Lesson Video: Hess’s Law Chemistry

In this video, we will learn how to define and use Hess’s law to calculate enthalpy changes.

13:15

Video Transcript

In this video, we’ll learn about Hess’s law, which is very useful in chemistry for calculating enthalpy changes. We’ll define Hess’s law and use it to calculate the enthalpy change for combustion and formation.

Let’s imagine that we’re attempting to climb a mountain. There might be multiple paths we can take to get to the summit of the mountain. It might take different amounts of time to climb the mountain, depending on which path we take. But because both paths are starting at the base of the mountain and finishing at the summit, the change in altitude will be the same no matter what path is taken. The change in energy during the course of a chemical reaction is similar to the altitude change when climbing a mountain. That is, if we start a reaction with some reactants and finish with some products, the change in energy will be the same, no matter which path we take to get from the reactants to the products. This is exactly what Hess’s law tells us. The enthalpy change of a chemical reaction is independent of the path taken.

So, let’s say we have some generic chemical reaction where we start with our reactants and form some products. One path would be going directly from the reactants to the products, but there might be a second path where we form some intermediates first before forming the products. Hess’s law tells us the change in enthalpy for path one is going to be equal to the change in enthalpy for path two. If we take a look at an enthalpy diagram for this reaction, the cause for Hess’s law becomes obvious. Here, we have the reactant state and the product state. The change in enthalpy to go from the reactants to the products is simply the difference in enthalpy between the product state and the reactant state, which is indicated by 𝛥𝐻 a.

In the second path, the intermediates are formed first. The change in enthalpy marked by 𝛥𝐻 b is the change in enthalpy going from the reactants to the intermediates. And 𝛥𝐻 c is the change in enthalpy to go from the intermediates to the products. The enthalpy change for the first path is just 𝛥𝐻 a. And we can find the enthalpy change for path two by adding 𝛥𝐻 b and 𝛥𝐻 c together, which would give us this change in enthalpy. As we can see, the change in enthalpy for path one is identical to the change in enthalpy for path two. This should be unsurprising because in both cases we’re starting with the reactants and ending with the products.

The overall enthalpy change is always determined by the relative positions of the reactants and products on the enthalpy diagram. Hess’s law is incredibly convenient in chemistry to help us determine the enthalpy changes of different reactions. For example, we might not know the change in enthalpy of going directly from the reactants to the products. But because the change in enthalpy is the same for both of these paths, we can calculate the enthalpy change that we’re interested in without performing an experiment, as long as we know the enthalpy change or changes for the other path.

Let’s see how we can use Hess’s law to calculate the enthalpy change of a reaction. Let’s say we want to know the standard enthalpy of formation of benzene. Recall that the standard enthalpy of formation is the enthalpy change when one mole of a substance is formed from its constituent elements in their standard states and under standard conditions. Standard conditions are defined as temperatures of 298 kelvin and pressures of one bar. You may also see pressures of one atmosphere for standard conditions because one bar and one atmosphere are fairly similar values.

So, if we want to know the standard enthalpy of formation for benzene, we’re describing the reaction where we form benzene directly from carbon in the form of graphite and hydrogen gas. We can always measure a change in enthalpy for a reaction by performing a calorimetry experiment. But it’s impossible to create benzene from graphite and hydrogen gas, so we can’t measure the enthalpy of formation for benzene. But we can measure the standard enthalpy of combustion for each of the chemical species involved in the reaction. As a refresher, the standard enthalpy of combustion is the enthalpy change when one mole of a substance that’s in its standard state burns completely in oxygen under standard conditions. So, these are the chemical reactions that we would measure to determine the enthalpy of combustion for each of the chemical species.

We’ll use these reactions and Hess’s law to calculate the enthalpy of formation for benzene by constructing a Hess cycle. The first step in constructing our Hess cycle is to write out the chemical equation that corresponds to the enthalpy change we want to know. Next, we need to include the chemical species that are involved in the other reactions that we’re using to calculate our enthalpy change. The big thing we need to include here is the products of these combustion reactions, the carbon dioxide and the water. We could include the oxygen in our Hess cycle, but it would clutter the screen. Besides, these reactions are being performed in excess oxygen, so the oxygen isn’t the most important chemical species to include in our Hess cycle.

The next thing we need to do to construct our Hess cycle is to draw arrows to connect our reactants and products. Graphite burns in oxygen to produce carbon dioxide. Hydrogen burns in oxygen to produce water. And benzene burns in oxygen to produce carbon dioxide and water. Next, we’ll put in enthalpy changes for each of the reactions we just put arrows for. This arrow represents the combustion of graphite. The enthalpy change for this arrow is the enthalpy change of combustion for graphite. But there are six moles of graphite in the reaction. So, we need to multiply this enthalpy change by six. And the enthalpy of combustion for graphite is negative 393.5 kilojoules per mole.

This next arrow represents the combustion of hydrogen. So, the enthalpy change for this arrow is three times the enthalpy of combustion of hydrogen because we have three moles of hydrogen in our Hess cycle. And the enthalpy of combustion for hydrogen is negative 285.8 kilojoules per mole. Finally, the last arrow represents the combustion of benzene. We only have one mole of benzene in our Hess cycle. So, the enthalpy change for this arrow is just the enthalpy change of combustion for benzene, negative 3267 kilojoules per mole.

