# What does Hess's law say about the enthalpy of a reaction?

Jun 22, 2014

The law states that the total enthalpy change during a reaction is the same whether the reaction is made in one step or in several steps.

In other words, if a chemical change takes place by several different routes, the overall enthalpy change is the same, regardless of the route by which the chemical change occurs (provided the initial and final condition are the same).

Hess' law allows the enthalpy change (ΔH) for a reaction to be calculated even when it cannot be measured directly. This is accomplished by performing basic algebraic operations based on the chemical equation of reactions using previously determined values for the enthalpies of formation.

Addition of chemical equations leads to a net or overall equation. If enthalpy change is known for each equation, the result will be the enthalpy change for the net equation.

EXAMPLE

Determine the heat of combustion, ΔH_"c", of CS₂, given the following equations.

1. C(s) + O₂(g) → CO₂(g); ΔH_"c" = -393.5 kJ
2. S(s) + O₂(g) → SO₂(g); ΔH_"c" = -296.8 kJ
3. C(s) + 2S(s) → CS₂(l); ΔH_"f" = 87.9 kJ

Solution

Write down the target equation, the one you are trying to get.

CS₂(l) + 2O₂(g) → CO₂(g) + 2SO₂(g)

Start with equation 3. It contains the first compound in the target (CS₂).

We have to reverse equation 3 and its ΔH to put the CS₂ on the left. We get equation A below.

A. CS₂(l) → C(s) + 2S(s); -ΔH_"f" = -87.9 kJ

Now we eliminate C(s) and S(s) one at a time. Equation 1 contains C(s), so we write it as Equation B below.

B. C(s) + O₂(g) → CO₂(g); ΔH_"c" = -393.5 kJ

We use Equation 2 to eliminate the S(s), but we have to double it to get 2S(s). We also double its ΔH. We then get equation C below.

C. 2S(s) + 2O₂(g) → 2SO₂(g); ΔH_"c" = -593.6 kJ

Finally, we add equations A, B, and C to get the target equation. We cancel things that appear on opposite sides of the reaction arrows.

A. CS₂(l) → C(s) + 2S(s); -ΔH_"f" = -87.9 kJ
B. C(s) + O₂(g) → CO₂(g); ΔH_"f" = -393.5 kJ
C. 2S(s) + 2O₂(g) → 2SO₂(g); ΔH_"f" = -593.6 kJ

CS₂(l) + 3O₂(g) → CO₂(g) + 2SO₂(g); ΔH_"c" = -1075.0 kJ