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>> So at UC Irvine we don't boast
about our athletic prowess very often [laughter].
That's partly because we don't have a football team [laughter].
But what we do have is probably the best men's volleyball
program in the country.
Did everybody know that?
I mean it sort of flies under the radar.
We've won two national championships
in the last five years on this campus.
National NCAA Championships
where we beat every other team in the country.
That pretty much means we're the best men's volleyball team,
collegiate men's volleyball team in the world.
Because let's face it, the US dominates in this sport.
So these guys beat Penn State last night?
And tomorrow they're going to beat USC [laughter].
Then we're going to have our third national championship
on this campus.
At least that's what I'm hoping happens.
So we can be very proud.
We should talk more about these guys.
Okay. So we sadly -- we're going to start talking
about the Gibbs Energy today.
Now, this is really a chapter 16 topic
and I'm not sure we'll come back to anything else in chapter 15.
I'm going to think about it over the weekend
but I'm guessing we're probably done with chapter 15.
We did it in sort of two lectures.
Okay? That material is important but sort of abstract to us
as chemists because where does the Carnell Cycle fit
in in chemistry?
How does it affect our daily lives as chemists?
I mean I can't answer that question.
It's a tenuous connection.
But the Gibbs Energy, for chemists
that the thermal dynamics,
that's where the rubber meets the road
in thermal dynamics is the Gibbs Energy.
It's going to allow us to tell whether a chemical reaction
happens or not, whether we're at equilibrium or not.
Right? This is what thermal dynamics is going
to do for us as chemists.
All right?
So we've really been building
up to this thing called the Gibbs Energy.
And today's lecture is extremely boring [laughter],
but important.
all right?
We're going to have some of those.
Right? Lots of symbols today.
All right?
But what we want to do is we want to figure
out where this Gibbs Energy comes from.
It was never really spelled out for me
in the physical chemistry class I had back in 1981.
All right?
It was just here's the Gibbs Energy, here's what it does.
All right?
Here's why it's important.
but no one ever really derived it.
But there is a nice airivation of the Gibbs Energy.
So, that's what we're going to try to do today
and we've only got 25 minutes.
So we may not get it -- we're not going to get all the way
through this lecture, and if we don't we'll just continue it
on Monday.
So don't worry about that.
But, all of these guys -- by the way, Clausius,
not an Austrian [laughter].
I saw that on a few forms.
German.
>> yeah.
>> That's what that's like right there.
All right, only one of these guys won the Nobel Prize.
This sounds like a quick question
for next week [laughter].
A, B, C, D. Which one of these guys won the Nobel Prize?
Anybody know?
>> [Inaudible].
They all did enough to win it but only one of them won it.
So there's really a mystery here.
Why did only one guy win the Nobel Prize first of all?
And which guy was it?
>> Lewis.
>> No, Gibbs and Lewis are good guesses
because those guys should have won the darn thing [laughter].
It was like the least famous guy on this slide.
>> [Inaudible].
>> Nerst [laughter].
Nerst won the Nobel Prize in 1920.
All right?
Now anybody know why?
I mean not why Nerst won but why these other guys didn't win.
I mean objectively they did more than Nerst
and they didn't win it.
>> Nerst survived until 1941.
>> The answer is, you know, the way the Nobel Prize works,
you do something really important
and then it takes a while.
There's an induction period while the rest
of the world tries to understand what you've done
and then once they understand it they have
to appreciate what you've done,
and then once they appreciate it they've got to get organized
to give you the award.
Right? And that process typically takes 20 years.
Right? When did the Novel Prizes start?
Anybody know?
>> [Inaudible].
>> 1901.
>> How do you know that [laughter]?
Did you just memorize that?
That's an amazing statistic to have on your fingertips.
That's the answer.
All right?
He died in 1896 and he, in his final will
and testament he endowed the Nobel Prize,
and the first one was given 1901 and they don't give it
to dead guys and most of these guys were dead [laughter].
Right? 1901 is here.
