Quick Notes Entropy

  • Entropy is a measure of disorder within a system, with the units JK-1mol -1.
    • If there are lots of possible of ways of arranging particles in a system, there is high disorder and it has a higher entropy.
    • If there are fewer possible ways of arranging particles in a system, there is less disorder and it has a lower entropy.
  • Solids have low entropies; gases have high entropies. Going from solid to gas increases the entropy of a system as there are then more possible ways to arrange the particles.

Full Notes Entropy

In chemistry, energy is involved in reactions. We know from basic kinetic theory that in order for particles to react, they have to collide with the required activation energy. The products formed are either at a lower or higher energy than the reactants.

RECAP. If the products of a reaction are at a lower energy than the reactants, the reaction is exothermic and the overall enthalpy change for the reaction will be negative (-ΔH). If the products of a reaction are at a higher energy than the reactants, the reaction is endothermic and the overall enthalpy change for the reaction will be positive (+ΔH).

Exothermic reactions generally occur more easily because they release energy, meaning no overall energy input is required. Nature is lazy, so reactions that do not require an overall input of energy are more likely to occur than those that do.

Endothermic reactions can and do occur in chemistry though because it’s not just enthalpy changes that determine whether a reaction can happen. Entropy is also a factor that determines how likely a reaction is to happen.

Very simply, entropy is a way of measuring how many ways we can arrange particles in a system. The more possible ways we can arrange the particles in space, the greater the ‘disorder’. A more detailed definition is given later!

Imagine a wardrobe with clothes in it. The more clothes you have, the more ways you can hang them in the wardrobe – there are more possible ways of ‘arranging’ the clothes in the system (the system here being everything inside the wardrobe).

entropy basics ways of arranging clothes wardrobe

A wardrobe with more clothes in would have a higher entropy than a wardrobe with fewer clothes in.

entropy increase with ways of arranging clothes in wardrobe

This same theory applies to particles in a system, except we also need to think about the state the particles are in (not just the number of particles).

In a solid, for example, particles cannot move around easily – they have to be in a fixed, regular order. As there are not many ways to arrange these particles in space, the entropy of the system would be low. The system has a low level of ‘disorder’.

In a system with gaseous particles, however, there are a vast number of ways to arrange these particles, so the entropy of the system would be high. The system has a high level of ‘disorder’.

entropy change with states of matter

It is important to note that entropy, like enthalpy, is only really useful as a relative term. Comparing the entropy of one system to another can give us a good idea as to whether a reaction is likely to happen.

Nature is lazy but also completely chaotic – nature prefers systems with higher entropy. See bottom of the page for why!

In simple terms, the total energy of a system is lower if there are more ways to arrange the particles within it. We know that nature prefers to form lower energy systems, which is why systems with high entropy are more likely to form than systems with low entropy.

It is not that simple though!

The total enthalpy change of a reaction also has an impact on whether a reaction can or cannot happen. Exothermic reactions are more likely to happen than endothermic reactions.

We now have two factors influencing whether a reaction is likely to happen: enthalpy change and entropy change.

To describe whether a reaction is likely to occur we have to link these two factors together.

Entropy – How is it linked to energy?

The above outline is a basic introduction to entropy and, combined with the other pages on chemistrystudent.com on entropy changes, should be enough for most exam specifications.

The idea that entropy is simply a measure of disorder is perhaps a little misleading as it doesn’t give any indication of how it is connected to energy. Below is a slightly more detailed, but still A-level relevant, outline to help clarify the above.

The units for entropy are JK-1. This tells us that energy (Joules, J) and temperature (Kelvin, K) are involved!

At any temperature above 0 Kelvin (absolute zero), particles have thermal energy. As particles hit each other, they exchange this energy with other particles. This means the energy ‘spreads’ out throughout the system. As it spreads out, it becomes less and less useful, until eventually it can’t really be used for anything. By less ‘useful’ we mean that it is unable to ‘do’ any work (unlike thermal energy, for example, which is able to be transferred between particles and trigger reactions).

This means the ‘useless’ energy can’t be measured in the same way thermal energy can, but we know it exists because energy cannot be created or destroyed. The total energy of a system must always have the same amount of energy within it.

Entropy, in a very simplistic sense, is the ‘useless’ energy that cannot be used for anything useful. This is why entropy has Joules within its units – we are, in fact, measuring energy!

Imagine giving everyone in the world the same number of coins. These coins will be transferred between people and, almost immediately, the distribution will not be even throughout everyone! But, some coins will naturally get lost and dropped in places where they will never be found or can’t be accessed (like down a drain!). The TOTAL number of coins will always be the same in the world, but the number of coins that can be transferred between people will slowly go down over time as more and more get ‘lost’.

Now, if no-one is allowed to move around they will be far less likely to lose their coins, this means the number of ‘lost’ coins will be smaller. The more that people are allowed to move and mix with other people, the more coins will be lost!

Entropy is like measuring the number of LOST coins in the world. It increases with the disorder of particles in the same way that the number of lost coins increases as people move around more.

Where does temperature fit with this?

At higher temperatures, particles move faster due to having more energy. Remember, it is through the movement of particles that energy is able to spread and get ‘distributed’ throughout a system. If the particles are moving faster, there are far more possible ways for the particles to bump into each other and transfer energy, meaning there are even more ways to distribute energy.

Because of this, at higher temperatures energy will get ‘spread’ out more than at lower temperatures, increasing the amount of ‘useful’ energy getting converted into ‘useless’ energy.

This is why entropy has temperature (Kelvin, K) in its units as it will always be linked to the temperature of a system.

Linking This

The possible distributions of energy within a system have an impact on the system's stability (linked to energy, measured in Joules, J).

The possible distributions of energy within a system change with temperature, so the above stability will change with temperature (Kelvin, K).

This is all still a simplistic view of, essentially, a mathematical concept. To go further at A-level would be of little benefit and only add to confusion. The idea that entropy changes with temperature is very important for A-level however, and forms the basis of entropy change calculations (see Entropy Changes).