How To Measure Disorder
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Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
INTRODUCTION The U.S. Army Corps of Engineers had an extravagant slogan during World War II: "The difficult we do at once; the impossible takes a little longer."
The central theme of this chapter is that a lowering of energy, and an increase in disorder, both are changes that tend to occur spontaneously.
This time division into the easy, the difficult, and the impossible also applies to chemical reactions. Some chemical reactions are very fast; others will take place eventually if you have the patience to wait. Yet a third class of chemical reactions will never go in a desired direction without outside help, even if you wait forever.
In the melting of the icicle, water can lose heat and go to a state of lower energy by freezing, but at a cost of increasing its order in the ice crystal.
If you want a particular reaction to occur, it is obviously of interest to be able to predict into which category the reaction falls. In the next two chapters we will see what governs how fast a reaction will go. In this chapter we are concerned with the simpler question of predicting whether a given reaction will ever occur by itself, given unlimited time. The key step will be learning how to measure the order or disorder that is produced when molecules interact, or the entropy of a reaction.
Conversely, a frozen icicle can go to a more disordered state by melting, but only if enough heat is supplied to break the hydrogen bonds in the ice crystal. The energy factors say "freeze," and the entropy factors say "melt". For reasons that we will explore in this chapter, energy is more important at low temperatures, and entropy, or disorder, dominates at higher temperatures. The temperature at which these two conflicting tendencies balance is the melting point of ice.
Whether a reaction ever will proceed by itself depends on two quantities that sometimes co-operate but more often conflict: heat or energy, and disorder or entropy.
Page 0 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/default.html
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
SPONTANEOUS REACTIONS Spontaneous reactions are those that will take place by themselves, given enough time. They do not have to be rapid; speed is not a factor in the definition of spontaneity. Explosions and many other spontaneous reactions are rapid, but other spontaneous processes, such as the precipitation of calcium carbonate in the stalactites of Mammoth Cave, require thousands of years. We recognize the irrelevance of time to the idea of spontaneity when we use the term "spontaneous combustion" for the slow smouldering of paint-soaked rags. The oxidation of newsprint is spontaneous, although we do not worry about our morning paper bursting into flames as we read it. At 25° C, the reaction of newsprint with oxygen is exceedingly slow, but the gradual browning of old newspapers in library files shows us that the process is spontaneous nevertheless. In contrast, the same reaction at the temperature of a lighted match is both spontaneous and rapid. By raising the temperature we have hastened the achievement of a chemical reaction, but the tendency for the reaction to take place was already there, even at room temperature. It is this tendency to react that we mean when we talk about spontaneity, and it is this tendency toward reaction that we would like to be able to predict.
One good reason for wanting to predict spontaneity is that, if a reaction is genuinely spontaneous but slow, we may be able to speed it up by changing the experimental conditions. Changing the temperature is one way that is particularly effective for oxidations. Finding a suitable catalyst is another. If a reaction is spontaneous, a catalyst will accelerate it. If the reaction is not spontaneous to begin with, then looking for a catalyst is a waste of time. This chapter is focused on one fundamental question: How can we tell in advance whether a reaction that has not been tried will be spontaneous?
Page 1 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page1.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTENEITY If we let a ball loose on a slope, it will roll spontaneously downhill (right). If we give one object a positive charge, it will be attracted spontaneously toward a second object with a negative charge. If we bring the north pole of a bar magnet near a compass needle, the needle will rotate to point its south pole toward the magnet. All three of these spontaneous processes are in the direction of lower energy lower gravitational energy for the ball on a slope, lower electrostatic energy for the two charged objects, and lower magnetic energy for the compass and magnet. Common sense seems to tell us that spontaneous processes are those that lead to a decrease in some form of energy. We would be surprised indeed to see boulders roll up a mountainside by themselves. There is a duck hunter's joke about a hardy breed of bird that always flies past the blind upside down, so that when they are hit, they fall up. We find this ridiculous because common sense tells us that things always happen spontaneously in the direction of lower, not higher, energy. But in predicting chemical reactions, common sense often is wrong.