All right, in principle Boltzmann
and Lewis could have won it
but by the time everyone understood what they had done,
they were dead.
All right?
Nerst hung on long enough [laughter]
to win the darn thing.
>> [Inaudible].
>> What's that?
>> [Inaudible].
>> Oh yeah, this bar is not quite right.
Yeah. Yeah, you're right.
>> [Inaudible].
>> There's no good reason why he didn't win the Nobel Prize.
>> [Inaudible].
>> It's one of those things where everybody
who wins this award deserves it and then there's another 50 guys
who should have won it who never did is sort
of the way this works I think.
Okay, that's the reason is the awards started here
and then it takes a while and, you know,
they only got their act together --
you're right, Lewis should have won the darn thing.
So this is Gibbs.
He's our hero in this whole thing
because he's the only American we're going
to be talking about pretty much.
C.M. Lewis was an American too.
G.N. Lewis rather.
But we're not going to -- you know we talk about him a lot
when we talk about bonding.
Lewis God structures.
That's the guy.
Right? But we mentioned him at the beginning
of the class probably -- you might not remember this
but he got his -- he got the first PhD
in engineering in the whole country.
The very first one that was given at Yale was
in 1863 right before or actually right during the Civil War.
Right? And then, you know, one of the sad realizations you come
to if you're an experimentalist is all the guys whose names are
attached to equations
and chemistry are all theoreticians pretty much.
All right?
So Lewis was a theoretician.
It's not the people in the lab mixing the chemicals together
and plotting the data.
It's the theoreticians that sit at their desks
with their pencils and figure stuff out.
He was a theoretician.
Like Einstein, Durack, Schrodinger; all right,
these guys never did an experiment outside of school.
Right? They just looked at other people's experiments
and figured them out.
So he had an appointment at Yale.
He graduated from Yale, he got appointed there without salary.
And this was common at that time.
If you hadn't proven yourself as a scholar it was not uncommon
to get hired by university.
You'd teach and do all this work
but they wouldn't pay you anything until you started
to publish, which was hard to do in those days.
Now, you write a paper, it's in your computer,
in 10 minutes you can submit it to a journal electronically.
All right?
Boom. It's a link on your --
your browser opens there's a link to the website,
it's gone, you're submitted.
In those days, you know, everything had
to be hand written manuscripts in triplicate,
delivered by horseback [laughter] to the journal office
which was somewhere on the east coast.
You know? I mean this process could take years
to publish a paper.
All right?
It's a lot different than it is now.
So it wasn't until he got an offer from Hopkins in Baltimore
that Yale, which is up in New Haven, Connecticut said okay,
well if Hopkins is going
to offer you $3,000 a year we'll give you $2,000
and that was enough for him to stay.
And then right after that he wrote his treaties
on the equilibrium of heterogeneous substance.
This basically spelled out everything we think
about as thermodynamics these days.
He spelled it out in one --
you know these days one of the standard strategies
that we all have as academics is you take some body of data
that you've got and you try to carve it
up into the smallest publishable unit.
So whatever you've done you can get the most papers out of.
Right? Because that's how you get promoted in this business.
He took everything that he had done and put it
into one 300-page paper and published it.
It's like the opposite of what we would do today.
He's even got a Facebook page [laughter].
If you write a 300-page paper you too can have a Facebook page
for your paper [laughter].
So here's his grave.
He's buried on the Yale campus because the Yale campus is one
of the coolest cemeteries that you've ever seen on it.
It's right on the campus.
It's called the Grove Street Cemetery.
Here it is.
All right, here's Grove Street.
But this is the Yale campus in New Haven.
New Haven is a dump [laughter].
Except for Yale.
All right?
It's -- you've got this beautiful university
in this town that is really not so beautiful anymore.
Getting better I guess.
Okay, so you can -- anybody who wants to can go and look
at this cemetery and the reason you might want to do that is
because Gibbs is buried there next to his dad.
Here's a map.
It's got a -- the cemetery has it's own website.
You can see the name of everybody who is buried
in this cemetery, what they did.
