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.[1] There is no standard temperature. Its symbol is Ξ”fH⦡. The superscript Plimsoll on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 Β°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.[2]

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 (kJ molβˆ’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 Ξ”fH⦡
298 K
.

Hess's 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's 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. Ξ”lattH corresponds to UL in the text. The downward arrow "electron affinity" shows the negative quantity –EAF, since EAF 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,

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

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

The sum of these enthalpies give the standard enthalpy of formation (ΔfH) 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:[3]

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:

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):

Applying Hess's law,

Solving for the standard of enthalpy of formation,

The value of is determined to be βˆ’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, Ξ½) 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:[4]

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, :

However 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 Ξ”H stays the same, but the sign changes.
  • When the balanced equation for a reaction is multiplied by an integer, the corresponding value of Ξ”H 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 Β°C

Thermochemical properties of selected substances at 298.15 K and 1 atm

Inorganic substances

Species Phase Chemical formula Ξ”fH⦡ /(kJ/mol)
Aluminium Solid Al 0
Aluminium chloride Solid AlCl3 βˆ’705.63
Aluminium oxide Solid Al2O3 βˆ’1675.5
Aluminium hydroxide Solid Al(OH)3 βˆ’1277
Aluminium sulphate Solid Al2(SO4)3 βˆ’3440
Barium chloride Solid BaCl2 βˆ’858.6
Barium carbonate Solid BaCO3 βˆ’1216
Barium hydroxide Solid Ba(OH)2 βˆ’944.7
Barium oxide Solid BaO βˆ’548.1
Barium sulfate Solid BaSO4 βˆ’1473.3
Beryllium Solid Be 0
Beryllium hydroxide Solid Be(OH)2 βˆ’903
Beryllium oxide Solid BeO βˆ’609.4
Boron trichloride Solid BCl3 βˆ’402.96
Bromine Liquid Br2 0
Bromide ion Aqueous Brβˆ’ βˆ’121
Bromine Gas Br 111.884
Bromine Gas Br2 30.91
Bromine trifluoride Gas BrF3 βˆ’255.60
Hydrogen bromide Gas HBr βˆ’36.29
Cadmium Solid Cd 0
Cadmium oxide Solid CdO βˆ’258
Cadmium hydroxide Solid Cd(OH)2 βˆ’561
Cadmium sulfide Solid CdS βˆ’162
Cadmium sulfate Solid CdSO4 βˆ’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 βˆ’443.04
Calcium Solid Ca 0
Calcium Gas Ca 178.2
Calcium(II) ion Gas Ca2+ 1925.90
Calcium(II) ion Aqueous Ca2+ βˆ’542.7
Calcium carbide Solid CaC2 βˆ’59.8
Calcium carbonate (Calcite) Solid CaCO3 βˆ’1206.9
Calcium chloride Solid CaCl2 βˆ’795.8
Calcium chloride Aqueous CaCl2 βˆ’877.3
Calcium phosphate Solid Ca3(PO4)2 βˆ’4132
Calcium fluoride Solid CaF2 βˆ’1219.6
Calcium hydride Solid CaH2 βˆ’186.2
Calcium hydroxide Solid Ca(OH)2 βˆ’986.09
Calcium hydroxide Aqueous Ca(OH)2 βˆ’1002.82
Calcium oxide Solid CaO βˆ’635.09
Calcium sulfate Solid CaSO4 βˆ’1434.52
Calcium sulfide Solid CaS βˆ’482.4
Wollastonite Solid CaSiO3 βˆ’1630
Carbon (Graphite) Solid C 0
Carbon (Diamond) Solid C 1.9
Carbon Gas C 716.67
Carbon dioxide Gas CO2 βˆ’393.509
Carbon disulfide Liquid CS2 89.41
Carbon disulfide Gas CS2 116.7
Carbon monoxide Gas CO βˆ’110.525
Carbonyl chloride (Phosgene) Gas COCl2 βˆ’218.8
Carbon dioxide (un–ionized) Aqueous CO2(aq) βˆ’419.26
Bicarbonate ion Aqueous HCO3– βˆ’689.93
Carbonate ion Aqueous CO32– βˆ’675.23
Monatomic chlorine Gas Cl 121.7
Chloride ion Aqueous Clβˆ’ βˆ’167.2
Chlorine Gas Cl2 0
Chromium Solid Cr 0
Copper Solid Cu 0
Copper(II) bromide Solid CuBr2 βˆ’138.490
Copper(II) chloride Solid CuCl2 βˆ’217.986
Copper(II) oxide Solid CuO βˆ’155.2
Copper(II) sulfate Aqueous CuSO4 βˆ’769.98
Fluorine Gas F2 0
Monatomic hydrogen Gas H 218
Hydrogen Gas H2 0
Water Gas H2O βˆ’241.818
Water Liquid H2O βˆ’285.8
