Standard enthalpy of reaction

The standard enthalpy of reaction (denoted formula_1 or formula_2) is the difference between total reactant and total product molar enthalpies due to a chemical reaction, from reactants in their standard states to products in their standard states. This can in turn be used to predict the heat liberated or absorbed during reaction when the enthalpy of mixing is also included. The enthalpy of mixing is zero for reactions involving only ideal gases and pure, un-mixed solids and liquids, but otherwise must be calculated or estimated to accurately predict or analyze enthalpy changes due to reaction. 
For a generic chemical reaction
the standard enthalpy of reaction formula_1 is related to the standard enthalpy of formation formula_5 values of the reactants and products by the following equation:
The enthalpy change is equal to the amount of heat absorbed or evolved in the transformation of the reactants at a given temperature and pressure into the products at the same temperature and pressure. In this equation, "formula_7p" and "formula_7r" 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. 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) and formula_9 mole/L (used in the field of biochemistry). For this reason it is important to note which standard concentration value is being used when consulting tables of enthalpies of formation.
Heat of reaction at constant volume and at constant pressure.
The heat of a reaction depends upon the conditions under which the reactions are carried out. There are two general conditions under which thermochemical measurements are made.
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 and so no work is involved.
From the first law of thermodynamics we have a relation, formula_13
That is, the heat of a reaction at constant volume is equal to the change in the internal energy formula_14 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.
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.
If formula_17 is only pressure–volume work, then
As enthalpy or heat content is defined by formula_21.
So we have, formula_22
When applied to a chemical reaction, this leads to the conclusion that the standard enthalpy of reaction is equal to the amount of heat generated by the reaction per mole of reactant (assuming that the reactant has a stoichiometric coefficient of 1).
At constant pressure, the heat of the reaction is exactly equal to the enthalpy change, formula_23, of the reacting system. Although this calculation is usually done at 25°C, adjustments can be made as needed if the temperature of interests varies significantly from 25°C using Kirchoff's Law of Thermochemistry. 
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 states.
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 of organic compounds by reaction with molecular oxygen (O2) to form carbon dioxide and water (H2O). The heat of combustion can be measured with a so-called bomb calorimeter, 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, its value is the same for any path between given initial and final states, so that the measured ΔH is the same as if the temperature stayed constant during the combustion.
For reactions which are incomplete, the equilibrium constant can be determined as a function of temperature. The enthalpy of reaction is then found from the van 't Hoff equation as formula_24. 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 formula_25 and thereby formula_26.
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 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.