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 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 Δ_fH^⦵. 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:

${\ce {C(s, graphite) + O2(g) -> CO2(g)}}$

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, represented by the symbol Δ_fH^⦵
_{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

Standard enthalpy change of formation in Born–Haber diagram for lithium fluoride. Δ_lattH corresponds to U_L in the text. The downward arrow "electron affinity" shows the negative quantity –EA_F, since EA_F is usually defined as positive.

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,

${\ce {Li(s) + 1/2 F2(g) -> LiF(s)}}$

may be considered as the sum of several steps, each with its own enthalpy (or energy, approximately):

1. H_sub, the standard enthalpy of atomization (or sublimation) of solid lithium.
2. IE_Li, the first ionization energy of gaseous lithium.
3. B(F–F), the standard enthalpy of atomization (or bond energy) of fluorine gas.
4. EA_F, the electron affinity of a fluorine atom.
5. U_L, the lattice energy of lithium fluoride.

The sum of these enthalpies give the standard enthalpy of formation (Δ_fH) of lithium fluoride:

$\Delta H_{\text{f}}=\Delta H_{\text{sub}}+{\text{IE}}_{\text{Li}}+{\frac {1}{2}}{\text{B(F–F)}}-{\text{EA}}_{\text{F}}+{\text{U}}_{\text{L}}.$

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:

$-U_{\text{L}}=\Delta H_{\text{sub}}+{\text{IE}}_{\text{Li}}+{\frac {1}{2}}{\text{B(F–F)}}-{\text{EA}}_{\text{F}}-\Delta H_{\text{f}}.$

Organic compounds

The formation reactions for most organic compounds are hypothetical. For instance, carbon and hydrogen will not directly react to form methane (CH₄), 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:

${\ce {CH4 + 2 O2 -> CO2 + 2 H2O}}$

is equivalent to the sum of the hypothetical decomposition into elements followed by the combustion of the elements to form carbon dioxide (CO₂) and water (H₂O):

${\ce {CH4 -> C + 2H2}}$

${\ce {C + O2 -> CO2}}$

${\ce {2H2 + O2 -> 2H2O}}$

Applying Hess's law,

$\Delta _{\text{comb}}H^{\ominus }({\text{CH}}_{4})=[\Delta _{\text{f}}H^{\ominus }({\text{CO}}_{2})+2\Delta _{\text{f}}H^{\ominus }({\text{H}}_{2}{\text{O}})]-\Delta _{\text{f}}H^{\ominus }({\text{CH}}_{4}).$

Solving for the standard of enthalpy of formation,

$\Delta _{\text{f}}H^{\ominus }({\text{CH}}_{4})=[\Delta _{\text{f}}H^{\ominus }({\text{CO}}_{2})+2\Delta _{\text{f}}H^{\ominus }({\text{H}}_{2}{\text{O}})]-\Delta _{\text{comb}}H^{\ominus }({\text{CH}}_{4}).$

The value of ⁠$\Delta _{\text{f}}H^{\ominus }({\text{CH}}_{4})$⁠ 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 (each being multiplied by its respective stoichiometric coefficient, ν) plus the sum of the standard enthalpies of formation of the products (each also multiplied by its respective stoichiometric coefficient), as shown in the equation below:

$\Delta _{\text{r}}H^{\ominus }=\sum \nu \Delta _{\text{f}}H^{\ominus }({\text{products}})-\sum \nu \Delta _{\text{f}}H^{\ominus }({\text{reactants}}).$

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, ${\ce {CH4 + 2O2 -> CO2 + 2H2O}}$:

$\Delta _{\text{r}}H^{\ominus }=[\Delta _{\text{f}}H^{\ominus }({\text{CO}}_{2})+2\Delta _{\text{f}}H^{\ominus }({\text{H}}_{2}{}{\text{O}})]-[\Delta _{\text{f}}H^{\ominus }({\text{CH}}_{4})+2\Delta _{\text{f}}H^{\ominus }({\text{O}}_{2})].$

However ${\ce {O2}}$ is an element in its standard state, so that $\Delta _{\text{f}}H^{\ominus }({\text{O}}_{2})=0$, and the heat of reaction is simplified to

$\Delta _{\text{r}}H^{\ominus }=[\Delta _{\text{f}}H^{\ominus }({\text{CO}}_{2})+2\Delta _{\text{f}}H^{\ominus }({\text{H}}_{2}{}{\text{O}})]-\Delta _{\text{f}}H^{\ominus }({\text{CH}}_{4}),$

which is the equation in the previous section for the enthalpy of combustion $\Delta _{\text{comb}}H^{\ominus }$.

