Jump to a key chapter

- This article is about
**calculating enthalpy change**in physical chemistry. - We'll start by
**defining enthalpy change**before giving its**units**. - We'll then recap certain
**types of enthalpy change**. - After that, we'll learn how you
**calculate enthalpy change****using****Hess' law**. - You'll first find out the
**method**, then you'll be able to apply your knowledge with our**worked examples**. - We include questions that use
**enthalpy of formation**,**enthalpy of combustion**, and**mean bond energy**.

## Calculating enthalpy change: definition, units, and types

Before we go any further, there are two important questions we need to answer:

- What is
**enthalpy change**? - What are
**standard enthalpy changes**?

**Enthalpy change (∆H)** is the amount of heat energy transferred during a chemical reaction at constant pressure. We measure it **kJ mol**^{-1}.

**Standard enthalpy changes (∆H ^{º})** are enthalpy changes measured under

**standard conditions**with the reactants and products in their

**standard states**.

(Units: **kJ mol**^{-1}**)**

### Types of enthalpy change

Although there are many types of enthalpy change, today we will discuss about **standard enthalpy changes of reaction, formation,** and **combustion****.**

The **standard ****enthalpy change** **of the reaction (∆ _{r}Hº)** is the enthalpy change when reactants form products in quantities given in the balanced chemical equation, under standard conditions and with all species in their standard states. Simply put, it is the

**enthalpy change that accompanies any standard reaction**.

The **standard enthalpy change of formation**** (∆ _{f}H°)** is the enthalpy change when one mole of a species is formed from its elements, under standard conditions and with all species in their standard states.

The **standard enthalpy change of combustion (∆ _{c}H°)** is the enthalpy change when one mole of a substance burns completely in oxygen under standard conditions, with all species in their standard states.

Find out more about enthalpy changes, further definitions and examples, over at **Enthalpy Changes**.

## Calculating enthalpy change using Hess' law

It is impossible to measure enthalpy change directly. Instead, we can calculate it in several ways. One way of doing this is by using **Hess' law**.

**Hess' law** states that the enthalpy change of a reaction is independent of the route taken.

Simply put, the **enthalpy change of a reaction is always the same**, no matter how many steps the reaction takes, which other species you go by, or how you get from start to finish.

Consider a reactant A whose product is B. You can start with A and end up with B in just one simple reaction-**the direct route**, or you can go through several different reactions ( A to Z, Z to Y, Y to X and X to B) to arrive at B- **the indirect route.** Either way, the enthalpy change remains the same since both the routes start with the same reactant and end with the same product.

**Hess' cycle.**

How does this help us?

We may not know the enthalpy change of the direct route, but we know all the enthalpy changes involved in the indirect route which can be used to calculate the enthalpy change of the direct route

In the above example, the direct route (going from A to B) is represented by the enthalpy change **ΔH**_{1}. The indirect route (going via Z, Y, and X) is represented by the enthalpy changes** ****ΔH**_{2}, **ΔH**_{3}, **ΔH**_{4}, and **ΔH**_{5}. Hess' law tells us that** ****ΔH**_{1}** = ****ΔH**_{2}** +**** ****ΔH**_{3}** +**** ****ΔH**_{4}** +**** ****ΔH**_{5}.

Visit **Hess' Law **for a comprehensive exploration of the topic. You can also learn about another method of calculating enthalpy change in the article **Measuring Enthalpy Changes**. This involves using a technique known as **calorimetry** to measure the heat energy transferred during a reaction, which we referred to in the introduction.

## Calculating enthalpy change of reaction

We will now see how Hess' law is used in **calculating enthalpy change.**

Hess's law allows us to **calculate the unknown enthalpy change of any reaction, provided we can represent it in terms of enthalpy changes that we do know**. At AS-level chemistry, this is typically limited to working out the

**standard enthalpy of reaction (∆**using

_{r}Hº)**standard enthalpy of formation (∆**and

_{f}Hº)**standard enthalpy of combustion (∆**.

_{c}Hº)The direct route of your Hess's cycle is always the reaction that you want to find the enthalpy change of. However, your indirect route looks slightly different depending on whether you use ∆_{f}Hº or ∆_{c}Hº:

- If you wish to calculate ∆
_{r}Hº using ∆_{f}Hº, your indirect route goes via the standard state elements that make up all the species in the reaction. - If you wish to calculate ∆
_{r}Hº using ∆_{c}Hº, your indirect route goes via the combustion products of all the species in the reaction.

For example, consider the hydrogenation of ethene: $$C_2H_4(g)+H_2(g)\rightarrow C_2H_6(g) $$

Here's what the two Hess's cycles look like:

Note the differences between the two cycles. For example, pay attention to the directions of the arrows. Also, note that we don't need to include the enthalpy of formation of H_{2}(g). This is because H_{2} is elemental and already in its standard state, so its ∆_{f}Hº has a value of +0.0 kJ mol^{-1}.

