Standard enthalpy of formation


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 is recommended by IUPAC, although prior to 1982 the value 1.00 atm 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.
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 at a pressure of 1 bar extrapolated from infinite dilution. For a pure substance or a solvent in a condensed state 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:
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, but also in kilocalorie per mole, joule per mole or kilocalorie per gram.
All elements in their reference states 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 .

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,
may be considered as the sum of several steps, each with its own enthalpy :
  1. , the standard enthalpy of atomization of solid lithium.
  2. , the first ionization energy of gaseous lithium.
  3. , the standard enthalpy of atomization of fluorine gas.
  4. , the electron affinity of a fluorine atom.
  5. , the lattice energy of lithium fluoride.
The sum of these enthalpies give the standard enthalpy of formation of lithium fluoride:
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:

Organic compounds

The formation reactions for most organic compounds are hypothetical. For instance, carbon and hydrogen will not directly react to form methane, so that the standard enthalpy of formation cannot be measured directly. However the standard enthalpy of combustion is readily measurable using bomb calorimetry. The standard enthalpy of formation is then determined using Hess's law. The combustion of methane:
is equivalent to the sum of the hypothetical decomposition into elements followed by the combustion of the elements to form carbon dioxide and water :
Applying Hess's law,
Solving for the standard of enthalpy of formation,
The value of is determined to be −74.8 kJ/mol. The negative sign shows that the reaction, if it were to proceed, would be exothermic; that is, methane is enthalpically more stable than hydrogen gas and carbon.
It is possible to predict heats of formation for simple unstrained organic compounds with the heat of formation group additivity method.

Use in calculation for other reactions

The standard enthalpy change of any reaction can be calculated from the standard enthalpies of formation of reactants and products using Hess's law. A given reaction is considered as the decomposition of all reactants into elements in their standard states, followed by the formation of all products. The heat of reaction is then minus the sum of the standard enthalpies of formation of the reactants plus the sum of the standard enthalpies of formation of the products, as shown in the equation below:
If the standard enthalpy of the products is less than the standard enthalpy of the reactants, the standard enthalpy of reaction is negative. This implies that the reaction is exothermic. The converse is also true; the standard enthalpy of reaction is positive for an endothermic reaction. This calculation has a tacit assumption of ideal solution between reactants and products where the enthalpy of mixing is zero.
For example, for the combustion of methane, CH4 + 2O2 -> CO2 + 2H2O:
However O2 is an element in its standard state, so that, and the heat of reaction is simplified to
which is the equation in the previous section for the enthalpy of combustion.

Key concepts for enthalpy calculations

  • When a reaction is reversed, the magnitude of ΔH stays the same, but the sign changes.
  • When the balanced equation for a reaction is multiplied by an integer, the corresponding value of ΔH must be multiplied by that integer as well.
  • The change in enthalpy for a reaction can be calculated from the enthalpies of formation of the reactants and the products
  • Elements in their standard states make no contribution to the enthalpy calculations for the reaction, since the enthalpy of an element in its standard state is zero. Allotropes of an element other than the standard state generally have non-zero standard enthalpies of formation.

