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The standard enthalpy of reaction (denoted \Delta_ H^\ominus or \Delta H_^\ominus) for a
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking ...
is the difference between total reactant and total product molar enthalpies, calculated for 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. This can in turn be used to predict the total chemical bond energy liberated or bound during reaction, as long as the enthalpy of mixing is also accounted for. For a generic chemical reaction :\nu_ \text + \nu_ \text ~+ ~... \rightarrow \nu_ \text + \nu_ \text ~+ ~... the standard enthalpy of reaction \Delta_ H^\ominus is related to the standard enthalpy of formation \Delta_ H^\ominus values of the reactants and products by the following equation: : \Delta_ H^\ominus = \sum_ \nu_p\Delta_ H_^ - \sum_ \nu_r\Delta_ H_^ In this equation, \nu_p and \nu_r are the stoichiometric coefficients of each product p and reactant r. The standard enthalpy of formation, which has been determined for a vast number of substances, 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. Standard states can be defined at any temperature and pressure, so both the standard temperature and pressure must always be specified. Most values of standard thermochemical data are tabulated at either (25°C, 1 bar) or (25°C, 1 atm). For ions in aqueous solution, the standard state is often chosen such that the aqueous H+ ion at a concentration of exactly 1 mole/liter has a standard enthalpy of formation equal to zero, which makes possible the tabulation of standard enthalpies for cations and anions at the same standard concentration. This convention is consistent with the use of the standard hydrogen electrode in the field of
electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an out ...
. However, there are other common choices in certain fields, including a standard concentration for H+ of exactly 1 mole/(kg solvent) (widely used in
chemical engineering Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials in ...
) and 10^ mole/L (used in the field of
biochemistry Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
). For this reason it is important to note which standard concentration value is being used when consulting tables of enthalpies of formation.


Introduction

Two initial thermodynamic systems, each isolated in their separate states of internal thermodynamic equilibrium, can, by a thermodynamic operation, be coalesced into a single new final isolated thermodynamic system. If the initial systems differ in chemical constitution, then the eventual thermodynamic equilibrium of the final system can be the result of chemical reaction. Alternatively, an isolated thermodynamic system, in the absence of some catalyst, can be in a metastable equilibrium; introduction of a catalyst, or some other thermodynamic operation, such as release of a spark, can trigger a chemical reaction. The chemical reaction will, in general, transform some chemical potential energy into thermal energy. If the joint system is kept isolated, then its internal energy remains unchanged. Such thermal energy manifests itself, however, in changes in the non-chemical state variables (such as temperature, pressure, volume) of the joint systems, as well as the changes in the mole numbers of the chemical constituents that describe the chemical reaction. Internal energy is defined with respect to some standard state. Subject to suitable thermodynamic operations, the chemical constituents of the final system can be brought to their respective standard states, along with transfer of energy as heat or through thermodynamic work, which can be measured or calculated from measurements of non-chemical state variables. Accordingly, the calculation of standard enthalpy of reaction is the most established way of quantifying the conversion of chemical potential energy into thermal energy.


Enthalpy of reaction for standard conditions defined and measured

The standard enthalpy of a reaction is defined so as to depend simply upon the standard conditions that are specified for it, not simply on the conditions under which the reactions actually occur. There are two general conditions under which
thermochemical 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 ...
measurements are actually made. : (a) Constant volume and temperature: heat Q_V = \Delta U , where U (sometimes written as E) is the internal energy of the system : (b) Constant pressure and temperature: heat Q_P = \Delta H , where H = U + PV is the
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 ...
of the system The magnitudes of the heat effects in these two conditions are different. In the first case the volume of the system is kept constant during the course of the measurement by carrying out the reaction in a closed and rigid container, and as there is no change in the volume no work is involved. From the first law of thermodynamics, \Delta U = Q - W , where W is the work done by the system. When only expansion work is possible for a process we have \Delta U = Q_V; this implies that the heat of reaction at constant volume is equal to the change in the internal energy \Delta U of the reacting system. The thermal change that occurs in a chemical reaction is only due to the difference between the sum of internal energy of the products and the sum of the internal energy of reactants. We have : \Delta U = \sum U_ - \sum U_ This also signifies that the amount of heat absorbed at constant volume could be identified with the change in the thermodynamic quantity internal energy. At constant pressure on the other hand, the system is either kept open to the atmosphere or confined within a container on which a constant external pressure is exerted and under these conditions the volume of the system changes. The thermal change at a constant pressure not only involves the change in the internal energy of the system but also the work performed either in expansion or contraction of the system. In general the first law requires that : Q = \Delta U + W (work) If W is only pressure–volume work, then at constant pressure : Q_P = \Delta U + P \Delta V Assuming that the change in state variables is due solely to a chemical reaction, we have : Q_P = \sum U_ - \sum U_ + P \left(\sum V_ - \sum V_\right) : Q_P = \sum \left(U_ + P V_ \right) - \sum \left(U_ + P V_ \right) As enthalpy or heat content is defined by H = U + PV , we have : Q_P = \sum H_ - \sum H_ = \Delta H By convention, the enthalpy of each element in its standard state is assigned a value of zero. If pure preparations of compounds or ions are not possible, then special further conventions are defined. Regardless, if each reactant and product can be prepared in its respective standard state, then the contribution of each species is equal to its molar enthalpy of formation multiplied by its stoichiometric coefficient in the reaction, and the enthalpy of reaction at constant (standard) pressure P^ and constant temperature (usually 298 K) may be written as : Q_ = \Delta_ H^\ominus = \sum_ \nu_\Delta_ H_^ - \sum_ \nu_\Delta_ H_^ As shown above, at constant pressure the heat of the reaction is exactly equal to the enthalpy change, \Delta_ H, of the reacting system.


