Suggested languages for you:
|
|

## All-in-one learning app

• Flashcards
• NotesNotes
• ExplanationsExplanations
• Study Planner
• Textbook solutions

# Entropy

Save
Print
Edit

Previously, you may have learned that entropy is a measure of disorder in a thermodynamic system. Why has the definition of entropy changed? Well, it turns out entropy is a little more complex than just a measure of disorder.

Entropy (S) is the number of possible ways energy can be distributed in a system of molecules.

• You will learn the definition of entropy.
• Why do we say entropy is about energy distribution between particles?
• You will also learn about spontaneous or feasible processes.
• Discover how the second law of thermodynamics helps to explain spontaneous reactions.
• Calculate the entropy change of a given reaction using standard entropy values.
• The meaning of total entropy.

## What is entropy?

To help you understand entropy, consider that molecules at equilibrium have the same average energy. However, if you could take snapshots of the molecules in a system at given instances in time, you would find that the molecules rarely have the exact same energy. This is because the molecules constantly interact and transfer energy with one another. Think of how gas particles constantly collide with each other and the walls of a container. Each collision causes some to speed up while others slow down. The faster particles have more energy than the slower ones. As a result, one molecule could have a certain amount of energy in one snapshot but have less in another one.

Gas particles constantly interact and transfer energy with each other. wikipedia.com

Energy exists in ‘packets’ which we call quanta. A particle can only have a whole number of quanta, never fractions of quanta. You must imagine that as the particles interact with each other, the quanta get distributed (or spread out) among them. In other words, every time you take a snapshot, there is a new arrangement of quanta between the molecules. The amount of quanta available to a particle in a system is limited to the total energy of the system. If you were to increase the amount of total energy in the system, for example by heating a gas, you would increase the number of available quanta that a particle can have.

Entropy, Olive [Odagbu] StudySmarter Originals

Essentially, you can say that the more energy a system has, the more ways there are to distribute energy between the molecules. As you have seen from the example of the gas particles, this energy is distributed randomly. So when we talk about entropy we are talking about the amount of possible ways energy can be distributed among the molecules in a system. The more ways there are, the higher the amount of entropy.

It might help to think of entropy in terms of how spread out the energy in a system is. The more spread out the energy is, the higher the entropy. When the particles in a system have more freedom to move around, the energy gets spread out more.

High entropy is related to energetic stability, because the energy in the system is better distributed among the particles.

This is why we say that liquids and gases have a higher entropy than solids. For example, the particles in a liquid move about more (or have more disorder) than in a solid, so there is a higher number of possible distributions of quanta between the particles.

### Units of entropy

Entropy is measure in joules, and not kilojoules. This is because a unit of entropy is smaller (in order of magnitude) than a unit of enthalpy. The official unit for entropy is .

## Entropy changes

Entropy change measures the change in disorder of a reaction.

Entropy is a state function, and like enthalpy we cannot measure it directly. We must understand it qualitatively, so we measure the change in entropy (𝚫S).

Standard entropy () is measured under standard conditions. In your exams, you will be given all the standard entropy values you will need to do calculations.

Unlike the standard enthalpy of formation of an element, the standard entropy values for elements is not 0. These values will be provided in your exams.

We can calculate the entropy change for a given reaction by entering standard entropy values in the following equation where sigma (∑) means “sum of” :

In a chemical reaction, the system is the species involved in the reaction. The surroundings are everything else- usually a test-tube or beaker and the air in the laboratory.

### What is total entropy change?

It’s great that you have now mastered calculating the entropy change of a given reaction, but have you noticed that something is missing? Remember the second law of thermodynamics? It says that in a spontaneous process, we have to take into consideration the system and the surroundings.

If a reaction is exothermic, heat is released to the surroundings which increases the surrounding entropy, whilst if a reaction is endothermic, it absorbs heat from the surroundings which decreases the surrounding entropy. So when we talk of a thermodynamic change in entropy, what we really mean is the change in total entropy- the combined change in entropy in the system and the surroundings.

The total entropy change () is the sum of the entropy changes in the system

() and the entropy change in the surroundings ().

We express total entropy change in the following equation:

For a reaction to be spontaneous (or feasible) must be positive.

Earlier we said that for a reaction to be feasible, energy must move in the direction of increasing total entropy. Essentially, a feasible or spontaneous reaction is one that is energetically possible. It may not happen automatically, because it might have a large activation energy that slows it down or stops it from taking place at a certain temperature. If the total entropy change is negative, then we say a reaction is not spontaneous.

As you can see, spontaneous reactions happen not only when the change in enthalpy (∆H) is negative (decreases). Some endothermic reactions happen spontaneously, like when dinitrogen tetroxide decomposes to nitrogen dioxide at room temperature. We can explain this spontaneous reaction by looking at the change in entropy (∆S). We say a reaction is spontaneous when the change in total entropy is positive (increases).

Clearly, we cannot predict if a reaction is feasible by only looking at the entropy change or just the enthalpy change. Gibbs free energy or free energy shows the relationship between entropy and enthalpy to help us predict the feasibility of a reaction.

## What is a spontaneous reaction?

Chemists are always asking: will a reaction take place? We call reactions that can take place without needing any intervention, spontaneous or feasible reactions.

A spontaneous process or reaction is one that takes place without any outside intervention given enough time.

Spontaneous reactions are also called feasible reactions. Some examiners may expect you to use one of the two, so it’s important for you to find out!

Some chemists prefer to use the term ‘feasible’ instead of ‘spontaneous’ because it gives the more accurate idea that we are talking about whether a reaction is possible. Spontaneous reactions do not have to happen all of a sudden or immediately. Some spontaneous processes can take years, like when an iron gate turns to rust.