### Method for calculating enthalpy change

Calculating an unknown enthalpy change of reaction using Hess' cycles:

- Decide whether you are going to use enthalpy of formation or enthalpy of combustion to find the unknown enthalpy change of reaction.
- Construct a Hess' cycle using the reaction's balanced chemical equation. This involves the direct route, which is the unknown enthalpy change of reaction you are trying to find out, and the indirect route, which goes via elemental forms or combustion products.
- Using either ∆
_{f}Hº or ∆_{c}Hº given in the question or in a data table, fill in the enthalpy changes involved in the indirect route. - Use the indirect route to calculate the enthalpy change of the direct route.

Here's a formula that might help you. However, some people prefer to draw a Hess' cycle out each time they try a question - experiment with different methods to find out what works for you.

In general:

$$\Delta _rH^\circ = -\Delta _fH^\circ (reactants) + -\Delta _fH^\circ (products)$$

$$\Delta _rH^\circ = \Delta _cH^\circ (reactants) -\Delta _cH^\circ (products)$$

### Example

Ready to give calculating enthalpy change of the reaction- ∆_{r}Hº a go?

Try this first example. It uses **standard enthalpies of formation** to find the standard enthalpy of reaction.

**Use the following information to calculate ∆ _{r}Hº of the forward reaction for the equilibrium given below:**

*$$CO(g)+2H_2(g)\rightleftharpoons CH_3OH(l)$$***Solution: **

Let's draw a Hess' cycle.

The direct route : CO and H_{2 }to CH_{3}OH.

The indirect route: CO and H_{2 }to their standard state elements, and from the elements to CH_{3}OH.

Note that this cycle features just one mole each of CO and CH_{3}OH. In addition, note that we don't have to include the ∆_{f}Hº of H_{2} - it is an elemental species in its standard state, and so has an enthalpy of formation of +0 kJ mol^{-1}.

We can now fill in the enthalpy changes of the indirect route:

Now, calculate the unknown enthalpy change of the direct route by adding together the enthalpy changes of the indirect route. This is the reverse of the enthalpy of formation of CO, added to the enthalpy of formation of CH_{3}OH:

$$-(-110.5)+(-238.0)=-90.5\space kJ\space mol^{-1}$$

Our final answer is **-127.5 kJ mol**^{-1}.

The next problem instead uses enthalpies of combustion to find an enthalpy of formation. We solve it using the same method as for our first example problem.

Use the following data to calculate the standard enthalpy of formation of propanol (C_{3}H_{7}OH):

**Solution**:We're given standard enthalpies of combustion and told to use them to find the standard enthalpy of formation of propane. First, we need to represent the unknown enthalpy change with a chemical equation, which we can then find the enthalpy change of reaction for:$$3C(s)+4H_2(g)+\frac{1}{2} O_2(g)\rightarrow C_3H_7OH(l)$$ Now, we can draw a Hess' cycle using the enthalpy changes of combustion given in the question:

Fig. 5: Hess' cycle for the formation of propanol using enthalpy of combustion, with the enthalpy changes within the indirect route filled in. StudySmarter Originals

If we follow the indirect route along, we can calculate ∆_{r}Hº, the enthalpy change of the direct route:

$$(3\times -393.5)+(4\times -285.8)-(-2021)=-302.7\space kJ\space mol^{-1}$$

Therefore, the enthalpy of formation of propanol is **-302.7 kJ mol**^{-1}.

## Calculating enthalpy change from bond energies

Hess' cycles don't just have to involve calculating ∆_{r}Hº from ∆_{f}Hº or ∆_{c}Hº. We can also calculate unknown enthalpy changes using **mean bond energy.**

**Mean bond energy** (also known as **mean bond enthalpy**) is the average energy required to break one mole of a specific covalent bond in the gaseous phase, averaged over a range of molecules.

Once again, the direct route in our Hess' cycle goes directly from reactants to products and represents the unknown enthalpy change. But this time, the indirect route goes via all the unbonded gaseous atoms that make up the species in the equation. When filling in the enthalpy changes of the indirect route, we consider the bond energy of all the covalent bonds in the reactants and products, and calculate the enthalpy change of the direct route accordingly.

Consider the hydrogenation of ethene once again. Here's our Hess' cycle:

Fig. 6 - Hess' cycle for the hydrogenation of ethene using mean bond energy.StudySmarter Originals

### Method

Here's how you calculate enthalpy change using bond energy:

- Construct a Hess's cycle using the reaction's balanced chemical equation. This involves the direct route, which is the unknown enthalpy change of reaction you are trying to find out, and the indirect route, which goes via unbonded atoms.
- Using mean bond energies given in the question or in a data table, fill in the enthalpy changes involved in the indirect route.
- Use the indirect route to calculate the direct route: the unknown enthalpy change of reaction.