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

Species	Phase	Chemical formula	ΔfH⦵ /(kJ/mol)
Aluminium	Solid	Al	0
Aluminium chloride	Solid	AlCl3	−705.63
Aluminium oxide	Solid	Al2O3	−1675.5
Aluminium hydroxide	Solid	Al(OH)3	−1277
Aluminium sulphate	Solid	Al2(SO4)3	−3440
Barium chloride	Solid	BaCl2	−858.6
Barium carbonate	Solid	BaCO3	−1216
Barium hydroxide	Solid	Ba(OH)2	−944.7
Barium oxide	Solid	BaO	−548.1
Barium sulfate	Solid	BaSO4	−1473.3
Beryllium	Solid	Be	0
Beryllium hydroxide	Solid	Be(OH)2	−903
Beryllium oxide	Solid	BeO	−609.4
Boron trichloride	Solid	BCl3	−402.96
Bromine	Liquid	Br2	0
Bromide ion	Aqueous	Br−	−121
Bromine	Gas	Br	111.884
Bromine	Gas	Br2	30.91
Bromine trifluoride	Gas	BrF3	−255.60
Hydrogen bromide	Gas	HBr	−36.29
Cadmium	Solid	Cd	0
Cadmium oxide	Solid	CdO	−258
Cadmium hydroxide	Solid	Cd(OH)2	−561
Cadmium sulfide	Solid	CdS	−162
Cadmium sulfate	Solid	CdSO4	−935
Caesium	Solid	Cs	0
Caesium	Gas	Cs	76.50
Caesium	Liquid	Cs	2.09
Caesium(I) ion	Gas	Cs+	457.964
Caesium chloride	Solid	CsCl	−443.04
Calcium	Solid	Ca	0
Calcium	Gas	Ca	178.2
Calcium(II) ion	Gas	Ca2+	1925.90
Calcium(II) ion	Aqueous	Ca2+	−542.7
Calcium carbide	Solid	CaC2	−59.8
Calcium carbonate (Calcite)	Solid	CaCO3	−1206.9
Calcium chloride	Solid	CaCl2	−795.8
Calcium chloride	Aqueous	CaCl2	−877.3
Calcium phosphate	Solid	Ca3(PO4)2	−4132
Calcium fluoride	Solid	CaF2	−1219.6
Calcium hydride	Solid	CaH2	−186.2
Calcium hydroxide	Solid	Ca(OH)2	−986.09
Calcium hydroxide	Aqueous	Ca(OH)2	−1002.82
Calcium oxide	Solid	CaO	−635.09
Calcium sulfate	Solid	CaSO4	−1434.52
Calcium sulfide	Solid	CaS	−482.4
Wollastonite	Solid	CaSiO3	−1630
Carbon (Graphite)	Solid	C	0
Carbon (Diamond)	Solid	C	1.9
Carbon	Gas	C	716.67
Carbon dioxide	Gas	CO2	−393.509
Carbon disulfide	Liquid	CS2	89.41
Carbon disulfide	Gas	CS2	116.7
Carbon monoxide	Gas	CO	−110.525
Carbonyl chloride (Phosgene)	Gas	COCl2	−218.8
Carbon dioxide (un–ionized)	Aqueous	CO2(aq)	−419.26
Bicarbonate ion	Aqueous	HCO3–	−689.93
Carbonate ion	Aqueous	CO32–	−675.23
Monatomic chlorine	Gas	Cl	121.7
Chloride ion	Aqueous	Cl−	−167.2
Chlorine	Gas	Cl2	0
Chromium	Solid	Cr	0
Copper	Solid	Cu	0