It's all people from like the 1800s.
It's pretty cool.
Noah Webster, yes, that Webster [laughter].
Number 16.
Right? Here's the gate that you go into.
It's really, really cool.
Huge grave markers like that.
So if you're ever in New Haven, Grove Street Cemetery.
Okay, so what we've been doing is learning the underpinnings
of thermodynamics.
That's what statistical mechanics is.
Right? It's the underpinnings of thermodynamics.
But as chemists what we really care about is equilibrium.
We haven't said the word yet.
Until today we haven't used the word equilibrium I don't think,
or maybe once or twice.
Okay, so we need to get to this because we're ready
to be done talking about this whole subject.
Aren't we?
All right, so let's get to the meat of the issue
and then we can put it behind us.
Now -- oops [inaudible] slip -- that's supposed to be up there.
So what we're going to try
to do today is derive the Gibbs function and there's going
to be a whole bunch of symbols
but I really think it's worth understanding this.
So here we go.
The system is running.
We talked about this already.
There's open systems, closed systems and isolated systems.
Everybody remember that?
Isolated systems, no matter or energy can change.
Closed systems, energy only.
Open, both energy and matter.
Most of what we said so far pertains to isolated systems
because they're easier to understand.
They're a lot simpler.
For isolated systems we've already derived
that the entropy increases.
Has to increase.
All right?
For any non-reversible process.
If the process reversible I'm going
to put an equal sign underneath that's greater
than or equal to zero.
Remember that?
Okay, so for an isolated system entropy increases during a
spontaneous process.
That's what that means.
We'll actually derive this again today.
If you're in either one of these two categories,
and we virtually always are.
All right?
If we're actually doing an experiment we're not
in an insolated system.
We're either in an open system or closed system.
All right?
We have to consider both the system
and the surroundings in this non-equality.
In other words it's the total entropy
of the universe that's got to get bigger.
All right?
And the universe includes the system that you care
about and everything else.
Okay? So there's two terms in this total entropy.
There's the system that you care about and everything outside
of it because your systems in communication
with the outside world either by exchanging matter
or by exchanging energy.
Okay, so if the system is an isolated entropy -- yes.
Now, this is the only thing that matters in terms
of understanding where something is spontaneous or not.
We're going to derive this Gibbs function
but the Gibbs function going to be derived from this.
It's all about entropy.
All right?
So if you remember nothing else about this lecture you need
to remember that spontaneity of a chemical process is
about entropy and the Gibbs energy is just a way
to parameterize in a convenient way the entropy for us.
That's all we're doing with the Gibbs function.
We're parameterizing the entropy in a convenient way.
Okay. So, if this is true then I can move that guy
over to the right hand side and put a minus sign on him.
Right? So that has to be true.
And we've already said we've got an expression for the entropy
in terms of the heat that's transferred in the temperature
and so I can make a substitution for the surroundings.
Minus DS here is going to be DQ.
It's plus DQ because there's normally a minus sign
that connects this minus DQ over T with DS.
Right? So if that's minus DS that's going
to be plus DQ over T surroundings.
Now, Q is a conserved quantity.
In other words if plus Q enters the system, minus Q is removed
from the surroundings.
Right? If Q goes into the system it has to come
from the surroundings.
Right? So if it's a plus for the system it's a minus
for the surroundings.
Right? Okay.
So what we've already beaten into the ground is that the DU,
we use the internal energy.
That equal DW plus DQ.
That means DQ is DU minus DW.
And so I can just plug this in for DQ
in this equation right here.
Right? DU minus DW.
And I've got this equation right here.
We haven't done anything fancy yet.
Everything's very simple.
And all I've done here is assume
that the only work that's being done is pressure volume work.
Okay? So I've got PDV here.
Now, let's multiple both sides by T surroundings.
When we do that we're going to get T surroundings on that side
and we're going to lose it
from the right side, and so here we go.
All right?
All I did is multiply by T surroundings.
So now it's on the left hand side
and it's gone from over here.
