AP Chemistry Spontaneity, Entropy, & Free Energy, Part I

Hello, and welcome back to Educator.com, and welcome back to AP Chemistry.0000

Today, we are going to start on a new chapter, and we are going to discuss spontaneity, entropy, and free energy.0004

We are going to be starting thermodynamics.0011

Now, if you remember, we did talk about thermodynamics a while back, when we were discussing calorimetry, and we mentioned the first law of thermodynamics.0014

We talked about enthalpy, heat, and work; that was sort of an introduction--just something to get you going, sort of starting to think about reactions and how heat is involved in chemical reactions.0021

Now, we are going to get much deeper into it; now we are going to talk about spontaneity, entropy, free energy--and we are going to tie all of those together into what is, for me personally, probably my favorite area of all of science, in fact.0036

When I was originally a chemistry student, I didn't care much for the thermodynamics, and probably the reason why is the reason why most people sort of have--0053

Well, to be in all honesty, thermodynamics is a strange topic, and strange--I mean, it's not always easy to wrap your mind around; it's a very elusive kind of thing.0066

There are certain aspects of the physical world that are both intuitive and sort of make sense naturally; thermodynamics is not one of them.0075

How heat and energy work, why certain things happen in one direction and why they don't--these are kind of elusive; they are very subtle concepts.0083

That is where the difficulty lies: there is nothing technically difficult about thermodynamics--in fact, it just comes down to a handful of equations, very simple equations.0091

And when I mean "handful," I mean maybe three.0100

So, there is certainly nothing mathematically strange; it's about what is going on.0103

Now, I'll be honest with you: we are not, of course, going to be able to get into the actual nuts and bolts, so in our discussion, there are a couple of things that I am going to ask you to just sort of take on faith.0108

Those of you that actually go on, let's say, as engineers or physicists or chemists, to take thermodynamic classes formally, you will actually go back and discuss why some of these things that we are discussing are true.0119

But for our purposes of chemistry, I'm hoping that we actually give you a really, really solid grounding in thermodynamics and why things happen the way that they happen.0130

Let's jump in and get started, and we'll start with a little bit of review of what we had done before.0140

OK, so let's recall some of our original discussion of thermodynamics: so, I'm just going to sort of list these as a series of things that we should know--just facts.0146

There are two ways to transfer energy, and that was heat and work.0157

Heat and work: so, when we are talking about anything in thermodynamics, we always talk about the system, and we talk about the surroundings.0171

The system is the thing that we are interested in--whatever it happens to be--whether it's a beaker of water, a block of concrete, a room filled with a certain gas.0179

And the surroundings is everything else.0187

There is a boundary somewhere between them; like, in a beaker of water, you might have the water being the system, the beaker itself--the glass--being the boundary, and the air outside being the surroundings.0190

So, let's sort of mention that: so we always have a system and surroundings.0202

OK, now we always (as chemists, anyway) consider the flow of energy from the system's point of view.0224

In other words, if this is the system, and out here is going to be (I'll put it, actually, in a little square like this)--this is the surroundings...and, of course, the whole thing, the system plus the surroundings, we call the universe...0250

This is just general thermodynamic nomenclature.0268

We are looking at it from the system's point of view, so from the system's point of view...well, actually, let's go ahead and give our main equation, or one of our primary equations.0271

The change in energy of a system is equal to the heat that flows into or out of the system, plus the work that is done onto or by the system.0282

Again, we said that heat and work are the only ways that energy can be transferred.0294

So, when we are talking about a given system, and there is a change in energy of that system, that means heat has gone in or out, work has gone in or out (or work has been done on the system or by the system), and that is it.0299

Those are the only two ways that energy can be transferred.0312

This is a statement of the first law of thermodynamics, essentially--the conservation of energy says that energy is constant.0315

Well, the first law of thermodynamics says, yes, it is constant; it can change form; and two ways that it can change form are heat and work.0323

But, the total energy has to remain the same.0331

OK, so let's see: heat flows into the system...our possibilities are: heat flows into the system (that means Q is positive; we are looking at it from the system's point of view, so if heat goes into the system, that means the system gets hotter)...0334

