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PROFESSOR NELSON: So, over the
last few lectures we've worked

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and struggled so formulate the
second and third laws

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of thermodynamics in
addition to the first.

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Last time we reach the third
law which is telling us that we

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can't quite get to zero degrees
Kelvin, but that as the

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temperature approaches zero
degrees Kelvin, the absolute

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entropy of a pure substance in
perfect crystalline

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form is zero.
 

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And what that corresponds to,
if you recall, is the idea that

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in a perfect crystal at zero
degrees Kelvin then you

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have no disorder at all.
 

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You have a perfectly
ordered system.

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And in that case, the
entropy is absolutely zero.

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And the bigger lesson from that
is that entropy, unlike energy

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u or enthalpy H, we could
define an absolutely

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number for it.
 

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The zero of it
wasn't arbitrary.

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Unlike the case for energy like
you've seen in lots and lots of

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disciplines, where you can
arbitrarily set the zero in

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a way that makes it
convenient for you.

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Entropy really is
not like that.

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There is an absolute zero
of entropy, and that's

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really what we learn.
 

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So now, now that we've got all
three of the major laws of

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thermodynamics, what I want to
start in on is a discussion of

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what happens spontaneously.
 

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We've seen that in just one
specialized case so far, but we

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should in a more general way be
able to tell when is a system

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at equilibrium, where there's
no net change taking place, and

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when is it still undergoing
spontaneous change towards

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some other state, presumably
toward an equilibrium state.

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How do we tell?
 

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So that's the topic that
I'd like to address today.

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So, that's the big
question, right?

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So let's say that we've got
our stuff in some state.

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A, whatever it is.
 

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And there's some other possible
state, B, whatever it is.

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And maybe if it some
well-defined temperature

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and pressure.
 

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What do we do to tell
whether that change will

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happen spontaneously?
 

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Do we calculate, you know,
delta S, delta u, delta H?

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What tells us whether or
not the change happens?

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Certainly in principle we know
how to calculate this and other

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stuff for a change in state
of this sort, for lots

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of changes of state.
 

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But calculating it alone
doesn't necessarily tell us

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whether or not it will just
happened of its own accord.

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And that's the issue that we'd
like to be able to address.

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Now, we have addressed
this in some cases.

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So, for example, we know that
if we take, you know, gas A and

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gas B with a barrier between
them, and we remove the

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barrier, they're going to mix.
 

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And we saw that and went
through it somewhat carefully

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and saw that if the system is
isolated, for that case we do

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have a criterion that tells us
whether change happens

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spontaneously.
 

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Namely, it's delta S
is greater than zero.

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That tells us whether the
change is spontaneous.

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And we saw that in fact in
this case delta S of mixing,

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we calculated it, saw
that it is positive.

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So, clearly, if we remove this
barrier mixing takes place, and

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obviously you know that that
happens from lots

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of experience.
 

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In general, the second law gave
us the Clausius inequality

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for spontaneous change.
 

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Namely dS is greater
than dq over T.

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I suppose we could specify the
surroundings temperature.

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We saw that in general dS is
greater than or equal to dq

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over T. if it's a reversible
process then the equality

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holds, but if it's
irreversible, which means it

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happens spontaneously, then
dS is greater than this.

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Just to illustrate the kind of
issues that we're up against

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here, let me just consider a
few different chemical

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reactions, all of which
happen spontaneously.

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So, I just want to write a few
examples down with a few values

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for delta u or delta H or delta
S, and see whether we can get

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any clues from what we see.
 

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So here are some spontaneous
chemical changes.

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Here's one.
 

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If we take hydrogen peroxide in
the liquid state, it can break

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down to form water and oxygen.
 

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If we look at the thermodynamic
quantities, the enthalpy and

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the entropy of the reaction,
what we find is delta H is

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minus 209 kiloJoules and
delta S is plus 132

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joules per Kelvin.
 

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So it seems like there's
a favorable change in

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entropy going this way.
 

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That is, you've got lower
energy on the right and

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also higher entropy.
 

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Higher entropy basically
because you're forming

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molecules of gas where there
weren't any before, and there's

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more disorder in the gas
phase than in the liquid.

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That is, the gas phase
molecules have more

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freedom to roam.
 

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Okay, that's one example.
 

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Here's another.
 

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Let's just take hydrogen
and nitrogen in the gas

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phase and form ammonia.
 

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Well, here we get, we
find that delta H is

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negative 92 kiloJoules.
 

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Delta S is negative 198
joules per Kelvin.

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This one also happens
spontaneously.

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One thing that makes it pretty
clear is that certainly delta S

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or the sign of it alone is not
dictating the outcome here.

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All right, here's
a third example.

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Let's take salt, solid, and
dissolve it in a bunch

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of liquid water.
 

