Hess Cycles

Video Lesson

Introduction

Before we learn about Hess Cycles, let's revisit some key concepts from thermochemistry.

Thermochemistry is the study of heat changes during chemical reactions. The heat change depends on the amount (number of moles) of reactants involved, and is measured in kJ mol⁻¹.

When a heat change is measured at constant pressure, it is called an enthalpy change, given the symbol ΔH.

When an enthalpy change is measured under standard conditions (pressure = 100 kPa, temperature = 298 K, with all substances in their standard states), it is written as:

ΔH°

Hess's Law

Germain Henri Hess was a 19th-century chemist who discovered that energy changes in chemical reactions do not depend on the route taken. His law states:

This is enormously useful. If you have a reaction whose enthalpy change is difficult to measure directly, you can calculate it indirectly by using a different route, provided you know the enthalpy changes for the individual steps in that route. This is where Hess Cycles come in.

Combustion Data Hess Cycle

If the exam question provides standard enthalpies of combustion, you should draw a combustion Hess Cycle. In this cycle, both reactants and products are combusted to form the same combustion products (usually CO₂ and H₂O), and the arrows point downwards.

The general layout looks like this:

• The unknown enthalpy change (ΔH) goes across the top, from reactants to products.
• Arrows point down from the reactants to combustion products (ΔH_c of reactants).
• Arrows point down from the products to the same combustion products (ΔH_c of products).

The formula to calculate the unknown enthalpy change is:

ΔH = ∑(ΔH_c reactants) − ∑(ΔH_c products)

Worked Example: Enthalpy of Formation of Butane

Use the combustion data below to calculate the standard enthalpy of formation of butane (C₄H₁₀).

Substance	Standard enthalpy of combustion / kJ mol−1
C	−394
H2	−286
C4H10	−2877

The formation reaction for butane is:

4C + 5H₂ → C₄H₁₀

Draw the Hess Cycle with the combustion products (4CO₂ + 5H₂O) at the bottom, then apply the formula:

ΔH = ∑(ΔH_c reactants) − ∑(ΔH_c products)

ΔH = [4(−394) + 5(−286)] − [−2877]

ΔH = [−1576 + (−1430)] − [−2877]

ΔH = −3006 + 2877

ΔH = −129 kJ mol⁻¹

Notice that the balanced equation requires 4 moles of C and 5 moles of H₂, so we multiply their combustion values accordingly. Always balance your cycle first.

Formation Data Hess Cycle

If the exam question provides standard enthalpies of formation, you should draw a formation Hess Cycle. In this cycle, the elements in their standard states sit at the bottom, and the arrows point upwards.

The general layout looks like this:

• The unknown enthalpy change (ΔH) goes across the top, from reactants to products.
• Arrows point up from the elements to the reactants (ΔH_f of reactants).
• Arrows point up from the elements to the products (ΔH_f of products).

The formula to calculate the unknown enthalpy change is:

ΔH = ∑(ΔH_f products) − ∑(ΔH_f reactants)

Worked Example: Enthalpy of Combustion of Benzene

Use the formation data below to calculate the standard enthalpy of combustion of benzene (C₆H₆).

Substance	Standard enthalpy of formation / kJ mol−1
C6H6	+49.2
CO2	−394
H2O	−286

The combustion reaction for benzene is:

C₆H₆ + 7.5O₂ → 6CO₂ + 3H₂O

Draw the Hess Cycle with the elements (6C + 3H₂ + 7.5O₂) at the bottom, then apply the formula:

ΔH = ∑(ΔH_f products) − ∑(ΔH_f reactants)

ΔH = [6(−394) + 3(−286)] − [+49.2]

ΔH = [−2364 + (−858)] − [+49.2]

ΔH = −3222 − 49.2

ΔH = −3271.2 kJ mol⁻¹

Note that oxygen is an element in its standard state, so its enthalpy of formation is zero. We only need the formation values for C₆H₆, CO₂, and H₂O.

Which Cycle Should I Use?

This is straightforward: look at the data you have been given in the question.

Data given	Cycle to draw	Arrow direction	Formula
Enthalpies of combustion	Combustion cycle	Down	ΔH = ∑ΔHc(reactants) − ∑ΔHc(products)
Enthalpies of formation	Formation cycle	Up	ΔH = ∑ΔHf(products) − ∑ΔHf(reactants)

Summary

• Hess's Law states that the enthalpy change of a reaction depends only on the initial and final states, not on the route taken.
• If given combustion data, draw a combustion Hess Cycle with arrows pointing down to the combustion products. Use: ΔH = ∑ΔH_c(reactants) − ∑ΔH_c(products).
• If given formation data, draw a formation Hess Cycle with arrows pointing up from the elements. Use: ΔH = ∑ΔH_f(products) − ∑ΔH_f(reactants).
• Always balance your cycle before calculating. The coefficients tell you which values to multiply.
• Remember: Combustion = Burn Down (arrows down) and Formation = Grow Up (arrows up).

Related Lessons

• Free Radical Substitution – learn the three-stage mechanism for how alkanes react with halogens.
• Moles & Avogadro’s Constant – revise mole calculations, which underpin Hess Cycle problems.