# Hess' Law

If you ever need to figure out the enthalpy change of something you can't measure directly, don't worry! There's something called Hess' Law that can help you out. This trick uses enthalpy changes that you do know to figure out the unknown value you're looking for. Hess' Law is a fancy term used in physical chemistry. It basically means that the enthalpy change of a reaction doesn't depend on the path you take. Another way to say it is Hess' Law of Constant Heat Summation. In this article, we're going to dive into Hess' Law. We'll explain how to represent it using energy diagrams and Hess' cycles. You'll also learn how to calculate unknown enthalpy changes by using enthalpy changes of combustion and formation. We'll even give you some examples to practice with.

## What is Hess' law?

A chemical reaction can have many different pathways. For instance, if you start with reactant A and want to reach product B, you can head straight from A to B. Alternatively, you can reverse your steps and go through the entire alphabet, passing through Z, X, Y, before finally arriving at B. Now, Hess' Law tells us that it doesn't matter how many steps you take, as long as you begin and end with the same species, the enthalpy change will be identical. This is because Hess' Law reinforces the first law of thermodynamics, which states that energy is always conserved in a chemical reaction. This principle is useful because it enables us to determine the unknown enthalpy change of a specific pathway using the known enthalpy changes of another pathway. In just a moment, we'll examine some examples. But before that, let's find out how we can demonstrate Hess' law.

## How do we show Hess' law?

To show Hess' law in action, we need to consider the different routes of a reaction. Like in the introduction above, let's say that we start with reactant A. It reacts directly to form product B. We can call this reaction route 1. However, A can also react to form intermediate Z, which reacts to form intermediate Y. Y then forms X and X in turn reacts to form B. We can call this indirect route, from A, all the way through Z, Y and X, and finally ending at B, route 2. In both cases, we started and ended with the same species. Hess' law tells us that the enthalpy changes of the two routes will be the same.

We can display the different routes a reaction can take in two ways: Using an energy diagram Using a Hess' cycle

### Energy diagrams

Energy diagrams show the energy level of species at different points in a reaction. The difference in energy levels between products and reactants gives us the enthalpy change of the reaction. Here, you can see that both routes start with A and end up at B. The overall enthalpy change is the same, even though route 1 went directly from A to B, whereas route 2 went through Z, X and Y.

### Hess' cycle

Hess' cycles are another simple way of showing the different routes of a reaction. You don't need to show the energy levels of the different species involved. Instead, you simply map out the two different routes like a flow chart.

It's essential to remember that routes 1 and 2 start with the same reactants and end with the same products. As a result, they both have the same overall enthalpy change. By including some of the enthalpy changes that we already know, we can determine an enthalpy change that we don't know.

So, what if we want to establish the enthalpy change of route 1? If we're aware of the enthalpy changes of all the reactions in route 2, we can compute the enthalpy change of route 1. The enthalpy change of route 1 is equal to the sum of all the enthalpy changes of route 2. Mathematically, it can be written as: enthalpy change of route 1 = enthalpy change of reaction A + enthalpy change of reaction B + enthalpy change of reaction C, Now, let's take a look at some examples of how Hess' Law works in real-life calculations.

### Hess' law and enthalpy of formation

The first type of calculation using Hess' Law involves utilizing enthalpies of formation to compute the enthalpy change of a reaction.

Enthalpy of formation, , is the enthalpy change that occurs when one mole of a substance is formed from its constituent elements, with all species in their standard states and under standard conditions.

In a chemical reaction, the reactants and products are always composed of the same elements. This means that we can construct a Hess' cycle with an indirect route that goes via these elements, employing enthalpies of formation to help us. Let's consider an example.

Calculate the enthalpy change of the following reaction using the given enthalpies of formation: Species (Propene) (Hydrogen) (Propane)+20.4+0.0-103.8

It's important to remember that the enthalpy of formation for any elemental molecule is always 0.

In this reaction, the direct route goes directly from the reactants, propene and hydrogen, to the product, propane. We'll refer to this as route 1. We don't know the enthalpy change of this route. However, we do know the enthalpies of formation for each of the species involved. We can use them to create an indirect route, route 2, that goes from reactants to elements to products, and determine the enthalpy change of that instead. Let's draw a Hess' cycle and include the enthalpies of formation that we know. We can ignore the enthalpy of formation of hydrogen since it is 0.

Make certain that you draw all of your arrows in the correct direction. Enthalpies of formation always move from the elements to the compounds.

