Thermochemical Cycles and Enthalpy Diagrams

Hess's law states that the enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same. This means enthalpy changes that cannot be measured directly can be calculated from other enthalpy changes.A thermochemical cycle links the reactants and products by two routes. The direct route is the reaction of interest, and the indirect route goes via intermediate substances, usually the elements (using enthalpies of formation) or the combustion products (using enthalpies of combustion). The total enthalpy change is the same for each route. When an arrow is followed backwards, the sign of its enthalpy change is reversed.An enthalpy level diagram shows the same information vertically, with each substance drawn on a line at its enthalpy. Exothermic changes point downwards and endothermic changes point upwards, so it is easy to see which substances are more energetically stable.For example, ethanol and methoxymethane are isomers with the formula C₂H₆O. Their enthalpies of formation as gases are -235 kJ mol^-1 and -184 kJ mol^-1. Both are formed from the same elements, so for CH₃OCH₃(g) → C₂H₅OH(g), ΔH = -235 - (-184) = -51 kJ mol^-1.On an enthalpy level diagram, ethanol sits 51 kJ mol^-1 below methoxymethane. This shows much more clearly than the cycle that ethanol has less energy and is more energetically stable.