How do you derive the enthalpy change for a formation reaction from combustion data?

The enthalpy change for a formation reaction can be derived from combustion data using Hess's Law of constant heat summation.

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the route by which the reaction takes place, as long as the initial and final conditions are the same. This principle allows us to calculate the enthalpy change of a reaction that is difficult to measure directly, such as a formation reaction, by using the enthalpy changes of other reactions that are easier to measure, such as combustion reactions.

To derive the enthalpy change for a formation reaction from combustion data, you need to know the enthalpy changes for the combustion reactions of the reactants and products involved in the formation reaction. The enthalpy change for the formation reaction is then calculated by subtracting the sum of the enthalpy changes for the combustion reactions of the reactants from the sum of the enthalpy changes for the combustion reactions of the products.

For example, consider the formation reaction of water from hydrogen and oxygen:

H2(g) + 1/2O2(g) → H2O(l)

The enthalpy change for this reaction can be calculated from the enthalpy changes for the combustion reactions of hydrogen and water:

H2(g) + 1/2O2(g) → H2O(l) ΔHc = -286 kJ/mol
H2(g) + O2(g) → H2O(l) ΔHc = -572 kJ/mol

The enthalpy change for the formation reaction is then calculated as follows:

ΔHf = ΔHc(products) - ΔHc(reactants)
= -286 kJ/mol - (-572 kJ/mol)
= 286 kJ/mol

This method of deriving the enthalpy change for a formation reaction from combustion data is a practical application of Hess's Law and is commonly used in thermochemistry. It allows us to calculate the enthalpy changes for reactions that are difficult to measure directly, and it provides a way to verify experimental results.