# Standard enthalpy change of formation

The standard enthalpy of formation or "standard heat of formation" of a compound is the change of enthalpy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states (the most stable form of the element at 101.325 kPa of pressure and the specified temperature, usually 298 K or 25 degrees Celsius). Its symbol is ΔHfO.

A similar type of enthalpy change, known as the standard enthalpy change of hydrogenation is defined as the enthalpy change observed when 1 mol of an unsaturated compound reacts with an excess of hydrogen to become fully saturated, all elements within the reaction being within their standard states.

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) + O2(g) → CO2(g)

The standard enthalpy change of formation is measured in units of energy per amount of substance. Most are defined in kilojoules per mole, or kJ mol-1, but can also be measured in calories per mole, joules per mole or kilocalories 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 in electronvolts 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 standard enthalpy change of formation is used in thermochemistry to find the standard enthalpy change of reaction. This is done by subtracting the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products, as shown in the equation below.

ΔHreactionO = ΣΔHfO (Products) - ΣΔHfO (Reactants)

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)Cl2(g) → NaCl(s)

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

File:BornHaberLiF.PNG
Standard enthalpy change of formation Born-Haber diagram for lithium fluoride.
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. 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.

#### Examples: Inorganic compounds (at 25 °C)

 Chemical Compound Phase (matter) Chemical formula Δ Hf0 in kJ/mol Ammonia (Ammonium Hydroxide) aq NH3 (NH4OH) -80.8 Ammonia g NH3 -46.1 Copper (II) sulfate aq CuSO4 -769.98 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 -469.6 Sodium hydroxide s NaOH -426.7 Sodium nitrate aq NaNO3 -446.2 Sodium nitrate s NaNO3 -424.8 Sulfur dioxide g SO2 -297 Sulfuric acid l H2SO4 -814 Silica s SiO2 -911 Nitrogen dioxide g NO2 +33 Nitrogen monoxide g NO +90 Water l H2O -286 Water g H2O -241.8 Carbon dioxide g CO2 -393.5 Hydrogen g H2 0 Fluorine g F2 0 Chlorine g Cl2 0 Bromine l Br2 0 Bromine g Br2 +31 Iodine s I2 0 Iodine g I2 +62 Zinc sulfate aq ZnSO4 -980.14
(State: g = gaseous; l = liquid; s = solid; aq = aqueous)