Page 2 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page2.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTANEITY It is true that in most spontaneous chemical reactions, energy or enthalpy falls. The energy that the chemical substances lose during reaction is given off as heat. Another way of expressing the situation is to say that most spontaneous chemical processes are exothermic. The combustion of gasoline, like all combustions, liberates heat, because the carbon dioxide and water molecules produced have lower energy than the gasoline and oxygen molecules from which they came. Is it valid to state as a general law that all spontaneous reactions go in the direction of lower energy, or that all spontaneous reactions are exothermic?
Page 3 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page3.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTANEITY The difficulty with general laws is that they are so hard to prove but so easy to disprove. If you are testing the proposition that "all Irishmen have red hair," then ten million red-haired Irishmen will not prove the law beyond challenge; they merely will make it more probable. But a single blond Irishman will wipe out the proposition completely. (All is not necessarily lost, however. If you look into the reasons for the yellow hair you may learn something about people.) The analogy is not facetious. Any number of spontaneous, heat emitting reactions will not rigorously prove the statement "all spontaneous reactions tend to minimize energy," yet one lone, spontaneous but heat-absorbing process will scuttle it. If we look more closely at why some heat-absorbing reactions are spontaneous, we will discover a new fundamental principle about chemical reactions.
Crystalline
N205
is
unstable
and
will
explode
spontaneously:
The remarkable aspect is that when N205 decomposes it absorbs 26 kcal of heat per mole. Here is a spontaneous and rapid reaction that clearly goes to a state of higher energy.
Exceptions to the principle that all spontaneous reactions emit heat are not hard to find. N205 is the oxide of nitrogen with its highest oxidation number, +5. The solid dissolves in water to form HNO3:
Page 4 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page4.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTANEITY Another example is the cooling effect when a salt such as ammonium chloride is dissolved in water (right). The reaction:
Ammonium Chloride Crystals dissolved in Water
absorbs enough heat to chill its surroundings, yet we do not expect an ammonium chloride solution to separate spontaneously into salt crystals and pure water just because in this direction the reaction gives off heat. An even simpler example is the vaporization of water. The heat of vaporization at room temperature is ∆H0= +10.5 kcal mole-1. Heats of vaporization for all liquids are positive because energy is required to break the attractive forces between molecules in the liquid and create a gas. Yet evaporation frequently is spontaneous. If only heat-yielding processes were spontaneous, then all gases in the universe would condense to liquids, all liquids would freeze to crystalline solids, and the world would be nothing but rock and ice. This obviously is not so, and energy obviously cannot be the only factor in making chemical reactions spontaneous.
Ammonium Chloride crytals dropped into water absorb heat from the surroundings as they dissolve. The tumbler feels cold to the touch.
Page 5 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page5.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTANEITY What is the missing factor? What do the N20, NH4Cl, and evaporation processes have in common with most exothermic reactions that X makes them take place spontaneously, even though these reactions are endothermic?
Disorder increases from ice to liquid to vapour, as more Hydrogen bonds are broken and as water molecules begin to move past one another.
The answer is that all of these reactions create disorder NO2 and O2 gas molecules are more disordered than crystals of N206. Hydrated ammonium and chloride ions in solution are more disordered than the regular array of NH4Cl ions in a crystal. H20 molecules moving about freely as water vapor are more disordered than the closely packed molecules of the liquid, or the frozen molecules of the solid . Most explosions are destructive precisely because they convert solids or liquids into gases that push out against their surroundings. (The expansion of the gases when they are heated by the reaction is another destructive factor.) A decrease in energy or enthalpy certainly is an important component in determining spontaneity, but the other aspect is the production of disorder.
Page 6 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page6.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
DISORDER AND SPONTANEITY How do we measure disorder? The means of doing this came originally from physics, not chemistry. During the middle of the last century, physicists were interested in the nature of heat and its manipulation, an understandable bias in an era of steam power. James Joule, Julius Mayer, and others concluded after careful experimental measurements that heat, work, and energy all were merely different aspects of the same thing. William Thomson (later Lord Kelvin, of the Kelvin or absolute temperature scale) and Rudolf Clausius were struck by the fact that the interconversion of heat and work is a one-way street. It is easy to convert the energy of work completely into heat, but the reverse transformation is never complete. Thomson's version of the second law of thermodynamics states that it is impossible by any cyclic, repeatable process to take heat and convert it entirely into work without losing some of this heat to a reservoir at a lower temperature. There can be no steam engines without condensing cylinders, and part of the available heat always is lost to the condenser instead of being converted to useful work. The second law in any of its forms makes heat look like the lowest or most degraded form of energy: easy to obtain but hard to reconvert.