Now again, heat is not temperature; so remember, temperature is a measure of the random motion of the molecules; when heat goes...heat is energy--it's a form of energy.0357

When heat goes into a system, like in an endothermic process (a system absorbs heat)--when it absorbs heat, that energy ends up making the molecules move faster, in turn raising the temperature.0368

So, heat is a transfer of energy; so if heat comes into the system, the heat is positive--that means the energy of the system has now gone up.0382

And, if heat flows out of the system, then Q is negative; that means the system had a certain amount of energy; a certain amount of energy flowed out as heat; now there is less energy, so it's negative; it lost heat--exothermic.0391

A gain of heat: endothermic process.0414

OK, now as far as work is concerned: work done by the system (in other words, if the system does work on the surroundings--for example, if a balloon actually is the system, and it expands--it is pushing against an external pressure--it is doing work on the surroundings)--in that case, work is negative.0417

When a system does work, it is as if it's losing energy; again, work is just another form of energy.0448

You can think of it as just something else that flows: heat is something that flows--if it flows out, well, that means the heat is negative from the system's point of view--it's losing heat.0455

Well, if the system does work, that means it's losing work; that is it--work is just something else that flows.0464

Don't think of work the way that we use it in daily language; work is just a form of energy that flows, either in or out, like heat, like water...anything else.0470

OK, now if work is done on the system (in other words, if the surroundings does work on the system--that means it is putting energy into the system), the work is positive.0480

Work is positive: so this change of energy--you can have both being positive, both being negative, one positive and one negative, or one positive and one negative.0494

There are four possibilities: and the sum of those is going to be the change in energy of the system.0502

So, this is our primary, first law of thermodynamics, basic equation.0508

OK, now let's define what a state function is (let me go ahead...no, that's OK; I can do it over here): So, a state function--I personally prefer to call it...I'm used to calling it a state function, but I think it's better to call it a state property.0515

Anytime I hear the word function, I think of some mathematical function, which is very odd.0533

It is just one of those words in science that is used, and I think it is more confusing; so when you see the word function in science, think "property," OK?0539

A state property (which makes more sense, when I actually define it) is a property of (you know what, I think I need to write a little bit better here, because this is important) the system that does not depend on the path the system took to get there.0546

The best way to think about it is this: if I start on the ground level of...let's say I have a 50-story building; if I start on the ground level, and if I go up to the 50^th level, and then I drop back down to the 10^th floor, and then I go up to the 20^th floor, and then I get out, well, I have gone up to the 20^th floor.0598

My change is just 20 floors; however, the path that I took was up to 50, down to 10, up another 10.0616

It doesn't matter how I got to the 20^th floor; what matters is now, as far as, like for example, my potential energy--it is just the difference between the ground level and the height of the 20^th floor.0623

It doesn't matter that I went all the way to 50 and all the way down to 10 and back up.0634

In between doesn't matter; all that matters is where I start and where I finish--my Initial and my Final.0639

Energy is a state function; that is what is important.0645

Energy is a state function.0652

Here is what is interesting: heat and work are not state functions.0660

Heat and work very much depend on the path that I take to get there; so, for example, if I'm pushing a rock up a hill, I can push it just directly up a hill, or I can push it around the mountain, around the mountain, around the mountain, and then finally, I get to a certain height.0671

Well, there is a big difference in the amount of work that I have done, believe me!0689

What is interesting is: if I measure the change in energy of the system, it actually doesn't matter; it's the same, no matter which path I take.0693

So, what is kind of curious is that energy is a state function: energy at the beginning of the system and energy at the end of the system, after something has happened--that change doesn't depend on how that change took place.0699

But the transfers of energy--the heat and the work--those actually are not state functions; it's very, very curious that that is the case.0711

OK, now let's talk about work: most work in chemistry will be pressure-volume work.0719

In other words, you will have a container; it is at a certain volume and has a certain pressure in it; let's say you push the piston down--you decrease the volume as you increase the pressure: pressure-volume work--there is work that is being done of a pressure-volume sort.0739

Well, the work that is done is equal to minus the pressure, times the change in volume.0754