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Hopefully you've got experience
saying that this happens,

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of course it does.
 

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If we measure the
thermodynamics, we discover

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that delta H is 4 kiloJoules,
plus 4 kiloJoules.

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Delta S is 45
joules per Kelvin.

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So now we have a different
sign for delta H and it

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still happens spontaneously.
 

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So clearly, we've got signs and
magnitudes of delta H and delta

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S, and if we wanted to put
delta u there, similar

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things would happen.
 

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They're all over the map.
 

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And yet, these things are
all spontaneous processes.

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And I didn't specify the
conditions, but if we were to

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do this under ordinary chemical
conditions of some, you'd say

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room temperature and pressure,
right, they all happen

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spontaneously.
 

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OK, clearly we'd be much better
off if we had some systematic

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quantitative way to tell
whether something would

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happen spontaneously.
 

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In other words, we need
criteria for equilibrium under

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more general conditions than
the ones that we've dealt with

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so far, than the one set of
conditions that we've

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dealt with so far, which
is isolated system.

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Most chemical changes, most
physical changes don't

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happen in isolated systems.
 

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So let's start by writing down
our definition of equilibrium.

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It's very simple.
 

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The equilibrium state is the
one, and it's just one, in

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which there are no spontaneous
changes that can take

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place to any other state.
 

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Now that's under whatever
constraints there are.

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There's a box around it.
 

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The temperature or the pressure
are fixed, what have you.

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But the point is, no
spontaneous changes can

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occur to any other state.
 

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So for example, when we remove
the barrier and the gases

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mix, you know it's over.
 

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Once the gases are mixed,
there's not going to

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be any further net
change in the system.

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It's at equilibrium, under
the new condition, that is

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with the barrier removed.
 

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OK, so now let's try to
formulate how to describe the

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equilibrium state and what
dictates spontaneity.

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So what we're going to do
is consider the first

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and second laws.
 

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So our first law,
du is dq plus dw.

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And our second law, dS is
greater than dq over the

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temperature of surroundings
for a change that

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happens spontaneously.
 

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And now, I want to combine
these two, which I

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of course can do.
 

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I can substitute dq from
this expression in here.

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I also want to assume for our
present purposes that there's

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only pressure volume work going
on, which is to say I want

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to put p dV in here
minus p dV for dw.

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So for combining for p V work,
what we see then is du has to

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be less than T surroundings
dS minus p external dV.

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Or we can rewrite this as
du plus external pressure

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dV minus T surroundings
dS is less than zero.

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Now this is fundamentally
important, and as you know that

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means that it warrants the
exalted distinction of being

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put up in colored chalk.
 

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And, in fact, since we're going
to reuse this again and again

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during today's lecture, I'm
going to put it over here and

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leave it sacrosanct for our
further use. du plus p external

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dV minus T surroundings
dS is less than zero.

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This Is our condition
for spontaneous change.

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Now this is a really
quite useful expression.

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For one thing what we have here
are all functions of state and

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parameters that we can control
like temperature and pressure.

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So that's a big help.
 

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And equilibrium happens when
there isn't any possible

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change of state that
would satisfy this.

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In other words, you've got
your system in some state.

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You know it's in some
state A, there are some

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other states around.
 

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Here is what we calculate
to tell whether it

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happens spontaneously.
 

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So we now have a real usable
criterion to help guide our

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understanding of whether things
happen by themselves of

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their own accord or not.
 

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Now, this is still a little bit
cumbersome, in part because of

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the variables involved,
including S.

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That is, most processes that
we're concerned with, they'll

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happen with something held
constant like pressure or

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temperature or maybe volume.
 

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So this isn't the most useful
form that we can have, but what

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we'll see shortly is that from
this, we can then derive

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further criteria for
essentially any set of

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variables or any set of
external constraints, like

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constant temperature or
pressure or volume and so

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forth that we might set.
 

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And so that's what
I now want to do.

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So I just want to use that
again and again, starting from

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that, for various different
sorts of conditions and derive

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the criterion for equilibrium
in each set of conditions.

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So first, let's start with the
one that we already know, and

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00:18:34 --> 00:18:43
make sure that it still works,
starting from here, mainly

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00:18:43 --> 00:18:45
our isolated system.
 

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So remember what that means?
 

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It means no heat, no work.
 

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Delta V is zero.
 

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Delta u is zero.
 

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So looking at this, du
is zero. dV is zero.

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So all that's left is negative
T dS is less than zero.

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In other words, T surrounding
dS has to be greater than zero,

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and of course temperature
is always positive.

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So dS for u and V fixed
is greater than zero.

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All right, so that's
sounds right.

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That's what we saw before.
 

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When we have an isolated
system, the criterion that

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determines whether something
happens spontaneously is the

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00:19:43 --> 00:19:49
entropy has to increase.
 

