From UCDavis Chemwiki

Perhaps because values of `DeltaH` are usually easier to measure than values of `DeltaU`, chemists have chosen to concentrate exclusively on `DeltaH` rather than on `DeltaU` as a way of recording thermochemical data. Though enthalpies of formation are easy to find, equivalent tables of internal energies are nonexistent. In many ways this insistence on `DeltaH` rather than on `DeltaU` is a pity. In particular, it suggests that somehow the enthalpy H has more fundamental significance on the molecular level than the internal energy U. It is important to realize that this is not the case. It is the internal energy which has a simple molecular interpretation, namely, the total energy of all the molecules in the system. By contrast the enthalpy includes not only the total energy of the molecules in the system but the potential energy of the atmosphere outside the system as well. We use the enthalpy so often because of its convenience rather than because of its molecular significance.

A further point worth making about the enthalpy is that the difference between `DeltaH` and `DeltaU` is not often of great chemical importance. This is particularly true of reactions which involve only gases, such as the decomposition of ozone. In a gaseous reaction the main factor determining both `DeltaU` and `DeltaH` is the change in electronic energy. Changes in molecular energy and also the expansion work `PDeltaV` are usually small compared with this change. In the decomposition of ozone, for example, the change in electronic energy is – 290.7 kJ per 2 mol ozone. The value of `DeltaU "is" –287.9 kJ`, while that of `DeltaH` is `–285.4 kJ`. The three quantities are all within a few percent of each other. For many purposes, differences of this order of magnitude are immaterial. When this is the case, we can equate both `DeltaU` and `DeltaH` to the change in electronic energy.
Relationship: Enthalpy (H) is the sum of the internal energy (U) and the product of pressure and volume (PV) given by the equation:

H=U+PV

When a process occurs at constant pressure, the heat evolved (either released or absorbed) is equal to the change in enthalpy. Enthalpy is a state function which depends entirely on the state functions T, P and U. Enthalpy is usually expressed as the change in enthalpy (`DeltaH`) for a process between initial and final states:

`DeltaH=DeltaU+ DeltaPV`

If temperature and pressure remain constant through the process and the work is limited to pressure-volume work, then the enthalpy change is given by the equation:

`DeltaH=DeltaU+PDeltaV`

Also at constant pressure the heat flow (q) for the process is equal to the change in enthalpy defined by the equation:

`DeltaH=q`

By looking at whether q is exothermic or endothermic we can determine a relationship between `DeltaH` and q. If the reaction absorbs heat it is endothermic meaning the reaction consumes heat from the surroundings so q>0(positive). Therefore, at constant temperature and pressure, by the equation above, if q is positive then `DeltaH` is also positive. And the same goes for if the reaction releases heat, then it is exothermic, meaning the system gives off heat to its surroundings, so q<0 (negative). If q is negative then `DeltaH` will also be negative.

Enthalpy Change Accompanying a Change in State of Matter

When a liquid vaporizes the liquid must absorb heat from its surroundings to replace the energy taken by the vaporizing molecules in order for the temperature to remain constant. This heat required to vaporize the liquid is called enthalpy of vaporization, or often, heat of vaporization. For example, the vaporization of one mole of water the enthalpy is given as:

`DeltaH = 44.0 kJ` at 298 K

When a solid melts, the required energy is similarly called enthalpy of fusion, or heat of fusion. For example, one mole of ice the enthalpy is given as:

`DeltaH = 6.01 kJ` at 273.15 K

`DeltaH=DeltaU+pDeltaV` (1)

Enthalpy can also be expressed as a molar enthalpy, DeltaH_m, by dividing the enthalpy or change in enthalpy by the number of moles. Enthalpy is a state function. This implies that when a system changes from one state to another, the change in enthalpy is independent of the path between two states of a system.

If there is no non-expansion work on the system and the pressure is still constant, then the change in enthalpy will equal the heat consumed or released by the system (q).

`DeltaH=q` (2)

This relationship can help to determine whether a reaction is endothermic or exothermic. At constant pressure, an endothermic reaction is when heat is absorbed. This means that the system consumes heat from the surroundings, so q is greater than zero. Therefore according to the second equation, the `DeltaH` will also be greater than zero. On the other hand, an exothermic reaction at constant pressure is when heat is released. This implies that the system gives off heat to the surroundings, so q is less than zero. Furthermore, `DeltaH` will be less than zero.