Standard enthalpy of formation

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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, with all substances in their standard states, and at a pressure of 1 bar (100 kPa). 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). Standard states are as follows:

  1. For a gas: the hypothetical state it would have assuming it obeyed the ideal gas equation at a pressure of 1 atm
  2. For a solute present in an ideal solution: a concentration of exactly one mole per liter (1 M) at a pressure of 1 atm
  3. 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 atm
  4. For an element: the form in which the element is most stable under 1 atm of pressure. One exception is phosphorus, for which the most stable form at 1 atm is black phosphorus, but white phosphorus is chosen as the standard reference state for zero enthalpy of formation.[1]

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)

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).

In physics the energy per particle is often expressed in electronvolts (eV), where 1 eV corresponds to 96.485 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 formation reaction is a constant pressure and constant temperature process. Since the pressure of the standard formation reaction is fixed at 1 atm, 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[edit]

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[edit]

Standard enthalpy change of formation in Born–Haber diagram for lithium fluoride.

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,

Li(s) + 12 F2(g) → LiF(s)

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

  1. The standard enthalpy of atomization (or sublimation) of solid lithium
  2. The first ionization energy of gaseous lithium
  3. The standard enthalpy of atomization (or bond energy) of fluorine gas
  4. The electron affinity of a fluorine atom
  5. The lattice energy of lithium fluoride

The sum of all these enthalpies will 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 in order to evaluate the lattice energy.[2]

Organic compounds[edit]

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 mesurable using bomb calorimetry. The standard enthalpy of formation is then determined using Hess's law. The combustion of methane (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 and water:

CH4 → C + 2 H2
C + O2 → CO2
2 H2 + O2 → 2 H2O

Applying Hess's law,

ΔcombH(CH4) = [ΔfH(CO2) + 2 ΔfH(H2O)] – ΔfH(CH4)

Solving for the standard of enthalpy of formation,

ΔfH(CH4) = [ΔfH(CO2) + 2 ΔfH(H2O)] – ΔcombH(CH4)

The value of ΔfH(CH4) is determined to be –74.8 kJ mol−1. The negative sign 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 heats of formation for simple unstrained organic compounds with the Heat of formation group additivity method.

Use in calculation for other reactions[edit]

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:

ΔrH = Σν ΔfH(products) − Σν ΔfH(reactants)[3]

If the standard enthalpy of the products is less than the standard enthalpy of the reactants, the standard enthalpy of reaction will be negative. This implies that the reaction is exothermic. The converse is also true; the standard enthalpy of reaction will be 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 + 2 O2 → CO2 + 2 H2O:

ΔrH = [ΔfH(CO2) + 2 ΔfH(H2O)] – [ΔfH(CH4) + 2 ΔfH(O2)]

However O2 is an element in its standard state, so that ΔfH(O2) = 0 and the heat of reaction is simplified to

ΔrH = [ΔfH(CO2) + 2 ΔfH(H2O)] – ΔfH(CH4),

which is the equation in the previous section for the enthalpy of combustion ΔcombH.

Key concepts for doing enthalpy calculations[edit]

  1. When a reaction is reversed, the magnitude of ΔH stays the same, but the sign changes.
  2. 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.
  3. The change in enthalpy for a reaction can be calculated from the enthalpies of formation of the reactants and the products
  4. 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[edit]

Thermochemical properties of selected substances at 298 K and 1 atm

Inorganic substances[edit]

