Standard enthalpy of formation

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 compound from its constituent elements, with all substances in their standard states at 1 atmosphere (1 atm or 101.3 kPa). Its symbol is ΔH_f^O or Δ_fH^O. The superscript theta (zero) on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 degrees Celsius or 298.15 K). Standard states are as follows:

1. For a gas: the standard state is a pressure of exactly 1 atm
2. For a solute present in an ideal solution: a concentration of exactly one mole/liter (M) at a pressure of 1 atm
3. 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 atm
4. For an element: the form in which the element is most stable under 1 atm of pressure. One exception is phosphorus, for which the most stable form at 1 atm is black phosphorus, but white phosphorus is chosen as the standard reference state for zero enthalpy of formation.^[1]

For example, the standard enthalpy of formation of carbon dioxide would be the enthalpy of the following reaction under the conditions above:

C_(s,graphite) + O_2(g) → CO_2(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 calorie per mole, joule per mole or kilocalorie per gram (any combination of these units conforming to the energy per mass or amount guideline). In physics the energy per particle is often expressed inelectronvolts which corresponds to about 100 kJ mol⁻¹.

All elements in their standard 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 atm, 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, represented by the symbol ΔH_f298^O .

The standard enthalpy of formation is equivalent to the sum of many separate processes included in the Born-Haber cycle of synthesis reactions. For example, to calculate the standard enthalpy of formation of sodium chloride, we use the following reaction:

Na_(s) + (1/2)Cl_2(g) → NaCl_(s)

This process is made of many separate sub-processes, each with its own enthalpy. Therefore, we must take into account:

1. The standard enthalpy of atomization of solid sodium
2. The first ionization energy of gaseous sodium
3. The standard enthalpy of atomization of chlorine gas
4. The electron affinity of chlorine atoms
5. The lattice enthalpy of sodium chloride

The sum of all these values will give the standard enthalpy of formation of sodium chloride.

Additionally, applying Hess's Law shows that the sum of the individual reactions corresponding to the enthalpy change of formation for each substance in the reaction is equal to the enthalpy change of the overall reaction, regardless of the number of steps or intermediate reactions involved. This is because enthalpy is a state function. In the example above the standard enthalpy change of formation for sodium chloride is equal to the sum of the standard enthalpy change of formation for each of the steps involved in the process. This is especially useful for very long reactions with many intermediate steps and compounds.

Chemists may use standard enthalpies of formation for a reaction that is hypothetical. For instance carbon and hydrogen will not directly react to form methane, yet the standard enthalpy of formation for methane is determined to be −74.8 kJ mol⁻¹ from using other known standard enthalpies of reaction with Hess's law. That it is negative shows that the reaction, if it were to proceed, would be exothermic; that is, it is enthalpically more stable than hydrogen gas and carbon.

It is possible to predict heat of formations for simple unstrained organic compounds with the Heat of formation group additivity method.

(State: g = gaseous; l = liquid; s = solid; aq = aqueous)

Standard Enthalpies of Formation (at 25°C, 298 K)

Chemical Compound	Phase (matter)	Chemical formula	Δ Hf0 in kJ/mol
Acetone	l	C3H6O	−248.4
Acetylene	g	C2H2	+227.4
Ammonia	g	NH3	−46.1
Ammonia (Ammonium Hydroxide)	aq	NH3 (NH4OH)	−80.8
Ammonium nitrate	s	NH4NO3	−365.6
Benzene	l	C6H6	+49.1
Bromine	l	Br2	0
Bromine	g	Br2	+31
Bromine	g	Br	+111.9
Calcium	s	Ca	0
Calcium carbonate	s	CaCO3	−1207.6
Calcium oxide	s	CaO	−634.9
Carbon	s	C (graphite)	0
Carbon	s	C (diamond)	+1.88
Carbon dioxide	g	CO2	−393.5
Carbon monoxide	g	CO	−110.5
Chlorine	g	Cl2	0
Chlorine	g	Cl	+121.3
Copper(II) sulfate	aq	CuSO4	−769.98
Ethane	g	C2H6	−84.68
Ethanol	l	C2H5OH	−277.6
Ethylene	g	C2H4	+52.4
Fluorine	g	F2	0
Fluorine	g	F	+79.38
Glucose	s	C6H12O6	−1273.3
Hydrogen	g	H2	0
Hydrogen bromide	g	HBr	−36.3
Hydrogen chloride	g	HCl	−92.3
Hydrogen fluoride	g	HF	−273.3
Iodine	s	I2	0
Iodine	g	I2	+62
Isopropanol	g	C3H7OH	−318.1
Methane	g	CH4	−74.87
Methanol	l	CH3OH	−238.6
Nitric oxide	g	NO	+91.3
Nitrogen	g	N2	0
Nitrogen dioxide	g	NO2	+33.2
Oxygen	g	O2	0
Ozone	g	O3	+142.7
Propane	g	C3H8	−103.85
Silica	s	SiO2	−911
Silver	s	Ag	0
Silver chloride	s	AgCl	−127.0
Sodium	s	Na	0
Sodium	g	Na	+107.5
Sodium bicarbonate	s	NaHCO3	−950.8
Sodium carbonate	s	Na2CO3	−1131
Sodium chloride (table salt)	aq	NaCl	−407
Sodium chloride (table salt)	s	NaCl	−411.12
Sodium chloride (table salt)	l	NaCl	−385.92
Sodium chloride (table salt)	g	NaCl	−181.42
Sodium hydroxide	aq	NaOH	−470.1
Sodium hydroxide	s	NaOH	−426.7
Sodium nitrate	aq	NaNO3	−446.2
Sodium nitrate	s	NaNO3	−424.8
Sucrose	s	C12H22O11	−2226.1
Sulfur (monoclinic)	s	S8	0.3
Sulfur (rhombic)	s	S8	0
Sulfur dioxide	g	SO2	−296.8
Sulfur trioxide	g	SO3	−395.7
Sulfuric acid	l	H2SO4	−814
Water	l	H2O	−285.8
Water vapor	g	H2O	−241.82
Zinc sulfate	s	ZnSO4	−980.14