All right, this doesn't look like our conservation
of entropy equations anymore does it?
It's starting to morph.
All right.
But we're still talking exclusively about entropy here.
Right? We've just made substitutions from symbols.
This equation is going to keep coming up.
We're going to call it the Pink equation.
What we're going to do is we're going
to find convenient expressions for DU,
plug them into the Pink equation and we're going to --
we're going to find the Gibbs equation,
we're going to find the Gibbs energy rather,
the Helmholtz energy.
Right? That's what we're going to do in the next 10 minutes.
All right, we're going to keep coming back
to the Pink equation.
Now, at equilibrium, right,
for an isolated system, blah, blah, blah.
For an isolated system DV equals DU equals zero.
In other words, the eternal energy
of the system doesn't change and the volume doesn't change,
and so if I prevent the volume from changing and I prevent DU
from changing, this term is zero and this term is zero
and in other words DS of the system is going to have
to be greater than equal to zero.
For an isolated system.
Right? So if I just take the Pink equation and I say
if my system is isolated, this term is zero
and this term is zero.
I divide by T surroundings, DS system's got to be greater
than or equal to zero.
So we've derived that now for an isolated system
from this Pink equation which came from this entropy argument.
The total entropy of the system and the surroundings has
to be greater than or equal to zero
for any chemical process if it's spontaneous.
Okay, now I'm going to stop writing sys every time I'm
talking about the system.
So if you see a big letter
with no subscript assume it means the system.
If I'm talking about the surroundings I'll keep
using that.
Boom. Okay.
Now, this is a general expression
for any system moving towards a new equilibrium.
That's what the non-equality means.
Right? It means that the system is in flux towards equilibrium.
All right?
And I'm going to explain in detail exactly why we --
how we think about that.
Okay? At equilibrium the external pressure
and the system pressure, and the external temperature
and the system temperature are equal to one another.
In other words, the temperature is the same outside
and inside the system.
The pressure's the same outside and inside the system.
I mean it's intuitively obvious this would have to be true
if we're talking about equilibrium.
Right? Okay.
So all this means is the pressure -- yes, okay.
So at equilibrium the Pink equation becomes the
Yellow equation.
Only thing that's different is the equals sign.
Right? So that's what the --
inequality means that we're evolving towards equilibrium.
When we get there we get an equal sign.
All right?
We'll come back to this equation.
All right?
This is the so-called master equation of thermodynamics,
but the Pink equation's actually more useful.
We'll keep coming back to the Pink equation, we won't continue
to mention the Yellow equation.
Okay. So, the Pink equation again,
it addresses many processes of interest.
For example, if volume and entropy are held constant,
if the volume and entropy are held constant,
volume and entropy.
If I hold that constant than DV is zero.
If I hold the entropy constant then DS is zero
and that means the DU has to be less than zero.
So, what does that mean?
It means that it's you that is minimized as we evolve
from a non-equilibrium state to an equilibrium state,
it's you that is minimized if and only if entropy
and volume are held constant.
Now, do we normally hold entropy
and volume constant when we do chemistry?
I don't know how you would [laughter].
All right?
I mean volume -- yes, you can do it but entropy, difficult.
All right?
So, it's not super useful for us as chemists
to use the internal energy as a marker for whether we're
at equilibrium or not because the internal energy is only
going to be a minimum when volume
and entropy are held constant.
We can't hold entropy constant very easily.
All right?
So we make note of this and we move on.
In other words a spontaneous process occurring
at constant volume and entropy will minimize the
internal energy.
This is true but not terribly useful.
Now, last week we talked about the enthalpy.
Maybe that's more useful.
Right? The enthalpy is U plus PV.
That's just a definition.
So if I take the total derivative of H, that's going
to be Du plus VDP plus PDV and I can just solve for U and plug it
into the Pink equation.
All right?
That's going to be our standard strategy
for the next six minutes.
Fine DU, plug it into the Pink equation,
rearrange these variables, got PU and what do we do?
