Editing Standard enthalpy of reaction (section)

==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 [[thermochemistry|thermochemical]] measurements are actually made.<ref name=Tinoco44>{{cite book |last1=Tinoco |first1=Ignacio Jr. |last2=Sauer |first2=Kenneth |last3=Wang |first3=James C. |title=Physical Chemistry: Principles and Applications in Biological Sciences |date=1995 |publisher=Prentice-Hall |isbn=0-13-186545-5 |page=44 |edition=3rd}}</ref>

: (a)	Constant volume and temperature: heat <math>Q_V = \Delta U </math>, where <math>U</math> (sometimes written as <math>E</math>) is the [[internal energy]] of the system
: (b)	Constant pressure and temperature: heat <math>Q_P = \Delta H </math>, where <math>H = U + PV</math> is the [[enthalpy]] 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, <math> \Delta U = Q - W </math>, where W is the work done by the system. When only expansion work is possible for a process we have <math> \Delta U = Q_V</math>; this implies that the heat of reaction at constant volume is equal to the change in the internal energy <math>\Delta U</math> of the reacting system.<ref name="Tinoco44" />

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 

:<math>
\Delta U = \sum U_\text{products} - \sum U_\text{reactants}
</math>

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

:<math>
Q = \Delta U + W
</math> (work)

If <math>W</math> is only [[Pressure-volume work|pressure–volume work]], then at constant pressure<ref name=Tinoco44/> 

:<math>
Q_P = \Delta U + P \Delta V
</math>

Assuming that the change in state variables is due solely to a chemical reaction, we have

:<math>
Q_P = \sum U_\text{products} - \sum U_\text{reactants} + P \left(\sum V_\text{products} - \sum V_\text{reactants}\right)
</math>

:<math>
Q_P =  \sum \left(U_\text{products} + P V_\text{products} \right) - \sum \left(U_\text{reactants} + P V_\text{reactants} \right)
</math>

As enthalpy or heat content is defined by <math>H = U + PV </math>, we have

:<math> Q_P = \sum H_\text{products} - \sum H_\text{reactants} = \Delta H</math>

By convention, the enthalpy of each element in its standard state is assigned a value of zero.<ref name=Tinoco48>{{cite book |last1=Tinoco |first1=Ignacio Jr. |last2=Sauer |first2=Kenneth |last3=Wang |first3=James C. |title=Physical Chemistry: Principles and Applications in Biological Sciences |date=1995 |publisher=Prentice-Hall |isbn=0-13-186545-5 |page=48 |edition=3rd}}</ref> 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 <math>P^{\ominus}</math> and constant temperature (usually 298 K) may be written as<ref name=Tinoco48/>  

:<math> 
Q_{P^{\ominus}} = \Delta_{\text {rxn}} H^\ominus = \sum_{\text{products},~p} \nu_{p}\Delta_{\text {f}} H_{p}^{\ominus} - \sum_{\text{reactants},~r} \nu_{r}\Delta_{\text {f}} H_{r}^{\ominus}
</math>

As shown above, at constant pressure the heat of the reaction is exactly equal to the enthalpy change, <math>\Delta_{\text {rxn}} H</math>, of the reacting system.<ref name=Tinoco44/>