# Heat of Formation Worked Problem

## Learn How to Calculate the Enthalpy Change Heat of formation is a measure of energy of a reaction. PM Images / Getty Images

Heat of formation is the enthalpy change that occurs when a pure substance forms from its elements under conditions of constant pressure. These are worked example problems calculating the heat of formation.

## Review

The symbol for the standard heat of formation (also known as the standard enthalpy of formation) is ΔHf or ΔHf° where:

Δ indicates a change

H indicates enthalpy, which is only measured as a change, not as an instantaneous value

° indicates thermal energy (heat or temperature)

f means "formed" or that a compound is being formed from its component elements

You may wish to review the Laws of Thermochemistry and endothermic and exothermic reactions before you begin. Tables are available for heats of formation of common compounds and ions in aqueous solution. Remember, heat of formation will tell you whether heat was absorbed or released and the quantity of heat.

## Problem 1

Calculate ΔH for the following reaction:

8 Al(s) + 3 Fe3O4(s) → 4 Al2O3(s) + 9 Fe(s)

Solution

ΔH for a reaction is equal to the sum of the heats of formation of the product compounds minus the sum of the heats of formation of the reactant compounds:

ΔH = Σ ΔHf products - Σ ΔHf reactants

Omitting terms for the elements, the equation becomes:

ΔH = 4 ΔHf Al2O3(s) - 3 ΔHf Fe3O4(s)

The values for ΔHf may be found in the Heats of Formation of Compounds table. Plugging in these numbers:

ΔH = 4(-1669.8 kJ) - 3(-1120.9 kJ)

ΔH = -3316.5 kJ

ΔH = -3316.5 kJ

## Problem 2

Calculate ΔH for the ionization of hydrogen bromide:

HBr(g) → H+(aq) + Br-(aq)

Solution

ΔH for a reaction is equal to the sum of the heats of formation of the product compounds minus the sum of the heats of formation of the reactant compounds:

ΔH = Σ ΔHf products - Σ ΔHf reactants

Remember, the heat of formation of H+ is zero. The equation becomes:

ΔH = ΔHf Br-(aq) - ΔHf HBr(g)

The values for ΔHf may be found in the Heats of Formation of Compounds of Ions table. Plugging in these numbers:

ΔH = -120.9 kJ - (-36.2 kJ)

ΔH = -120.9 kJ + 36.2 kJ

ΔH = -84.7 kJ