Now, we need to construct two paths around our diagram so that we can apply Hess’s law to our Hess cycle. When we make these paths, the arrow should go in the same direction. So, one path we can start with carbon and hydrogen and follow the arrows to carbon dioxide and water. For our other path, we’ll again start with carbon and hydrogen and finish the arrow going the other way at carbon dioxide and water.

Hess’s law tells us that the enthalpy change for path one is equal to the enthalpy change for path two. The total enthalpy change for path one is the enthalpy of formation of benzene plus the enthalpy of combustion of benzene, negative 3267 kilojoules per mole. The total enthalpy change for path two is the sum of six times negative 393.5 kilojoules per mole and three times negative 285.8 kilojoules per mole.

Now, we have everything we need to solve for the enthalpy of formation of benzene. Let’s first isolate the enthalpy of formation by adding 3267 kilojoules per mole to both sides. Now, we can solve for the enthalpy of formation of benzene, which gives us 48.6 kilojoules per mole. Now, we know how to use Hess’s law to construct Hess cycles so that we can calculate enthalpy changes of reactions that we’re interested in.

Perhaps, the most common application of Hess’s law is calculating the enthalpy change of a reaction from enthalpies of formation. For example, let’s determine the enthalpy change associated with this reaction. This is the reaction involved in cellular respiration, where glucose is used to produce energy for our cells. We’ll need the enthalpies of formation for each of the chemical species involved in this reaction. Remember that the enthalpies of formation correspond to forming each of the chemical species from the elements that make them up.

To construct our Hess cycle, we’ll need to include the elements that make up each of the chemical species. Before I do that, I’m going to remove the standard enthalpy of formation for oxygen from this table so that we can save some screen space. After all, the standard enthalpy of formation for any element in its standard state is zero. So, it’s not providing much information here. To form the chemical species on either side of our chemical reaction from their standard states, we would need six carbon as graphite, nine oxygen gas, and six hydrogen gas.

The next step in constructing our Hess cycle is to connect everything with arrows. The direction of our arrows in the Hess cycle need to match the reaction arrows in these reactions that correspond to the enthalpies of formation. Glucose is formed from carbon, oxygen, and hydrogen, carbon dioxide is formed from oxygen and carbon, and water is formed from hydrogen and oxygen. We don’t need to worry about including oxygen gas in our Hess cycle because the enthalpy of formation of oxygen is zero.

Next, let’s attach the correct enthalpy changes to the arrows we just drew. This arrow is the enthalpy of formation of glucose, which is negative 1273.3 kilojoules per mole. This arrow corresponds to the enthalpy of formation of carbon dioxide, actually six times the enthalpy of formation of carbon dioxide because we have six moles of carbon dioxide in our reaction equation. The enthalpy of formation of carbon dioxide is negative 393.5 kilojoules per mole. And this final arrow matches the enthalpy of formation for water. And again, this will be six times the enthalpy of formation for water because we have six moles of water in our reaction equation. And we can plug in the enthalpy of formation of water, negative 285.8 kilojoules per mole.

Now, we need to draw our paths around our Hess cycle, making sure the arrow direction matches. So, one of our paths can go this way around the Hess cycle and our other path can go this way. According to Hess’s law, the enthalpy change for both of these paths needs to be equal. The total enthalpy change for path one is the sum of negative 1273.3 kilojoules per mole and the standard enthalpy for the reaction that we’re interested in calculating. And the total enthalpy change for path two is the sum of six times negative 393.5 kilojoules per mole and six times negative 285.8 kilojoules per mole.

Now, we can solve for the 𝛥𝐻 of the reaction. We can isolate the enthalpy change we’re trying to solve for by adding 1273.3 kilojoules per mole to both sides. Multiplying and adding everything together gives us negative 2802.5 kilojoules per mole for the enthalpy change of the reaction.

In the past, we might’ve calculated the enthalpy change for reaction using bond enthalpies. That is, we take the sum of the bond enthalpies for the bonds that are broken in the reactants and we subtract the bond enthalpies for the bonds that are formed in the products. And now we’ve seen how to calculate the same quantity using standard enthalpies of formation. So, which of these approaches is better? Should we calculate the enthalpy change of a reaction using bond enthalpies or enthalpies of formation?

We can look up the values of bond enthalpies and enthalpies of formation in tables and use them to calculate the enthalpy of reaction. But where do these tabulated values come from? Enthalpies of formation are measured directly in experiments or calculated using experimental data. And these experiments are performed in standard conditions. Bond enthalpies are simply average values for a bond of that type. But in reality, bond enthalpies change depending on the rest of the molecule that bond is in. Also, bond enthalpies aren’t measured under standard conditions. So, the best way to calculate an enthalpy change for reaction is using the standard enthalpies of formation because they are more accurate.

Now, let’s wrap up this video by summarizing what we learned. Hess’s law states that the enthalpy change of a chemical reaction is independent of the path taken. We can use Hess cycles to calculate an enthalpy change. We saw how to calculate enthalpies of formation from enthalpies of combustion using Hess cycles and how to calculate the enthalpy of a reaction using enthalpies of formation. But we could construct more complicated Hess cycles for other reactions. We can also calculate the enthalpy change of a reaction using bond enthalpies, but the results won’t be as accurate as a calculation that uses standard enthalpies of formation.

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