Copper(II) bromide	Solid	CuBr2	−138.490
Copper(II) chloride	Solid	CuCl2	−217.986
Copper(II) oxide	Solid	CuO	−155.2
Copper(II) sulfate	Aqueous	CuSO4	−769.98
Fluorine	Gas	F2	0
Monatomic hydrogen	Gas	H	218
Hydrogen	Gas	H2	0
Water	Gas	H2O	−241.818
Water	Liquid	H2O	−285.8
Hydrogen ion	Aqueous	H+	0
Hydroxide ion	Aqueous	OH−	−230
Hydrogen peroxide	Liquid	H2O2	−187.8
Phosphoric acid	Liquid	H3PO4	−1288
Hydrogen cyanide	Gas	HCN	130.5
Hydrogen bromide	Liquid	HBr	−36.3
Hydrogen chloride	Gas	HCl	−92.30
Hydrogen chloride	Aqueous	HCl	−167.2
Hydrogen fluoride	Gas	HF	−273.3
Hydrogen iodide	Gas	HI	26.5
Iodine	Solid	I2	0
Iodine	Gas	I2	62.438
Iodine	Aqueous	I2	23
Iodide ion	Aqueous	I−	−55
Iron	Solid	Fe	0
Iron carbide (Cementite)	Solid	Fe3C	5.4
Iron(II) carbonate (Siderite)	Solid	FeCO3	−750.6
Iron(III) chloride	Solid	FeCl3	−399.4
Iron(II) oxide (Wüstite)	Solid	FeO	−272
Iron(II,III) oxide (Magnetite)	Solid	Fe3O4	−1118.4
Iron(III) oxide (Hematite)	Solid	Fe2O3	−824.2
Iron(II) sulfate	Solid	FeSO4	−929
Iron(III) sulfate	Solid	Fe2(SO4)3	−2583
Iron(II) sulfide	Solid	FeS	−102
Pyrite	Solid	FeS2	−178
Lead	Solid	Pb	0
Lead dioxide	Solid	PbO2	−277
Lead sulfide	Solid	PbS	−100
Lead sulfate	Solid	PbSO4	−920
Lead(II) nitrate	Solid	Pb(NO3)2	−452
Lead(II) sulfate	Solid	PbSO4	−920
Lithium fluoride	Solid	LiF	−616.93
Magnesium	Solid	Mg	0
Magnesium ion	Aqueous	Mg2+	−466.85
Magnesium carbonate	Solid	MgCO3	−1095.797
Magnesium chloride	Solid	MgCl2	−641.8
Magnesium hydroxide	Solid	Mg(OH)2	−924.54
Magnesium hydroxide	Aqueous	Mg(OH)2	−926.8
Magnesium oxide	Solid	MgO	−601.6
Magnesium sulfate	Solid	MgSO4	−1278.2
Manganese	Solid	Mn	0
Manganese(II) oxide	Solid	MnO	−384.9
Manganese(IV) oxide	Solid	MnO2	−519.7
Manganese(III) oxide	Solid	Mn2O3	−971
Manganese(II,III) oxide	Solid	Mn3O4	−1387
Permanganate	Aqueous	MnO− 4	−543
Mercury(II) oxide (red)	Solid	HgO	−90.83
Mercury sulfide (red, cinnabar)	Solid	HgS	−58.2
Nitrogen	Gas	N2	0
Ammonia (ammonium hydroxide)	Aqueous	NH3 (NH4OH)	−80.8
Ammonia	Gas	NH3	−46.1
Ammonium nitrate	Solid	NH4NO3	−365.6
Ammonium chloride	Solid	NH4Cl	−314.55
Nitrogen dioxide	Gas	NO2	33.2
Hydrazine	Gas	N2H4	95.4
