All molecules at temperatures above absolue zero possess thermal energyˇX the randomized kinetic energy associated with the various motions the molecules as a whole, and also the atoms within them, can undergo. Polyatomic molecules also possess potential energy in the form of chemical bonds. Molecules are thus both vehicles for storing and transporting energy, and the means of converting it from one form to another when the formation, breaking, or rearrangement of the chemical bonds within them is accompanied by the uptake or release of heat.

Chemical Energy
Chemical substances are made of atoms, or more generally, of positively charged nuclei surrounded by negatively charged electrons. A molecule such as dihydrogen, H2, is held together by electrostatic attractions mediated by the electrons shared between the two nuclei. The total potential energy of the molecule is the sum of the repulsions between like charges and the attractions between electrons and nuclei:
In other words, the potential energy of a molecule depends on the time-averaged relative locations of its constituent nuclei and electrons. This dependence is expressed by the familiar potential energy curve which serves as an important description of the chemical bond between two atoms.

In gaseous hydrogen, for example, the molecules will be moving freely from one location to another; this is called translational motion, and the molecules therefore possess translational kinetic energy KE_trans = mv^2/2, in which v stands for the average velocity of the molecules; you may recall from your study of gases that v, and therefore KE_trans, depends on the temperature.

In addition to translation, molecules can possess other kinds of motion. Because a chemical bond acts as a kind of spring, the two atoms in H2 will have a natural vibrational frequency. In more complicated molecules, many different modes of vibration become possible, and these all contribute a vibrational term KE_vib to the total kinetic energy. Finally, a molecule can undergo rotational motions which give rise to a third term KE_rot. Thus the total kinetic energy of a molecule is the sum

The total energy of the molecule (its internal energy U) is just the sum:

Energetics of chemical reactions
The rearrangement of atoms that occurs in a chemical reaction is virtually always accompanied by the liberation or absorption of heat. If the purpose of the reaction is to serve as a source of heat, such as in the combustion of a fuel, then these heat effects are of direct and obvious interest. We will soon see, however, that a study of the energetics of chemical reactions in general can lead us to a deeper understanding of chemical equilibrium and the basis of chemical change itself.

In chemical thermodynamics, we define the zero of the enthalpy and internal energy as that of the elements as they exist in their stable forms at 298K and 1 atm pressure. Thus the enthalpies H of Xe(g), O2(g) and C(diamond) are all zero, as are those of H2 and Cl2 in the reaction.


The enthalpy of two moles of HCl is smaller than that of the reactants, so the difference is released as heat. Such a reaction is said to be exothermic. The reverse of this reaction would absorb the same quantity of heat from the surroundings and be endothermic.

Changes in enthalpy and internal energy
We can characterize any chemical reaction by the change in the internal energy or enthalpy:

The significance of this can hardly be exaggerated because ŁGH, being a state function, is entirely independent of how the system gets from the initial state to the final state. In other words, the value of ŁGH or ŁGU for a given change in state is independent of the pathway of the process.

Consider, for example, the oxidation of a lump of sugar to carbon dioxide and water:

This process can be carried out in many ways, for example by burning the sugar in air, or by eating the sugar and letting your body carry out the oxidation. Although the mechanisms of the transformation are completely different for these two pathways, the overall change in the enthalpy of the system (the atoms of carbon, hydrogen and oxygen that were originally in the sugar) will be identical, and can be calculated simply by looking up the standard enthalpies of the reactants and products and calculating the difference



The same quantity of heat is released whether the sugar is burnt in the air or oxidized in a series of enzyme-catalyzed steps in your body.

Enthalpy of formation
The enthalpy change for a chemical reaction is the difference:

If the reaction in question represents the formation of one mole of the compound from its elements in their standard states, as in
then we can arbitrarily set the enthalpy of the elements to zero and write

which defines the standard enthalpy of formation of water at 298K.

The standard enthalpy of formation of a compound is defined as the heat associated with the formation of one mole of the compound from its elements in their standard states.

Hess' law and thermochemical calculations
You probably know that two or more chemical equations can be combined algebraically to give a new equation. Even before the science of thermodynamics developed in the late nineteenth century, it was observed that the heats associated with chemical reactions can be combined in the same way to yield the heat of another reaction. For example, the standard enthalpy changes for the oxidation of graphite and diamond can be combined to obtain ŁGH˘X for the transformation between these two forms of solid carbon, a reaction that cannot be studied experimentally.

Subtraction of the second reaction from the first (i.e., writing the second equation in reverse and adding it to the first one) yields

This principle, known as Hess' law of independent heat summation is a direct consequence of the enthalpy being a state function. Hessˇ¦ law is one of the most powerful tools of chemistry, for it allows the change in the enthalpy (and in other thermodynamic functions) of huge numbers of chemical reactions to be predicted from a relatively small base of experimental data.

Because most substances cannot be prepared directly from their elements, heats of formation of compounds are seldom determined by direct measurement. Instead, Hessˇ¦ law is employed to calculate enthalpies of formation from more accessible data. The most important of these are the standard enthalpies of combustion. Most elements and compounds combine with oxygen, and many of these oxidations are highly exothermic, making the measurement of their heats relatively easy.


Source:
Stephen Lower, chem1 virtual textbook, a reference text for General Chemistry, Simon Fraser University.