# Standard enthalpy of reaction

The standard enthalpy of reaction (denoted ΔHr) is the enthalpy change that occurs in a system when matter is transformed by a given chemical reaction, when all reactants and products are in their standard states.

For a generic chemical reaction

vA A + −vB B + ... → vP P + vQ Q ...

the standard enthalpy of reaction ΔHr is related to the standard enthalpy of formation ΔHf of the reactants and products by the following equation neglecting the heat of mixing of reagents and products or assuming ideal solutions involved:

${\displaystyle \Delta H_{\mathrm {r} }^{\ominus }=\sum _{B}{v_{B}\Delta H_{\mathrm {f} }^{\ominus }(B)}}$

In this equation, vB is the stoichiometric number of entity B. 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.

The enthalpy change of any reaction under any conditions can be computed from the above equation, given the standard enthalpy of formation of the reactants and products. The enthalpy change is defined as 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.

## Heat of reaction at constant pressure and at constant volume

The heat of a reaction depends upon the conditions under which the reaction is carried out. There are two general conditions under which thermochemical measurements are made.

(a) Constant volume and temperature: heat ${\displaystyle Q_{v}=\Delta E}$
(b) Constant pressure and temperature: heat ${\displaystyle Q_{p}=\Delta H}$

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 also involved.

From the first law of thermodynamics we have a relation, ${\displaystyle \Delta E=Q_{v}}$

That is, the heat of a reaction at constant volume is equal to the change in the internal energy (Δ E) of the reacting system.

The thermal change that occurs in a chemical reaction is only due to the difference in the sum of internal energy of the products and the sum of the internal energy of reactants.

${\displaystyle \Delta E=\sum E_{products}-\sum E_{reactants}}$

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.

${\displaystyle Q_{p}=\Delta E+W}$ (work)

If ‘W’ is only pressure-volume work, then

${\displaystyle Q_{p}=\Delta H=\Delta E+P\Delta V}$
${\displaystyle Q_{p}=\left(\sum E_{p}-\sum E_{r}\right)+P\left(V_{p}-V_{r}\right)}$
${\displaystyle Q_{p}=\left(\sum E_{p}+PV_{p}\right)-\left(\sum E_{r}+PV_{r}\right)}$

As enthalpy or heat content is defined by ${\displaystyle H=E+PV}$.

So we have, ${\displaystyle Q_{p}=\sum H_{p}-\sum H_{r}=\Delta H}$

At constant pressure, the heat of the reaction is exactly equal to the enthalpy change, ${\displaystyle \Delta H}$, of the reacting system.

## Subcategories

In each case the word standard implies that all reactants and products are in their standard states.

• Standard enthalpy of neutralization is the change in enthalpy that occurs when an acid and base undergo a neutralization reaction to form one mole of water.
• Standard enthalpy of sublimation, or heat of sublimation, is defined as the enthalpy required to sublime one mole of the substance.
• Standard enthalpy of solution (or enthalpy change of dissolution or heat of solution) is the enthalpy change associated with the dissolution of a substance in a solvent at constant pressure.
• Standard enthalpy of hydrogenation is defined as the enthalpy change observed when one mole of an unsaturated compound reacts with an excess of hydrogen to become fully saturated.