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Now, what this means too is if
we imagine a bunch of different

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00:20:05 --> 00:20:09
states, and this is the entropy
of them, so this could be any

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sort of variable but the point
is there are a bunch of

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possible states around,
whichever one has the maximum

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entropy, that's the
equilibrium state.

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In other words, you know we've
got the two gases on either

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side of that partition.
 

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We remove the partition,
and they mix.

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Well, the equilibrium
state is the one with the

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gases completely mixed.
 

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Of course there are lots of
states that would have maybe

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local pockets of one substance
in excess and another substance

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in excess somewhere else.
 

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00:20:56 --> 00:20:59
In other words, there would
be lots of states nearby

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to the equilibrium state.
 

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00:21:01 --> 00:21:03
That is, the chain, they could
they could be approached with

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very little change from
the equilibrium state.

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00:21:06 --> 00:21:09
They aren't the
equilibrium state.

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00:21:09 --> 00:21:12
The entropy in all of those
states will be lower than

252
00:21:12 --> 00:21:18
the entropy of the
fully mixed state.

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00:21:18 --> 00:21:22
So the point is, once you're at
equilibrium none of the other

254
00:21:22 --> 00:21:26
states, they're accessible, the
system could rearrange itself

255
00:21:26 --> 00:21:31
to form them, but there is no
accessible state that has

256
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higher entropy than the
equilibrium state.

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OK, that's our familiar
isolated system.

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Now let's try moving to
unfamiliar territory and

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00:21:58 --> 00:22:08
extending what we know.
 

260
00:22:08 --> 00:22:19
So, let's try constant
entropy and volume.

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00:22:19 --> 00:22:24
And the motivation for choosing
a pair like that is easy

262
00:22:24 --> 00:22:26
to see, if we look at our
condition for spontaneous

263
00:22:26 --> 00:22:28
change or general condition.
 

264
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Well, entropy and volume
constant means dV and

265
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dS are equal to zero.
 

266
00:22:32 --> 00:22:33
What does that say?
 

267
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It means du is less than zero.
 

268
00:22:35 --> 00:22:39
That's our condition.
 

269
00:22:39 --> 00:22:46
So we immediately get
du at constant S and

270
00:22:46 --> 00:22:51
V is less than zero.
 

271
00:22:51 --> 00:23:01
That's our condition for
spontaneous change.

272
00:23:01 --> 00:23:05
In other words, if we don't
have to worry about entropy or

273
00:23:05 --> 00:23:09
volume equilibrium is achieved
when energy is at a minimum.

274
00:23:09 --> 00:23:12
Now this is what you learn
in elementary physics

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00:23:12 --> 00:23:14
and in mechanics, right.
 

276
00:23:14 --> 00:23:16
You're not worried
about entropy.

277
00:23:16 --> 00:23:22
So, you know, if you've got a
hill or valley and there's a

278
00:23:22 --> 00:23:28
cart on wheels, it's going
to go down to the bottom.

279
00:23:28 --> 00:23:31
The spontaneous change
lowers the potential

280
00:23:31 --> 00:23:36
energy in that case.
 

281
00:23:36 --> 00:23:50
So this is a simple condition
that's very familiar.

282
00:23:50 --> 00:23:54
Now, the reason this condition
always holds in ordinary

283
00:23:54 --> 00:23:58
mechanics is because you're
never, in that case, concerned

284
00:23:58 --> 00:24:02
with a huge statistical
population of particles where

285
00:24:02 --> 00:24:06
the disorder among
them is an issue.

286
00:24:06 --> 00:24:09
We're not worrying then about
the fact that, well like in the

287
00:24:09 --> 00:24:16
case of gas molecules mixing,
the macroscopic state of the

288
00:24:16 --> 00:24:19
whole thing, all those
molecules, how many different

289
00:24:19 --> 00:24:21
microscopic configurations
are there?

290
00:24:21 --> 00:24:24
Remember, I mentioned then
we'll go further later on

291
00:24:24 --> 00:24:27
into this, that entropy
can be related to the

292
00:24:27 --> 00:24:28
extent of disorder.
 

293
00:24:28 --> 00:24:32
That is, how many different
possible configurations of all

294
00:24:32 --> 00:24:35
those molecules there would
be for a particular state.

295
00:24:35 --> 00:24:40
The reason the entropy of the
mixed gases is the highest is

296
00:24:40 --> 00:24:43
because that has the most
possible configurations.

297
00:24:43 --> 00:24:48
If you start segregating the
gases, there are fewer possible

298
00:24:48 --> 00:24:51
configurations that the whole
system can be in because

299
00:24:51 --> 00:24:58
you're forcing a particular
set of circumstances.

