Standard enthalpy of formation

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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 ΔfH. 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).

Contents

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 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 ΔfH
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. DlattH corresponds to UL in the text. The downward arrow "electron affinity" shows the negative quantity -EAF, since EAF is usually defined as positive. Born-haber cycle LiF.svg
Standard enthalpy change of formation in Born–Haber diagram for lithium fluoride. ΔlattH 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 −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: [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

Examples: standard enthalpies of formation at 25 °C

Thermochemical properties of selected substances at 298.15 K and 1 atm

Inorganic substances

SpeciesPhaseChemical formulaΔfH /(kJ/mol)
Aluminium SolidAl0
Aluminium chloride SolidAlCl3−705.63
Aluminium oxide SolidAl2O3−1675.5
Aluminium hydroxide SolidAl(OH)3−1277
Aluminium sulphate SolidAl2(SO4)3−3440
Barium chloride SolidBaCl2−858.6
Barium carbonate SolidBaCO3−1216
Barium hydroxide SolidBa(OH)2−944.7
Barium oxide SolidBaO−548.1
Barium sulfate SolidBaSO4−1473.3
Beryllium SolidBe0
Beryllium hydroxide SolidBe(OH)2−903
Beryllium oxide SolidBeO−609.4
Boron trichloride SolidBCl3−402.96
Bromine LiquidBr20
Bromide ion AqueousBr−121
Bromine GasBr111.884
Bromine GasBr230.91
Bromine trifluoride GasBrF3−255.60
Hydrogen bromide GasHBr−36.29
Cadmium SolidCd0
Cadmium oxide SolidCdO−258
Cadmium hydroxide SolidCd(OH)2−561
Cadmium sulfide SolidCdS−162
Cadmium sulfate SolidCdSO4−935
Caesium SolidCs0
Caesium GasCs76.50
Caesium LiquidCs2.09
Caesium(I) ionGasCs+457.964
Caesium chloride SolidCsCl−443.04
Calcium SolidCa0
Calcium GasCa178.2
Calcium(II) ionGasCa2+1925.90
Calcium(II) ionAqueousCa2+−542.7
Calcium carbide SolidCaC2−59.8
Calcium carbonate (Calcite)SolidCaCO3−1206.9
Calcium chloride SolidCaCl2−795.8
Calcium chloride AqueousCaCl2−877.3
Calcium phosphate SolidCa3(PO4)2−4132
Calcium fluoride SolidCaF2−1219.6
Calcium hydride SolidCaH2−186.2
Calcium hydroxide SolidCa(OH)2−986.09
Calcium hydroxide AqueousCa(OH)2−1002.82
Calcium oxide SolidCaO−635.09
Calcium sulfate SolidCaSO4−1434.52
Calcium sulfide SolidCaS−482.4
Wollastonite SolidCaSiO3−1630
Carbon (Graphite)SolidC0
Carbon (Diamond)SolidC1.9
Carbon GasC716.67
Carbon dioxide GasCO2−393.509
Carbon disulfide LiquidCS289.41
Carbon disulfide GasCS2116.7
Carbon monoxide GasCO−110.525
Carbonyl chloride (Phosgene)GasCOCl2−218.8
Carbon dioxide (un–ionized)AqueousCO2(aq)−419.26
Bicarbonate ionAqueousHCO3−689.93
Carbonate ionAqueousCO32–−675.23
Monatomic chlorineGasCl121.7
Chloride ionAqueousCl−167.2
Chlorine GasCl20
Chromium SolidCr0
Copper SolidCu0
Copper(II) bromide SolidCuBr2−138.490
Copper(II) chloride SolidCuCl2−217.986
Copper(II) oxide SolidCuO−155.2
Copper(II) sulfate AqueousCuSO4−769.98
Fluorine GasF20
Monatomic hydrogenGasH218
Hydrogen GasH20
Water GasH2O−241.818
Water LiquidH2O−285.8
Hydrogen ion AqueousH+0
Hydroxide ion AqueousOH−230
Hydrogen peroxide LiquidH2O2−187.8
Phosphoric acid LiquidH3PO4−1288
Hydrogen cyanide GasHCN130.5
Hydrogen bromide LiquidHBr−36.3
Hydrogen chloride GasHCl−92.30
Hydrogen chloride AqueousHCl−167.2
Hydrogen fluoride GasHF−273.3
Hydrogen iodide GasHI26.5
Iodine SolidI20
Iodine GasI262.438
Iodine AqueousI223
Iodide ionAqueousI−55
Iron SolidFe0
Iron carbide (Cementite)SolidFe3C5.4
Iron(II) carbonate (Siderite)SolidFeCO3−750.6
Iron(III) chloride SolidFeCl3−399.4
Iron(II) oxide (Wüstite)SolidFeO−272
Iron(II,III) oxide (Magnetite)SolidFe3O4−1118.4
Iron(III) oxide (Hematite)SolidFe2O3−824.2
Iron(II) sulfate SolidFeSO4−929
Iron(III) sulfate SolidFe2(SO4)3−2583
Iron(II) sulfide SolidFeS−102
Pyrite SolidFeS2−178
Lead SolidPb0
Lead dioxide SolidPbO2−277
Lead sulfide SolidPbS−100
Lead sulfate SolidPbSO4−920
Lead(II) nitrate SolidPb(NO3)2−452
Lead(II) sulfate SolidPbSO4−920
Lithium fluoride SolidLiF−616.93
Magnesium SolidMg0
Magnesium ionAqueousMg2+−466.85
Magnesium carbonate SolidMgCO3−1095.797
Magnesium chloride SolidMgCl2−641.8
Magnesium hydroxide SolidMg(OH)2−924.54
Magnesium hydroxide AqueousMg(OH)2−926.8
Magnesium oxide SolidMgO−601.6
Magnesium sulfate SolidMgSO4−1278.2
Manganese SolidMn0
Manganese(II) oxide SolidMnO−384.9
Manganese(IV) oxide SolidMnO2−519.7
Manganese(III) oxide SolidMn2O3−971
Manganese(II,III) oxide SolidMn3O4−1387
Permanganate AqueousMnO
4
−543
Mercury(II) oxide (red)SolidHgO−90.83
Mercury sulfide (red, cinnabar)SolidHgS−58.2
Nitrogen GasN20
Ammonia (ammonium hydroxide)AqueousNH3 (NH4OH)−80.8
AmmoniaGasNH3−46.1
Ammonium nitrate SolidNH4NO3−365.6
Ammonium chloride SolidNH4Cl−314.55
Nitrogen dioxide GasNO233.2
Hydrazine GasN2H495.4
Hydrazine LiquidN2H450.6
Nitrous oxide GasN2O82.05
Nitric oxide GasNO90.29
Dinitrogen tetroxide GasN2O49.16
Dinitrogen pentoxide SolidN2O5−43.1
Dinitrogen pentoxide GasN2O511.3
Nitric acid AqueousHNO3−207
Monatomic oxygenGasO249
Oxygen GasO20
Ozone GasO3143
White phosphorus SolidP40
Red phosphorus SolidP−17.4 [5]
Black phosphorus SolidP−39.3 [5]
Phosphorus trichloride LiquidPCl3−319.7
Phosphorus trichloride GasPCl3−278
Phosphorus pentachloride SolidPCl5−440
Phosphorus pentachloride GasPCl5−321
Phosphorus pentoxide SolidP2O5−1505.5 [6]
Potassium bromide SolidKBr−392.2
Potassium carbonate SolidK2CO3−1150
Potassium chlorate SolidKClO3−391.4
Potassium chloride SolidKCl−436.68
Potassium fluoride SolidKF−562.6
Potassium oxide SolidK2O−363
Potassium nitrate SolidKNO3−494.5
Potassium perchlorate SolidKClO4−430.12
Silicon GasSi368.2
Silicon carbide SolidSiC−74.4, [7] −71.5 [8]
Silicon tetrachloride LiquidSiCl4−640.1
Silica (Quartz)SolidSiO2−910.86
Silver bromide SolidAgBr−99.5
Silver chloride SolidAgCl−127.01
Silver iodide SolidAgI−62.4
Silver oxide SolidAg2O−31.1
Silver sulfide SolidAg2S−31.8
Sodium SolidNa0
SodiumGasNa107.5
Sodium bicarbonate SolidNaHCO3−950.8
Sodium carbonate SolidNa2CO3−1130.77
Sodium chloride AqueousNaCl−407.27
Sodium chloride SolidNaCl−411.12
Sodium chloride LiquidNaCl−385.92
Sodium chloride GasNaCl−181.42
Sodium chlorate SolidNaClO3−365.4
Sodium fluoride SolidNaF−569.0
Sodium hydroxide AqueousNaOH−469.15
Sodium hydroxide SolidNaOH−425.93
Sodium hypochlorite SolidNaOCl−347.1
Sodium nitrate AqueousNaNO3−446.2
Sodium nitrate SolidNaNO3−424.8
Sodium oxide SolidNa2O−414.2
Sulfur (monoclinic)SolidS80.3
Sulfur (rhombic)SolidS80
Hydrogen sulfide GasH2S−20.63
Sulfur dioxide GasSO2−296.84
Sulfur trioxide GasSO3−395.7
Sulfuric acid LiquidH2SO4−814
Titanium GasTi468
Titanium tetrachloride GasTiCl4−763.2
Titanium tetrachloride LiquidTiCl4−804.2
Titanium dioxide SolidTiO2−944.7
Zinc GasZn130.7
Zinc chloride SolidZnCl2−415.1
Zinc oxide SolidZnO−348.0
Zinc sulfate SolidZnSO4−980.14

