Reaction Enthalpies

The standard enthalpy of formation is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states (most stable allotropes at 298 K and 1 bar). By definition, ΔH°f = 0 for all elements in their standard states. For example, the formation of liquid water: H₂(g) + ½O₂(g) → H₂O(l), ΔH°f = −285.8 kJ mol⁻¹. The strict requirement of 'one mole of product' means fractional coefficients for reactants are acceptable and necessary. Tables of standard enthalpies of formation are used with Hess's Law to calculate ΔH°rxn = Σ[ΔH°f(products)] − Σ[ΔH°f(reactants)].

The standard enthalpy of combustion is the enthalpy change when one mole of a substance undergoes complete combustion in excess oxygen under standard conditions, with all products in their standard states (CO₂(g) and H₂O(l) for organic compounds). Values are always negative (exothermic). For methane: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), ΔH°comb = −890.3 kJ mol⁻¹. Combustion enthalpies are measured directly using a bomb calorimeter and are critical for evaluating energy density of fuels. The more carbon–hydrogen bonds a molecule contains, the more negative (larger magnitude) its ΔH°comb.

The standard enthalpy of atomization is the enthalpy change when one mole of gaseous atoms is formed from an element or compound in its standard state. For elements: it represents breaking all bonds to produce isolated gas-phase atoms. For example, for carbon: C(graphite) → C(g), ΔH°at = +715 kJ mol⁻¹; for hydrogen: ½H₂(g) → H(g), ΔH°at = +218 kJ mol⁻¹. Note that atomization is always endothermic since bonds must be broken. Atomization enthalpies are indispensable in Born–Haber cycles and in calculating mean bond enthalpies, allowing chemists to estimate bond strengths across different molecules.

The standard enthalpy of sublimation is the enthalpy change when one mole of a solid substance converts directly to the gaseous phase under standard conditions, without passing through the liquid phase: X(s) → X(g). This process is always endothermic (ΔH°sub > 0) because intermolecular (or interionic/interatomic) forces must be overcome. For iodine: I₂(s) → I₂(g), ΔH°sub = +62.4 kJ mol⁻¹; for sodium: Na(s) → Na(g), ΔH°sub = +107 kJ mol⁻¹. In Born–Haber cycles, the sublimation enthalpy of a metal is the first step converting a solid metal into gaseous atoms before ionization.

Hess's Law states that the total enthalpy change of a reaction is independent of the route taken, provided initial and final states are the same (a consequence of enthalpy being a state function). This allows us to combine known ΔH values algebraically: reactions can be reversed (changing the sign of ΔH) or multiplied by a scalar (scaling ΔH proportionally). The formula ΔH°rxn = Σ[ΔH°f(products)] − Σ[ΔH°f(reactants)] is the most common application. Alternatively, using mean bond enthalpies: ΔH°rxn ≈ Σ(bonds broken) − Σ(bonds formed), where bond breaking is endothermic (+) and bond forming is exothermic (−).

• \Delta H^\circ_{\text{rxn}} — Standard enthalpy of reaction (kJ mol⁻¹): The heat exchanged with the surroundings at constant pressure and standard conditions for the reaction as written.
• \Delta H^\circ_f — Standard enthalpy of formation (kJ mol⁻¹): Enthalpy change for forming one mole of substance from elements in their standard states. Zero for all pure elements in standard states.
• n, m — Stoichiometric coefficients (dimensionless (mol)): The molar coefficients of products (n) and reactants (m) as they appear in the balanced chemical equation.

Problem. Calculate the standard enthalpy of combustion of ethanol, C₂H₅OH(l), using standard enthalpies of formation. Given: ΔH°f[C₂H₅OH(l)] = −277.7 kJ mol⁻¹, ΔH°f[CO₂(g)] = −393.5 kJ mol⁻¹, ΔH°f[H₂O(l)] = −285.8 kJ mol⁻¹.

Answer. The standard enthalpy of combustion of ethanol is −1366.7 kJ mol⁻¹.

• Hess's Law — Hess's Law is the mathematical framework used to combine standard enthalpies of formation, combustion, and atomization to calculate any reaction enthalpy indirectly.
• Calorimetry — Calorimetry is the experimental technique used to directly measure enthalpies of combustion and other reaction enthalpies using bomb calorimeters and coffee-cup calorimeters.
• Bond Enthalpies — Mean bond enthalpies provide an alternative route to estimating ΔH°rxn and are directly related to atomization enthalpies, connecting molecular bonding to thermochemical cycles.
• Born–Haber Cycle — Born–Haber cycles use enthalpies of formation, atomization, sublimation, and ionization in a thermochemical cycle to calculate lattice energies of ionic compounds.
• First Law of Thermodynamics — The conservation of energy (First Law) is the fundamental principle that justifies Hess's Law and the concept that enthalpy is a state function independent of reaction pathway.