OK, therefore, the ΔE, we know, is q + w; well, w is -PΔV, so ΔE is equal to q, minus PΔV.0762

There you go: the change in energy of the system is a sum of the heat that is transferred in or out as heat, and the work that is done by any pressure-volume change.0782

Add those two, and that will tell you what the change in energy of the system is.0795

OK, here is what is important about this particular P: the P in PΔV is always, always the external pressure.0799

OK, that is very, very important; it's not the internal pressure of the system--it is the external pressure.0820

It is the pressure that causes a compression--the external pressure--or which resists an expansion.0827

The pressure on the inside is trying to push out; well, the pressure on the outside is trying to keep it from pushing out--it's like you trying to open a door.0857

It's the external pressure; so P in this PΔV always is external pressure.0864

Any time you are given a problem, and you are not exactly sure what this P is supposed to be, unless it specifically says "the pressure in the system" (which, in the case of pressure-volume work, will never say that), this P is always the external pressure.0869

Just know that: it will save you a lot of grief, I promise.0885

OK, so again, we are just reviewing some of the things that we did before; so, now we are going to talk about this thing that we mentioned earlier, called enthalpy--the ΔH.0890

I personally don't like the word enthalpy: heat--let's just call it the heat, and I will actually show you why it is the heat.0900

The definition of enthalpy is the following: the enthalpy of a system is equal to the energy of the system, plus the pressure of the system, times its volume.0907

If I take the energy of a system, and if I can somehow measure it, and then if I measure the pressure and the volume of that system, multiply the pressure and volume, and add it to the energy that is there, I get something called enthalpy.0919

Now, a change in enthalpy from initial state (which is really what we measure in science: we measure changes in things): ΔH is equal to ΔE + ΔPV (right?--just Δs across the board).0931

Well, if we do constant pressure, if we keep P constant, we can pull it out--there is no change in pressure, so it's only a change in volume; and this equation becomes the following.0948

ΔH = ΔE + PΔV.0966

Well, what is ΔE? ΔE is just q-PΔV.0974

ΔH=q-PΔV + PΔV; the PΔVs cancel, and what we get is: at constant pressure, the enthalpy of the system happens to be the same as the heat of the system that is transferred in or out.0980

That is what is amazing; so this is at constant pressure--very, very important.1006

If they say "constant volume," not "constant pressure," this is not true: constant volume is a different process altogether.1012

Those of you that go on to study engineering, thermodynamics, or as physicists, you will discuss constant volume processes; but in chemistry, we generally like to keep the pressure constant; it's easy to keep the pressure constant, because, well, if you are running a reaction in a beaker, the pressure of the atmosphere is constant--it doesn't really change much: so "at constant pressure" is very, very important.1018

For those of you who want the fancy name for it in science, it is called isobaric.1041

OK, but it's best probably not to throw around words like that; just say "constant pressure"; it's better to go like that.1046

OK, so let's see: Enthalpy is also a state function; it doesn't matter how you get to where you are going.1054

Remember Hess's Law, where, if you have a reaction...if you have a bunch of reactions that you can add to get to the final reaction, the enthalpy is just--add the enthalpies together.1064

The change in enthalpy will be the same; how you got there doesn't matter; so enthalpy is a state function--is a state property.1073

OK, now I probably should have told you this in the beginning of this particular lesson: this lesson and, more than likely, the next lesson, are going to be more discussions; they are going to be more qualitative things.1090

We want to be able to wrap our mind around what is going on.1103

Remember earlier, when we were discussing equilibrium and things: it was really, really important that you understood the chemistry.1107

If you understood the chemistry, you could decide what is going to happen next, and you can adjust the mathematics to make it match the chemistry, as opposed to wondering what I do mathematically.1113

This lesson and the next lesson are going to be ways of wrapping our mind around these things that are new, things that we have never really thought about before.1123

We are going to introduce entropy in a minute: energy, enthalpy, all of these things floating around, and later free energy...so there is going to be a fair amount of discussion.1132

I just wanted you to sort of be aware of that; we will get to the math eventually, but I want to lay a reasonably good foundation; it's very, very important.1142

