Entropy

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.

• 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 each other. 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.

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.

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.

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.

Entropy changes

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 need to do calculations.

Another thing to remember about entropy change is that we measure it 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 . The following tables show the standard entropy values for a few common substances in their given states.

Standard entropy values of common substances in their given states. Olive [Odagbu] StudySmarter Originals

Entropy changes of reactions

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

Try the following examples to get the hang of these calculations.

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? 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. Also, 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.

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 only 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. Learn more in Free Energy.