Aliphatic hydrocarbons

FormulaNameΔfH /(kcal/mol)ΔfH /(kJ/mol)
Straight-chain
CH4 Methane −17.9−74.9
C2H6 Ethane −20.0−83.7
C2H4 Ethylene 12.552.5
C2H2 Acetylene 54.2226.8
C3H8 Propane −25.0−104.6
C4H10n-Butane −30.0−125.5
C5H12n-Pentane −35.1−146.9
C6H14n-Hexane −40.0−167.4
C7H16n-Heptane −44.9−187.9
C8H18n-Octane −49.8−208.4
C9H20n-Nonane −54.8−229.3
C10H22n-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

SpeciesPhaseChemical formulaΔfH /(kJ/mol)
Acetone LiquidC3H6O−248.4
Benzene LiquidC6H648.95
Benzoic acid SolidC7H6O2−385.2
Carbon tetrachloride LiquidCCl4−135.4
Carbon tetrachloride GasCCl4−95.98
Ethanol LiquidC2H5OH−277.0
Ethanol GasC2H5OH−235.3
Glucose SolidC6H12O6−1271
Isopropanol GasC3H7OH−318.1
Methanol (methyl alcohol)LiquidCH3OH−238.4
Methanol (methyl alcohol)GasCH3OH−201.0
Methyl linoleate (Biodiesel)GasC19H34O2−356.3
Sucrose SolidC12H22O11−2226.1
Trichloromethane (Chloroform)LiquidCHCl3−134.47
Trichloromethane (Chloroform)GasCHCl3−103.18
Vinyl chloride SolidC2H3Cl−94.12

See also

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