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 from the formation of 1 mole of the compound from its constituent elements, with all substances in their standard states at 101.3 kPa and 298 K. Its symbol is ΔHfO or ΔfHO. The superscript theta (zero) on this symbol indicates that the process has been carried out under standard conditions. Standard States are as follows:

  1. For a gas: standard state is a pressure of exactly 1 atmosphere
  2. For a substance present in a solution: a concentration of exactly 1 M at a pressure of 1 atm
  3. For a pure substance in a condensed state (a liquid or a solid): 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 and the specified temperature. (Usually 25 degrees Celsius or 298.15 K) One exception is phosphorus: most stable under 1 atm is black phosphorus, but white phosphorus is used as the reference 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)

Note that 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. Most are defined in kilojoules per mole (kJ mol−1), but can also be measured in calories per mole, joules per mole or kilocalories 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 which corresponds to about 100 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.

Mechanics[edit]

The standard enthalpy of formation is equivalent to the sum of many separate processes included in the Born-Haber cycle of synthesis reactions. For example, to calculate the standard enthalpy of formation of sodium chloride, we use the following reaction:

Na(s) + (1/2)Cl2(g) → NaCl(s)

This process is made of many separate sub-processes, each with their own enthalpies. Therefore, we must take into account:

Standard enthalpy change of formation Born-Haber diagram for lithium fluoride.
  1. The standard enthalpy of atomization of solid sodium
  2. The first ionization energy of gaseous sodium
  3. The standard enthalpy of atomization of chlorine gas
  4. The electron affinity of chlorine atoms
  5. The lattice enthalpy of sodium chloride

The sum of all these values will give the standard enthalpy of formation of sodium chloride.

Additionally, applying Hess's Law shows that the sum of the individual reactions corresponding to the enthalpy change of formation for each substance in the reaction is equal to the enthalpy change of the overall reaction, regardless of the number of steps or intermediate reactions involved. This is because enthalpy is a state function. In the example above the standard enthalpy change of formation for sodium chloride is equal to the sum of the standard enthalpy change of formation for each of the steps involved in the process. This is especially useful for very long reactions with many intermediate steps and compounds.

Chemists may use standard enthalpies of formation for a reaction that is hypothetical. For instance carbon and hydrogen will not directly react to form methane, yet the standard enthalpy of formation for methane is determined to be -74.8 kJ mol−1 from using other known standard enthalpies of reaction with Hess's law. That it is negative 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 heat of formations for simple unstrained organic compounds with the Heat of formation group additivity method.

Standard enthalpy of reaction[edit]

The standard enthalpy of formation is used in thermochemistry to find the standard enthalpy change of reaction. This is done by subtracting the sum of the standard enthalpies of formation of the reactants (each being multiplied by its respective stoichiometric coefficient, ν) from 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:

ΔH° = Σ(ν × ΔHf°) (products) - Σ(ν × ΔHf°) (reactants)

For example, for the reaction CH4 + 2 O2 → CO2 + 2 H2O:

ΔHr° = [(1 × ΔHf°(CO2)) + (2 × ΔHf°(H2O))] (products) - [(1 × ΔHf°(CH4)) + (2 × ΔHf°(O2))] (reactants)

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.

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 are not included in the enthalpy calculations for the reaction since the enthalpy of an element in its standard state is zero.

Subcategories[edit]

Examples: Inorganic compounds (at 25°C, 298 K)[edit]

Chemical CompoundPhase (matter)Chemical formulaΔ Hf0 in kJ/mol
Ammonia (Ammonium Hydroxide)aqNH3 (NH4OH)-80.8
AmmoniagNH3-46.1
Copper (II) sulfateaqCuSO4-769.98
Sodium carbonatesNa2CO3-1131
Sodium chloride (table salt)aqNaCl-407
Sodium chloride (table salt)sNaCl-411.12
Sodium chloride (table salt)lNaCl-385.92
Sodium chloride (table salt)gNaCl-181.42
Sodium hydroxideaqNaOH-470.1
Sodium hydroxidesNaOH-426.7
Sodium nitrateaqNaNO3-446.2
Sodium nitratesNaNO3-424.8
Sulfur dioxidegSO2-297
Sulfuric acidlH2SO4-814
SilicasSiO2-911
Nitrogen dioxidegNO2+33.2
Nitrogen monoxidegNO+91.3
WaterlH2O-285.8
WatergH2O-241.82
Carbon dioxide(CO2)gCO2-393.5
HydrogengH20
FluorinegF20
ChlorinegCl20
BrominelBr20
BrominegBr2+31
IodinesI20
IodinegI2+62
Zinc sulfatesZnSO4-980.14
(State: g = gaseous; l = liquid; s = solid; aq = aqueous)

See also[edit]

External links[edit]

References[edit]

[2]

  1. ^ Principles of Modern Chemistry 547p
  2. ^ Zumdahl, Steven (2009). Chemical Principles, Ed. 6 p. 384-387. Houghton Mifflin, Boston. New York. ISBN 978-0-547-19626-8.