It is easy to change coordinated motion into random motion but impossible to turn uncoordinated motion completely back into uniform motion. When we heat a can of soup, all the molecules begin moving faster but in a random manner. What is the probablility that, purely by chance, all the molecules in the soup will begin to move faster in the same direction, taking the pan and the kitchen wall with them.
We know what Thomson and Clausius a century ago did not. On a molecular level, kinetic energy is the coordinated motion of all of the molecules in a solid in the same direction (right). Heat in a solid is the disunited motion of individual moleculed about their equilibrium positions. Kinetic energy is organised, coherent motion and heat is random incoherent motion.
Page 7 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page7.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
DISORDER AND SPONTANEITY As any good statistical physicist or cook can tell you, the chance of this happening is effectively zero. If every one of n molecules has an equal chance of moving up or down in the soup, or a 50% chance of being found moving upward, the probability that at some instant all n molecules will move upward in unison is given by the expression (½)n. For the n = 1.7 x 1025 molecules in a half litre of soup, this is an unimaginably small number.
It is true that, given enough time, the most unlikely events could happen by chance. Order could come from molecular disorder spontaneously, and an array of monkeys could type all the books in the British Museum. Neither is worth waiting for in the real world.
Arthur Eddington expressed these probabilities vividly in 1928 in his book The Nature of the Physical World. Speaking of the mathematically identical problem of the probability of finding all of the molecules of a gas in one half of a container at the same time, he said: "The reason why we ignore this chance may be seen by a rather classical illustration. If I let my fingers wander idly over the keys of a typewriter it might happen that my screed made an intelligible sentence. If an army of monkeys were strumming on typewriters they might write all the books in the British Museum. The chance of their doing so is decidedly more favourable than the chance of the molecules all moving to one half of the vessel."
Page 8 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page8.htm
2006/12/11
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
INTRODUCTION The U.S. Army Corps of Engineers had an extravagant slogan during World War II: "The difficult we do at once; the impossible takes a little longer."
The central theme of this chapter is that a lowering of energy, and an increase in disorder, both are changes that tend to occur spontaneously.
This time division into the easy, the difficult, and the impossible also applies to chemical reactions. Some chemical reactions are very fast; others will take place eventually if you have the patience to wait. Yet a third class of chemical reactions will never go in a desired direction without outside help, even if you wait forever.
In the melting of the icicle, water can lose heat and go to a state of lower energy by freezing, but at a cost of increasing its order in the ice crystal.
If you want a particular reaction to occur, it is obviously of interest to be able to predict into which category the reaction falls. In the next two chapters we will see what governs how fast a reaction will go. In this chapter we are concerned with the simpler question of predicting whether a given reaction will ever occur by itself, given unlimited time. The key step will be learning how to measure the order or disorder that is produced when molecules interact, or the entropy of a reaction.
Conversely, a frozen icicle can go to a more disordered state by melting, but only if enough heat is supplied to break the hydrogen bonds in the ice crystal. The energy factors say "freeze," and the entropy factors say "melt". For reasons that we will explore in this chapter, energy is more important at low temperatures, and entropy, or disorder, dominates at higher temperatures. The temperature at which these two conflicting tendencies balance is the melting point of ice.
Whether a reaction ever will proceed by itself depends on two quantities that sometimes co-operate but more often conflict: heat or energy, and disorder or entropy.
Page 0 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/default.html
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
SPONTANEOUS REACTIONS Spontaneous reactions are those that will take place by themselves, given enough time. They do not have to be rapid; speed is not a factor in the definition of spontaneity. Explosions and many other spontaneous reactions are rapid, but other spontaneous processes, such as the precipitation of calcium carbonate in the stalactites of Mammoth Cave, require thousands of years. We recognize the irrelevance of time to the idea of spontaneity when we use the term "spontaneous combustion" for the slow smouldering of paint-soaked rags. The oxidation of newsprint is spontaneous, although we do not worry about our morning paper bursting into flames as we read it. At 25° C, the reaction of newsprint with oxygen is exceedingly slow, but the gradual browning of old newspapers in library files shows us that the process is spontaneous nevertheless. In contrast, the same reaction at the temperature of a lighted match is both spontaneous and rapid. By raising the temperature we have hastened the achievement of a chemical reaction, but the tendency for the reaction to take place was already there, even at room temperature. It is this tendency to react that we mean when we talk about spontaneity, and it is this tendency toward reaction that we would like to be able to predict.