Please trust me on this.1149

OK, so enthalpy is a state property: and I'll just put, "Recall Hess's Law."1151

OK, so one last thing: exothermic--an exothermic reaction: that means it loses heat from the system's point of view; that means heat is going away.1162

That means the heat is negative; so that means the enthalpy, which is the heat, is less than 0.1178

When I see an enthalpy less than 0, that means it is an exothermic process--or when I calculate an enthalpy, based on the thermodynamic data that you have at the back of your book, that lists ΔHs, ΔGs, and entropy values--when you calculate it that way (remember, products minus reactants?), it's going to be negative for an exothermic process.1183

Endothermic process: well, an endothermic process absorbs heat; we are always looking from the system's point of view--that means heat is positive.1207

Heat is enthalpy; enthalpy is positive--it's greater than 0.1215

I hope that makes sense.1219

There we go; OK, so let's just take a look at a quick example here.1222

We will take the combustion of methane: CH₄ (which is methane, a standard gaseous hydrocarbon), plus two moles of oxygen, forms one mole of CO₂, plus two moles of water.1228

Any kind of combustion forms carbon dioxide and water.1243

The ΔH of this reaction is equal to -803 kilojoules.1246

That means 803,000 Joules of energy as heat is released; that is why, when you burn something, it is hot--that is what you are feeling: you are feeling the release of energy.1253

OK, ΔH (well...that's fine; I'll go ahead and just draw): in case you are wondering where I got this value, I took 2 times the enthalpy of this, plus 1 times the enthalpy of that, minus twice the enthalpy of this times one times the enthalpy of that.1266

Remember, products minus reactants: just go back to Hess's Law; go back to finding ΔHs, and that is how I got that.1292

It basically says this: When we have CH₄, and we have O₂, there is a certain amount of energy associated with the bonds in those molecules.1301

Once I ignite it and I convert it to CO₂ and H₂O, there is a certain amount of energy associated with the bonds in these molecules.1313

Well, the energy in the bonds of these molecules is a lot lower than the energy in these.1325

What happens to that excess energy as it goes from here to here?1331

That is the ΔH; that is what equals q, heat.1337

It is released as heat: energy flows out of the system.1344

OK, so here is our sort of take-home lesson: the first law (which is essentially what we have been talking about) of thermodynamics (we'll just call it the first law) gives us an accounting tool, a way of keeping track of energy flow and the different forms it can take.1350

That is it; that is really all the first law is--the change in energy, heat, work, heat released, heat gained, exothermic, endothermic...we are just keeping track of where the energy is going and how it's going.1401

Total energy is actually conserved.1413

OK, all right: Total E is constant (which, of course, you know: energy is conserved).1416

So, this is concerned with how much energy is involved in a change; that is it--this is what the first law tells us--it tells us how much energy is involved in a process.1426

So, in the process, CH₄ and O₂ going to CO₂ and H₂O, well, the amount of heat that is involved in the process is 803 kilojoules.1444

There you go: it tells us "Is energy flow into or out of a system?"1452

In this case, it's exothermic: it's out of a system--the system is releasing heat.1469

And 3: What is the final form of the energy involved?1475

That is an important one, also: it's all important.1479

What is the final form of the energy (of the energies, I should say) involved?1482

Well, we have two forms here: we have a whole bunch of energy here; here, we have energy in terms of bonds, and we have energy in terms of heat (so two types of energy going on).1502

If this release of heat actually ended up doing some kind of work (let's say you had it in some container, and you did something with that container, and it ended up actually expanding the container, and the piston did work on it--like a gas engine), well, now it's not only heat, not only bonds--but it's also work: so, three forms of energy.1513

OK, so that is what the first law tells us, and that was pretty much what we discussed when we originally discussed thermodynamics in the context of thermochemistry.1538

So now, we want to look at another question that we want to answer: How do we answer the following question?1548

Here is another question we want to ask--so now that we can account for the energy and find out how it's leaving, how it's coming, how much is involved...well, why does a given process take place at all?1569

Why does a given process happen at all?1587

Or (or I should say "and," not "or"--there are actually two questions that we want to answer)--and, why does it happen in the direction that it does happen?1600