Hydrogen ion Aqueous H+ 0
Hydroxide ion Aqueous OHβˆ’ βˆ’230
Hydrogen peroxide Liquid H2O2 βˆ’187.8
Phosphoric acid Liquid H3PO4 βˆ’1288
Hydrogen cyanide Gas HCN 130.5
Hydrogen bromide Liquid HBr βˆ’36.3
Hydrogen chloride Gas HCl βˆ’92.30
Hydrogen chloride Aqueous HCl βˆ’167.2
Hydrogen fluoride Gas HF βˆ’273.3
Hydrogen iodide Gas HI 26.5
Iodine Solid I2 0
Iodine Gas I2 62.438
Iodine Aqueous I2 23
Iodide ion Aqueous Iβˆ’ βˆ’55
Iron Solid Fe 0
Iron carbide (Cementite) Solid Fe3C 5.4
Iron(II) carbonate (Siderite) Solid FeCO3 βˆ’750.6
Iron(III) chloride Solid FeCl3 βˆ’399.4
Iron(II) oxide (WΓΌstite) Solid FeO βˆ’272
Iron(II,III) oxide (Magnetite) Solid Fe3O4 βˆ’1118.4
Iron(III) oxide (Hematite) Solid Fe2O3 βˆ’824.2
Iron(II) sulfate Solid FeSO4 βˆ’929
Iron(III) sulfate Solid Fe2(SO4)3 βˆ’2583
Iron(II) sulfide Solid FeS βˆ’102
Pyrite Solid FeS2 βˆ’178
Lead Solid Pb 0
Lead dioxide Solid PbO2 βˆ’277
Lead sulfide Solid PbS βˆ’100
Lead sulfate Solid PbSO4 βˆ’920
Lead(II) nitrate Solid Pb(NO3)2 βˆ’452
Lead(II) sulfate Solid PbSO4 βˆ’920
Lithium fluoride Solid LiF βˆ’616.93
Magnesium Solid Mg 0
Magnesium ion Aqueous Mg2+ βˆ’466.85
Magnesium carbonate Solid MgCO3 βˆ’1095.797
Magnesium chloride Solid MgCl2 βˆ’641.8
Magnesium hydroxide Solid Mg(OH)2 βˆ’924.54
Magnesium hydroxide Aqueous Mg(OH)2 βˆ’926.8
Magnesium oxide Solid MgO βˆ’601.6
Magnesium sulfate Solid MgSO4 βˆ’1278.2
Manganese Solid Mn 0
Manganese(II) oxide Solid MnO βˆ’384.9
Manganese(IV) oxide Solid MnO2 βˆ’519.7
Manganese(III) oxide Solid Mn2O3 βˆ’971
Manganese(II,III) oxide Solid Mn3O4 βˆ’1387
Permanganate Aqueous MnOβˆ’
4
βˆ’543
Mercury(II) oxide (red) Solid HgO βˆ’90.83
Mercury sulfide (red, cinnabar) Solid HgS βˆ’58.2
Nitrogen Gas N2 0
Ammonia (ammonium hydroxide) Aqueous NH3 (NH4OH) βˆ’80.8
Ammonia Gas NH3 βˆ’46.1
Ammonium nitrate Solid NH4NO3 βˆ’365.6
Ammonium chloride Solid NH4Cl βˆ’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 βˆ’43.1
Dinitrogen pentoxide Gas N2O5 11.3
Nitric acid Aqueous HNO3 βˆ’207
Monatomic oxygen Gas O 249
Oxygen Gas O2 0
Ozone Gas O3 143
White phosphorus Solid P4 0
Red phosphorus Solid P βˆ’17.4[5]
Black phosphorus Solid P βˆ’39.3[5]
Phosphorus trichloride Liquid PCl3 βˆ’319.7
Phosphorus trichloride Gas PCl3 βˆ’278
Phosphorus pentachloride Solid PCl5 βˆ’440
Phosphorus pentachloride Gas PCl5 βˆ’321
Phosphorus pentoxide Solid P2O5 βˆ’1505.5[6]
Potassium bromide Solid KBr βˆ’392.2
Potassium carbonate Solid K2CO3 βˆ’1150
Potassium chlorate Solid KClO3 βˆ’391.4
Potassium chloride Solid KCl βˆ’436.68
Potassium fluoride Solid KF βˆ’562.6
Potassium oxide Solid K2O βˆ’363
Potassium nitrate Solid KNO3 βˆ’494.5
Potassium perchlorate Solid KClO4 βˆ’430.12
Silicon Gas Si 368.2
Silicon carbide Solid SiC βˆ’74.4,[7] βˆ’71.5[8]
Silicon tetrachloride Liquid SiCl4 βˆ’640.1
Silica (Quartz) Solid SiO2 βˆ’910.86
Silver bromide Solid AgBr βˆ’99.5
Silver chloride Solid AgCl βˆ’127.01
Silver iodide Solid AgI βˆ’62.4
Silver oxide Solid Ag2O βˆ’31.1
Silver sulfide Solid Ag2S βˆ’31.8
Sodium Solid Na 0
Sodium Gas Na 107.5
Sodium bicarbonate Solid NaHCO3 βˆ’950.8
Sodium carbonate Solid Na2CO3 βˆ’1130.77
Sodium chloride Aqueous NaCl βˆ’407.27
Sodium chloride Solid NaCl βˆ’411.12
Sodium chloride Liquid NaCl βˆ’385.92
Sodium chloride Gas NaCl βˆ’181.42
Sodium chlorate Solid NaClO3 βˆ’365.4
Sodium fluoride Solid NaF βˆ’569.0
Sodium hydroxide Aqueous NaOH βˆ’469.15
Sodium hydroxide Solid NaOH βˆ’425.93
Sodium hypochlorite Solid NaOCl βˆ’347.1
Sodium nitrate Aqueous NaNO3 βˆ’446.2
Sodium nitrate Solid NaNO3 βˆ’424.8
Sodium oxide Solid Na2O βˆ’414.2
Sulfur (monoclinic) Solid S8 0.3
Sulfur (rhombic) Solid S8 0
Hydrogen sulfide Gas H2S βˆ’20.63
Sulfur dioxide Gas SO2 βˆ’296.84
Sulfur trioxide Gas SO3 βˆ’395.7
Sulfuric acid Liquid H2SO4 βˆ’814
Titanium Gas Ti 468
Titanium tetrachloride Gas TiCl4 βˆ’763.2
Titanium tetrachloride Liquid TiCl4 βˆ’804.2
Titanium dioxide Solid TiO2 βˆ’944.7
Zinc Gas Zn 130.7
Zinc chloride Solid ZnCl2 βˆ’415.1
Zinc oxide Solid ZnO βˆ’348.0
Zinc sulfate Solid ZnSO4 βˆ’980.14

