Have you ever thought about how a reaction that makes more moles of products than reactants be thermodynamically stable? Or why do certain combination reactions happen by themselves, whilst others are extremely rare? These are the types of questions that concern the disorder of a system, and we call that entropy. Here, we will explore entropy changes in different contexts.
- This article is about entropy changes in chemistry.
- We'll begin with the definition of entropy (S) and entropy change (∆S).
- We'll then explore the characteristics of entropy changes, including how entropy changes in reactions involving change of state, change in temperature, and change in the number of moles of gas.
- After that, we'll look at entropy changes in irreversible (and reversible) processes, as well as taking a deep dive into entropy changes for ideal gases.
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.
Entropy (S) is a measure of disorder in a thermodynamic system. It is also defined as the number of possible ways that particles and their energy can be distributed in a system. It is measured in J K-1 mol-1.
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.
Return to the two species from before: a solid and a liquid. As we know, the molecules or particles within the solid are arranged in neat rows, whilst those within the liquid move about randomly. We can see how the solid has much more order than the liquid. Conversely, you could say that the liquid has more disorder than the solid. This is quantified and described through entropy - the liquid has greater entropy than the solid.
Fig. 1 - A diagram showing the arrangement of particles in a solid and a liquid.StudySmarter Originals
Another context where entropy can be visualised is in certain chemical reactions, where the number of moles on each side of the reaction changes. If there are more molecules present, there is an increase in the disorder of the system, as there are more ways in which the molecules can be arranged. Thus, there is a greater entropy.
One key difference between entropy and other thermodynamic constants, such as enthalpy, is that it is possible to know the absolute value of entropy for a system. Absolute entropy is simply the entropy of a species compared to its entropy at 0 K. In contrast, absolute enthalpy can't be measured directly. This is because enthalpy involves components that we still don't completely understand and can't measure accurately.
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:
Standard entropy is the entropy of a pure substance under standard conditions of pressure and temperature. Usually, we define the standard molar entropy, which is the entropy of one mole of substance under standard conditions.
For a more in-depth introduction to the idea of entropy, check out the article Entropy. You can also learn about standard conditions in Enthalpy Changes.
Entropy change
Now, let's look at entropy change.
Entropy change (∆S) is the change in the disorder (entropy) within a system as the result of a chemical or physical process. Like entropy, it is also measured in J K-1 mol-1.
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:
| Physical process | Entropy change |
| Melting (solid to liquid) | Positive |
| Boiling (solid to gas) | Positive |
| Freezing (liquid to solid) | Negative |
| Sublimation (solid to gas) | Positive |
| Condensing (gas to liquid) | Negative |
| Dissolving | Increase |
| Decomposition | Increase |
| Crystallisation | Decrease |
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.
Consider the reverse of the Haber Process:
$$2NH_3(g)\rightarrow N_2(g)+3H_2(g)$$
Can you see how, in the reaction above, two moles of gases become four? If you are creating more moles of gases than you started with, then there are many more ways that they can move around and interact with each other, and so you are creating more disorder in your system. This means that the system's entropy increases.
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:
| Type/feature of reaction | Entropy change |
| Change of state (melting, evaporating, or sublimation) | Increase |
| Change of state (condensing or freezing) | Decrease |
| Temperature increase | Increase |
| Temperature decrease | Decrease |
| Increase in the number of moles of gas | Increase |
| Decrease in the number of moles of gas | Decrease |
Here are some further characteristics of entropy changes.
Change in complexity
Other characteristics of entropy changes rely on the complexity of compounds. Generally, the more complex the molecule involved (meaning the more atoms and groups it has) the larger its entropy.
For example, CaO has a lower entropy than CaCO3 because it has fewer atoms per mole.
Change in strength
The last thing to look at is allotropes of the same compound or element. Harder substances usually have a lower entropy than softer (or less definitively arranged) substances.