So, those are the next two questions that we want to answer.1637

"Why does a given process take place at all?"1640

Why do we age? why does a ball roll down a hill--it doesn't roll up a hill naturally?--yes, you could invoke gravity for that, but there is actually something deeper going on, believe it or not.1643

Why is it that, when you burn wood, it turns into carbon dioxide and water? What happens if I take carbon dioxide and water and try to heat it up again in a flask--why doesn't it turn back into wood?1656

These are very, very valid questions; so we know, from our experience in life, that things tend to happen in a given direction, that if we want it to go in the opposite direction, one of two possibilities: 1) It's really, really hard to go in the opposite direction, to reverse something (but if we put enough energy into it, and enough effort, we can actually make it go in reverse), or it's completely impossible to actually make something go in reverse.1670

For example, aging is a perfect example: we don't know how to reverse the aging process.1700

Why is it that we would age?--these are very, very valid questions; there is something going on here.1706

Well, as it turns out, we do have an answer for it; and that is what we are going to discuss.1712

So, let me just throw out a couple of other things--a couple of other examples.1717

If I take some iron, and I just sort of leave it out there in the rain and air, it rusts; you know that; but why is it that rust never turns back into metal--never turns back into iron?1723

Iron rusts, but iron oxide (which is rust) never goes back to iron.1735

That is kind of annoying; just naturally speaking, why does it go in only one direction and not the other?1740

Well, OK: here is one of those times when I am going to throw something out, and it is going to feel like I just sort of pulled it out of the sky; but I am going to ask you to take it on faith that this is what it is.1747

I am going to introduce a new thermodynamic property, and it is going to be this property that is going to answer these questions.1763

And again, I think, as we sort of go on to discuss this property, it might make a little more sense--it might be a little more satisfactory of an answer.1771

But, this is sort of part and parcel of the elusive nature of thermodynamics--that we are able to identify this particular property that we are going to mention, and in some sense, it may be easy to understand, and in another sense, it's not really sort of easy to completely wrap your mind around.1781

It is not exactly intuitive; so again, I just wanted to warn you: this property that I am going to introduce--I'm just going to introduce it as: that's it.1798

I'm just going to put it in front of you and say, "This is the reason why something happens," "why these things happen in a given direction," or "why something happens in one direction and not in reverse."1806

OK, so I'm going to actually do this in red, I think; let's go with red...actually, we are...yes, OK.1816

So, the property for driving certain processes spontaneously forward (and this word, spontaneous, is going to be very, very important in a minute), and others not, is a property called entropy.1825

Absolutely very, very important; the symbol for entropy is S; and we also speak of a change in entropy, ΔS.1872

OK, here is what entropy is: you are going to love this definition--I'm not sure if it is going to make much sense, but here it comes: it is a measure of the disorder of a system.1889

I'm going to use another word, and I personally like thinking about it this way.1915

It is a measure of the chaos in a system.1921

And, as we do some of our problems in the future lessons, you will understand why it's better to think of things in terms of chaos, as opposed to disorder; but essentially, it's the same thing.1927

OK, now, let's start with some important equations: the entropy of a given universe is equal to the entropy of the system, plus the entropy of the surroundings.1937

OK, so we have a system; we have surroundings; we have a universe.1958

And the same with ΔS: ΔS of universe is equal to ΔS of the system, plus the ΔS of the surroundings.1961

That means, as it turns out, when we speak about entropy, we are often talking about the entire universe.1973

When we want to measure the change in the chaos of a given universe, it is made of two components: we have to measure the change of chaos in the system, and we have to measure the change in chaos of the surroundings of that system.1980

And again, both can be positive; both can be negative; one can be positive, one could be negative; and this is what we are going to investigate.1992

OK, I'm going to state the second law of thermodynamics, and then we'll move forward from there.2001

I don't know if I should do in on top or on the bottom; you know what, I'm just going to do it down here.2008

So, second law: In any (actually, you know what, did I)...you know what I am going to do--actually, before I write the second law, I'm going to actually define...because I have used the word spontaneous, I'm going to actually define what I mean by a spontaneous process, just to be complete here--because a "spontaneous" process is not what we think of when we think of "spontaneous" in normal daily living.2014

