How to Calculate the Heat of Combustion of Propane

The heat of combustion of propane (C3H8) is a crucial parameter in understanding the energy content and efficiency of this important fuel. To calculate the heat of combustion of propane, we need to determine the enthalpy change (ΔH) when 1 mole of propane is completely burned in oxygen to form carbon dioxide and water. This can be achieved by using Hess’s law and the given data on the enthalpies of formation.

Step 1: Understand the Balanced Chemical Equation

The balanced chemical equation for the combustion of propane is:

C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g)

This equation shows that 1 mole of propane (C3H8) reacts with 5 moles of oxygen (O2) to produce 3 moles of carbon dioxide (CO2) and 4 moles of water (H2O).

Step 2: Find the Enthalpy of Formation of CO2 and H2O

The enthalpy of formation (ΔHf°) is the change in enthalpy when 1 mole of a compound is formed from its constituent elements in their standard states. We need to know the enthalpy of formation for carbon dioxide (CO2) and water (H2O):

• CO2(g): ΔHf° = -393.5 kJ/mol
• H2O(g): ΔHf° = -241.8 kJ/mol

Step 3: Write the Balanced Equation for Propane Formation

To find the enthalpy of formation of propane (ΔHf°(C3H8)), we need to write the balanced chemical equation for the formation of 1 mole of propane from its constituent elements in their standard states:

3C(s) + 4H2(g) → C3H8(g)

Step 4: Use Hess’s Law to Find ΔHf°(C3H8)

We can use the following Hess’s law cycle to determine the enthalpy of formation of propane:

1. C(s) + O2(g) → CO2(g) (1)
2. H2(g) + 1/2O2(g) → H2O(l) (2)
3. 3C(s) + 4H2(g) → C3H8(g) (3)
4. 3CO2(g) + 4H2O(l) → C3H8(g) + 5O2(g) (4)

The sum of reactions (1), (2), and (3) is equal to reaction (4) but in reverse. Therefore, the enthalpy change of reaction (4) is equal to the negative sum of the enthalpy changes of reactions (1), (2), and (3).

Enthalpy change of reaction (4) = -[ΔHf°(CO2) * 3 + ΔHf°(H2O) * 4 + ΔHf°(C3H8)]

Enthalpy change of reaction (4) = -[-393.5 * 3 – 241.8 * 4 – ΔHf°(C3H8)]

Solving for ΔHf°(C3H8), we get:

ΔHf°(C3H8) = -2219.2 kJ/mol

Step 5: Calculate the Heat of Combustion

The heat of combustion of propane is the negative of the enthalpy of formation (ΔHf°) of propane:

Heat of combustion of propane = -ΔHf°(C3H8) = -(-2219.2 kJ/mol) = 2219.2 kJ/mol

Therefore, the heat of combustion of propane is 2219.2 kJ/mol.