Chemguide: Support for CIE A level Chemistry

Learning outcome 23: Chemical energetics

23.3: Entropy change, ΔS

Learning outcome 23.3.1

Before you go on, find and read the statement in your syllabus.

The syllabus defines entropy, S, as

"the number of possible arrangements of the particles and their energy in a given system".

At this level, in the past, we have usually just described entropy as a measure of the amount of disorder in a system. A very regular, highly ordered system (diamond, for example) will have a very low entropy. A very disordered system (a mixture of gases at a high temperature, for example) will have a high entropy.

The CIE statement has now got more formal than this. Let's look at this with a couple of thought experiments . . .

The first one would be criticised by people who know about these things because it only relates to arrangement in space, and not to energy - but it is a useful starting point.

Suppose you held a stack of ten coins between your finger and thumb. That's a fairly ordered state for them to be in. And then you dropped them on the floor. Every time you did this, you would get a different random pattern of coins on the floor - arranged just by chance. That is now a disordered system.

Now, it is just imaginable that when you dropped them, by chance they would fall into a neat stack of coins like the one you started with, but the probability of that happening, compared to all the other ways that the coins might fall, is so very, very tiny that you would be totally amazed if it happened.

Technically, entropy applies to disorder in energy terms - not just to disordered arrangements in space. But we often just quickly look at how disordered a system is in space in order to make a judgement about its entropy. A system which is more disordered in space will tend to have more disorder in the way the energy is arranged as well.

Suppose you managed to arrange some gaseous molecules in a container so that they were all exactly evenly spaced and so that they all had exactly the same energy - a fairly ordered state. And then you let them go and do what molecules do - move around, and bump into each other and the walls of the container.

Each collision between two molecules will cause them to change direction, and it will probably speed up one of them, and slow down the other. After a very short time, their arrangement in space will be chaotic, and so will the way energy is shared between them. The faster moving particles have more energy; the slower ones less.

The "number of possible arrangements of the particles and their energy in a given system" has increased. And so the entropy has increased because of the more random distribution of the energy.

A previous CIE syllabus said "explain that . . . a system becomes more stable when its energy is spread out in a more disordered state".

That is really all you need to know. If you look in textbooks or on the web, you will find explanations of increasing difficulty - some very scary indeed! Don't waste time on these at this level.

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© Jim Clark 2020