Species Phase Chemical formula ΔfH /(kJ/mol)
Aluminium
Aluminium Solid Al 0
Aluminium chloride Solid AlCl3 −705.63
Aluminium oxide Solid Al2O3 −1669.8
Aluminium hydroxide Solid Al(OH)3 −1277
Aluminium sulphate Solid Al2(SO4)3 −3440
Ammonia (ammonium hydroxide) Aqueous NH3 (NH4OH) −80.8
Ammonia Gas NH3 −46.1
Ammonium nitrate Solid NH4NO3 −365.6
Barium
Barium chloride Solid BaCl2 −858.6
Barium carbonate Solid BaCO3 −1213
Barium hydroxide Solid Ba(OH)2 −944.7
Barium oxide Solid BaO −548.1
Barium sulfate Solid BaSO4 −1473.2
Beryllium
Beryllium Solid Be 0
Beryllium hydroxide Solid Be(OH)2 −902.9999
Beryllium oxide Solid BeO −609.4(25)
Boron
Boron trichloride Solid BCl3 −402.96
Bromine
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
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
Calcium
Calcium Solid Ca 0
Calcium Gas Ca 178.2
Calcium(II) ion Gas Ca2+ 1925.90
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
Caesium
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
Carbon
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
Chlorine
Monatomic chlorine Gas Cl 121.7
Chloride ion Aqueous Cl −167.2
Chlorine Gas Cl2 0
Chromium
Chromium Solid Cr 0
Copper
Copper Solid Cu 0
Copper(II) oxide Solid CuO −155.2
Copper(II) sulfate Aqueous CuSO4 −769.98
Fluorine
Fluorine Gas F2 0
Hydrogen
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
Iodine Solid I2 0
Iodine Gas I2 62.438
Iodine Aqueous I2 23
Iodide ion Aqueous I −55
Iron
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
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
Magnesium
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
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
Mercury(II) oxide (red) Solid HgO −90.83
Mercury sulfide (red, cinnabar) Solid HgS −58.2
Nitrogen
Ammonia Aqueous NH3 −80.8
Ammonia Gas NH3 −45.90
Ammonium chloride Solid NH4Cl −314.55
Nitrogen dioxide Gas NO2 33.2
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
Oxygen
Monatomic oxygen Gas O 249
Oxygen Gas O2 0
Ozone Gas O3 143
Phosphorus
White phosphorus Solid P4 0
Red phosphorus Solid P –17.4[4]
Black phosphorus Solid P –39.3[4]
Phosphorus trichloride Liquid PCl3 −319.7
Phosphorus trichloride Gas PCl3 −278
Phosphorus pentachloride Solid PCl5 −440
Potassium
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 perchlorate Solid KClO4 −430.12
Silicon
Silicon Gas Si 368.2
Silicon carbide Solid SiC −73.22
Silicon tetrachloride Liquid SiCl4 −640.1
Silica (Quartz) Solid SiO2 −910.86
Silver
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
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 fluoride Solid NaF −569.0
Sodium hydroxide Aqueous NaOH −469.15
Sodium hydroxide Solid NaOH −425.93
Sodium nitrate Aqueous NaNO3 −446.2
Sodium nitrate Solid NaNO3 −424.8
Sodium oxide Solid Na2O −414.2
Sulfur
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
Tin
Titanium
Titanium Gas Ti 468
Titanium tetrachloride Gas TiCl4 −763.2
Titanium tetrachloride Liquid TiCl4 −804.2
Titanium dioxide Solid TiO2 −944.7
Zinc
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[edit]

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[edit]

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[edit]

References[edit]

  1. ^ Oxtoby, David W; Pat Gillis, H; Campion, Alan (2011). Principles of Modern Chemistry. p. 547. ISBN 0-8400-4931-5. 
  2. ^ Moore, Stanitski, and Jurs. Chemistry: The Molecular Science. 3rd edition. 2008. ISBN 0-495-10521-X. pages 320-321.
  3. ^ http://www.science.uwaterloo.ca/~cchieh/cact/c120/heatreac.html
  4. ^ a b Housecroft, C. E.; Sharpe, A. G. (2004). Inorganic Chemistry (2nd ed.). Prentice Hall. p. 392. ISBN 978-0130399137. 
  • Zumdahl, Steven (2009). Chemical Principles (6th ed.). Boston. New York: Houghton Mifflin. pp. 384–387. ISBN 978-0-547-19626-8. 

External links[edit]