300
00:24:58 --> 00:25:01
When you don't have to worry
about criteria like that,

301
00:25:01 --> 00:25:05
ordinary, mechanical energy
rules supreme, and

302
00:25:05 --> 00:25:10
that's dictating where
equilibrium lies.

303
00:25:10 --> 00:25:14
But of course, most chemical
and biological systems aren't

304
00:25:14 --> 00:25:18
that simple precisely because
you have to worry about many

305
00:25:18 --> 00:25:22
particles and their statistics
and the way they might

306
00:25:22 --> 00:25:25
order or disorder.
 

307
00:25:25 --> 00:25:31
So, and of course, you know,
keeping entropy as a fixed

308
00:25:31 --> 00:25:35
variable for a system like
that is extremely cumbersome.

309
00:25:35 --> 00:25:38
As soon as you allow anything
to mix, like you might if you

310
00:25:38 --> 00:25:41
want to do any chemistry,
entropy changes.

311
00:25:41 --> 00:25:46
If you change the temperature
entropy changes and so on.

312
00:25:46 --> 00:25:47
So let's go on.
 

313
00:25:47 --> 00:26:01
Let's consider a few
other examples.

314
00:26:01 --> 00:26:07
Let's hang on for a little
while longer to a set

315
00:26:07 --> 00:26:11
of conditions where we
will maintain constant

316
00:26:11 --> 00:26:24
entropy, namely constant
entropy and pressure.

317
00:26:24 --> 00:26:33
So, the dS term is zero,
but the other two are not.

318
00:26:33 --> 00:26:46
So, du plus p dV is
less than zero.

319
00:26:46 --> 00:26:56
I can write this as d(u
+ pV) less than zero.

320
00:26:56 --> 00:26:58
Normally I couldn't do that
because this term would have

321
00:26:58 --> 00:27:04
p dV plus V dp, but we've
specified the pressure is

322
00:27:04 --> 00:27:09
constant, so the
dp part is zero.

323
00:27:09 --> 00:27:12
And this is a quantity
that you know, right?

324
00:27:12 --> 00:27:15
What's u plus pV?
 

325
00:27:15 --> 00:27:18
STUDENT: dH.
 

326
00:27:18 --> 00:27:27
PROFESSOR NELSON: dH less
than zero, criterion

327
00:27:27 --> 00:27:34
for spontaneous change.
 

328
00:27:34 --> 00:27:44
In the case where S and
p are held constant.

329
00:27:44 --> 00:27:51
Now, once again, like I
illustrated for entropy, and I

330
00:27:51 --> 00:27:58
could have done the same for
energy here, you know, if we

331
00:27:58 --> 00:28:02
again look at a bunch of
different states, and look at

332
00:28:02 --> 00:28:07
their enthalpy, well, like
before, they'll be invariably

333
00:28:07 --> 00:28:21
lots of possible states.
 

334
00:28:21 --> 00:28:24
And now, what is this saying,
the equilibrium state is the

335
00:28:24 --> 00:28:28
one with the lowest
possible enthalpy.

336
00:28:28 --> 00:28:32
In the case here, that I just
illustrated with the little

337
00:28:32 --> 00:28:34
cart going down the valley,
would be exactly the same

338
00:28:34 --> 00:28:37
with regular energy, the
equilibrium state is one

339
00:28:37 --> 00:28:39
of lowest energy, right.
 

340
00:28:39 --> 00:28:41
And of course there are
lots of nearby states.

341
00:28:41 --> 00:28:46
The cart could be a little ways
up the hill, and in this case,

342
00:28:46 --> 00:28:48
it's enthalpy, but again,
there would be lots

343
00:28:48 --> 00:28:51
of accessible states.
 

344
00:28:51 --> 00:28:54
But if the system is in
equilibrium, none of those

345
00:28:54 --> 00:28:58
states has lower enthalpy.
 

346
00:28:58 --> 00:29:00
It's already in the
lowest enthalpy state.

347
00:29:00 --> 00:29:06
That is the equilibrium state.
 

348
00:29:06 --> 00:29:15
OK, well, now, let's
get to the big ones.

349
00:29:15 --> 00:29:18
That is, in real life, the
variables that you'd normally

350
00:29:18 --> 00:29:24
control aren't some combination
of entropy and these variables,

351
00:29:24 --> 00:29:28
but really their temperature,
volume and pressure, any couple

352
00:29:28 --> 00:29:31
of those, might be what
you'd really have under

353
00:29:31 --> 00:29:34
experimental control.
 

354
00:29:34 --> 00:30:04
So now let's go to them.
 

355
00:30:04 --> 00:30:06
Let's control T and V.
 

356
00:30:06 --> 00:30:24
So, all right, so now
we're getting serious.

357
00:30:24 --> 00:30:29
All right, well, there's
our equilibrium criterion.

