Revision notes thermodynamics-energetics - introduction to entropy and direction of change - for Advanced Level Theoretical-Physical Chemistry:
Doc Brown's A Level Chemistry Advanced Level Theoretical Physical Chemistry – AS A2 Level Revision Notes – Basic Thermodynamics
GCE Thermodynamics–thermochemistry sub–index links below
Part 3: ΔS Entropy Changes and ΔG Free Energy Changes
This page introduces the student to the concept of entropy and is fundamental as to why a physical or chemical change is possible. The entropy of a system does seem at first sight to be about how chaotic or random it seems to be BUT it is more to do with how many ways it is possible for a system to exist i.e. the what is the state of the system in which enables its energy to be distributed in the maximum number of ways. Its not an east concept to come to terms with and the page starts by pointing out the limitations of enthalpy changes in predicting whether a reaction will occur or not?
3.1 An Introduction to Entropy
Entropy and the direction of physical change or chemical change
Why do chemical reactions occur? Why does magnesium react with hydrochloric acid? Why doesn't hydrogen react with magnesium chloride solution? Why does ice melt at 273 K (0oC)?
These are questions not concerned with the rates of change (kinetics), even though this may have a bearing on their apparent spontaneity, but the above questions have everything to do with the energy changes which are possible i.e. what changes are feasible and why? and what is the 'energetic' driving force of these changes?
3.1a Events that happen, are the ones most likely to happen i.e. the most probable outcome!
3.1b The more ways an event can happen, the more probable is that event and the higher the entropy of a system
3.1c The entropy of a system not at equilibrium will always try to increase, determining the direction of change
immiscible liquid layers VERSUS miscible liquids
3.1d The entropy of substances increases gas > liquid >> solid Why?
3.1e Heat Capacity, energy distribution and entropy
Molecules possess three forms of kinetic energy:
Translation – moving from one place to another as in a gas or liquid (virtually no translation in solids).
Rotation – the molecule or a grouping in the molecule spinning around.
Vibration – all atoms constituting bonds vibrate in some way either by stretching–compression along the bond axis or bending–relaxing movement.
All of these forms of energy are quantised, that is, only specific KE energies of translation, rotation and vibration are allowed and the more energy absorbed in raising the temperature of a substance the more of the higher quantum levels of KE are accessible i.e. more ways in which the energy can be distributed i.e. an entropy increase. Note that we are now talking about the distribution of energy and not just the possible spatial arrangements and freedom to move around.
The order of these three types of quantum level is vibrational > rotation > translational
The translational quantum levels are so close together that virtually any measurable KE or velocity is likely to be observed – but it does seem strange to think of this motion in a quantised way. Although not required at advanced level, it is possible to show by direct experiment that freely moving electrons, atoms or molecules behave as a wave as well as particle – but the quantum world is 'wacky one' so don't expect the reality of our macro physical world to match with the quantum world. However, the quantisation of vibrational and rotational levels shouldn't present a conceptual problem – just think that the vibrations and rotations can only occur at specific frequencies determined by the quantum number rules – which you don't have to worry about. Also, remember microwave absorption is due to rotational quantum level changes and infra–red absorption is due to vibrational level changes.
As you heat a substance more and more of these 'kinetic energy' quantum levels can be accessed as the temperature of the substance increases, therefore more ways to distribute the energy, therefore a higher entropy state is obtained.
3.1f Electronic energy levels and entropy
If you continue to heat a substance eventually the kinetic energy of collisions–vibrations etc. is sufficient to cause electronic energy quantum level changes. Molecules can be raised to an 'excited' state when an electron is raised to a higher quantum level, and, if raised sufficiently highly, bond breaking will occur. This does not necessarily increase the temperature of substance because electronic quantum level changes do not affect the motion of the molecules i.e. the kinetic energy of the molecules. However, what it does mean is that yet more 'energy levels' are available in which to distribute the energy absorbed i.e. yet again this will lead to a higher entropy level being attained.
So the complete order of the four types of quantum level is electronic > vibrational > rotation > translation and, depending on the physical state and temperature of a substance, there is continuous interchange of energy between the possible energy levels e.g. via particle collision – remember energy cannot be created or destroyed, but can be changed in 'form' or 'distribution'.
There is a further conceptual quantum level complication because these types of quantum levels, although specific for a given bond or molecule etc. are not independent of each other. Each electronic level has its own set of associated vibrational levels, each vibrational level has its own set of associated rotational levels and each rotational level has its own set of translational levels. BUT don't worry about this! the point is that when a system–substance absorbs energy, the energy will be distributed in the maximum possible number of ways i.e. to attain the highest possible entropy state.
3.1g A summing up so far before we get into examples and then calculations!
We have considered the concept of the entropy state of a substance in terms of :–
A substance/system not at 'equilibrium' (i.e. a 'no net change state') will try to attain the highest entropy state by physical or chemical change. We can envisage the entropy of a substance in terms of the spatial distribution of the particles in the substance and the distribution of the energy of individual particles between the available translational, rotational, vibrational and electronic energy levels of each particle.
Therefore, entropy is a measure of the number of ways particles can be spatially distributed AND the number of ways the quanta of energy can be distributed i.e. the way the energy is 'arranged' in the system.
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