Plug it into the Pink equation,
and what the Pink equation tells us --
now what I do, I've got this whole thing now
that I'm going to plug into there.
There it is.
Okay? And the first thing that we notice is
that these two terms will cancel if the pressures are equal
and let's just imagine
that we're approaching the equilibrium state
and they are equal.
All right?
They won't necessarily be equal until that's true
but when we're close to equilibrium, this term
and this term will cancel.
I hope you'll agree.
And then, if pressure and entropy are now held constant.
Right? We held volume and entropy constant earlier.
All right?
Now we're going to hold pressure and entropy constant.
That is not more useful to us by the way.
But if we do that, entropy -- so that goes to zero.
Pressure, to that goes to zero.
These guys canceled with one another so we're left with D.
so the enthalpy is the variable that we're going to care
about if we can control
and maintain constant the entropy and the pressure.
Now is that a useful thing for us to know as chemists?
Well, it's a useful thing to know
but as a practical matter we're not going
to be constantly doing this.
Enthalpy is not going to tell us when we're
at equilibrium most of the time.
We can't satisfy this requirement
of maintain the entropy constant.
Okay. Now, temperature actually is a variable
that we frequently hold constant as chemists.
So if we consider DT equal to zero and DV equal zero,
then hey, those are requirements that we are sometimes going
to be able to satisfy in the laboratory.
All right?
We can do an experiment at constant temperature
and we can do an experiment at constant volume.
All right?
And in principle that's actually going to be quasi useful for us
to understand whether we're at equilibrium
under those conditions.
So, the thermodynamic variable we're going to care
about here is something called the Helmholtz energy,
and all we're going to do here is write a definition for it.
Helmholtz energy is called A [inaudible] minus TS.
That's just how it's defined.
Right? That equation doesn't really mean anything to us.
All right?
It wasn't -- we didn't derive it from any place.
We just defined the Helmholtz energy.
That's what it is.
Then what we do is write the derivative of that equation.
All right?
Da minus DU is DTS, which is minus TDS minus SDT.
Solve for DU, and what are we going to do?
[ Inaudible ]
Plug it into the Pink equation is the right answer.
All right?
There's the Pink equation again.
We put this guy in for DU, and there it is.
All right?
Right there.
Okay, and now what we're talking about --
all right, so that's going to cancel
that without thinking too hard.
If we assume we're close to equilibrium
and these two temperatures are going
to be equal to one another.
That's the system temperature, that's the surroundings.
Okay? And then if we further assume that DT is zero
and DV is zero, that goes away and DV, that guy goes away.
Okay, and so DA, the Helmholtz energy ends up being the thing
that we're going to care about.
All right?
If the Helmholtz energy is getting lower it should
be spontaneous.
If the Helmholtz energy is getting higher,
that should be non-spontaneous
for any system that we care about.
Right? So if we're able to maintain temperature
and volume constant A is going to be our go to variable.
Now, the way that you do that is by using one of these guys.
In case you're wondering.
Right? This is a parr bomb.
It's universally called a parr bomb even though there's
like five companies that make these things.
But Parr makes the best ones.
All this is, is a stainless steel container
into which there's a glass jacket that goes inside here
and these are gas inlets and outlets.
And you see these two tubes right there?
Those are pressure -- those are over pressure valves.
Right? They're thin aluminum membranes and if the pressure
of this thing goes above 3,000 ATM those blow.
Right? And it sounds like a gunshot when they go off.
Right? You're heating something in here,
this needle goes all the way up to here and when this thing is
about to blow up those two valves prevent
that from happening.
But when they go off by golly it's spectacular [laughter].
All right?
But I think you'll agree,
this thing can maintain constant volume no matter what the
pressure is doing as long as the pressure stays below 3,000 ATM.
Boom, that's your -- that's how you do constant volume
and constant temperature.
All right?
Now most of the time we're not going to use this guy.
All right?
So we have to still talk about the Gibbs energy,
but we'll do that on Monday. ------------------------------612f1750100d--