Entropy & spontaneity
15.2 Entropy & spontaneity (4 hours)
Pause for thought
Entropy is paradoxically probably one of the hardest and one of the easiest topics to teach! 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.
If you tell your students that 'nature tends to disorder' which is a very simplified form of the second law of thermodynamics (The total entropy change of an isolated system must be positive) this will generally suffice. It is actually better to explain that it 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 explain why complex, highly ordered arrangements of molecules such as ice crystals form when water is cooled or even why humans exist. They 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. Sometimes when students have difficulty answering a question it is 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 (right) 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.
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.
Learning outcomesAfter studying this topic students should be able to: Understand
Apply their knowledge to:
| Clarification notesVarious reaction conditions that affect the value and sign of ΔG should be examined. International-mindednessThe UN sustainable energy initiative has the goal of doubling of global sustainable energy resources by 2030. |
Teaching tipsMy teaching room has a door leading to a resource room. I like to start entropy by asking students why, if one room was filled with oxygen and the other with nitrogen, the two gases mix when the door is opened even though no enthalpy change takes place. Alternatively, could the air currently in the rooms arrange itself so that all the nitrogen went to one room and all the oxygen stayed in the other room? I then relate the idea of disorder to all the possible random combinations in the ways the individual molecule making up the air disperse. In theory one combination is that all the nitrogen molecules would be in one room and all the oxygen molecules in the other. The chance of this one specific possibility is infinitesimally small and is never likely to happen and even if it did it would only be for a minute fraction of a second. Discuss with them the ideas of order and disorder and the concept of subsystems and total isolated systems. They should understand that, unlike enthalpy (H At this level impress upon them that changes of state usually cause the largest entropy changes. For this reason, most IB questions where they ask whether the change is positive or negative involve either changes of state or an increase or decrease in the total number of molecules present. It is difficult to do much meaningful IB practical work with entropy. You could tell them to tidy up their room at home - it is a lot easier to make it untidy (more disordered) than it is to tidy it! Up to this point students tend to only think of the energy of a reaction in terms of enthalpy change. I like to introduce spontaneity by returning to the example of why gases mix (or do not unmix) even though there is no enthalpy change. This impresses upon them that there are other driving forces to a reaction or process other than just an enthalpy change. The concept of free energy - the energy available to do work - can then be explained. The key to this sub-topic is the relationship ΔG⦵ = ΔH⦵ – TΔS⦵ and it is worth stressing that this is one of the most important relationships in the whole of Chemistry. Even so, many students get it wrong when they try to use it as they ignore the fact that the units of enthalpy are kJ mol-1 whereas the units of entropy are J K-1 mol-1. The K-1 is easily taken care of by quoting the temperature as its absolute (or Kelvin) value. The problem usually is that students forget to either convert the enthalpy change into J mol-1 by multiplying by 1000 or convert the entropy change to kJ K-1 mol-1 by dividing by 1000 before substituting the values into the equation (see Understanding and using ΔG). Get them to work out all the possibilities for when ΔH Stress that just because ΔG The relationship between ΔG | Study guide
Page 43 - 44 QuestionsFor ten 'quiz' multiple choice questions with the answers explained see MC test: Entropy & spontaneity. For short-answer questions which can be set as an assignment for a test, homework or given for self study together with model answers see Entropy & spontaneity questions. Vocabulary listEntropy, S IM, TOK, 'Utilization' etc.See separate page which covers all of Topic 5 & 15. Practical workMost practicals simply do traditional calorimeter experiments to find ΔH for a reaction then use data tables for entropy values to calculate ΔG. For example, you could adapt for IB use the |
Teaching slides
Teachers may wish to share these slides with students for learning or for reviewing key concepts.
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Other resources
1. For a bit of fun how about 'Entropy set to music' by Stevethedinosaur.
2. 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.
3. 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.
4. A better explanation with some specific example given by Paul Andersen.
5. If your students can follow the conversation as he speaks very fast this crashcourse video covers most of what is needed for understanding entropy at IB level.