Try to visualise carbon in both diamond and graphite. Graphite is much softer than diamond and has free-moving electrons, whilst diamond contains a dense lattice of carbon atoms. All these factors mean that graphite has a greater entropy value than diamond.
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.
The equation below shows the reaction between nitrogen and hydrogen to make ammonia, and the corresponding entropy values of each species:
$$N_2 + 3H_2 \rightarrow 2NH_3$$
- S°(NH3) = 192.5 J K-1 mol-1
- S°(H2) = 130.6 J K-1 mol-1
- S°(N2) = 191.5 J K-1 mol-1
Calculate the entropy change of the reaction.
Well, if we look at the overall entropy formula, we can see that entropy change equals the entropy of the products minus the entropy of the reactants:
$$\Delta S^\circ _{system} = \sum S^\circ _{products} - \sum S^\circ _{reactants}$$
Now we just need to find the entropy of the products and the entropy of the reactants using the information in the question, and substitute these values into the formula:
$$\sum S^\circ _{products}=2 \times 192.5=385.0\space J\space K^{-1} \space mol^{-1} $$
$$\sum S^\circ _{reactants}= 191.5+(3\times 130.6)=583.3\space J\space K^{-1} \space mol^{-1} $$
$$\Delta S^\circ _{system}=385.0-583.3$$
$$\Delta S^\circ _{system}=-198.3\space J\space K^{-1} \space mol^{-1} $$
Thus, the overall entropy change for the production of ammonia is -198.3 J K-1 mol-1. As it is a negative value, in this reaction, entropy decreases.
Note that this formula helps you calculate the entropy change of a system. However, reactions in a system also cause an entropy change in their surroundings. Combining the entropy change of a system and the entropy change of its surroundings gives you the total entropy change:
$$\Delta S^\circ _{surroundings} = \frac{-\Delta H^\circ _{reaction}}{T} $$
$$\Delta S^\circ _{total}=\Delta S^\circ _{system} + \Delta S^\circ _{surroundings} $$
Total entropy change becomes important when we look at entropy changes in reversible reactions, below.
Check which formulae your exam board requires you to know.
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.
A reversible reaction is one in which the reactants form the products whilst the products simultaneously reform the reactants. In other words, the reaction occurs in two directions - both forwards and backwards.
An irreversible reaction is one that is not reversible, meaning that it does not promote the backwards reaction. In contrast, it only proceeds in one direction.
Feel free to check out our article on Reversible Reactions for more on this topic.
What does reversibility have to do with entropy, though? Well, it involves the second law of thermodynamics.
The second law of thermodynamics states that total entropy cannot decrease.
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.
Spontaneous reactions are reactions that occur without outside intervention, such as the input of energy. They are also called feasible reactions.
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.
Here's the formula. Note that the initial volume is given by Vi and the final volume by Vf:
$$\Delta S = nR \ln \frac{V_f}{V_i}$$
In addition, ideal gases always have a larger absolute entropy than real gases, because of the lack of interactions between particles.
Check out our article on the Ideal Gas Law for more about ideal gases.
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.
Entropy Changes - Key takeaways
- Entropy (S) is a measure of disorder and chaos in a system.
- Entropy change (∆S) is the change in the disorder (entropy) within a system as the result of a chemical or physic and
- Both entropy and entropy change have the units J K-1 mol-1.
- Key characteristics of entropy change include:
- Entropy increases with melting, evaporating, and sublimation.
- Entropy decreases with condensing and freezing.
- Entropy increases with an increase in temperature.
- Entropy increases with an increase in the number of moles of gas.
- The entropy change of a system is given by the formula \(\Delta S^\circ _{system} = \sum S^\circ _{products} - \sum S^\circ _{reactants}\)
- Total entropy change is given by the equation \(\Delta S^\circ _{total}=\Delta S^\circ _{system} + \Delta S^\circ _{surroundings} \)
- Total entropy increases in irreversible reactions and during the expansion of ideal gases.
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