Calculating Enthalpy Change

Calculating enthalpy change: definition, units, and types

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

1. What is enthalpy change?
2. What are standard enthalpy changes?

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.

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.

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.

Fig. 1 - An example of Hess' cycle. The direct and indirect routes are labelled accordingly.StudySmarter Originals

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 ΔH₁. The indirect route (going via Z, Y, and X) is represented by the enthalpy changes ΔH₂, ΔH₃, ΔH₄, and ΔH₅. Hess' law tells us that ΔH₁ = ΔH₂ + ΔH₃ + ΔH₄ + ΔH₅.

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 (∆_rHº) using standard enthalpy of formation (∆_fHº) and standard enthalpy of combustion (∆_cHº).

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 ∆_fHº or ∆_cHº:

• If you wish to calculate ∆_rHº using ∆_fHº, your indirect route goes via the standard state elements that make up all the species in the reaction.
• If you wish to calculate ∆_rHº using ∆_cHº, 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:

Fig. 2 - Hess' cycles for the hydrogenation of ethene. The left-hand cycle uses enthalpy of formation whilst the right-hand cycle uses enthalpy of combustion.StudySmarter Originals

Method for calculating enthalpy change

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

1. Decide whether you are going to use enthalpy of formation or enthalpy of combustion to find the unknown enthalpy change of reaction.
2. 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.
3. Using either ∆_fHº or ∆_cHº given in the question or in a data table, fill in the enthalpy changes involved in the indirect route.
4. Use the indirect route to calculate the enthalpy change of the direct route.

Example

Ready to give calculating enthalpy change of the reaction- ∆_rHº 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 ∆_rHº of the forward reaction for the equilibrium given below:

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

Solution:

The question asks us to calculate the enthalpy of reaction for a hypothetical case of methanol production. It gives us some enthalpies of formation, and we'll use these to find the unknown enthalpy change.

Let's draw a Hess' cycle.

The direct route : CO and H₂ to CH₃OH.

The indirect route: CO and H₂ to their standard state elements, and from the elements to CH₃OH.

Note that this cycle features just one mole each of CO and CH₃OH. In addition, note that we don't have to include the ∆_fHº of H₂ - it is an elemental species in its standard state, and so has an enthalpy of formation of +0 kJ mol^-1.

Fig. 3: Hess' cycle for Methanol production | StudySmarter Originals

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

Fig. 4: Hess' Cycle for methanol production with enthalpy of formations for indirect route filled in | StudySmarter Originals

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 CH₃OH:

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

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.

Calculating enthalpy change from bond energies

Hess' cycles don't just have to involve calculating ∆_rHº from ∆_fHº or ∆_cHº. We can also calculate unknown enthalpy changes using mean bond energy.

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:

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.

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.