# Calculating Energy Change

As you learned on the previous page, the energy change associated with a chemical reaction is expressed by heat of reaction, ∆H. These values can be can be calculated a couple of ways.

## Hess’ Law Remember that when the direction of a thermochemical equation is reversed, the sign of the enthalpy of the reaction is reversed. When an equation is doubled, tripled, cut in half, etc., the quantity of ∆H changes by that same ratio. When reactions are mathematically manipulated in this way, we are actually using the concept known as Hess’ Law. Hess’ Law says that the total enthalpy of a reaction is independent of the reaction pathway. This means that if a reaction is carried out in a series of steps, the enthalpy change (∆H) for the overall reaction will be equal to the sum of the enthalpy changes for the individual steps.

To better understand this concept, think about climbing a mountain. To get to the top, you can take the road that goes around the mountain. Or, you can hike straight up the side.

Regardless of the path you choose, your change in elevation will be the same. ∆H is the same way in that its value is independent of the path taken to establish its value.

The advantage of Hess Law is that it allows us to calculate the enthalpy change for a chemical reaction in which the enthalpy data is not directly known.

Watch the following video to see how to use Hess’ Law to calculate ∆Hrxn.

The rules for applying Hess’s law are below:
1. When an equation is revered, the value of ΔH° must also be reversed.
2. Any formula that is cancelled from both sides of the equation must be identical, even in the same physical state.
3. If the coefficients of a reaction are multiplied or divided, the value of ΔH° must also be multiplied or divided by the same factor.
PRACTICE!
Find the ΔH° for the reaction, Cusub2O(s) + 1/2 Osub2 (g) → Cusub 2 O(s) from this data:
2 Cu(s) + O2 (g) → 2 CuO(s)    ΔH° = -310 kJ
2 Cu(s) + 1/2 O2 (g) → Cu2O (s)   ΔH° = -169 kJ

By inspecting the two equations, it is easy to see that the second equation needs to be reversed, because Cu2O(s) is a reactant in the final equation. When the reaction is reversed, the sign for ΔH° must be changed.

Step 1:

2 Cu(s) + O2 (g) → 2 CuO(s)    ΔH° = -310 kJ
2 Cu(s) + 1/2 O2 (g) → Cu2O (s)   ΔH° = +169 kJ

Hess’ Law can be shown visually through an enthalpy diagram. The one shown here represents the above reaction. The change in enthalpy, ΔH, is represented by the distance between the horizontal lines. It is important to note that we cannot know the actual H values (the horizontal lines) for any chemical since it is impossible for us to measure total heat content, H. But, through calorimetry, we can measure ∆Hrxn.

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