First, we go from propene and hydrogen to their elements. This is the inverse of one of the enthalpy changes that we do know - the enthalpy of formation of propene. We know it's the inverse since the black arrow showing the reaction's enthalpy change goes in the opposite direction. Therefore, we need to take the negative of this enthalpy change. So far, route 2's enthalpy change is .

Now, we need to go from the elements to propane. This is one of the enthalpy changes that we know - the enthalpy of formation of propane. This time, we are following the black arrow in the right direction, so we add this enthalpy value to route 2's current enthalpy change. It now appears like this:

We've done it! We've successfully gone from our reactants, propene and hydrogen, to our product, propane, via the indirect route, and have calculated an enthalpy change: . Hess' Law states that the enthalpy change of a reaction is always the same, regardless of the path taken. Therefore, the enthalpy change of the direct route, route 1, is also .

### Hess' law and enthalpy of combustion

Both sides of a chemical reaction always combust to produce the same products. This means that instead of creating an indirect route that goes via elements, we can go through their combustion products instead. This involves using enthalpies of combustion.

Enthalpy of combustion, , is the enthalpy change that occurs when one mole of a substance is completely burned in oxygen under standard conditions.

Let's calculate the enthalpy change of the following reaction using the given enthalpies of combustion: Species-394-286-1560

To begin, let's draw a Hess' cycle. The direct route goes directly from the reactants, carbon and hydrogen, to the product, ethane. The indirect route goes through their combustion products, which are the same for both sides of the reaction. Therefore, we don't have to write them out - we can just put 'Combustion products.' However, note that in our equation, we have two moles of carbon and three moles of hydrogen. Our indirect route therefore needs to feature two enthalpies of combustion of carbon and three enthalpies of combustion of hydrogen.

Hess' cycle for the formation of ethane.

By following route 2 from carbon and hydrogen to the combustion products, we get an enthalpy change of .

To go from the combustion products to ethane, we need the reverse of the enthalpy of combustion of ethane. Therefore, route 2's overall enthalpy change is . This implies that route 1's enthalpy change, which is the enthalpy of formation of ethane, is also .

This is our final answer.

As we saw earlier, some enthalpy changes are difficult to measure. We can use Hess' Law to calculate these instead. Examples include calculating lattice enthalpies, the enthalpy of formation of benzene, and the enthalpy change when graphite turns into diamond.

In summary, Hess' Law states that the enthalpy change of a reaction is independent of the route taken. It is also known as Hess' Law of constant heat summation. We can use Hess' Law to calculate unknown enthalpy changes using enthalpy changes that we do know. We can represent Hess' Law using an energy diagram or a Hess' cycle. Hess' Law calculations often involve enthalpies of formation and enthalpies of combustion.

## Hess' Law

What is Hess' law?

Hess' law is a relationship used in physical chemistry. It states that the enthalpy change of a reaction is independent of the route taken.

How do you do Hess' law calculations?

To do Hess' law calculations, you draw a Hess' cycle. This shows a direct route, going from reactants to products, and an indirect route, going via intermediates. You write in the enthalpy changes of the indirect route involving the products, reactants, and intermediates, and use them to calculate the enthalpy change of the direct route.

How is Hess' law applied in calculating enthalpy?

Hess' law states that the enthalpy change of a reaction is independent of the route taken. This means that we can calculate the enthalpy change of the direct route of a reaction using the enthalpy changes of an indirect route. For example, say you want to calculate the enthalpy change of the reaction between ethene and hydrogen to form ethane. You can work this out using the enthalpy changes of formation of the three species involved.

Can Hess' law be applied to Gibbs free energy?

Hess' law also extends to Gibbs free energy. The overall change in Gibbs free energy in a reaction is always the same, regardless of the route taken. Take the direct route of the reaction A + B → D. Let's say that the indirect route consists of the reactions A + B → 2C and 2C → D. The changes in Gibbs free energy for these two reactions are ΔGo1 and ΔGo2 respectively. The overall change in Gibbs free energy of the direct route is therefore ΔGo1 + ΔGo2.

How do you use Hess' law?

Hess' law states that the enthalpy change of a reaction is independent of the route taken. This means that we can use it to calculate an enthalpy change that we don't know, using enthalpy changes that we do know. For example, you might want to calculate the enthalpy change of a reaction. You can do this using the enthalpy changes of formation of all of the reactants and products involved.

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