One good reason for wanting to predict spontaneity is that, if a reaction is genuinely spontaneous but slow, we may be able to speed it up by changing the experimental conditions. Changing the temperature is one way that is particularly effective for oxidations. Finding a suitable catalyst is another. If a reaction is spontaneous, a catalyst will accelerate it. If the reaction is not spontaneous to begin with, then looking for a catalyst is a waste of time. This chapter is focused on one fundamental question: How can we tell in advance whether a reaction that has not been tried will be spontaneous?
Page 1 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page1.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTENEITY If we let a ball loose on a slope, it will roll spontaneously downhill (right). If we give one object a positive charge, it will be attracted spontaneously toward a second object with a negative charge. If we bring the north pole of a bar magnet near a compass needle, the needle will rotate to point its south pole toward the magnet. All three of these spontaneous processes are in the direction of lower energy lower gravitational energy for the ball on a slope, lower electrostatic energy for the two charged objects, and lower magnetic energy for the compass and magnet. Common sense seems to tell us that spontaneous processes are those that lead to a decrease in some form of energy. We would be surprised indeed to see boulders roll up a mountainside by themselves. There is a duck hunter's joke about a hardy breed of bird that always flies past the blind upside down, so that when they are hit, they fall up. We find this ridiculous because common sense tells us that things always happen spontaneously in the direction of lower, not higher, energy. But in predicting chemical reactions, common sense often is wrong.
Page 2 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page2.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTANEITY It is true that in most spontaneous chemical reactions, energy or enthalpy falls. The energy that the chemical substances lose during reaction is given off as heat. Another way of expressing the situation is to say that most spontaneous chemical processes are exothermic. The combustion of gasoline, like all combustions, liberates heat, because the carbon dioxide and water molecules produced have lower energy than the gasoline and oxygen molecules from which they came. Is it valid to state as a general law that all spontaneous reactions go in the direction of lower energy, or that all spontaneous reactions are exothermic?
Page 3 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page3.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTANEITY The difficulty with general laws is that they are so hard to prove but so easy to disprove. If you are testing the proposition that "all Irishmen have red hair," then ten million red-haired Irishmen will not prove the law beyond challenge; they merely will make it more probable. But a single blond Irishman will wipe out the proposition completely. (All is not necessarily lost, however. If you look into the reasons for the yellow hair you may learn something about people.) The analogy is not facetious. Any number of spontaneous, heat emitting reactions will not rigorously prove the statement "all spontaneous reactions tend to minimize energy," yet one lone, spontaneous but heat-absorbing process will scuttle it. If we look more closely at why some heat-absorbing reactions are spontaneous, we will discover a new fundamental principle about chemical reactions.
Crystalline
N205
is
unstable
and
will
explode
spontaneously:
The remarkable aspect is that when N205 decomposes it absorbs 26 kcal of heat per mole. Here is a spontaneous and rapid reaction that clearly goes to a state of higher energy.
Exceptions to the principle that all spontaneous reactions emit heat are not hard to find. N205 is the oxide of nitrogen with its highest oxidation number, +5. The solid dissolves in water to form HNO3:
Page 4 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page4.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTANEITY Another example is the cooling effect when a salt such as ammonium chloride is dissolved in water (right). The reaction:
Ammonium Chloride Crystals dissolved in Water
absorbs enough heat to chill its surroundings, yet we do not expect an ammonium chloride solution to separate spontaneously into salt crystals and pure water just because in this direction the reaction gives off heat. An even simpler example is the vaporization of water. The heat of vaporization at room temperature is ∆H0= +10.5 kcal mole-1. Heats of vaporization for all liquids are positive because energy is required to break the attractive forces between molecules in the liquid and create a gas. Yet evaporation frequently is spontaneous. If only heat-yielding processes were spontaneous, then all gases in the universe would condense to liquids, all liquids would freeze to crystalline solids, and the world would be nothing but rock and ice. This obviously is not so, and energy obviously cannot be the only factor in making chemical reactions spontaneous.