A spontaneous process is a process that happens under a given set of (oops, wow, that was interesting--those crazy lines again) circumstances, without any outside intervention.2055

OK, so a spontaneous process is a process that happens under a given set of circumstances, without any outside intervention.2103

OK, one other statement that I want to make about spontaneity: Spontaneous does not mean fast.2112

For example, diamond is pure carbon; graphite is pure carbon; if you set a piece of diamond on a table, the change from diamond to graphite is a spontaneous process at standard temperature and pressure.2136

In other words, if I left that thing alone for a very, very, very long time (certainly much longer than our lifetime), it will eventually turn to graphite without any intervention at all.2156

It is going to take millions of years, but it will happen.2166

The thermodynamics says that it will happen, and it will happen; but again, it doesn't mean it is going to happen fast.2170

That means I don't have to do anything, and it will happen; that is what "spontaneous" means--that, under a given set of circumstances, if I just leave it alone, it will happen.2176

The thermodynamics says that it will; so, that is what thermodynamics does--it tells us whether something will happen spontaneously.2186

It doesn't tell us anything about how fast it will happen; remember, that is the domain of kinetics.2196

Two different domains: kinetics is the study of how fast things happen; thermodynamics is about whether they can happen under a given set of circumstances.2201

OK, so now, let's go back and talk about the second law; let me define...let me actually write it down.2211

So, the second law: In any spontaneous process (this is profoundly important), there is always an increase in the entropy of the universe.2219

In other words, ΔS of the universe is always greater than 0.2256

Stop and think about this for a second: in any spontaneous process, the entropy of the universe is always greater than 0.2263

If I have a given system, and if I happen to measure the change in entropy, and it ends up being a positive value, that means that that process is spontaneous as written.2276

That means I don't have to do anything to it; it will happen naturally.2285

It may not happen quickly, but it will happen naturally.2289

That is what we mean by "spontaneous"; the second law of thermodynamics is profoundly important.2294

Essentially, what it is saying is that life and the universe is unfolding as it does; because it is doing so, that means that the entropy of the universe is actually increasing.2302

It is not constant--this is very different: the first law of thermodynamics says that the energy, the total energy of everything, is constant.2319

Energy can change forms, but it can never be created or destroyed.2328

The second law says that the entropy of the universe is actually increasing; the universe, each day that things unfold in life--every aspect of life--the chaos of the universe is increasing.2331

Now, it's true that certain systems might become less chaotic; but I can promise you that (remember, the ΔS of the universe has two components: the ΔS of the system and the ΔS of the universe)--as a system or series of systems become more ordered, less chaotic, I promise you, there is a greater increase in the disorder and the chaos of the universe.2345

That is the whole idea: in any spontaneous process and the unfolding of the universe, the unfolding of life as it is, there is actually an increase of entropy.2369

This is the underlying reason for why we age.2379

Yes, it is true: we eat and we do things, so we are actually sort of maintaining the order that is this amazing human body.2382

However, our surroundings--the entropy of our surroundings is constantly increasing more than our entropy of our system is decreasing.2391

The entropy of the universe--our body plus our surroundings--is always greater than 0: that is why we age.2400

OK, so let's consider the following: OK, so ΔS: remember, we said that the ΔS of the universe is equal to the ΔS of the system, plus the ΔS of the surroundings.2409

When we are considering whether something is spontaneous, we have to consider both the entropy of the system and the entropy of the surroundings.2428

Both might be positive; both might be negative; one is positive, one is negative; one is negative, one is positive; it depends--both of them have a say in what the total outcome is.2435

So, once again, if ΔS universe is greater than 0, our process is spontaneous (let me see, where are we here? OK); if ΔS of the universe is less than 0, it's spontaneous in reverse.2446

And, if ΔS of the universe equals 0 (I had better write that out a little bit better), that means the system is at equilibrium.2474

So, we are not done with equilibrium: equilibrium is going to haunt us for the rest of our life--and that's good: equilibrium is a great thing.2490