Hydrazine	Liquid	N2H4	50.6
Nitrous oxide	Gas	N2O	82.05
Nitric oxide	Gas	NO	90.29
Dinitrogen tetroxide	Gas	N2O4	9.16
Dinitrogen pentoxide	Solid	N2O5	−43.1
Dinitrogen pentoxide	Gas	N2O5	11.3
Nitric acid	Aqueous	HNO3	−207
Monatomic oxygen	Gas	O	249
Oxygen	Gas	O2	0
Ozone	Gas	O3	143
White phosphorus	Solid	P4	0
Red phosphorus	Solid	P	−17.4
Black phosphorus	Solid	P	−39.3
Phosphorus trichloride	Liquid	PCl3	−319.7
Phosphorus trichloride	Gas	PCl3	−278
Phosphorus pentachloride	Solid	PCl5	−440
Phosphorus pentachloride	Gas	PCl5	−321
Phosphorus pentoxide	Solid	P2O5	−1505.5
Potassium bromide	Solid	KBr	−392.2
Potassium carbonate	Solid	K2CO3	−1150
Potassium chlorate	Solid	KClO3	−391.4
Potassium chloride	Solid	KCl	−436.68
Potassium fluoride	Solid	KF	−562.6
Potassium oxide	Solid	K2O	−363
Potassium nitrate	Solid	KNO3	−494.5
Potassium perchlorate	Solid	KClO4	−430.12
Silicon	Gas	Si	368.2
Silicon carbide	Solid	SiC	−74.4, −71.5
Silicon tetrachloride	Liquid	SiCl4	−640.1
Silica (Quartz)	Solid	SiO2	−910.86
Silver bromide	Solid	AgBr	−99.5
Silver chloride	Solid	AgCl	−127.01
Silver iodide	Solid	AgI	−62.4
Silver oxide	Solid	Ag2O	−31.1
Silver sulfide	Solid	Ag2S	−31.8
Sodium	Solid	Na	0
Sodium	Gas	Na	107.5
Sodium bicarbonate	Solid	NaHCO3	−950.8
Sodium carbonate	Solid	Na2CO3	−1130.77
Sodium chloride	Aqueous	NaCl	−407.27
Sodium chloride	Solid	NaCl	−411.12
Sodium chloride	Liquid	NaCl	−385.92
Sodium chloride	Gas	NaCl	−181.42
Sodium chlorate	Solid	NaClO3	−365.4
Sodium fluoride	Solid	NaF	−569.0
Sodium hydroxide	Aqueous	NaOH	−469.15
Sodium hydroxide	Solid	NaOH	−425.93
Sodium hypochlorite	Solid	NaOCl	−347.1
Sodium nitrate	Aqueous	NaNO3	−446.2
Sodium nitrate	Solid	NaNO3	−424.8
Sodium oxide	Solid	Na2O	−414.2
Sulfur (monoclinic)	Solid	S8	0.3
Sulfur (rhombic)	Solid	S8	0
Hydrogen sulfide	Gas	H2S	−20.63
Sulfur dioxide	Gas	SO2	−296.84
Sulfur trioxide	Gas	SO3	−395.7
Sulfuric acid	Liquid	H2SO4	−814
Titanium	Gas	Ti	468
Titanium tetrachloride	Gas	TiCl4	−763.2
Titanium tetrachloride	Liquid	TiCl4	−804.2
Titanium dioxide	Solid	TiO2	−944.7
Zinc	Gas	Zn	130.7
Zinc chloride	Solid	ZnCl2	−415.1
Zinc oxide	Solid	ZnO	−348.0
Zinc sulfate	Solid	ZnSO4	−980.14

