# 5.3 Enthalpy  (Page 2/25)

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As discussed, the relationship between internal energy, heat, and work can be represented as Δ U = q + w . Internal energy is a type of quantity known as a state function    (or state variable), whereas heat and work are not state functions. The value of a state function depends only on the state that a system is in, and not on how that state is reached. If a quantity is not a state function, then its value does depend on how the state is reached. An example of a state function is altitude or elevation. If you stand on the summit of Mt. Kilimanjaro, you are at an altitude of 5895 m, and it does not matter whether you hiked there or parachuted there. The distance you traveled to the top of Kilimanjaro, however, is not a state function. You could climb to the summit by a direct route or by a more roundabout, circuitous path ( [link] ). The distances traveled would differ (distance is not a state function) but the elevation reached would be the same (altitude is a state function).

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 ( U ) and the mathematical product of its pressure ( P ) and volume ( V ):

$H=U+PV$

Since it is derived from three state functions ( U , P , and V ), enthalpy is also 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:

$\text{Δ}H=\text{Δ}U+P\text{Δ}V$

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

$P\text{Δ}V=\text{−}w$

Substituting this equation and the definition of internal energy into the enthalpy-change equation yields:

$\begin{array}{l}\text{Δ}H=\text{Δ}U+P\text{Δ}V\\ ={q}_{\text{p}}+w-w\\ ={q}_{\text{p}}\end{array}$

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, then the heat flow ( q p ) and enthalpy change (Δ H ) for the process are equal.

The heat given off when you operate 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. On the other hand, the heat produced by a reaction measured in a bomb calorimeter ( [link] ) is not equal to Δ H because the closed, constant-volume metal container prevents expansion work from occurring. Chemists usually perform experiments under normal atmospheric conditions, at constant external pressure with q = Δ H , which makes enthalpy the most convenient choice for determining heat.

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