Because many of the chemical reactions we wish to describe take place in contact with the ambient atmosphere, we are particularly interested in isobaric (constant pressure) applications of thermodynamics. In this case, work is easy to calculate. You simply determine the change in volume of your system

ΔV = V_final - V_initial

and measure the ambient atmospheric pressure, P. Because your system expands or contracts against the constant atmospheric pressure, work is done against/by a constant P_ex equal to the pressure of the atmosphere

w = - P ΔV

Although it is important to take work into account in any application of the first law, the 'PV' work done by or on the system as it expands or contracts is not particularly interesting in chemistry. We can generate a new state function that does not include the 'PV' work by defining H, the enthalpy

H = U + PV

The symbol '=' indicates that this is a definition and is true under all circumstances, even those in which the pressure varies. Like the internal energy, U, H depends only on the state variables, temperature (T), pressure (P) and volume (V). Changes in enthalpy, ΔH, will only depend on the final and initial states, and not on the way the change takes place; Δ H will be path-independent.

Under constant pressure conditions, we can express the change of enthalpy

ΔH = ΔU + P ΔV

If we use the first law of thermodynamics, Δ U = q + w, to substitute for Δ U

ΔH = q + w + PΔV

and then substitute for w at constant pressure

ΔH = q - PΔV + PΔV

we get the very simple result that the change in enthalpy is equal to the heat

ΔH = q_p

To emphasis that the pressure is constant, we have added a subscript 'p' to the heat in the equation above. Remember that this is not an exotic condition. It is a good approximation when reactions are run in containers open to the atmosphere like a laboratory desk top or even a furnace in a house.

In teaching energy concepts at the high school and college general chemistry level, you will probably spend more time talking about enthalpy than about internal energy. One important concept at this level is whether a chemical reaction produces energy when it occurs or requires that energy be supplied for it to occur. For example, when you burn natural gas in a furnace you expect that heat will be liberated. Natural gas is mostly methane, CH₄, and the combustion reaction is

CH_{4 (g)} + 2 O_{2 (g)} --> CO_{2 (g)} + 2 H₂O _(l) Δ H =- 891 kJ

This equation states that when one mole of methane gas combines with two moles of oxygen gas to produce one mole of carbon dioxide gas and two moles of liquid water, 891 kilojoules of enthalpy will be liberated. The value given for enthalpy assumes that the reaction is carried out at 100 kPa (1 bar) and 298 K. The minus sign indicates that the system will lose 891 kJ of enthalpy and the surroundings (your house) will gain 891 kJ of enthalpy. Since the reaction takes place at constant pressure (in air), the change of enthalpy will be entirely in the form of heat. Reactions, such as the combustion of methane, that give off heat are called exothermic.

Some reactions require heat. Reactions for which ΔH is positive are called endothermic. You can make any exothermic reaction into an endothermic one by reversing the reaction

CO_{2 (g)} + 2 H₂O _(l) --> CH_{4 (g)} + 2 O _{2 (g)} Δ H = 891 kJ

Note that whether a reaction requires heat (endothermic) or liberates heat (exothermic) says absolutely nothing about whether it is spontaneous or not. Some reactions that occur spontaneously are exothermic. The combustion of methane at 1 bar and 298 K is one such reaction. However, many heats of solution, e.g.

NH₄NO_3  (s) --> NH₄⁺_(aq) + NO₃^-_(aq) ΔH = 26 kJ

are endothermic under these conditions, as are some reaction that involve the making and breaking of chemical bonds. One example of this is the photosynthesis reaction

6 CO ₂+ 6 H₂O + energy --> C₆H₁₂O₆ + 6 O₂

As the temperature is increased, more and more endothermic reactions become spontaneous as we supply the energy, in the form of thermal motion, necessary to drive them.

Enthalpy is an intrinsic property; it depends upon the amount of chemicals you have. If you burn 1/3 mole of methane, your combustion reaction would be

1/3 CH _{4 (g)} + 2/3 O_{2 (g)} --> 1/3 CO_{2 (g)} + 2/3 H₂O _(l) ΔH =- 297 kJ

and 297 kJ of heat would be liberated. One gram of methane (1.0 g / 16 g/mole = 0.062 moles) would generate 55 kilojoules of heat (Δ H =- 55 kJ), provided there is sufficient oxygen to burn it completely.

Sometimes, the exothermicity or endothermicity of a reaction is depicted graphically, as shown on the chart to the right. In this chart, the enthalpy is depicted along the y-axis and the reaction proceeds from left to right along the x-axis. For the reaction to occur, chemical bonds first must be broken and, since this requires energy, the reaction must first surmount an energy 'hill' to a higher enthalpy state before the products can form. The graph to the right depicts an endothermic reaction, in which the enthalpy of the products is lower than that of the reactants. For a discussion of rates of reactions and other examples of energy diagrams, including the appearance of exothermic energy diagrams, click here. It is often possible to make a qualitative estimate of whether a chemical process is endothermic or exothermic. For example, melting ice (or changing any solid into its liquid) takes energy. If you want to melt a solid isobarically, you need to put energy into it in the form of heat. This is because the solid phase of a particular chemical will have much stronger intermolecular interactions than will a liquid phase of the same chemical. Similarly, boiling water takes energy because to transform a liquid into a gas, you have to break the intermolecular interactions holding the liquid together. Both of these processes are endothermic. Perhaps not so obvious is that when water vapor condenses to a liquid under constant pressure conditions, heat is given off. Remember that condensation is the reverse reaction of vaporization. If vaporization (boiling) is exothermic (requires heat), condensation must be endothermic (gives off heat).

A web page that describes demonstrations of exothermic and endothermic reactions can be accessed by clicking here.

The enthalpy of a chemical reaction can also be estimated by considering the bonds that need to be broken to separate the atoms in the molecular reactants and the bonds that need to be formed from these atoms to create the product. You can even get a semi-quantitative measure of the enthalpy of reaction by using tabulated bond enthalpies. These bond energies are defined as the enthalpy of breaking an average bond which is always positive (exothermic). Combining enthalpies is possible because enthalpy is a state functions which is independent of path. A reaction can be thought of as many steps separating all bonds and then forming the new bonds. This distorted picture of the actual reaction path can be used because enthalpy depends only on the initial and final state and not the pathway.

Reaction enthalpies are estimated by summing enthalpies of all of the bonds broken. Then enthalpies of all of the bonds formed are subtracted from the total.

Σ Enthalpies of bonds broken - Σ Enthalpies of bonds formed = Enthalpy of reaction

Reaction enthalpies calculated in this manner are only approximate because different molecules will have slightly different energies for even what appear to be similar bonds. Furthermore, keep in mind that enthalpies are both temperature and pressure dependent. Although the dependency on pressure is usually weak, the dependence on temperature can be very substantial.

You can practice problems Using Bond Energies at this site with immediate feedback.