Representing Enthalpy Changes
Method 1: Thermochemical Equations with Energy Terms
The first way to describe the enthalpy change in a chemical reaction: include it as a term in a thermochemical equation.

• If a reaction is endothermic, it requires a certain quantity of energy to be supplied to the reactants. This energy (like the reactants) is “consumed” as the reaction progresses and is listed along with the reactants.
• If a reaction is exothermic, energy is released as the reaction proceeds and is listed along with the products.

For example, in the electrolysis of water, energy is absorbed.
H2O (l) + 285.8 kJ → H2 (g) + ½ O2 (g)

For example, magnesium burns in oxygen as follows:
Mg(s) + ½  O2 (g) → MgO(s) + 601.6 kJ

Method 2: Thermochemical Equations with _H Values
A second way to describe the enthalpy change in a reaction is to write a balanced chemical equation and then the ΔH value beside it, making sure that ΔH is given the correct sign.

Thus, the production of methanol from carbon monoxide and hydrogen could be written as:
CO (g) + 2 H2 (g) → CH3OH (l)         ∆H =  –128.6 kJ

Note that the units for the enthalpy change are kilojoules (not kJ/mol), because the enthalpy change applies to the reactants and products as written, with the numbers of moles of reactants and products given in the equation. The same equation could be written as:
½ CO (g) +  H2 (g) → ½ CH3OH (l)         ∆H =  –64.3 kJ

Method 4: Potential Energy Diagrams

Chemists sometimes explain observed energy changes in chemical reactions in terms of chemical potential energy. This stored energy is related to the relative positions of particles and the strengths of the bonds between them.

Potential energy is stored or released as the positions of the particles change, just as it is when a spring is stretched and then released. As bonds break and re-form and the positions of atoms are altered, changes occur in potential energy.

We can visually communicate this energy transferred by using a potential energy diagram. In this theoretical description, the energy transferred during a change is represented as changes in the chemical potential energy of the particles as bonds are broken or formed.

The vertical axis on the diagram represents the potential energy of the system. Since the reactants are written on the left and the products on the right, the horizontal axis is sometimes called a reaction coordinate or reaction progress.