Enthalpy

Q: What is enthalpy in simple terms?

Enthalpy (H) is a thermodynamic quantity that measures the total heat content of a system at constant pressure. The change in enthalpy (ΔH) tells you how much heat a chemical reaction releases or absorbs. ΔH 0 means endothermic (absorbs heat).

Q: What's the difference between enthalpy and energy?

Internal energy U is the total energy stored in a system. Enthalpy H = U + PV adds in the pressure-volume work term. At constant volume (sealed container), heat flow equals ΔU. At constant pressure (open container, atmospheric pressure), heat flow equals ΔH. Since most chemistry happens at constant atmospheric pressure, ΔH is the more directly measurable quantity.

Q: How does Hess's law work?

Hess's law says the total enthalpy change for a reaction is independent of the path taken. If a reaction can be split into intermediate steps, the total ΔH equals the sum of ΔH for each step. This is a consequence of enthalpy being a state function. Hess's law lets you calculate ΔH for reactions that are hard to measure directly by combining ΔH values from related reactions.

Q: What is the standard enthalpy of formation?

ΔH_f° is the enthalpy change when 1 mole of a compound forms from its constituent elements in their standard states (1 atm, 298 K). By convention, ΔH_f° of any element in its standard state is zero. Tabulated values let you compute ΔH for any reaction using: ΔH_rxn = Σ ΔH_f(products) - Σ ΔH_f(reactants).

Q: Why isn't every exothermic reaction spontaneous?

Because spontaneity is determined by Gibbs free energy ΔG = ΔH - TΔS, which combines enthalpy and entropy. Even an endothermic reaction (ΔH > 0) can be spontaneous if it produces enough entropy increase. Ammonium nitrate dissolving in water absorbs heat (cools the solution) but is spontaneous because the entropy gain dominates. Enthalpy alone doesn't predict direction.

Enthalpy is a thermodynamic quantity that measures the total heat content of a system at constant pressure. The change in enthalpy ($ \Delta H $) tells you how much heat a chemical reaction releases or absorbs. Exothermic reactions have $ \Delta H < 0 $ (release heat to the surroundings). Endothermic reactions have $ \Delta H > 0 $ (absorb heat). Combustion, neutralization, condensation are exothermic; melting, vaporization, photosynthesis are endothermic. Enthalpy is the central thermodynamic property tracked by almost every chemistry textbook because reactions at constant atmospheric pressure (which is most lab and industrial chemistry) make $ \Delta H $ directly equal to heat flow.

Enthalpy diagram for an exothermic reaction — Enthalpy change ΔH for an exothermic reaction — energy is released from reactants to products.

Definition

Enthalpy $ H $ is defined as:

$$ H = U + PV $$

where $ U $ is internal energy, $ P $ is pressure, and $ V $ is volume. The product $ PV $ is the ‘work’ contribution from the system pushing against its surroundings at constant pressure.

For a process at constant pressure, the change in enthalpy equals the heat exchanged:

$$ \Delta H = q_p $$

This is why enthalpy is so practical — laboratory and industrial chemistry mostly happens at constant atmospheric pressure, so measuring heat flow directly tells you $ \Delta H $.

Sign Convention

$ \Delta H < 0 $: exothermic. Energy flows OUT of the system as heat. Products have lower energy than reactants. Examples: combustion, neutralization, freezing, condensation.
$ \Delta H > 0 $: endothermic. Energy flows INTO the system as heat. Products have higher energy than reactants. Examples: melting, boiling, photosynthesis, dissolving ammonium nitrate in water.

Hess’s Law

Hess’s law: the total enthalpy change for a reaction is independent of the pathway taken. If a reaction can be broken into intermediate steps, $ \Delta H $ for the overall reaction equals the sum of $ \Delta H $ for each step. This is a direct consequence of enthalpy being a state function (it depends only on the initial and final states, not on the path).

Example. To find $ \Delta H $ for $ \text{C}(s) + \tfrac{1}{2}\text{O}_2 \to \text{CO}(g) $ (hard to measure directly), use known data for $ \text{C}(s) + \text{O}_2 \to \text{CO}_2 $ ($ \Delta H = -393.5 $ kJ) and $ \text{CO}(g) + \tfrac{1}{2}\text{O}_2 \to \text{CO}_2 $ ($ \Delta H = -283.0 $ kJ). The target reaction’s $ \Delta H = -393.5 – (-283.0) = -110.5 $ kJ. Hess’s law lets you compute enthalpies of reactions that can’t be measured directly.

