1.5.5 Hess’s Law

• 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)

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

Calculating ΔH_r from ΔH_f 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 + ΔH_r

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 + ΔH_r

Therefore,

ΔH_r = ΔH₂ – ΔH₁

Worked example: Calculating the enthalpy change of reaction

• Step 1: Write the balanced equation at the top

• Step 2: Draw the cycle with the elements at the bottom

• Step 3: Draw in all arrows, making sure they go in the correct directions. Write the standard enthalpy of formations

• Step 4: Apply Hess’s Law

Calculating ΔH_f  from ΔH_c 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 = ΔH_f + 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 = ΔH_f + ΔH₂

Therefore,

ΔH_f  = ΔH₁ – ΔH₂

Worked example: Calculating the enthalpy change of formation of ethane

• Step 1: Write the equation for enthalpy change of formation at the top and add oxygen on both sides

• Step 2: Draw the cycle with the combustion products at the bottom

• Step 3: Draw all arrows in the correct direction

• Step 4: Apply Hess’s Law

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 (ΔH_at^ꝋ ) is the enthalpy change when one mole of gaseous atoms is formed from its elements under standard conditions.
  • Eg. ΔH_at^ꝋ [H₂] relates to the equation:

½ H₂(g) → H(g)

Worked example: Calculating average C-H bond energy

• Step 1: Write down the equation for the dissociation of methane at the top

• Step 2: Write down the elements at the bottom

• Step 3: Draw all arrows in the correct direction

• Step 4: Apply Hess’s Law

• Step 5: Since there are 4 C-H bonds in methane: