DP Chemistry: 15.2 Entropy & spontaneity

15.2 Entropy & spontaneity

Written specifically for students to provide help and support for the IB Diploma chemistry programme this page provides full coverage of the syllabus content of Topic 15.2 Entropy & spontaneity. It encourages you to think critically and provides many questions with full worked answers so that you can monitor and improve your knowledge and understanding.

Learning outcomes

After studying this topic you should be able to:

Understand

  • Entropy (S) is related to the distribution of available energy among the relevant particles. The more ways the energy can be distributed the higher the entropy.
  • The Gibbs free energy change (ΔG) is the energy obtained from a chemical reaction that is available to do work. It is related to the change in enthalpy (ΔH), the change in entropy (ΔS), and the absolute temperature (T).
  • Under the same conditions the entropy of a gas is greater than the entropy of a liquid which in turn is greater than the entropy of a solid.

Apply your knowledge to:

  • Predict, by considering the states of the reactants and products, whether a change will result in an increase or decrease in entropy.
  • Calculate entropy changes (ΔS) from standard entropy values (S⦵).
  • Apply the equation ΔG⦵ = ΔH⦵ – TΔS⦵ to predict spontaneity and calculate the various conditions of enthalpy and temperature that will affect this.
  • Relate the value and sign of ΔG to the position of equilibrium of a reaction.

Relationships & vocabulary

Nature of science

The idea of entropy has evolved over the years due to developments in statistics and probability. This is an example of how theories develop and can be superseded over time.

International-mindedness

The UN sustainable energy initiative has the goal of doubling of global sustainable energy resources by 2030.

For more examples and links to International mindedness, Theory of knowledge, utilization etc. see separate page which covers all of Topics 5 & 15: Energetics/thermochemistry.

Vocabulary

entropy, Sstandard entropy change, ΔS⦵disorderisolated systemsubsystem
spontaneousGibbs free energy change, ΔG⦵spontaneitythermodynamically stablekinetically stable

Learning slides

You can use this slide gallery for learning or for reviewing concepts and information. It covers all the key points in the syllabus for this sub-topic.

  

Something to think about

Entropy is paradoxically probably one of the hardest and one of the easiest topics to learn! Hardest because a full understanding of entropy really requires knowledge of statistical thermodynamics; easiest because at this level it can be related simply to the idea of disorder and the questions asked in the examination are usually very straightforward.

 'Nature tends to disorder' is a very simplified form of the second law of thermodynamics (The total entropy change of an isolated system must be positive) will generally suffice to deduce whether an entropy change is positive or negative. It is actually better to understand that entropy refers to the distribution of available energy among the particles. The more ways the energy can be distributed the higher the entropy. However it can be quite difficult to understand why complex, highly ordered arrangements of molecules such as ice crystals form when water is cooled or even why humans exist. You need to understand the difference between an isolated system and a subsystem. While the entropy change within a subsystem (ice or humans) may become negative (i.e. more ordered) the total entropy change within the larger isolated system will be positive.

ΔStotal = ΔSsubsystem + ΔSsurroundings


Consider what happens when ice is added to water to cool a drink (left). When the ice melts it becomes more disordered (ΔS> 0) but the surrounding water in the glass becomes lower in temperature so therefore becomes more ordered (ΔS< 0). The heat gained by the ice must be equal to the heat lost by the water but overall the increase in disorder due to the ice melting is greater than the increase in order due to the surrounding water cooling.

The word 'spontaneous' provides a good example to use when discussing the importance of the correct use of language in chemistry. Language is one of the eight ways of knowing addressed in the TOK syllabus. Some students may have difficulty answering a question because they have not understood the language used in the question rather than the underlying chemical theory (see Language of Chemistry). In everyday English spontaneous means 'off the cuff' or carrying out an action or thought without prior preparation or considering all the consequences beforehand. In Chemistry it has a very different and highly specific meaning. According to sub-topic 15.2 all a Higher Level IB student needs to know is that a reaction will be spontaneous when ΔG is negative - but what does this really mean?

A spontaneous reaction is one that once initiated can proceed in a given direction without needing to be driven by the input of an external source of energy. In other words a spontaneous reaction releases free energy - that is energy that is available to do work1. It does not necessarily mean the reaction must be exothermic or that there must be an increase in entropy as it depends upon a combination of both of these factors according to the equation ΔG = ΔH – TΔS.

Notice the use of the word 'can' rather than 'will' in the definition. In English spontaneous usually implies something done quite quickly. In chemistry there is no concept of time in the use of the word spontaneous. It says nothing about the rate of the reaction. Often a spontaneous reaction may not proceed at any measurable rate as the activation energy is so high. A good example is the combustion of carbon. Diamonds are pure carbon. In 2007 the artist Damien Hirst made a skull of diamonds (see image in 'Learning outcomes' above) called 'For the love of God'. Luckily for the group that bought it for one hundred million US dollars, diamonds are extremely stable kinetically in air even though, as ΔG for the combustion of carbon is negative, they are thermodynamically unstable and spontaneously burn to form carbon dioxide.

1. Strictly speaking it is the ability to do external work. This is because ΔH is the enthalpy change at constant pressure and if there is a volume increase then internal work is done as the volume expands. This is beyond the syllabus as the IB does not distinguish between ΔH and the enthalpy change at constant volume, ΔU.

Test your understanding of this topic

(Note that your teacher may have restricted your access to some or all of these questions and worked answers if they are going to use them as a class test or set them as an assignment.)

For ten 'quiz' multiple choice questions with the answers explained see MC test: Entropy & spontaneity.

For short-answer questions see Entropy & spontaneity questions.

More resources

1. See Understanding and using ΔG  

2. For a bit of fun how about 'Entropy set to music' by Stevethedinosaur.

Entropy (1)

3. For a more serious explanation of entropy with a good example using sand and a sandcastle try Professor Brian Cox - taken from his excellent BBC series on the wonders of the universe.

Entropy (2)

4. A student giving a tutorial on Gibbs Free Energy. It is an interesting video as the student shows clearly how to work out the change in free entropy for a particular reaction and relates it to the IB definition of spontaneous. However it is clear that there is no actual understanding of what a spontaneous reaction is as there is confusion between kinetic and thermodynamic stability.

Gibbs free energy (1)  

5. A better explanation with some specific example given by Paul Andersen.

Gibbs free energy (2)  

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