358
00:30:29 --> 00:30:31
We're still going back to it.
 

359
00:30:31 --> 00:30:32
It still holds.
 

360
00:30:32 --> 00:30:37
So we've now got the dV
part equal to zero.

361
00:30:37 --> 00:30:48
So what this says is that du
minus T dS is less than zero,

362
00:30:48 --> 00:30:55
and we can combine those to say
d(u - TS) is less than zero.

363
00:30:55 --> 00:30:58
And again, just like before,
we can do that although this

364
00:30:58 --> 00:31:04
normally would say this has
T dS and also minus S dT.

365
00:31:04 --> 00:31:05
T is fixed.
 

366
00:31:05 --> 00:31:08
So that part is zero.
 

367
00:31:08 --> 00:31:11
So this is really the
equivalent of this.

368
00:31:11 --> 00:31:17
So when we did this here, we
conveniently found that that

369
00:31:17 --> 00:31:22
quantity u plus pV is something
we know and love, and

370
00:31:22 --> 00:31:23
we're familiar with it.
 

371
00:31:23 --> 00:31:24
It's our enthalpy H.
 

372
00:31:24 --> 00:31:28
So we could write that
criterion as dH less than zero.

373
00:31:28 --> 00:31:35
So here, let's combine these
to define a new quantity.

374
00:31:35 --> 00:31:38
It obviously has importance
because what it's going to say

375
00:31:38 --> 00:31:42
is that that's the quantity
that defines equilibrium, that

376
00:31:42 --> 00:31:47
tells us about equilibrium,
under the very important

377
00:31:47 --> 00:31:52
practical constraints of having
fixed temperature and volume.

378
00:31:52 --> 00:31:55
Realistically, the more
likely constraints

379
00:31:55 --> 00:31:57
than either of those.
 

380
00:31:57 --> 00:32:08
So let's -- we'll go to a
brand new color, define

381
00:32:08 --> 00:32:13
A as u minus TS.
 

382
00:32:13 --> 00:32:26
it's called the
Helmholtz free energy.

383
00:32:26 --> 00:32:30
OK, and then our criterion for
equilibrium under these

384
00:32:30 --> 00:32:39
conditions is dA, V and T equal
to the temperature of the

385
00:32:39 --> 00:32:47
surroundings, is
less than zero.

386
00:32:47 --> 00:32:58
OK, and once again, you know if
we wanted to look at a bunch of

387
00:32:58 --> 00:33:10
states that could be accessed,
well, we would find lots of

388
00:33:10 --> 00:33:15
states near by, in character
to the equilibrium state.

389
00:33:15 --> 00:33:19
The one that is at equilibrium,
there is only one macroscopic

390
00:33:19 --> 00:33:21
state at equilibrium.
 

391
00:33:21 --> 00:33:31
It has the lowest A.
 

392
00:33:31 --> 00:33:35
In some sense, that's one
reason to associate this as a

393
00:33:35 --> 00:33:42
kind of energy, just like
mechanical energy u or enthalpy

394
00:33:42 --> 00:33:47
H, it's the minimum free
energy state that is the

395
00:33:47 --> 00:34:02
equilibrium state under
the relevant conditions.

396
00:34:02 --> 00:34:06
Now, let's take the step
to the biggest set of

397
00:34:06 --> 00:34:08
conditions of all.
 

398
00:34:08 --> 00:34:11
What is it when you run a
chemical reaction under

399
00:34:11 --> 00:34:18
ordinary circumstances,
what's constant?

400
00:34:18 --> 00:34:18
STUDENT: [UNINTELLIGIBLE]
 

401
00:34:18 --> 00:34:20
PROFESSOR NELSON:
A little louder.

402
00:34:20 --> 00:34:21
STUDENT: Pressure
and temperature.

403
00:34:21 --> 00:34:21
PROFESSOR NELSON: Pressure
and temperature, right.

404
00:34:21 --> 00:34:23
You're running, you're
shaking a beaker up here

405
00:34:23 --> 00:34:27
at room temperature.
 

406
00:34:27 --> 00:34:49
So let's look at that
set of conditions.

407
00:34:49 --> 00:34:51
All right, there it is.
 

408
00:34:51 --> 00:34:54
This is the condition for
really the lion's share of

409
00:34:54 --> 00:34:58
chemistry, biology, and other
kinds of changes we'll

410
00:34:58 --> 00:35:00
be concerned with.
 

411
00:35:00 --> 00:35:07
So, there's our condition
for equilibrium.

412
00:35:07 --> 00:35:11
We don't get to set any
of them to zero, right?