Standard Enthalpies of Formation

The standard enthalpy of formation $ \Delta H_f^\circ $ is the enthalpy change when 1 mole of a compound forms from its constituent elements in their standard states (1 atm, 298 K). By convention, $ \Delta H_f^\circ $ of an element in its standard state is zero.

Tabulated values let you compute $ \Delta H $ for any reaction:

$$ \Delta H_{rxn} = \sum n_p \Delta H_f^\circ(\text{products}) – \sum n_r \Delta H_f^\circ(\text{reactants}) $$

where $ n_p $ and $ n_r $ are the stoichiometric coefficients. A table of $ \Delta H_f^\circ $ values is the chemistry student’s most useful single resource for enthalpy calculations.

Bond Enthalpies

Each chemical bond has a characteristic enthalpy required to break it (in the gas phase). Average bond enthalpies:

Bond	Average enthalpy (kJ/mol)	Bond	Average enthalpy (kJ/mol)
H-H	436	C-C	346
O=O	498	C=C	614
N≡N	945	C-O	358
O-H	463	C-H	414

Reaction enthalpy can be estimated as: $ \Delta H \approx \sum(\text{bonds broken}) – \sum(\text{bonds formed}) $. Bonds broken require energy input (positive contribution); bonds formed release energy (negative contribution). Less precise than tabulated formation enthalpies but useful for rough estimates and intuition.

Why Exothermic Doesn’t Mean Spontaneous

A common student misconception: that exothermic (\$ \\Delta H < 0 \$) reactions are always spontaneous. They aren't. Spontaneity depends on the Gibbs free energy change $ \\Delta G = \\Delta H - T\\Delta S $, which combines enthalpy and entropy. Even an endothermic reaction can be spontaneous if it produces enough entropy increase (e.g., dissolving ammonium nitrate cools the solution because \$ \\Delta H > 0 \$ but the entropy gain makes \$ \\Delta G < 0 \$).

This is why you need both enthalpy and entropy to predict reaction direction. Enthalpy alone is incomplete.

Frequently Asked Questions

What is enthalpy in simple terms?

Enthalpy (H) is a thermodynamic quantity that measures the total heat content of a system at constant pressure. The change in enthalpy (ΔH) tells you how much heat a chemical reaction releases or absorbs. ΔH 0 means endothermic (absorbs heat).

What’s the difference between enthalpy and energy?

Internal energy U is the total energy stored in a system. Enthalpy H = U + PV adds in the pressure-volume work term. At constant volume (sealed container), heat flow equals ΔU. At constant pressure (open container, atmospheric pressure), heat flow equals ΔH. Since most chemistry happens at constant atmospheric pressure, ΔH is the more directly measurable quantity.

How does Hess’s law work?

Hess’s law says the total enthalpy change for a reaction is independent of the path taken. If a reaction can be split into intermediate steps, the total ΔH equals the sum of ΔH for each step. This is a consequence of enthalpy being a state function. Hess’s law lets you calculate ΔH for reactions that are hard to measure directly by combining ΔH values from related reactions.

What is the standard enthalpy of formation?

ΔH_f° is the enthalpy change when 1 mole of a compound forms from its constituent elements in their standard states (1 atm, 298 K). By convention, ΔH_f° of any element in its standard state is zero. Tabulated values let you compute ΔH for any reaction using: ΔH_rxn = Σ ΔH_f(products) – Σ ΔH_f(reactants).

Why isn’t every exothermic reaction spontaneous?

Because spontaneity is determined by Gibbs free energy ΔG = ΔH – TΔS, which combines enthalpy and entropy. Even an endothermic reaction (ΔH > 0) can be spontaneous if it produces enough entropy increase. Ammonium nitrate dissolving in water absorbs heat (cools the solution) but is spontaneous because the entropy gain dominates. Enthalpy alone doesn’t predict direction.

What are bond enthalpies used for?

Bond enthalpies estimate reaction enthalpies as: ΔH ≈ Σ(bonds broken) – Σ(bonds formed). Bond breaking is endothermic (positive); bond formation is exothermic (negative). The method is less precise than tabulated formation enthalpies (because bond enthalpies are averages over many molecules) but useful for quick estimates and for building chemical intuition about which reactions release the most energy.