Calculating Enthalpy Changes Using Hess's Law

Hess's Law, also known as "Hess's Law of Constant Heat Summation," states that the total enthalpy of a chemical reaction is the sum of the enthalpy changes for the steps of the reaction. Therefore, you can find enthalpy change by breaking a reaction into component steps that have known enthalpy values. This example problem demonstrates strategies for how to use Hess's Law to find the enthalpy change of a reaction using enthalpy data from similar reactions.

Hess's Law Enthalpy Change Problem

What is the value of ΔH for the following reaction?

CS₂(l) + 3 O₂(g) → CO₂(g) + 2 SO₂(g)

Given:

C(s) + O₂(g) → CO₂(g); ΔH_f = -393.5 kJ/mol
S(s) + O₂(g) → SO₂(g); ΔH_f = -296.8 kJ/mol
C(s) + 2 S(s) → CS₂(l); ΔH_f = 87.9 kJ/mol

Solution

Hess's Law says the total enthalpy change does not rely on the path taken from beginning to end. Enthalpy can be calculated in one grand step or multiple smaller steps.

To solve this type of problem, organize the given chemical reactions where the total effect yields the reaction needed. There are a few rules that you must follow when manipulating a reaction.

1. The reaction can be reversed. This will change the sign of ΔH_f.
2. The reaction can be multiplied by a constant. The value of ΔH_f must be multiplied by the same constant.
3. Any combination of the first two rules may be used.

Finding a correct path is different for each Hess's Law problem and may require some trial and error. A good place to start is to find one of the reactants or products where there is only one mole in the reaction. You need one CO₂, and the first reaction has one CO₂ on the product side.

C(s) + O₂(g) → CO₂(g), ΔH_f = -393.5 kJ/mol

This gives you the CO₂ you need on the product side and one of the O₂ moles you need on the reactant side. To get two more O₂ moles, use the second equation and multiply it by two. Remember to multiply the ΔH_f by two as well.

2 S(s) + 2 O₂(g) → 2 SO₂(g), ΔH_f = 2(-326.8 kJ/mol)

Now you have two extra S's and one extra C molecule on the reactant side that you don't need. The third reaction also has two S's and one C on the reactant side. Reverse this reaction to bring the molecules to the product side. Remember to change the sign on ΔH_f.

CS₂(l) → C(s) + 2 S(s), ΔH_f = -87.9 kJ/mol

When all three reactions are added, the extra two sulfur and one extra carbon atoms are canceled out, leaving the target reaction. All that remains is adding up the values of ΔH_f.

ΔH = -393.5 kJ/mol + 2(-296.8 kJ/mol) + (-87.9 kJ/mol)
ΔH = -393.5 kJ/mol - 593.6 kJ/mol - 87.9 kJ/mol
ΔH = -1075.0 kJ/mol

Answer: The change in enthalpy for the reaction is -1075.0 kJ/mol.

Facts About Hess's Law

• Hess's Law takes its name from Russian chemist and physician Germain Hess. Hess investigated thermochemistry and published his law of thermochemistry in 1840.
• To apply Hess's Law, all of the component steps of a chemical reaction need to occur at the same temperature.
• Hess's Law may be used to calculate entropy and Gibb's energy in addition to enthalpy.