In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their reference state, with all substances in their standard states. The standard pressure value p⦵ = 105 Pa (= 100 kPa = 1 bar) is recommended by IUPAC, although prior to 1982 the value 1.00 atm (101.325 kPa) was used. There is no standard temperature. Its symbol is ΔfH⦵. The superscript Plimsoll on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 °C or 298.15 K). Standard states are defined for various types of substances. For a gas, it is the hypothetical state the gas would assume if it obeyed the ideal gas equation at a pressure of 1 bar. For a gaseous or solid solute present in a diluted ideal solution, the standard state is the hypothetical state of concentration of the solute of exactly one mole per liter (1 M) at a pressure of 1 bar extrapolated from infinite dilution. For a pure substance or a solvent in a condensed state (a liquid or a solid) the standard state is the pure liquid or solid under a pressure of 1 bar. For elements that have multiple allotropes, the reference state usually is chosen to be the form in which the element is most stable under 1 bar of pressure. One exception is phosphorus, for which the most stable form at 1 bar is black phosphorus, but white phosphorus is chosen as the standard reference state for zero enthalpy of formation. For example, the standard enthalpy of formation of carbon dioxide is the enthalpy of the following reaction under the above conditions:
C ( s , graphite ) + O 2 ( g ) ⟶ CO 2 ( g ) {\displaystyle {\ce {C(s, graphite) + O2(g) -> CO2(g)}}}
All elements are written in their standard states, and one mole of product is formed. This is true for all enthalpies of formation. The standard enthalpy of formation is measured in units of energy per amount of substance, usually stated in kilojoule per mole (kJ mol−1), but also in kilocalorie per mole, joule per mole or kilocalorie per gram (any combination of these units conforming to the energy per mass or amount guideline). All elements in their reference states (oxygen gas, solid carbon in the form of graphite, etc.) have a standard enthalpy of formation of zero, as there is no change involved in their formation. The formation reaction is a constant pressure and constant temperature process. Since the pressure of the standard formation reaction is fixed at 1 bar, the standard formation enthalpy or reaction heat is a function of temperature. For tabulation purposes, standard formation enthalpies are all given at a single temperature: 298 K, and are represented by the symbol ΔfH⦵298 K (or ΔH⦵f,298 K).
Hess' law For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. The enthalpy of reaction can then be analyzed by applying Hess' law, which states that the sum of the enthalpy changes for a number of individual reaction steps equals the enthalpy change of the overall reaction. This is true because enthalpy is a state function, whose value for an overall process depends only on the initial and final states and not on any intermediate states. Examples are given in the following sections.
Ionic compounds: Born–Haber cycle
For ionic compounds, the standard enthalpy of formation is equivalent to the sum of several terms included in the Born–Haber cycle. For example, the formation of lithium fluoride,
Li ( s ) + 1 2 F 2 ( g ) ⟶ LiF ( s ) {\displaystyle {\ce {Li(s) + 1/2 F2(g) -> LiF(s)}}}
may be considered as the sum of several steps, each with its own enthalpy (or energy, approximately):
Hsub, the standard enthalpy of atomization (or sublimation) of solid lithium. IELi, the first ionization energy of gaseous lithium. B(F–F), the standard enthalpy of atomization (or bond energy) of fluorine gas. EAF, the electron affinity of a fluorine atom. UL, the lattice energy of lithium fluoride. The sum of these enthalpies give the standard enthalpy of formation (ΔHf) of lithium fluoride:
Δ H f = Δ H sub + IE Li + 1 2 B(F–F) − EA F + U L . {\displaystyle \Delta H_{\text{f}}=\Delta H_{\text{sub}}+{\text{IE}}_{\text{Li}}+{\frac {1}{2}}{\text{B(F–F)}}-{\text{EA}}_{\text{F}}+{\text{U}}_{\text{L}}.}
In practice, the enthalpy of formation of lithium fluoride can be determined experimentally, but the lattice energy cannot be measured directly. The equation is therefore rearranged to evaluate the lattice energy:
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