# Enthalpy

Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume multiplied by the pressure. Enthalpy is a quantifiable state function, and the total enthalpy of a system cannot be measured directly; the enthalpy change of a system is measured instead. Enthalpy is a thermodynamic potential, and is useful particularly for nearly-constant pressure process, where any energy input to the system must go into internal energy or the mechanical work of expanding the system.

## Equations

Enthalpy is defined by the following equation:

[itex]H = U + PV \,[itex]

where

H is the enthalpy, measured in joules
U is the internal energy, measured in joules
P is the pressure of the system, measured in pascals
V is the volume, measured in cubic metres

The total enthalpy of a system cannot be measured directly; the enthalpy change of a system is measured instead. Enthalpy change is defined by the following equation:

[itex]\Delta H = H_{final} - H_{initial} \,[itex]

where

ΔH is the enthalpy change, measured in joules
Hfinal is the final enthalpy of the system, measured in joules. In a chemical reaction, Hfinal is the enthalpy of the products.
Hinitial is the initial enthalpy of the system, measured in joules. In a chemical reaction, Hinitial is the enthalpy of the reactants.

Enthalpy is most useful when pressure is held constant through exposure to the surroundings, to analyse reactions that increase the volume of the system, causing it to do mechanical work on the surroundings and lose energy. Conversely, reactions that cause a decrease in volume cause the surroundings to do work on the system, and an increase in the energy of the system. In this case, enthalpy change may be expressed as:

DH = DU + P DV

where

D may indicate an infinitesimal change (often denoted "d") or a finite difference (often denoted "Δ").

Regardless of whether the external pressure is constant, infinitesimal enthalpy change obeys:

dH = T dS + V dP

(where S is the entropy) so long as the only work done is through volume change. Since the expression T dS always represents transfer of heat, it makes sense to treat the enthalpy as a measure of the total heat in the system, so long as the pressure is held constant; this explains the term heat content.

For an exothermic reaction at constant pressure, the system's change in enthalpy is equal to the energy released in the reaction, including the energy retained in the system and that lost through expansion against the surroundings. Similarly, for an endothermic reaction, the system's change in enthalpy is equal to the energy absorbed in the reaction, including the energy lost by the system and that gained through expansion against the surroundings.

## Standard enthalpy

Main article: Standard enthalpy.

The standard enthalpy change of reaction (denoted Ho or HO)is the enthalpy change that occurs in a system when 1 equivalent of matter is transformed by a chemical reaction under standard conditions.

A common standard enthalpy change is the standard enthalpy change of formation, which has been determined for a vast number of substances. The enthalpy change of any reaction under any conditions can be computed, given the standard enthalpy change of formation of all of the reactants and products. Other reactions with standard enthalpy change values include combustion (standard enthalpy change of combustion) and neutralisation (standard enthalpy change of neutralisation).

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