Ammonium Chloride crytals dropped into water absorb heat from the surroundings as they dissolve. The tumbler feels cold to the touch.
Page 5 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page5.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
ENERGY AND SPONTANEITY What is the missing factor? What do the N20, NH4Cl, and evaporation processes have in common with most exothermic reactions that X makes them take place spontaneously, even though these reactions are endothermic?
Disorder increases from ice to liquid to vapour, as more Hydrogen bonds are broken and as water molecules begin to move past one another.
The answer is that all of these reactions create disorder NO2 and O2 gas molecules are more disordered than crystals of N206. Hydrated ammonium and chloride ions in solution are more disordered than the regular array of NH4Cl ions in a crystal. H20 molecules moving about freely as water vapor are more disordered than the closely packed molecules of the liquid, or the frozen molecules of the solid . Most explosions are destructive precisely because they convert solids or liquids into gases that push out against their surroundings. (The expansion of the gases when they are heated by the reaction is another destructive factor.) A decrease in energy or enthalpy certainly is an important component in determining spontaneity, but the other aspect is the production of disorder.
Page 6 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page6.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
DISORDER AND SPONTANEITY How do we measure disorder? The means of doing this came originally from physics, not chemistry. During the middle of the last century, physicists were interested in the nature of heat and its manipulation, an understandable bias in an era of steam power. James Joule, Julius Mayer, and others concluded after careful experimental measurements that heat, work, and energy all were merely different aspects of the same thing. William Thomson (later Lord Kelvin, of the Kelvin or absolute temperature scale) and Rudolf Clausius were struck by the fact that the interconversion of heat and work is a one-way street. It is easy to convert the energy of work completely into heat, but the reverse transformation is never complete. Thomson's version of the second law of thermodynamics states that it is impossible by any cyclic, repeatable process to take heat and convert it entirely into work without losing some of this heat to a reservoir at a lower temperature. There can be no steam engines without condensing cylinders, and part of the available heat always is lost to the condenser instead of being converted to useful work. The second law in any of its forms makes heat look like the lowest or most degraded form of energy: easy to obtain but hard to reconvert.
It is easy to change coordinated motion into random motion but impossible to turn uncoordinated motion completely back into uniform motion. When we heat a can of soup, all the molecules begin moving faster but in a random manner. What is the probablility that, purely by chance, all the molecules in the soup will begin to move faster in the same direction, taking the pan and the kitchen wall with them.
We know what Thomson and Clausius a century ago did not. On a molecular level, kinetic energy is the coordinated motion of all of the molecules in a solid in the same direction (right). Heat in a solid is the disunited motion of individual moleculed about their equilibrium positions. Kinetic energy is organised, coherent motion and heat is random incoherent motion.
Page 7 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page7.htm
2006/12/11
Foundations to Chemistry - adapted from "Chemistry, Matter and the Universe"
13. How To Measure Disorder
Page 1 of 1
Online Multimedia Links
DISORDER AND SPONTANEITY As any good statistical physicist or cook can tell you, the chance of this happening is effectively zero. If every one of n molecules has an equal chance of moving up or down in the soup, or a 50% chance of being found moving upward, the probability that at some instant all n molecules will move upward in unison is given by the expression (½)n. For the n = 1.7 x 1025 molecules in a half litre of soup, this is an unimaginably small number.
It is true that, given enough time, the most unlikely events could happen by chance. Order could come from molecular disorder spontaneously, and an array of monkeys could type all the books in the British Museum. Neither is worth waiting for in the real world.
Arthur Eddington expressed these probabilities vividly in 1928 in his book The Nature of the Physical World. Speaking of the mathematically identical problem of the probability of finding all of the molecules of a gas in one half of a container at the same time, he said: "The reason why we ignore this chance may be seen by a rather classical illustration. If I let my fingers wander idly over the keys of a typewriter it might happen that my screed made an intelligible sentence. If an army of monkeys were strumming on typewriters they might write all the books in the British Museum. The chance of their doing so is decidedly more favourable than the chance of the molecules all moving to one half of the vessel."
Page 8 of 45
http://neon.chem.ox.ac.uk/vrchemistry/entropy/page8.htm
2006/12/11
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