    Examples: standard enthalpies of formation at 25 °C

Thermochemical properties of selected substances at 298.15 K and 1 atm

Inorganic substances

SpeciesPhaseChemical formulaΔfH⦵ /
AluminiumSolidAl0
Aluminium chlorideSolidAlCl3−705.63
Aluminium oxideSolidAl2O3−1675.5
Aluminium hydroxideSolidAl3−1277
Aluminium sulphateSolidAl23−3440
Barium chlorideSolidBaCl2−858.6
Barium carbonateSolidBaCO3−1216
Barium hydroxideSolidBa2−944.7
Barium oxideSolidBaO−548.1
Barium sulfateSolidBaSO4−1473.3
BerylliumSolidBe0
Beryllium hydroxideSolidBe2−903
Beryllium oxideSolidBeO−609.4
Boron trichlorideSolidBCl3−402.96
BromineLiquidBr20
Bromide ionAqueousBr−−121
BromineGasBr111.884
BromineGasBr230.91
Bromine trifluorideGasBrF3−255.60
Hydrogen bromideGasHBr−36.29
CadmiumSolidCd0
Cadmium oxideSolidCdO−258
Cadmium hydroxideSolidCd2−561
Cadmium sulfideSolidCdS−162
Cadmium sulfateSolidCdSO4−935
CaesiumSolidCs0
CaesiumGasCs76.50
CaesiumLiquidCs2.09
Caesium ionGasCs+457.964
Caesium chlorideSolidCsCl−443.04
CalciumSolidCa0
CalciumGasCa178.2
Calcium ionGasCa2+1925.90
Calcium ionAqueousCa2+−542.7
Calcium carbideSolidCaC2−59.8
Calcium carbonate SolidCaCO3−1206.9
Calcium chlorideSolidCaCl2−795.8
Calcium chlorideAqueousCaCl2−877.3
Calcium phosphateSolidCa32−4132
Calcium fluorideSolidCaF2−1219.6
Calcium hydrideSolidCaH2−186.2
Calcium hydroxideSolidCa2−986.09
Calcium hydroxideAqueousCa2−1002.82
Calcium oxideSolidCaO−635.09
Calcium sulfateSolidCaSO4−1434.52
Calcium sulfideSolidCaS−482.4
WollastoniteSolidCaSiO3−1630
Carbon SolidC0
Carbon SolidC1.9
CarbonGasC716.67
Carbon dioxideGasCO2−393.509
Carbon disulfideLiquidCS289.41
Carbon disulfideGasCS2116.7
Carbon monoxideGasCO−110.525
Carbonyl chloride GasCOCl2−218.8
Carbon dioxide AqueousCO2−419.26
Bicarbonate ionAqueousHCO3–−689.93
Carbonate ionAqueousCO32–−675.23
Monatomic chlorineGasCl121.7
Chloride ionAqueousCl−−167.2
ChlorineGasCl20
ChromiumSolidCr0
CopperSolidCu0
Copper bromideSolidCuBr2−138.490
Copper chlorideSolidCuCl2−217.986
Copper oxideSolidCuO−155.2
Copper sulfateAqueousCuSO4−769.98
FluorineGasF20
Monatomic hydrogenGasH218
HydrogenGasH20
WaterGasH2O−241.818
WaterLiquidH2O−285.8
Hydrogen ionAqueousH+0
Hydroxide ionAqueousOH−−230
Hydrogen peroxideLiquidH2O2−187.8
Phosphoric acidLiquidH3PO4−1288
Hydrogen cyanideGasHCN130.5
Hydrogen bromideLiquidHBr−36.3
Hydrogen chlorideGasHCl−92.30
Hydrogen chlorideAqueousHCl−167.2
Hydrogen fluorideGasHF−273.3
Hydrogen iodideGasHI26.5
IodineSolidI20
IodineGasI262.438
IodineAqueousI223
Iodide ionAqueousI−−55
IronSolidFe0
Iron carbide SolidFe3C5.4
Iron carbonate SolidFeCO3−750.6
Iron chlorideSolidFeCl3−399.4
Iron oxide SolidFeO−272
Iron oxide SolidFe3O4−1118.4
Iron oxide SolidFe2O3−824.2
Iron sulfateSolidFeSO4−929
Iron sulfateSolidFe23−2583
Iron sulfideSolidFeS−102