The system is at equilibrium.2497

We exist for as long as we do--we are alive--because of equilibrium.2501

The body does everything it can to maintain an equilibrium; it doesn't like it when things are off balance--it's always trying to maintain an equilibrium.2508

In some sense, you can actually define life as a system at equilibrium.2516

OK, now let's give a slightly better sense of what it is that we mean by entropy: so, I'm going to give you some examples, and I think this one example should suffice.2520

I wouldn't lose any sleep over this: think about a little bit; try to wrap your mind around it; but if not, it is not the end of the world--you can still work with the stuff--you can still do the problems.2531

OK, now entropy (I'm going to do this in red) is--we said it is a measure of the randomness of a system.2544

It is a measure of chaos: OK, it is a measure of the number of ways a given state can exist; that is what it is--that is what an entropy is: it is a measure of the number of ways that a given state can exist.2554

The more ways that a particular state that I specify can exist, that means the system is more chaotic.2585

And, the tendency toward the state--so entropy is a measure of the number of ways a given state can exist, and the tendency toward the state that has more ways available to it.2594

We will see what we mean in just a minute.2633

OK, so we have a container, and that container has a little wall in between, and a little bit of a hole in between; so there are actually two compartments in this container.2636

OK, we have 4 items: we will just call them 1, 2, 3, and 4.2654

The question is: How many different ways are there to arrange those four items in this container?2659

OK, so how many different ways are there to arrange it, where all four items are on one side?2672

Well, basically, 1, 2, 3, and 4, right?--there is only one way, so we will just call this arrangement 1: all on one side.2679

There is one way; OK.2696

Now, how many different ways are there to arrange it so that we have one thing on one side and three on the other?2700

One on one side, three on the other: well, fundamentally, we can do 1, 2, 3, 4; we can do 1, 2, 4, 3; we can do 1, 3, 4, 2; and we can do 2, 3, 4, 1.2711

We will call this arrangement 2, and we have four ways.2758

Well now, how about two on one side, two on the other?--1, 2, 3, 4, 5, 6; so, we can have 1, 2, 3, 4; we can have 1, 3, 2, 4; we can have 1, 4, 3, 2; we can have 2, 3, 1, 4; 3, 4, 1, 2; 2, 4, 1, 3.2765

Interesting: so this is...now, I don't want you to worry so much about what it is that we are doing here; the idea that I want you to take home is--now, I want you to think of this in terms of a...like let's say I had this container, this glass container, and in between, I had this wall with a little bit of a stop-caulk, and I put a whole bunch of gas--I put four particles of gas--in one side of the container.2820

Well, OK: if I open up the stop-caulk--if I just open this up, what is going to happen?2851

You know from your experience that the gas is going to distribute itself evenly.2858

Well, the reason it does that is the following: if all of the gas were to just stay on one side, there is only one way for that gas to be there.2862

Basically, that is one arrangement; all of the gas molecules have to be here.2872

If one particle of gas were to go to the other side--well, there are four different arrangements that it can have; so, probabilistically speaking, it is more likely that the system is going to end up here, because it has more states, more individual states, available to it, to actually satisfy...one on one side, three on the other.2876

Well, now, how about two gas particles on one side and two gas particles on the other side--which is what your intuition tells you, as far as how a gas distributes itself when you open up a container and allow it to sort of move over here?2898

So now, we have 1, 2, 3, 4, 5, 6--now, there are 6 ways: well, imagine if you had one mole of gas, 6.02x10²³ particles.2914

Well, there is only one way for all of those particles to arrange themselves in one container; however, you can just imagine, with that many particles, how many ways there are to arrange themselves, to distribute themselves evenly, half of them on the left, half of them on the right, with the gas moving back and forth, in and out.2924

So, because there are billions and billions of ways that that is possible, the probability of finding it in this configuration is virtually nil; it is not going to happen.2942

You are never going to find all of the gas in one container; it is statistically impossible.2952

But, it is statistically probable that it is going to be in one of these arrangements; in each case, you have half of it on one side, half on the other.2957

But, because there are so many possibilities for half and half, the probability that it will be in one of these states outweighs the other probabilities--that is why a gas distributes itself evenly when you open a stop-caulk and allow it to escape into the other end of the container.2968