### Example

Let's put the method into practice. Try the following question and compare your answer to our worked solution.

**Calculate the enthalpy change of the hydrogenation of ethene, shown below:**

*$$C_2H_4(g)+H_2(g)\rightarrow C_2H_6(g)$$*

Use the following data table of bond energies to help you:

Solution:

You'll notice that this is the same reaction that we considered when we introduced the topic of mean bond energy. We've already drawn a Hess' cycle - we just need to fill in the enthalpy changes using the data table given:

Now, we can follow the indirect route along to calculate the enthalpy change of the direct route. We need the bond energies of the reactants, added to the reverse of the bond energies of the products:

$$(4\times 412)+614+436-(348+(6\times 412))=-122\space kJ\space mol^{-1}$$

Our final answer is **-122 kJ mol**^{-1}.

This next problem is slightly different. Here, we work backward and calculate one particular bond energy using a known enthalpy change of reaction, and other mean bond energies.

**Calculate the mean bond energy of the N-H bond, using the following information:**

*$$N_2(g)+3H_2(g)\rightarrow 2NH_3(g)\qquad \Delta H^\circ =-91.8\space kJ\space mol^{-1}$$*

**Solution: **

We start by drawing a Hess' cycle. But instead of trying to find an enthalpy change of reaction, here we want to find a particular bond energy: the N-H bond energy. We are given the enthalpy change of reaction for the production of NH_{3}, and the N≡N and H-H bond energies. The direct route of our Hess' cycle goes from NH_{3} to unbonded N and H atoms. The indirect route goes from NH_{3} to N_{2} and H_{2} (using ∆_{r}Hº), and from N_{2} and H_{2} to unbonded atoms (using N≡N and H-H bond energies). Here is our Hess' cycle, with known enthalpy changes filled in:

Follow the indirect route along:

$$-(-91.8)+(941+3(436))=2340.8\space kJ\space mol^{-1}$$

This gives us the enthalpy change for the direct route. However, note that the indirect route tells us the enthalpy change when six moles of N-H bonds are broken. The question asks us to find the bond energy of N-H, which is the enthalpy change when just one mole of N-H bonds is broken. Therefore, we divide the enthalpy change of the direct route by 6:

$$\frac{2340.8}{6} =390.13\space kJ\space mol^{-1}$$

Our final answer is **390 kJ mol**^{-1}.

Make sure to give your answer to the correct number of significant figures. Here, the smallest number of significant figures used in the question is three, and so we give our answer to three significant figures .

## Calculating Enthalpy Change - Key takeaways

**Enthalpy change (∆H)**is the amount of heat energy transferred during a chemical reaction at constant pressure. We typically measure it**kJ mol**^{-1}.- We can calculate enthalpy change using
**Hess' law**. This states that the enthalpy change of a reaction is independent of the route taken. It allows us to calculate an unknown enthalpy change using known enthalpy changes. - To calculate an unknown enthalpy change:
- Construct a Hess' cycle using the reaction's balanced chemical equation. This involves the direct route, which is the unknown enthalpy change of reaction you are trying to find out, and the indirect route, which involves known enthalpy changes.
- Use data given in the question to fill in the enthalpy changes involved in the indirect route.
- Use the indirect route to calculate the enthalpy change of the direct route.

- Calculating enthalpy change often involves working with
**standard enthalpy of reaction**,**formation**, and**combustion**, as well as**mean bond energy**.

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##### Frequently Asked Questions about Calculating Enthalpy Change

How do you calculate enthalpy change?

You calculate enthalpy change using either a calorimetry experiment or Hess' law. Hess' law tells you that the enthalpy change of a reaction is always the same, independent of the route taken. This means that you can use an indirect route involving known enthalpy changes to calculate the unknown enthalpy change of the direct route of a reaction.

What is a Hess' law calculation?

Hess' law calculations are mathematical calculations used to find an unknown enthalpy change. You do this by representing a chemical reaction using a direct route and an indirect route. Hess' law tells you that the enthalpy change of a reaction is always the same, independent of the route taken. This means that if you know all the enthalpy changes involved in the indirect route, you can use them to calculate the unknown enthalpy change of the direct route.

How do you calculate enthalpy change in an experiment?

You calculate enthalpy change in an experiment using calorimetry. This involves measuring the heat energy transferred during a certain chemical reaction. Check out the article **Calorimetry** for a more detailed look at the technique.

How do you calculate enthalpy change using Hess's law?

Hess' law tells you that the enthalpy change of a reaction is always the same, independent of the route taken. You calculate enthalpy changes using Hess' law by representing a reaction with an unknown enthalpy change using a direct route and an indirect route. Provided that you know all the enthalpy changes involved in the indirect route, you can use them to calculate the unknown enthalpy change of the direct route.

What is the unit for enthalpy change?

The unit of enthalpy change is kJ mol^{-1}.

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