PyriteSolidFeS2−178
LeadSolidPb0
Lead dioxideSolidPbO2−277
Lead sulfideSolidPbS−100
Lead sulfateSolidPbSO4−920
Lead nitrateSolidPb2−452
Lead sulfateSolidPbSO4−920
Lithium fluorideSolidLiF−616.93
MagnesiumSolidMg0
Magnesium ionAqueousMg2+−466.85
Magnesium carbonateSolidMgCO3−1095.797
Magnesium chlorideSolidMgCl2−641.8
Magnesium hydroxideSolidMg2−924.54
Magnesium hydroxideAqueousMg2−926.8
Magnesium oxideSolidMgO−601.6
Magnesium sulfateSolidMgSO4−1278.2
ManganeseSolidMn0
Manganese oxideSolidMnO−384.9
Manganese oxideSolidMnO2−519.7
Manganese oxideSolidMn2O3−971
Manganese oxideSolidMn3O4−1387
PermanganateAqueous−543
Mercury oxide SolidHgO−90.83
Mercury sulfide SolidHgS−58.2
NitrogenGasN20
Ammonia AqueousNH3 −80.8
AmmoniaGasNH3−46.1
Ammonium nitrateSolidNH4NO3−365.6
Ammonium chlorideSolidNH4Cl−314.55
Nitrogen dioxideGasNO233.2
HydrazineGasN2H495.4
HydrazineLiquidN2H450.6
Nitrous oxideGasN2O82.05
Nitric oxideGasNO90.29
Dinitrogen tetroxideGasN2O49.16
Dinitrogen pentoxideSolidN2O5−43.1
Dinitrogen pentoxideGasN2O511.3
Nitric acidAqueousHNO3−207
Monatomic oxygenGasO249
OxygenGasO20
OzoneGasO3143
White phosphorusSolidP40
Red phosphorusSolidP−17.4
Black phosphorusSolidP−39.3
Phosphorus trichlorideLiquidPCl3−319.7
Phosphorus trichlorideGasPCl3−278
Phosphorus pentachlorideSolidPCl5−440
Phosphorus pentachlorideGasPCl5−321
Phosphorus pentoxideSolidP2O5−1505.5
Potassium bromideSolidKBr−392.2
Potassium carbonateSolidK2CO3−1150
Potassium chlorateSolidKClO3−391.4
Potassium chlorideSolidKCl−436.68
Potassium fluorideSolidKF−562.6
Potassium oxideSolidK2O−363
Potassium nitrateSolidKNO3−494.5
Potassium perchlorateSolidKClO4−430.12
SiliconGasSi368.2
Silicon carbideSolidSiC−74.4, −71.5
Silicon tetrachlorideLiquidSiCl4−640.1
Silica SolidSiO2−910.86
Silver bromideSolidAgBr−99.5
Silver chlorideSolidAgCl−127.01
Silver iodideSolidAgI−62.4
Silver oxideSolidAg2O−31.1
Silver sulfideSolidAg2S−31.8
SodiumSolidNa0
SodiumGasNa107.5
Sodium bicarbonateSolidNaHCO3−950.8
Sodium carbonateSolidNa2CO3−1130.77
Sodium chlorideAqueousNaCl−407.27
Sodium chlorideSolidNaCl−411.12
Sodium chlorideLiquidNaCl−385.92
Sodium chlorideGasNaCl−181.42
Sodium chlorateSolidNaClO3−365.4
Sodium fluorideSolidNaF−569.0
Sodium hydroxideAqueousNaOH−469.15
Sodium hydroxideSolidNaOH−425.93
Sodium hypochloriteSolidNaOCl−347.1
Sodium nitrateAqueousNaNO3−446.2
Sodium nitrateSolidNaNO3−424.8
Sodium oxideSolidNa2O−414.2
Sulfur SolidS80.3
Sulfur SolidS80
Hydrogen sulfideGasH2S−20.63
Sulfur dioxideGasSO2−296.84
Sulfur trioxideGasSO3−395.7
Sulfuric acidLiquidH2SO4−814
TitaniumGasTi468
Titanium tetrachlorideGasTiCl4−763.2
Titanium tetrachlorideLiquidTiCl4−804.2
Titanium dioxideSolidTiO2−944.7
ZincGasZn130.7
Zinc chlorideSolidZnCl2−415.1
Zinc oxideSolidZnO−348.0
Zinc sulfateSolidZnSO4−980.14