# 1.5.5 Hess’s Law

### Hess Cycles

• Hess’s Law states that:
“The total enthalpy change in a chemical reaction is independent of the route by which the chemical reaction takes place as long as the initial and final conditions are the same.”
• This means that whether the reaction takes place in one or two steps, the total enthalpy change of the reaction will still be the same The diagram above illustrates Hess’ Law: the enthalpy change of the direct route, going from reactants (A+B) to product (C) is equal to the enthalpy change of the indirect routes

• Hess’ Law is used to calculate enthalpy changes which can’t be found experimentally using calorimetry, eg:

3C (s) + 4H2 (g) → C3H8(g)

• ΔHf (propane) can’t be found experimentally as hydrogen and carbon don’t react under standard conditions

#### Calculating ΔHr from ΔHf using Hess’s Law energy cycles

• The products can be directly formed from the elements = ΔH2

OR

• The products can be indirectly formed from the elements = ΔH1 + ΔHr The enthalpy change from elements to products (direct route) is equal to the enthalpy change of elements forming reactants and then products (indirect route)

• Equation

ΔH2 = ΔH1 + ΔHr

Therefore,

ΔHr = ΔH2 – ΔH1

#### Calculating ΔHffrom ΔHc using Hess’s Law energy cycles

• The combustion products can be formed directly from elements to combustion products = ΔH1

OR

• The combustion products can be formed indirectly from elements to compound to combustion products = ΔHf+ ΔH2 The enthalpy change going from elements to products (direct route) is equal to the enthalpy change of elements forming reactants and then products (indirect route)

• Equation

ΔH1 = ΔHf + ΔH2

Therefore,

ΔH= ΔH1 – ΔH2

#### Calculating average bond energies using Hess’s cycles

• Bond energies cannot be found directly so enthalpy cycles are used to find the average bond energy
• This can be done using enthalpy changes of atomisation and combustion or formation
• The enthalpy change of atomisation (ΔHat ) is the enthalpy change when one mole of gaseous atoms is formed from its elements under standard conditions.
• Eg. ΔHat [H2] relates to the equation:

½ H2(g) → H(g)

#### Exam Tip

Remember to take into account the number of moles of each reactant and product.

For example, there are two moles of NaHCO3(s) so the ΔHf value is multiplied by 2. ### Author: Francesca

Fran has taught A level Chemistry in the UK for over 10 years. As head of science, she used her passion for education to drive improvement for staff and students, supporting them to achieve their full potential. Fran has also co-written science textbooks and worked as an examiner for UK exam boards.
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