Aliphatic hydrocarbons

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

Other organic compounds

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

See also

References

  1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "standard pressure". doi:10.1351/goldbook.S05921
  2. ^ Oxtoby, David W; Pat Gillis, H; Campion, Alan (2011). Principles of Modern Chemistry. Cengage Learning. p. 547. ISBN 978-0-8400-4931-5.
  3. ^ Moore, Stanitski, and Jurs. Chemistry: The Molecular Science. 3rd edition. 2008. ISBN 0-495-10521-X. pages 320–321.
  4. ^ "Enthalpies of Reaction". www.science.uwaterloo.ca. Archived from the original on 25 October 2017. Retrieved 2 May 2018.
  5. ^ a b Housecroft, C. E.; Sharpe, A. G. (2004). Inorganic Chemistry (2nd ed.). Prentice Hall. p. 392. ISBN 978-0-13-039913-7.
  6. ^ Green, D.W., ed. (2007). Perry's Chemical Engineers' Handbook (8th ed.). Mcgraw-Hill. pp. 2–191. ISBN 9780071422949.
  7. ^ Kleykamp, H. (1998). "Gibbs Energy of Formation of SiC: A contribution to the Thermodynamic Stability of the Modifications". Berichte der Bunsengesellschaft fΓΌr physikalische Chemie. 102 (9): 1231–1234. doi:10.1002/bbpc.19981020928.
  8. ^ "Silicon Carbide, Alpha (SiC)". March 1967. Retrieved 5 February 2019.
  • Zumdahl, Steven (2009). Chemical Principles (6th ed.). Boston. New York: Houghton Mifflin. pp. 384–387. ISBN 978-0-547-19626-8.

External links