Apply Hess's law and bond enthalpy data to calculate enthalpy changes for reactions.

What this dot point is asking

TASC expects you to use Hess's law with energy cycles and standard enthalpies of formation, and to estimate enthalpy changes from average bond enthalpies.

Hess's law

Because enthalpy is a state function, the energy change depends only on the start and end points, not the path between them.

You can therefore construct an energy cycle: if a direct reaction is hard to measure, go via intermediate steps whose enthalpies are known and add them up. Reversing a step changes the sign of its $\Delta H$; multiplying a step multiplies its $\Delta H$.

Using enthalpies of formation

The standard enthalpy of formation $\Delta H_f^\circ$ is the enthalpy change when one mole of a compound forms from its elements in their standard states. Elements in their standard state have $\Delta H_f^\circ = 0$.

Using bond enthalpies

A reaction breaks bonds in the reactants (requiring energy) and makes bonds in the products (releasing energy):

Bond enthalpies are averages over many molecules, so this method gives an estimate, not an exact value, and it strictly applies only to gaseous species.

Why bond enthalpies give only an estimate

Bond enthalpy data are average values measured across many different molecules, so the energy of, say, a $\text{C}-\text{H}$ bond in methane differs slightly from one in ethanol. When you use average bond enthalpies you are therefore approximating, and the result usually differs by a few percent from a value calculated using exact enthalpies of formation. Bond enthalpies also apply strictly to species in the gas phase, because they describe breaking bonds in isolated gaseous molecules; if a reactant or product is a liquid or solid, the additional enthalpy of vaporisation or sublimation is ignored, adding further error. For an exact answer, formation data or Hess cycles built from measured combustion enthalpies are preferred.

Building a Hess cycle

When formation data are not directly available, you can construct an energy cycle from any set of reactions that share common intermediates, typically combustion reactions or formation reactions. Write the target reaction, then arrange the known equations (reversing or scaling as needed) so that adding them reproduces the target exactly. The sum of the adjusted enthalpies is the target $\Delta H$. This is the method used in the benzene and propan-1-ol questions above, and it works because enthalpy is a state function: the route does not matter, only the start and end states.

In the exam, write the balanced equation first, label which method you are using, multiply every term by its coefficient, and check the sign against whether you expect the reaction to be exothermic or endothermic.