Hess’s Law

· Hess’s law: the overall enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same.
· This works because enthalpy change, ΔH, is a state function: it depends only on the starting substances and final substances, not the pathway.
· Used to calculate enthalpy changes that cannot be measured directly by experiment, e.g. reactions that are too slow, incomplete, unsafe, or difficult to control.
· In Hess cycles, the sum of ΔH values around alternative routes must be equal.
· Always include correct signs: exothermic ΔH is negative, endothermic ΔH is positive.

This diagram shows a simple Hess cycle, where the same overall enthalpy change can be reached by different routes. It reinforces that ΔH is independent of pathway. Source

Constructing Hess Cycles

· Write the target equation clearly first: this is the reaction whose ΔH you need to find.
· Place the reactants and products at the top of the cycle.
· Add a common reference level, usually either elements in their standard states or combustion products.
· Draw arrows in the direction of the enthalpy changes given in the question.
· Apply the rule: the enthalpy change by one route = the enthalpy change by the alternative route.
· If an arrow is followed against its direction, change the sign of ΔH.
· If an equation is multiplied, multiply its ΔH by the same factor.

This figure shows reactants and products connected by both a direct path and an indirect path. It illustrates that the heat/enthalpy change is the same overall when the start and finish are unchanged. Source

Formation Cycles

· Use a formation cycle when data are standard enthalpy changes of formation, ΔHf⦵.
· ΔHf⦵ = enthalpy change when 1 mole of a compound is formed from its elements in their standard states under standard conditions.
· In formation cycles, the common reference point is usually the elements in their standard states.
· Exam shortcut:
· ΔHr⦵ = ΣΔHf⦵(products) − ΣΔHf⦵(reactants)
· Remember to multiply each ΔHf⦵ by the number of moles in the balanced equation.
· For an element in its standard state, ΔHf⦵ = 0.

Combustion Cycles

· Use a combustion cycle when data are standard enthalpy changes of combustion, ΔHc⦵.
· ΔHc⦵ = enthalpy change when 1 mole of a substance is completely burned in oxygen under standard conditions.
· In combustion cycles, the common reference point is usually the combustion products.
· For organic compounds, combustion products are usually CO₂ and H₂O.
· Exam shortcut:
· ΔHr⦵ = ΣΔHc⦵(reactants) − ΣΔHc⦵(products)
· Be careful: this is the opposite order from formation data.
· Oxygen may appear in the equations but often cancels out in the cycle.

Using Bond Energy Data

· Hess’s law can also be applied using bond energy data.
· Bond breaking is endothermic, so energy is absorbed and ΔH is positive.
· Bond making is exothermic, so energy is released and ΔH is negative.
· Key equation:
· ΔHr = Σ(bond energies of bonds broken) − Σ(bond energies of bonds formed)
· Count every bond in the balanced equation carefully.
· Bond energy calculations often use average bond energies, so answers are usually estimates, not exact experimental values.

Exam Calculation Method

· Step 1: Write the balanced target equation.
· Step 2: Identify whether the data are formation, combustion, or bond energy data.
· Step 3: Draw a clear Hess cycle with arrows in the correct direction.
· Step 4: Multiply enthalpy values by the correct stoichiometric coefficients.
· Step 5: Reverse signs when using an equation backwards.
· Step 6: Add/subtract values so the cycle gives the required ΔH.
· Step 7: Give the final answer with the correct sign, units: kJ mol⁻¹, and suitable significant figures.

Common Exam Traps

· Forgetting that ΔH changes sign when a reaction is reversed.
· Forgetting to multiply ΔH when the chemical equation is multiplied.
· Mixing up the shortcuts: formation = products − reactants, but combustion = reactants − products.
· Using unbalanced equations, causing incorrect mole ratios.
· Omitting state symbols when they affect the enthalpy term given.
· Writing + for an exothermic value or − for an endothermic value without checking the reaction direction.
· Giving an answer without kJ mol⁻¹.