You’ve probably seen spontaneous reactions happen many times, but never noticed because they seem so natural. For example, you know that if you let go of an untied inflated balloon, the gas inside will escape quickly to diffuse in the surroundings until the balloon is deflated. Or if you leave an iron gate exposed to the air long enough, the iron reacts with oxygen in the air and eventually starts to rust. You have experienced these processes and know what direction they take. What about other processes you haven’t any experience with?

Exothermic reactions take place in the direction that forms a product that is more energetically stable than the reactants. That is to say, there is a decrease in enthalpy. Some reactions move in the direction that achieves equilibrium. For example, in the dimerisation of nitrogen dioxide (), shown below, the forward exothermic reaction produces dinitrogen tetroxide ().

At room temperature though, the reaction reaches equilibrium where some of the spontaneously decomposes back to and enthalpy increases. How do we explain the backwards endothermic reaction? The second law of thermodynamics can help.

### What is the second law of thermodynamics?

You may have heard the second law of thermodynamics stated as “in a spontaneous process, entropy always increases.” This way of stating the second law isn’t exactly factual. Consider the reaction between ammonia () and hydrogen chloride gas (HCl) below. Does the entropy increase or decrease?

Clearly entropy decreases in this reaction since two gases react to form a solid, yet at room temperature, this reaction is spontaneous. What is increasing is the total entropy. So a more correct way to say the second law is:

In a spontaneous process, the total entropy change for a system and its surroundings is positive.

In other words, in a spontaneous reaction, energy moves in the direction of increasing total entropy.

Often we don't know the entropy change of the surroundings. However, we can estimate it using the reaction's enthalpy change and temperature. These values help us work out something called Gibbs free energy, which is another way of measuring the spontaneity of a reaction.

#### Gibbs Free Energy

As mentioned previously, a way in which feasibility can be determined is by using Gibbs Free Energy. But what is that? In this section we will briefly explore Gibbs Free Energy. This is the energy that becomes 'free' in a reaction and factors in enthalpy changes, entropy changes and temperature. This is explored in another article.

The equation is as follow:

ΔG = ΔH - TΔS

Where:

ΔG = Free energy

ΔH = Change in enthalpy

T = Temperature

ΔS = Change in entropy

This equation will be explored further in other articles, which will include examples.

## Entropy - Key takeaways

• Entropy is the number of possible ways energy can be distributed in a system of molecules.
• A spontaneous reaction is one that takes place without outside intervention given enough time.
• The second law of thermodynamics states that in a spontaneous process, the total entropy change for a system and its surroundings is always positive.
• Entropy is measured in .
• The symbol for standard entropy is .
• We calculate the entropy change in a system as .
• The total entropy change is the sum of the entropy change in the system and the surroundings .

Total entropy change is the sum of entropy change in the system and the surroundings. We calculate it using the following equation:

∆S (total) = ∆S (system) + ∆S (surroundings)

Entropy is the number of possible ways quanta (packets of energy) can be distributed between the particles in a system. The more ways there are, the higher the entropy.

Quanta get distributed when the particles in a system interact with each other and transfer energy. The more freely moving the particles in a system are, the more energy is spread about the system. We say liquids have a higher entropy than solids because the particles in a liquid move about more than in a solid i.e., the particles in a liquid are more disordered. So there is a higher distribution of quanta between the particles.

## Final Entropy Quiz

Question

What is entropy?

Entropy is the number of possible ways energy can be distributed between the particles in a system.

Show question

Question

What is a spontaneous or feasible change?

A spontaneous or feasible change is one that takes place on its own without outside intervention, given enough time.

Show question

Question

What is the second law of thermodynamics?

In spontaneous changes, the total entropy change for a system and its surroundings is always positive.

Show question

Question

Select factors that can make a reaction feasible?

Negative enthalpy change

Show question

Question

Which of the following is the unit we use for entropy?

Show question

Question

Arrange the following in order of increasing entropy: Gas, solid, liquid.

Solid, liquid, gas.

Show question

Question

The equation shows how hydrogen is made from a reaction involving steam and methane. Use the table below to calculate the change in entropy for the reaction.

Show question

Question

The graph below shows the entropy of a sample of water changing with the temperature. Give a reason for the larger change in entropy at T2.

The particles have greater disorder at T2. This could be due to vaporisation.

Show question

Question

What is total entropy?

The total entropy change  is the sum of the entropy change in the system  and the entropy change in the surroundings .

OR

Show question

Question

How do we calculate the entropy change of a given reaction?

Show question

Question

Which has more entropy?

Solid

Show question

Question

Which has more entropy?

Liquid

Show question

Question

Which has more entropy?

Solid

Show question

Question

What is the correct equation for Gibbs Free Energy?

ΔG = ΔH - TΔS

Show question

Question

What is Gibbs Free Energy?

The energy that becomes 'free' in a reaction and factors in enthalpy changes, entropy changes and temperature.

Show question

60%

of the users don't pass the Entropy quiz! Will you pass the quiz?

Start Quiz

## Study Plan

Be perfectly prepared on time with an individual plan.

## Quizzes

Test your knowledge with gamified quizzes.

## Flashcards

Create and find flashcards in record time.

## Notes

Create beautiful notes faster than ever before.

## Study Sets

Have all your study materials in one place.

## Documents

Upload unlimited documents and save them online.

## Study Analytics

Identify your study strength and weaknesses.

## Weekly Goals

Set individual study goals and earn points reaching them.

## Smart Reminders

Stop procrastinating with our study reminders.

## Rewards

Earn points, unlock badges and level up while studying.

## Magic Marker

Create flashcards in notes completely automatically.

## Smart Formatting

Create the most beautiful study materials using our templates.

Just Signed up?

No, I'll do it now