalpy Calculations
Bond enthalpies are average values derived from many compounds. They work well for hydrocarbons and simple organic molecules but become less accurate for compounds with unusual bonding or significant resonance stabilization. Benzene, with its delocalized pi electrons, has different bond strengths than the average C-C and C=C values suggest.
Standard enthalpies of formation provide more accurate results than bond enthalpy estimates because they account for the specific molecular environment. However, bond enthalpies remain valuable for quick estimates when detailed thermodynamic data is unavailable.
Calorimetry in Biological Systems
Biological calorimetry measures the heat produced by living organisms. Direct calorimetry places a subject in an insulated chamber and measures heat output. Indirect calorimetry measures oxygen consumption and CO2 production to calculate metabolic rate, using the stoichiometry of nutrient oxidation.
Isothermal titration calorimetry (ITC) measures the heat released or absorbed when molecules bind. A single ITC experiment determines the binding constant, stoichiometry, enthalpy change, and entropy change for biomolecular interactions. This technique has been invaluable for understanding enzyme-substrate binding, protein-DNA interactions, and drug-target recognition.
Frequently Asked Questions
What is the difference between exothermic and endothermic reactions? Exothermic reactions release heat (ΔH negative, surroundings get warmer). Endothermic reactions absorb heat (ΔH positive, surroundings get cooler).
Can a reaction be spontaneous at one temperature but not another? Yes. When ΔH and ΔS have the same sign, spontaneity depends on temperature. The reaction becomes spontaneous when T > ΔH/ΔS or T < ΔH/ΔS depending on the signs.
What does ΔG = 0 mean? It means the system is at equilibrium — the forward and reverse reaction rates are equal, and there is no net change in the composition of the system.
Why is entropy important for predicting spontaneity? Many reactions are enthalpy-driven (exothermic), but entropy can overcome unfavorable enthalpy. Dissolving ammonium nitrate in water is spontaneous despite being endothermic because the entropy increase is large enough.
What is the difference between heat and temperature? Heat is energy transfer due to temperature difference. Temperature is a measure of average kinetic energy. A large object at moderate temperature can contain more heat than a small object at high temperature.
How do you calculate the enthalpy change for a reaction? Use the standard enthalpies of formation: ΔH°rxn = Σ(n × ΔH°f products) - Σ(n × ΔH°f reactants). Alternatively, use bond enthalpies for approximate values.
Stoichiometry Guide — Chemical Equilibrium — Chemical Kinetics