413
00:35:11 --> 00:35:21
So, okay and we can handle
that. du plus p dV minus T dS

414
00:35:21 --> 00:35:28
is less than zero, but we do
get to simplify in writing this

415
00:35:28 --> 00:35:36
as d(u + pV - TS) is less than
zero, and just like we've seen

416
00:35:36 --> 00:35:41
before, yes, this has p dV and
V dp, but the dp is

417
00:35:41 --> 00:35:43
zero because we're at
constant pressure.

418
00:35:43 --> 00:35:49
This has minus T dS minus S dT,
but the dT part is zero because

419
00:35:49 --> 00:35:52
we're at constant temperature.
 

420
00:35:52 --> 00:35:56
So the result is we can combine
all of these as a single

421
00:35:56 --> 00:35:59
differential, and just like
we've seen before, what that

422
00:35:59 --> 00:36:04
suggests is that we define
another new quantity given

423
00:36:04 --> 00:36:07
by this expression.
 

424
00:36:07 --> 00:36:13
And that is the last one
we're going to describe.

425
00:36:13 --> 00:36:21
And that is G, u
plus pV minus TS.

426
00:36:21 --> 00:36:28
 


427
00:36:28 --> 00:36:34
The Gibbs free energy.
 

428
00:36:34 --> 00:36:38
Notice, we could also
write, let's rewrite that.

429
00:36:38 --> 00:36:46
G is u plus the pV minus
TS, but u plus pV is H.

430
00:36:46 --> 00:36:53
So we also can write this as H
minus TS and u minus TS is what

431
00:36:53 --> 00:36:56
we just defined a
minute ago as A.

432
00:36:56 --> 00:37:01
So we can also write
this as A plus pV.

433
00:37:01 --> 00:37:05
 


434
00:37:05 --> 00:37:09
And the main thing of crucial
importance is what, by defining

435
00:37:09 --> 00:37:16
this in the way we have, what
that's saying is that dG at

436
00:37:16 --> 00:37:37
constant p and T is
less than zero.

437
00:37:37 --> 00:37:49
There's our condition for
equilibrium at constant

438
00:37:49 --> 00:37:56
temperature and pressure.
 

439
00:37:56 --> 00:37:58
Boy, is that going to be
important for the whole

440
00:37:58 --> 00:38:02
rest of the course.
 

441
00:38:02 --> 00:38:14
So, and of course, I hardly
need to emphasize further, but

442
00:38:14 --> 00:38:19
we could do the exact same
consideration that we have

443
00:38:19 --> 00:38:26
for H and A, there's G.
 

444
00:38:26 --> 00:38:28
There's our equilibrium state.
 

445
00:38:28 --> 00:38:34
It's the state that has the
lowest Gibbs free energy.

446
00:38:34 --> 00:38:38
All these things though
are incredibly practical,

447
00:38:38 --> 00:38:40
useful criteria.
 

448
00:38:40 --> 00:38:47
This is only defined in
terms of state functions.

449
00:38:47 --> 00:38:51
And just like we saw before for
the case of entropy in an

450
00:38:51 --> 00:38:56
isolated system, now we have
something we can calculate.

451
00:38:56 --> 00:39:01
It's a state function, so we're
at constant temperature and

452
00:39:01 --> 00:39:05
pressure, and now we want to
consider some chemical change

453
00:39:05 --> 00:39:08
or a phase transition
or you name it.

454
00:39:08 --> 00:39:10
Does it happen of
its own accord?

455
00:39:10 --> 00:39:14
Well now we know what
needs to be calculated in

456
00:39:14 --> 00:39:17
order to determine that.
 

457
00:39:17 --> 00:39:23
So this one is so uniquely
pervasive, let's just really

458
00:39:23 --> 00:39:28
explicitly write it all out.
 

459
00:39:28 --> 00:39:39
For constant pressure and
temperature delta G is less

460
00:39:39 --> 00:39:50
than zero, means A going to B
is, all right, let's consider

461
00:39:50 --> 00:40:01
some process state
A and state B.

462
00:40:01 --> 00:40:09
If delta G is less than zero,
it happens spontaneously.

463
00:40:09 --> 00:40:29
If delta G equals zero, then
we're already in equilibrium.

464
00:40:29 --> 00:40:37
And if delta G is greater
than zero, then it goes

465
00:40:37 --> 00:40:49
spontaneously in the
other direction.

466
00:40:49 --> 00:40:54
Any questions about
any of this?

467
00:40:54 --> 00:40:58
Let me just give a
couple of examples.

468
00:40:58 --> 00:41:01
If we go back to any of those
chemical reactions that I wrote

469
00:41:01 --> 00:41:07
on the board before, right,
well certainly we can calculate

470
00:41:07 --> 00:41:11
what delta G would be
for each one of them.

471
00:41:11 --> 00:41:15
Because we know how to
calculate all the parts of it.

472
00:41:15 --> 00:41:18
It's state functions, it's
composed of state functions

473
00:41:18 --> 00:41:20
that we know how to calculate.
 