Variation with temperature or pressure

The variation of the enthalpy of reaction with temperature is given by Kirchhoff's Law of Thermochemistry, which states that the temperature derivative of ΔH for a chemical reaction is given by the difference in
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat cap ...
(at constant pressure) between products and reactants: :\left(\frac\right)_p = \Delta C_p. Integration of this equation permits the evaluation of the heat of reaction at one temperature from measurements at another temperature. :\Delta H^\circ \! \left( T \right) = \Delta H^\circ \! \left( T^\circ \right) + \int_^ \Delta C_P^\circ \, \mathrm T Pressure variation effects and corrections due to mixing are generally minimal unless a reaction involves non-ideal gases and/or solutes, or is carried out at extremely high pressures. The enthalpy of mixing for a solution of ideal gases is exactly zero; the same is true for a reaction where the reactants and products are pure, unmixed components. Contributions to reaction enthalpies due to concentration variations for solutes in solution generally must be experimentally determined on a case by case basis, but would be exactly zero for ideal solutions since no change in the solution's average intermolecular forces as a function of concentration is possible in an ideal solution.


Subcategories

In each case the word ''standard'' implies that all reactants and products are 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. * Standard enthalpy of combustion is the enthalpy change when one mole of an organic compound reacts with molecular
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 ...
(O2) to form carbon dioxide and liquid water. For example, the standard enthalpy of combustion of ethane gas refers to the reaction C2H6 (g) + (7/2) O2 (g) → 2 CO2 (g) + 3 H2O (l). * Standard enthalpy of formation is the enthalpy change when one mole of any compound is formed from its constituent elements in their standard states. The enthalpy of formation of one mole of ethane gas refers to the reaction 2 C (graphite) + 3 H2 (g) → C2H6 (g). * Standard enthalpy of
hydrogenation Hydrogenation is a chemical reaction between molecular hydrogen (H2) and another compound or element, usually in the presence of a catalyst such as nickel, palladium or platinum. The process is commonly employed to reduce or saturate organic ...
is defined as the enthalpy change observed when one mole of an unsaturated compound reacts with an excess of hydrogen to become fully saturated. The hydrogenation of one mole of
acetylene Acetylene ( systematic name: ethyne) is the chemical compound with the formula and structure . It is a hydrocarbon and the simplest alkyne. This colorless gas is widely used as a fuel and a chemical building block. It is unstable in its pure ...
yields ethane as a product and is described by the equation C2H2 (g) + 2 H2 (g) → C2H6 (g). *
Standard enthalpy of neutralization In chemistry and thermodynamics, the enthalpy of neutralization () is the change in enthalpy that occurs when one equivalent of an acid and a base undergo a neutralization reaction to form water and a salt. It is a special case of the enth ...
is the change in enthalpy that occurs when an acid and base undergo a neutralization reaction to form one mole of water. For example in aqueous solution, the standard enthalpy of neutralization of
hydrochloric acid Hydrochloric acid, also known as muriatic acid, is an aqueous solution of hydrogen chloride. It is a colorless solution with a distinctive pungent smell. It is classified as a strong acid. It is a component of the gastric acid in the dige ...
and the base magnesium hydroxide refers to the reaction HCl (aq) + 1/2 Mg(OH)2 → 1/2 MgCl2 (aq) + H2O(l).


Evaluation of reaction enthalpies

There are several methods of determining the values of reaction enthalpies, involving either measurements on the reaction of interest or calculations from data for related reactions. For reactions which go rapidly to completion, it is often possible to measure the heat of reaction directly using a calorimeter. One large class of reactions for which such measurements are common is the
combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combus ...
of
organic compound In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. Th ...
s by reaction with molecular oxygen (O2) 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 (H2O). The heat of combustion can be measured with a so-called
bomb calorimeter A bomb is an explosive weapon that uses the exothermic reaction of an explosive material to provide an extremely sudden and violent release of energy. Detonations inflict damage principally through ground- and atmosphere-transmitted mechanica ...
, in which the heat released by combustion at high temperature is lost to the surroundings as the system returns to its initial temperature. Since 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 ...
, its value is the same for any path between given initial and final states, so that the measured Δ''H'' is the same as if the temperature stayed constant during the combustion. For reactions which are incomplete, the
equilibrium constant The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
can be determined as a function of temperature. The enthalpy of reaction is then found from the van 't Hoff equation as \Delta_ H^\ominus = \frac \ln K_\mathrm. A closely related technique is the use of an electroanalytical voltaic cell, which can be used to measure the Gibbs energy for certain reactions as a function of temperature, yielding K_\mathrm(T) and thereby \Delta_ H^\ominus . It is also possible to evaluate the enthalpy of one reaction from the enthalpies of a number of other reactions whose sum is the reaction of interest, and these not need be formation reactions. This method is based on Hess's law, which states that the enthalpy change is the same for a chemical reaction which occurs as a single reaction or in several steps. If the enthalpies for each step can be measured, then their sum gives the enthalpy of the overall single reaction. Finally the reaction enthalpy may be estimated using
bond energies In chemistry, bond energy (''BE''), also called the mean bond enthalpy or average bond enthalpy is the measure of bond strength in a chemical bond. IUPAC defines bond energy as the average value of the gas-phase bond-dissociation energy (usually ...
for the bonds which are broken and formed in the reaction of interest. This method is only approximate, however, because a reported bond energy is only an average value for different molecules with bonds between the same elements.Petrucci, Harwood and Herring, pages 422–423


References

{{Reflist Enthalpy Thermochemistry Thermodynamics pl:Standardowe molowe ciepło tworzenia