Some chemical reactions give off tremendous heat and perform work on the surroundings, such as the combustion of rocket fuel causing a space shuttle to lift off from the ground.

The sum of heat “*q,*” and work “*w*,” is the change in internal energy, “Δ*E*,” as given by the first law of thermodynamics.

For chemical reactions involving gases that occur at atmospheric pressure, the work done is the mechanical work associated with volume changes — either expansion or contraction. Work is therefore equal to the negative value of the pressure times the change in volume.

Substituting for *w* in the first law of thermodynamics and rearranging the terms in the equation shows that *q* = Δ*E* + *P*Δ*V*, giving the expression for heat flow under constant pressure.

In other chemical reactions, such as the burning of wood to cook food, it is more relevant to quantify the heat given off to facilitate cooking, than to measure the amount of expansion work done on the surrounding.

Since internal energy accounts for both heat and work, Δ*E* is not used for constant pressure conditions. To exclusively discuss the energy flow in the form of heat, a new thermodynamic function – enthalpy – is defined.

Enthalpy, *H*, equals the sum of internal energy, *E*, and pressure-volume work, *P*–*V*. Because energy, pressure, and volume are state functions, enthalpy is also a state function.

Absolute enthalpy values for specific substances cannot be measured. Only the change in enthalpy can be determined. Enthalpy change, Δ*H*, equals the change in internal energy, Δ*E *+ *P*Δ*V*.

Recalling that the change in energy is the sum of heat and pressure-volume work the equations can be combined to show that under constant pressure conditions Δ*H *equals the heat, *q*, gained, or lost by the system.

If the system loses energy to the surroundings in the form of heat — as in the burning of wood — the temperature of the surroundings rises. This is described by a negative sign convention for *q*. Consequently, Δ*H* becomes negative, and the process is described as exothermic.

On the contrary, if the system gains energy from the surroundings in the form of heat — such as the reaction occurring in a chemical cold pack — the temperature of the surroundings falls. The heat, in this case, is described by a positive sign convention. This makes Δ*H* positive, and the process is called endothermic.

Chemists ordinarily use a property known as enthalpy (*H*) to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum of a system’s internal energy (*E*) and the mathematical product of its pressure (*P*) and volume (*V*):

Enthalpy is a state function. Enthalpy values for specific substances cannot be measured directly; only enthalpy changes for chemical or physical processes can be determined. For processes that take place at constant pressure (a common condition for many chemical and physical changes), the enthalpy change (Δ*H*) is:

The mathematical product *P*Δ*V* represents work (*w*), namely, expansion or pressure-volume work. By their definitions, the arithmetic signs of Δ*V* and w will always be opposite:

Substituting this equation and the definition of internal energy at constant pressure (Δ*E* = *q*_{p} + *w*) into the enthalpy-change equation yields:

where *q*_{p} is the heat of reaction under conditions of constant pressure.

And so, if a chemical or physical process is carried out at constant pressure with the only work done caused by expansion or contraction (*P-V* work), then the heat flow (*q*_{p}) and enthalpy change (Δ*H*) for the process are equal.

The heat given off while operating a Bunsen burner is equal to the enthalpy change of the methane combustion reaction that takes place since it occurs at the essentially constant pressure of the atmosphere. Chemists usually perform experiments under normal atmospheric conditions, at constant external pressure with *q*_{p} = Δ*H*, which makes enthalpy the most convenient choice for determining heat changes for chemical reactions.

A negative value of an enthalpy change, Δ*H* < 0, indicates an exothermic reaction (heat given off to the surroundings); a positive value, Δ*H* > 0, indicates an endothermic reaction (heat absorbed from the surroundings). If the direction of a chemical equation is reversed, the arithmetic sign of its Δ*H* is changed (a process that is endothermic in one direction is exothermic in the opposite direction).

Conceptually, Δ*E* (a measure of heat and work) and Δ*H* (a measure of heat at constant pressure) both represent changes in a state function for the system. In processes where the volume change, Δ*V*, is small (melting of ice), and Δ*E* and Δ*H* are identical. However, if the volume change is significant (evaporation of water), the amount of energy transferred as work will be significant; thus, Δ*E* and Δ*H* have significantly different values.

*This text is adapted from Openstax, Chemistry 2e, Section 5.3: Enthalpy.*

- Canagaratna, Sebastian G. "A visual aid in enthalpy calculations."
*Journal of Chemical Education*77, no. 9 (2000): 1178. - Howard, Irmgard K. "H is for enthalpy, thanks to Heike Kamerlingh Onnes and Alfred W. Porter."
*Journal of chemical education*79, no. 6 (2002): 697. - Van Ness, Hendrick C.
*Classical thermodynamics of non-electrolyte solutions.*Elsevier, 2015.

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