474
00:41:20 --> 00:41:23
So we could tell.
 

475
00:41:23 --> 00:41:28
When delta G is zero, you know,
it doesn't mean that you've got

476
00:41:28 --> 00:41:33
all of one side, all reactants
and zero products or all

477
00:41:33 --> 00:41:36
products and zero reactants.
 

478
00:41:36 --> 00:41:38
There is some mixture of them.
 

479
00:41:38 --> 00:41:44
What this will tell
us is what mixture.

480
00:41:44 --> 00:41:46
You know the stuff is in there
in equilibrium, you know

481
00:41:46 --> 00:41:50
the hydrogen and nitrogen
that will form ammonia.

482
00:41:50 --> 00:41:53
And in the end, when it's at
equilibrium, and you look and

483
00:41:53 --> 00:41:55
you'd make a measurement,
right, you could

484
00:41:55 --> 00:41:56
do spectroscopy.
 

485
00:41:56 --> 00:42:00
You could easily see how much
of each thing is there.

486
00:42:00 --> 00:42:06
It doesn't go all the way to
absolutely 100 percent ammonia,

487
00:42:06 --> 00:42:09
zero hydrogen zero nitrogen if
they were mixed together

488
00:42:09 --> 00:42:10
with the right ratios.
 

489
00:42:10 --> 00:42:11
Doesn't happen.
 

490
00:42:11 --> 00:42:14
There would be some
of the reactants and

491
00:42:14 --> 00:42:17
some of the products.
 

492
00:42:17 --> 00:42:20
In the biochemical reactions
that are taking place in your

493
00:42:20 --> 00:42:26
body, there is equilibrium
between a whole myriad of

494
00:42:26 --> 00:42:29
reactants and products, and
thank heavens that

495
00:42:29 --> 00:42:33
gets maintained.
 

496
00:42:33 --> 00:42:36
So that's what this will guide
us through, and of course

497
00:42:36 --> 00:42:42
that's incredibly,
incredibly important.

498
00:42:42 --> 00:42:45
Here's another thing that's
worth thinking about.

499
00:42:45 --> 00:42:51
There's a balance here
between ordinary energy

500
00:42:51 --> 00:42:58
or enthalpy and entropy.
 

501
00:42:58 --> 00:43:02
Energy means, you know,
chemical reactions happen, and

502
00:43:02 --> 00:43:06
you end up with something that
might be exothermic, that

503
00:43:06 --> 00:43:09
is, the products are more
stable then the reactants.

504
00:43:09 --> 00:43:13
You burn methane, and it
combines with oxygen to

505
00:43:13 --> 00:43:19
form water, to form CO2.
 

506
00:43:19 --> 00:43:21
And if you work out the
energetics as we've gone

507
00:43:21 --> 00:43:23
with thermochemistry,
you discover there's a

508
00:43:23 --> 00:43:27
huge negative delta H.
 

509
00:43:27 --> 00:43:30
In other words, the bonds
are much stronger.

510
00:43:30 --> 00:43:34
CO2 is really a
stable molecule.

511
00:43:34 --> 00:43:37
Methane, there are certainly
some solid bonds there, but

512
00:43:37 --> 00:43:43
breaking those to form CO2
and water, well it's worth

513
00:43:43 --> 00:43:45
it, right, energetically.
 

514
00:43:45 --> 00:43:53
Still, the actual equilibrium
depends on entropy also,

515
00:43:53 --> 00:43:55
not only on the energy.
 

516
00:43:55 --> 00:43:57
And that's why, when I put
up those three different

517
00:43:57 --> 00:44:02
reactions, and we saw
the signs could vary.

518
00:44:02 --> 00:44:05
It's because there's a
balance between the two.

519
00:44:05 --> 00:44:10
Energy may be favoring reaction
in one direction, toward

520
00:44:10 --> 00:44:13
let's say products that
have lower energy.

521
00:44:13 --> 00:44:17
But at the same time, entropy
is going to be favoring

522
00:44:17 --> 00:44:22
whichever side has higher
entropy, has more disorder,

523
00:44:22 --> 00:44:26
and there's a balance
that's achieved.

524
00:44:26 --> 00:44:30
And that's why all those
reactions, first of all, in

525
00:44:30 --> 00:44:34
some sense what I put up was
kind of a trivial statement in

526
00:44:34 --> 00:44:39
actual fact saying they all
happen spontaneously, because I

527
00:44:39 --> 00:44:43
didn't specify what we were
starting with exactly,

528
00:44:43 --> 00:44:45
what concentrations we
were starting with.

529
00:44:45 --> 00:44:47
Even something quite
unfavorable might happen

530
00:44:47 --> 00:44:49
at least a little
bit spontaneously.

531
00:44:49 --> 00:44:51
You'll have equilibrium.
 

