In
chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
and
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...
, the standard enthalpy of formation or standard heat of formation of a
compound is the change of
enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
during the formation of 1
mole of the substance from its constituent
elements in their reference state, with all substances in their
standard state
In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. A superscript circle ° (degree symbol) or a Plimsoll (⦵) character is use ...
s. The standard
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
value is recommended by
IUPAC
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
, although prior to 1982 the value 1.00
atm (101.325 kPa) was used. There is no standard temperature. Its symbol is . 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:
# For a gas: the hypothetical state it would have assuming it obeyed the
ideal gas equation at a pressure of 1 bar
# For a gaseous or solid
solute present in a diluted
ideal solution
In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to ze ...
: 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
A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
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
Phosphorus is a chemical element with the symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but because it is highly reactive, phosphorus is never found as a free element on Ea ...
, for which the most stable form at 1 bar is
black phosphorus
Elemental phosphorus can exist in several allotropes, the most common of which are white and red solids. Solid violet and black allotropes are also known. Gaseous phosphorus exists as diphosphorus and atomic phosphorus.
White phosphorus
White ...
, 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
Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is t ...
would be the enthalpy of the following reaction under the above conditions:
:
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
The joule per mole (symbol: J·mol−1 or J/mol) is the unit of energy per amount of substance in the International System of Units (SI), such that energy is measured in joules, and the amount of substance is measured in moles.
It is also an S ...
(kJ mol
−1), but also in
kilocalorie per mole
The kilocalorie per mole is a unit to measure an amount of energy per number of molecules, atoms, or other similar particles. It is defined as one kilocalorie of energy (1000 thermochemical gram calories) per one mole of substance. The unit symb ...
,
joule
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force appli ...
per mole or kilocalorie per
gram
The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram.
Originally defined as of 1795 as "the absolute weight of a volume of pure water equal to th ...
(any combination of these units conforming to the energy per mass or amount guideline).
All elements in their reference states (
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
gas, solid
carbon
Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
in the form of
graphite
Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on la ...
, 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 .
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
The standard enthalpy of reaction (denoted \Delta_ H^\ominus or \Delta H_^\ominus) for a chemical reaction is the difference between total reactant and total product molar enthalpies, calculated for substances in their standard states. This can i ...
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
In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system ...
, 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
![Born-haber cycle LiF](https://upload.wikimedia.org/wikipedia/commons/f/fe/Born-haber_cycle_LiF.svg)
For ionic compounds, the standard enthalpy of formation is equivalent to the sum of several terms included in the
Born–Haber cycle
The Born–Haber cycle is an approach to analyze reaction energies. It was named after the two German scientists Max Born and Fritz Haber, who developed it in 1919. It was also independently formulated by Kasimir Fajans and published concurrently ...
. For example, the formation of
lithium fluoride
Lithium fluoride is an inorganic compound with the chemical formula LiF. It is a colorless solid, that transitions to white with decreasing crystal size. Although odorless, lithium fluoride has a bitter-saline taste. Its structure is analogous to ...
,
:
Li(s) + 1/2F2(g) -> LiF(s)
may be considered as the sum of several steps, each with its own enthalpy (or energy, approximately):
# , the
standard enthalpy of atomization (or
sublimation) of solid lithium.
# , the
first ionization energy
First or 1st is the ordinal form of the number one (#1).
First or 1st may also refer to:
*World record, specifically the first instance of a particular achievement
Arts and media Music
* 1$T, American rapper, singer-songwriter, DJ, and rec ...
of gaseous lithium.
# , the standard
enthalpy of atomization
In chemistry, the enthalpy of atomization (also atomisation in British English) is the enthalpy change that accompanies the total separation of all atoms in a chemical substance (either an element or a compound). This is often represented by th ...
(or bond energy) of fluorine gas.
# , the
electron affinity
The electron affinity (''E''ea) of an atom or molecule is defined as the amount of energy released when an electron attaches to a neutral atom or molecule in the gaseous state to form an anion.
::X(g) + e− → X−(g) + energy
Note that this is ...
of a fluorine atom.
# , the
lattice energy
In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bind ...
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:
:
Organic compounds
The formation reactions for most organic compounds are hypothetical. For instance, carbon and hydrogen won't directly react to form
methane
Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Eart ...
(), so that the standard enthalpy of formation cannot be measured directly. However the
standard enthalpy of combustion is readily measurable using
bomb calorimetry
In chemistry and thermodynamics, calorimetry () is the science or act of measuring changes in '' state variables'' of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, to chemical react ...
. 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
Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is t ...
() and water ():
:
CH4 -> C + 2H2
:
C + O2 -> CO2
:
2H2 + O2 -> 2H2O
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
In thermodynamics, an exothermic process () is a thermodynamic process or reaction that releases energy from the system to its surroundings, usually in the form of heat, but also in a form of light (e.g. a spark, flame, or flash), electricity (e ...
; 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, ) ''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:
:
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
In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to ze ...
between reactants and products where the
enthalpy of mixing
In thermodynamics, the enthalpy of mixing (also heat of mixing and excess enthalpy) is the enthalpy liberated or absorbed from a substance upon mixing. When a substance or compound is combined with any other substance or compound, the enthalpy o ...
is zero.
For example, for the combustion of methane,
CH4 + 2O2 -> CO2 + 2H2O:
:
However
O2 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 doing enthalpy calculations
# When a reaction is reversed, the magnitude of Δ''H'' stays the same, but the sign changes.
# When the balanced equation for a reaction is multiplied by an integer, the corresponding value of Δ''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.
Allotropy, 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
Aliphatic hydrocarbons
Other organic compounds
See also
*
Calorimetry
In chemistry and thermodynamics, calorimetry () is the science or act of measuring changes in ''state variables'' of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, to chemical reacti ...
*
Enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
*
Heat of combustion
The heating value (or energy value or calorific value) of a substance, usually a fuel or food (see food energy), is the amount of heat released during the combustion of a specified amount of it.
The ''calorific value'' is the total energy relea ...
*
Thermochemistry
Thermochemistry is the study of the heat energy which is associated with chemical reactions and/or phase changes such as melting and boiling. A reaction may release or absorb energy, and a phase change may do the same. Thermochemistry focuses on ...
References
* {{Cite book, last1=Zumdahl, first1= Steven , year=2009, title= Chemical Principles, edition= 6th , pages=384–387, publisher= Houghton Mifflin, location= Boston. New York, isbn= 978-0-547-19626-8
External links
NIST Chemistry WebBook
Enthalpy
Thermochemistry
de:Enthalpie#Standardbildungsenthalpie