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Hess's Law: Definition, Formula & Examples

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

In this lesson, we will learn about Hess's Law and how to use enthalpy of formation and enthalpy of combustion to calculate the change in enthalpy using Hess's Law.

Chemical Reactions

Most chemical reactions are actually a series of reactions. Take for example the breakdown of sugar into energy:

Glucose reaction

This actually occurs over dozens of steps. Glucose is first changed into glucose-6-phospahte, and eventually into pyruvate and then into carbon dioxide. Some of the electrons are put onto ADP to make ATP. When these electrons are removed for energy oxygen is used. Through this entire process, we end up losing water. But it is a lot easier and more efficient to simplify it into one reaction. Everything that ends up being both a product and reactant gets canceled out until we end up with sugar and oxygen as reactants and carbon dioxide and water as products.

Let's look at a simple example using A's and B's. Let's say that:

A+B = AB

And

AB + C = ABC

Then we can say that A+B+AB+C=AB + ABC. But since AB is both a product and reactant we can cancel those out and simplify this further into A+B+C=ABC.

Hess's Law

This doesn't just make it easier to write chemical formulas. It also simplifies the process of determining the total enthalpy change. Hess's Law states that no matter the multiple steps or intermediates in a reaction the total enthalpy change is equal to the sum of each individual reaction. It is also known as the conservation of energy law. So this means that we can determine the total enthalpy change of A+B+C=ABC by determining this actual reaction's enthalpy change. Or we can determine the enthalpy change for A+B=AB and AB+C=ABC and then add these two together.

Another way to look at this is with a graph. Let's say that it takes a lot of energy for A and B to form AB. But then once it combines with C into ABC it releases a lot of energy:

Change in energy graph

So we can determine the enthalpy change by simply looking at delta H1, or we can add delta H2 and delta H3. This may not make sense at first. Why we would add delta H2 and delta H3 instead of subtracting delta H2 from delta H3? But we need to remember that delta H1 and delta H3 are negative (because they go down on the enthalpy chart) while delta H2 is positive (because it goes up on the enthalpy chart), so the adding and subtracting is already worked in by making the numbers either positive or negative.

Enthalpy Change

Before we look at some actual examples, let's review what enthalpy is. Enthalpy is the amount of energy, or heat, in a compound at a specific pressure. So the change in enthalpy is how much the total enthalpy changes from reactants to products. If energy is released, then the change in enthalpy is negative because energy was released into the environment, so there is less energy in the products than in the reactants. If energy is used then the change in enthalpy is positive because energy was taken from the environment, so there is more energy in the products than in the reactants.

In regards to Hess's Law enthalpy of formation and enthalpy of combustion are very important. Enthalpy of formation is the change in enthalpy required to create one mole of the substance from its pure elements. While Enthalpy of combustion is the change in enthalpy required to break down one mole of the substance into its pure elements. You can find tables which list the enthalpy of formation and combustion. The enthalpy of combustion for a compound will always be the same as the enthalpy of formation except the sign will be switched (so if the enthalpy of formation for carbon dioxide is -394 kJ then the enthalpy of combustion of carbon dioxide is 394 kJ).

Heat of Formation table

Example

Let's start with methane combusting into carbon dioxide and water.

Methane reaction

When we look at the table of enthalpy of formation we see that the heat of formation of methane is -74.8 kJ/mol, since methane is on the products side; we want the heat of combustion, so it is 74.8 kJ/mol. For oxygen it is 0 kJ/mol. Carbon dioxide is -393.5 kJ/mol; we don't need to switch this sign because we use the heat of formation for products. And for water, it is -241.8 kJ/mol. Notice that we use the heat of formation of gaseous water because that is what is used in the equation.

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