Entropy Change

Entropy change: definition and meaning

Here we will discuss the core concepts of entropy changes. However, before we get into a discussion of what entropy changes are, we should first define entropy itself.

Entropy

What happens when you melt a solid? Its temperature increases, thanks to an enthalpy change. But its structure and arrangement of molecules also change, too. The atoms in the solid are held together much more tightly than those in the liquid, which in contrast can move freely around. You could say that the solid is relatively ordered, whilst the liquid is extremely disordered. This is an example of entropy.

Disorder might be an unfamiliar idea. Other words used to describe the concept are randomness, uncertainty, and most importantly, chaos. Here are two examples of entropy to help you understand it a little more clearly.

Standard entropy

Let's now start thinking about standard entropy as a concept before moving on to entropy changes. We can define standard entropy as such:

Entropy change

Now, let's look at entropy change.

Certain types of reactions are accompanied by specific entropy changes. Let's take a couple of examples for you to understand how entropy might change during a chemical reaction by looking at the characteristics of entropy change. This will help you predict entropy change just by looking at a chemical equation.

Entropy change characteristics

Here, we will describe some standard phenomena that occur regarding entropy changes during different reactions.

Change of state

Firstly, think about chemical reactions that involve a change in state of matter. Reactions typically increase or decrease in entropy based on the change in state.

Take a look at the conversion of water from its solid state (a snowflake, say) to its liquid state (a puddle of melted water):

$$H_2O(s) \rightarrow H_2O(l)$$

In the reaction above, you go from a solid to a liquid. The solid has a fixed organisation of molecules which gives it its shape, whilst in a liquid, the molecules can move around in a free, disordered way. In this example, the entropy has increased. If the liquid were to turn into a gas, the molecules would be able to move around even more freely, and thus, entropy would increase further. You can take a look at the figure below to get a more visual understanding of this topic:

Fig. 2 - An image showing the change of state from ice to water. Here, entropy increases.StudySmarter Originals

We can conclude that the entropy of different states of matter increases as you move from solid to liquid to gas. The increase in entropy is due to the increasing disorder between the molecules in the different states:

• Solids have the lowest entropy because their particles are held in an ordered arrangement.
• Liquids typically have a higher entropy because their particles can move about more randomly.
• Gases have the highest entropy out of all three by a significant margin because their particles are free to move about however they like, in a totally disordered way..

All the physical changes of states are characterized by positive (an increase in entropy) or negative (a decrease in entropy) entropy changes. You can see the entropy changes of physical processes in the table below:

In general: reactions that feature melting, boiling, or sublimation typically have a positive entropy change, whilst reactions that feature freezing or condensing have a negative entropy change.

Change in temperature

Similarly, think about what happens to the entropy of a system if you increase its temperature but don't change the state of the substances within. Heating gives the particles within the system more kinetic energy. This means that in the case of solids, the particles vibrate on the spot more rapidly, whilst in the case of liquids and gases, the particles move around more quickly. In both cases, the disorder of the system increases. Thus, if you increase the temperature of a system, you increase its entropy.

In general: endothermic reactions feature a positive entropy change.

Change in number of moles

Another cause of an entropy change is a change in the number of moles during a chemical reaction. Specifically, we look at the number of moles of gas because gases have significantly higher entropies than solids and liquids. Systems that contain more moles of gas tend to have a higher entropy than those with fewer moles of gas.

In general: reactions that contain a larger number of moles of gases in the products than in the reactants typically have a positive entropy change.

Summary

The following table summarises the general entropy changes that characterise certain types and features of chemical reactions:

Entropy change formula

You should now be able to look at a chemical reaction and predict the entropy change that takes place within the system. In this next section, we will explore one formula, which you can use to calculate this entropy change quantitively. Make sure to look through our examples as you go along - you need to know this topic thoroughly!

Take a look at the formula below:

$$\Delta S^\circ _{system} = \sum S^\circ _{products} - \sum S^\circ _{reactants}$$

The basic overview of the formula above is similar to any thermodynamic reaction you will come across. It basically states that the overall change in entropy for a reaction is equal to the total absolute entropy of all the products, minus the total absolute entropy of all the reactants. Let's take an example to see how to deal with this formula.

Entropy changes in an irreversible process

Before we finish, let's explore two further ideas involving entropy changes. We'll start with entropy changes in irreversible and reversible processes.

When discussing entropy, there are two types of processes we can look at: reversible and irreversible.

What does reversibility have to do with entropy, though? Well, it involves the second law of thermodynamics.

Consider reversible and irreversible reactions again. Entropy is a state function, which means that the total entropy of a certain system should always be the same, no matter how you get to that system. But we know that for any reaction, be it reversible or irreversible, total entropy cannot decrease. This means that if going from reactants to products increases the total entropy, then you can't go back from products to reactants. Thus, reactions with a positive total entropy change are irreversible: total entropy increases during an irreversible reaction. We say that these reactions are spontaneous.

However, if going from reactants to products has no overall total entropy change, then you can move back from products to reactants. That means that the reaction is reversible. Thus, reversible reactions have a total entropy change of 0 J mol^-1 K^-1: total entropy doesn't change during a reversible reaction.

Entropy change for ideal gases

Finally, you might be interested in entropy changes of ideal gases. For example, how does entropy change differ for ideal gases compared to real gases? It will help to look at the definition of an ideal ga as.

Working with ideal gases is often much simpler than working with real gases because we can ignore the effects of phenomena that are hard to calculate, such as interactions between particles. In fact, the behaviour of ideal gases can generally be derived solely from just one simple equation:

$$PV=nRT$$

Calculating entropy changes for ideal gases is much simpler than for real gases for this exact reason. For example, we can easily calculate entropy change for an ideal gas that is expanding froThe to another, and thus changing pressure, using just n, R, and the initial and final volumes. You should find that the entropy of an ideal gas increases as its volume increases.

In addition, ideal gases always have a larger absolute entropy than real gases, because of the lack of interactions between particles.

Now that you understand different aspects of entropy changes, you should be ready to tackle real-life entropy calculations, as well as predict the entropy change that takes place in different situations and processes.