It isn't because of pressure or other things like that, or a vacuum; no, it's because of statistics; it's a probability.2986

It is about entropy: this is a highly-ordered system--it has a very low entropy.2994

This is a highly-disordered system; it has a high entropy.3000

The system tends toward the series of states that have a higher entropy; that is why it goes this way naturally.3005

It will move in this direction: if you take a gas and put it in a container that has a separation with a little hole in it, the gas will not all of a sudden go to one end of the container and all collect on the left or on the right.3015

It won't happen spontaneously, because the entropy going from here to here is going to decrease; in a spontaneous process, entropy always increases.3030

Therefore, from here to here, entropy definitely increases; therefore, this will happen spontaneously.3041

I don't have to do anything; in fact, all I do is open a stop-caulk, and the gas will rush out and distribute itself evenly.3047

Again, it doesn't happen for physical reasons; it happens because the underlying probabilities make it so; it's because the entropy is that property that drives certain systems forward.3054

In fact, the entropy is the only thing that drives all systems spontaneously forward--absolutely everything--and to this day, we have not found one single exception to any of the laws of thermodynamics.3065

It is pretty extraordinary: it has been about 150, 160 years that this is the case, and we have not found any exceptions.3078

If you remember, in the earlier part of the 20^th century, classical mechanics was supplanted by relativity and quantum mechanics; but thermodynamics has not changed in 150 years; it is still just as valid.3085

Now, granted, we sort of use quantum mechanics to get a deeper atomic molecular view of thermodynamics; but all of the original ideas--the first law and the second law--they are still valid.3098

This is what is going on with entropy: I hope that helps a little bit.3113

Final words here: because there are more ways available for arrangement 3, you are more likely to find the system in arrangement 3; that is it--that is all that is going on.3119

Like we said, there are a whole bunch of ways that a mole of gas particles can distribute themselves in two containers; there is only one way for a mole of particles to be on one side of a container.3169

Because you have a multitude--billions and billions--of ways for it to be distributed evenly, you are going to find the system in that arrangement.3184

That is why we see the behavior that we see.3192

All process, all spontaneous processes, display an increase in entropy.3196

If you see something happen naturally, you can guarantee that the change in entropy of that system, in going from state 1 to state 2, has increased; it is greater than 0.3203

That is the whole idea.3213

I cannot even begin to tell you how profound and how deep this is--this notion of entropy.3214

It is truly extraordinary; and for me, after all these years, I am still, still fascinated by it; and there is still so much that I just...well, anyway--it's amazing.3224

OK, so a couple more things: if you start at arrangement 1, you will spontaneously tend toward arrangement 3, because arrangement 3 is more chaotic.3233

Arrangement 1 is highly ordered; arrangement 3 is more disordered--there is more movement--there is more freedom of movement with the atoms.3263

Particles can be here and there; there are just more things available to it.3272

OK, if you start at state 3--if you start at arrangement 3--the system will not spontaneously tend to arrangement, because there is going to be a decrease in entropy; it's not going to happen.3277

It is just not going to happen, ever.3308

My final advice regarding thermodynamics (OK, you know what, I'm not going to write this down; I think that is...): My advice with thermodynamics is, don't wrap your mind over trying to understand this conceptually.3314

There is a very, very famous saying with regard to thermodynamics: a very famous scientist in the early part of the century said, "Nobody really understands thermodynamics; we just get used to it."3337

There is a lot to be said for that; and, in a lot of ways, that is exactly true.3348

It is true for a lot of things; there are a lot of things that we may not completely understand, but we get used to them.3352

And we can work with them, and we can use them, and we can do practical things with them.3356

So again, don't lose any sleep if you don't necessarily understand; if you were able to follow what it is that I have discussed in today's lesson, and it at least made sense to you--if the arguments were plausible--that is it; you are in a good place.3360

You are ahead of the curve; that is all it needs to be.3374

So, don't worry too much about it.3377

OK, thank you for joining us here at Educator.com.3379

We'll see you next time for a further discussion of spontaneity, entropy, and free energy.3382

Take care; goodbye.3387