Chemguide: Support for CIE A level Chemistry

Learning outcome 23: Chemical energetics

23.3: Entropy change, ΔS

Learning outcome 23.3.2

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

This is about the entropy changes which occur during certain physical or chemical changes.

Statement 23.3.2(a)

This covers entropy changes during a change of state, including solid to liquid, liquid to gas and solid to aqueous solution.

Entropy is given the symbol S, and standard entropy (measured at 298 K and a pressure of 1 bar) is given the symbol S°. You might find the pressure quoted as 1 atmosphere rather than 1 bar in less recent sources. Don't worry about it - they are nearly the same. 1 bar is 100 kPa; 1 atmosphere is 101.325 kPa. Use whatever units the examiners give you.

Here are some standard entropies for a few solids, all with the units J K-1mol-1:

carbon (as diamond)2.4
calcium fluoride68.9
calcium carbonate92.9

These all have low entropies because they are highly ordered solids, but notice that the entropy usually increases as the solid gets more complicated.

What happens during change of state? The following figures are for the standard entropy of water in different states.

ice (approximate value)48
liquid water69.9

The entropy increases as the molecules become more disordered as you go from solid to liquid to gas.

Notice that there isn't very big jump in entropy when ice turns to water. That's because the hydrogen bonding between the liquid molecules imposes a fair amount of order on them even in the liquid.

. . . and for benzene:

liquid benzene173
benzene vapour269

Notice that the benzene values are bigger than those of water-steam. This is because benzene is a more complicated molecule. There are more ways of arranging the energy of the molecule in a disordered way over bigger molecules than smaller ones.

What happens when an ionic solid dissolves in water?

The ionic solid is highly ordered, and so has a relatively low entropy. Pure liquid water also has a certain amount of order as explained above. But when the solid dissolves in water, the whole system becomes highly disordered as the crystal breaks up and the ions find their way between the water molecules. Entropy increases.

Note:  Notice that I have taken a short cut here. I have gone straight from an increase in disorder in space and movement to an increase in entropy without specifically thinking about it in energy terms. We often do this at this level. The increase in disorder in space and movement is associated with an increase in disorder in energy terms, but is much easier to imagine.

Statement 23.3.2(b)

This covers the change in entropy during a temperature change.

Obviously if increasing the temperature involves a change of state in the material, then you have increased the entropy . . . and we have already looked at that.

Suppose there isn't a change of state.

Think about having some gas particles in a container with a high degree of disorder both in their spacial arrangement, and in their energies - they are moving at all sorts of different speeds, changing all the time.

If you add more energy by heating the gas, the number of different possibilities for arranging the energy over the molecules increases. And so increasing the temperature increases the entropy of the system.

Statement 23.3.2(c)

This covers changes in entropy in reactions involving at least some gas molecules.

Gases have higher entropies than solids or liquids because of their disordered movement. That means that during a reaction in which there is a change in the number of molecules of gas present, entropy will change.

Reactions involving an increase in the number of gas molecules

For example, the effect of heat on calcium carbonate, or the reaction between a carbonate and an acid:

In both cases, there are no gases on the left-hand side of the equation, but carbon dioxide appears on the right. Entropy will increase during such a reaction, because of the increased disorder.

Reactions involving a decrease in the number of gas molecules

For example, the production of ammonia:

In this case, there is a decrease in entropy during the forward reaction because there are fewer gas molecules than you had to start with. That means that there fewer ways of arranging the energy of the system over those molecules, and so entropy decreases.

Examples of making predictions

In all of these examples, I am using the simplification that an increase in physical disorder will be associated with an increase in energetic disorder and so an increase in entropy (and vice versa for a decrease in physical disorder). I don't honestly think there is any other way you can do this quickly at this level.

This is just a crystalline solid going into solution. The solid is highly ordered; the solution is disordered. There is an increase in entropy.

The water is changing from the highly disordered gas into a more ordered liquid. The entropy will fall.

Look carefully at the state symbols. Water is a liquid.

There are three moles of gas on the left-hand side of the equation, but only one on the right. The starting materials are more disordered than the products, and so there is a decrease in entropy.

Notice that if the water had been formed as steam, you couldn't easily predict whether there was an increase or a decrease in entropy, because there would be three moles of gas on each side.

The presence of the five moles of liquid water on the left-hand side means that there will be far more disorder before the change than there is in the products. The copper(II) sulphate crystals formed will be very ordered. Entropy will decrease.

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© Jim Clark 2020