532
00:44:51 --> 00:44:53
In those cases, though, you'd
have quite a reasonable

533
00:44:53 --> 00:44:57
equilibrium, spontaneously,
that is there would be a lot of

534
00:44:57 --> 00:45:00
reaction that went if you
simply started under practical

535
00:45:00 --> 00:45:03
conditions and let it go.
 

536
00:45:03 --> 00:45:07
Even though the signs of the
enthalpy changed, and the signs

537
00:45:07 --> 00:45:10
of the entropy changed because
it's a combination of

538
00:45:10 --> 00:45:11
the two that matters.
 

539
00:45:11 --> 00:45:14
Here's a really simple example.
 

540
00:45:14 --> 00:45:19
Mixing of oil and water.
 

541
00:45:19 --> 00:45:21
You know from experience
if you've ever mixed them

542
00:45:21 --> 00:45:25
to make salad dressing,
they don't mix too well.

543
00:45:25 --> 00:45:28
And you may know that
if you heat them up,

544
00:45:28 --> 00:45:33
they mix much better.
 

545
00:45:33 --> 00:45:35
Why?
 

546
00:45:35 --> 00:45:39
You know, we've done a bunch of
thermochemistry, and we've kind

547
00:45:39 --> 00:45:44
of seen that the energy of
mixing, your energetics

548
00:45:44 --> 00:45:48
don't change too much as a
function of temperature.

549
00:45:48 --> 00:45:49
What's changing?
 

550
00:45:49 --> 00:45:56
Why does it mix better
when you warm it up?

551
00:45:56 --> 00:46:00
But, you know, looking at our
definition of Gibbs free

552
00:46:00 --> 00:46:09
energy, here it is,
right, or here.

553
00:46:09 --> 00:46:13
Let me just say, actually if
you calculated delta S for

554
00:46:13 --> 00:46:17
the mixing as a function of
temperature, it doesn't

555
00:46:17 --> 00:46:18
change all that much.
 

556
00:46:18 --> 00:46:20
You know, the amount of
disorder upon mixing is

557
00:46:20 --> 00:46:22
not really sensitive
to temperature.

558
00:46:22 --> 00:46:27
What does change though?
 

559
00:46:27 --> 00:46:33
T, and the entropy is weighted
by the temperature, so the

560
00:46:33 --> 00:46:38
entropy matters more and
more the hotter it gets.

561
00:46:38 --> 00:46:40
And that's consistent
with other things that

562
00:46:40 --> 00:46:41
we've seen, right?
 

563
00:46:41 --> 00:46:44
Remember the whole thing about
the perfect crystal at zero

564
00:46:44 --> 00:46:48
degrees Kelvin has
zero entropy.

565
00:46:48 --> 00:46:49
It's completely ordered.
 

566
00:46:49 --> 00:46:51
Entropy doesn't matter anymore.
 

567
00:46:51 --> 00:46:55
It'll go to the
lowest energy state.

568
00:46:55 --> 00:47:03
Raise the temperature, and now
entropy plays a bigger role.

569
00:47:03 --> 00:47:07
So the point is, this balance
between energy that you could

570
00:47:07 --> 00:47:12
think of as say bond energies
in chemical reactions, and

571
00:47:12 --> 00:47:15
entropy that you can think of
in terms of disorder, how many

572
00:47:15 --> 00:47:19
different possible combinations
or configurations of something

573
00:47:19 --> 00:47:22
wrong, will dictate where
the equilibrium lies.

574
00:47:22 --> 00:47:26
And knowing now how to
calculate these free energies

575
00:47:26 --> 00:47:29
especially the Helmholtz and
the Gibbs free energies, that's

576
00:47:29 --> 00:47:32
what's going to guide us
in really calculating

577
00:47:32 --> 00:47:37
quantitatively, OK, where
will equilibrium lie.

578
00:47:37 --> 00:47:42
And before long, we'll start
in on discussing chemical

579
00:47:42 --> 00:47:46
equilibrium, does
deriving where they lie

580
00:47:46 --> 00:47:47
phase equilibrium?
 

581
00:47:47 --> 00:47:50
Does stuff change phase to
go from liquid to solid

582
00:47:50 --> 00:47:51
and so forth, right?
 

583
00:47:51 --> 00:47:54
And where does that happen,
at what temperature and

584
00:47:54 --> 00:47:56
pressure and so forth.
 

585
00:47:56 --> 00:48:01
And it's always going to come
down to calculating the

586
00:48:01 --> 00:48:05
appropriate free energy, and
how it changes in the process.

587
00:48:05 --> 00:48:09
So this is going to be a guide
for us for essentially all

588
00:48:09 --> 00:48:11
that we're going to do
in the rest of the term.

589
00:48:11 --> 00:48:12