Aliphatic hydrocarbons

Formula	Name	ΔfH⦵ /(kcal/mol)	ΔfH⦵ /(kJ/mol)
Straight-chain
CH4	Methane	−17.9	−74.9
C2H6	Ethane	−20.0	−83.7
C2H4	Ethylene	12.5	52.5
C2H2	Acetylene	54.2	226.8
C3H8	Propane	−25.0	−104.6
C4H10	n-Butane	−30.0	−125.5
C5H12	n-Pentane	−35.1	−146.9
C6H14	n-Hexane	−40.0	−167.4
C7H16	n-Heptane	−44.9	−187.9
C8H18	n-Octane	−49.8	−208.4
C9H20	n-Nonane	−54.8	−229.3
C10H22	n-Decane	−59.6	−249.4
C4 Alkane branched isomers
C4H10	Isobutane (methylpropane)	−32.1	−134.3
C5 Alkane branched isomers
C5H12	Neopentane (dimethylpropane)	−40.1	−167.8
C5H12	Isopentane (methylbutane)	−36.9	−154.4
C6 Alkane branched isomers
C6H14	2,2-Dimethylbutane	−44.5	−186.2
C6H14	2,3-Dimethylbutane	−42.5	−177.8
C6H14	2-Methylpentane (isohexane)	−41.8	−174.9
C6H14	3-Methylpentane	−41.1	−172.0
C7 Alkane branched isomers
C7H16	2,2-Dimethylpentane	−49.2	−205.9
C7H16	2,2,3-Trimethylbutane	−49.0	−205.0
C7H16	3,3-Dimethylpentane	−48.1	−201.3
C7H16	2,3-Dimethylpentane	−47.3	−197.9
C7H16	2,4-Dimethylpentane	−48.2	−201.7
C7H16	2-Methylhexane	−46.5	−194.6
C7H16	3-Methylhexane	−45.7	−191.2
C7H16	3-Ethylpentane	−45.3	−189.5
C8 Alkane branched isomers
C8H18	2,3-Dimethylhexane	−55.1	−230.5
C8H18	2,2,3,3-Tetramethylbutane	−53.9	−225.5
C8H18	2,2-Dimethylhexane	−53.7	−224.7
C8H18	2,2,4-Trimethylpentane (isooctane)	−53.5	−223.8
C8H18	2,5-Dimethylhexane	−53.2	−222.6
C8H18	2,2,3-Trimethylpentane	−52.6	−220.1
C8H18	3,3-Dimethylhexane	−52.6	−220.1
C8H18	2,4-Dimethylhexane	−52.4	−219.2
C8H18	2,3,4-Trimethylpentane	−51.9	−217.1
C8H18	2,3,3-Trimethylpentane	−51.7	−216.3
C8H18	2-Methylheptane	−51.5	−215.5
C8H18	3-Ethyl-3-Methylpentane	−51.4	−215.1
C8H18	3,4-Dimethylhexane	−50.9	−213.0
C8H18	3-Ethyl-2-Methylpentane	−50.4	−210.9
C8H18	3-Methylheptane	−60.3	−252.5
C8H18	4-Methylheptane	?	?
C8H18	3-Ethylhexane	?	?
C9 Alkane branched isomers (selected)
C9H20	2,2,4,4-Tetramethylpentane	−57.8	−241.8
C9H20	2,2,3,3-Tetramethylpentane	−56.7	−237.2
C9H20	2,2,3,4-Tetramethylpentane	−56.6	−236.8
C9H20	2,3,3,4-Tetramethylpentane	−56.4	−236.0
C9H20	3,3-Diethylpentane	−55.7	−233.0

Other organic compounds

Species	Phase	Chemical formula	ΔfH⦵ /(kJ/mol)
Acetone	Liquid	C3H6O	−248.4
Benzene	Liquid	C6H6	48.95
Benzoic acid	Solid	C7H6O2	−385.2
Carbon tetrachloride	Liquid	CCl4	−135.4
Carbon tetrachloride	Gas	CCl4	−95.98
Ethanol	Liquid	C2H5OH	−277.0
Ethanol	Gas	C2H5OH	−235.3
Glucose	Solid	C6H12O6	−1271
Isopropanol	Gas	C3H7OH	−318.1
Methanol (methyl alcohol)	Liquid	CH3OH	−238.4
Methanol (methyl alcohol)	Gas	CH3OH	−201.0
Methyl linoleate (Biodiesel)	Gas	C19H34O2	−356.3
Sucrose	Solid	C12H22O11	−2226.1
Trichloromethane (Chloroform)	Liquid	CHCl3	−134.47
Trichloromethane (Chloroform)	Gas	CHCl3	−103.18
Vinyl chloride	Solid	C2H3Cl	−94.12

See also

• Calorimetry
• Thermochemistry

References

• Zumdahl, Steven (2009). Chemical Principles (6th ed.). Boston. New York: Houghton Mifflin. pp. 384–387. ISBN 978-0-547-19626-8.

External links

• NIST Chemistry WebBook