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# Gibbs free energy and spontaneity

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We've learned over the last
several videos that if we have a system undergoing constant
pressure, or it's in an environment with constant
pressure, that its change in enthalpy is equal to the heat
added to the system. And I'll write this little
p here, because that's at constant pressure. So if you have a reaction, let's
say A plus B yields C and our change in enthalpy-- so
our enthalpy in this state minus the change in the enthalpy
in that state-- so let's say our change in enthalpy
is less than 0, we know that this is exothermic. Why is that? And once again, I'm assuming
constant pressure. How do we know this is
exothermic, that we're releasing energy? Because change in enthalpy,
when we're dealing with a constant pressure system, is
heat added to the system. If the heat added to the system
is negative, we must be releasing heat. So we're releasing
heat or energy. So plus energy. And we learned in the last
video, I think it was either the last video or a couple of
videos ago, we call this an exothermic reaction. And then if you have a reaction
that needs energy-- so let's say you have A plus B
plus some energy yields C, then what does that mean? Well, that means that the
system absorbed energy. The amount of energy
you absorb is your change in enthalpy. So your delta H is going
to be positive. Your change in enthalpy
is positive. You've absorbed energy
into the system. And we call these endothermic
reactions. You're absorbing heat. Now, if we wanted to figure
out whether reaction just happens by itself-- whether it's
spontaneous-- it seems like this change in enthalpy
is a good candidate. Obviously, if I'm releasing
energy, I didn't need any energy for this reaction to
happen, so maybe this reaction is spontaneous. And likewise, since I'd have to
somehow add energy into the system, my gut tells me that
this maybe isn't spontaneous. But there's a little part of me
that says, well, you know, what if the particles are
running around really fast, and they have a lot of kinetic
energy that can be used to kind of ram these particles
together, maybe all of a sudden this would
be spontaneous. So maybe enthalpy by itself
wouldn't completely describe what's going to happen. So in order to get a little
intuition, and to maybe build up our sense of whether
a reaction happens spontaneously, let's think about
the ingredients that probably matter. We already know that delta
H probably matters. If we release energy-- you know,
delta H less than 0, that tends to make me think
it might be spontaneous. But what if our delta S, what
if our entropy goes down? What if things become
more ordered? We've already learned from the
second law of thermodynamics, that that doesn't tend
to be the case. And just from personal
experience, we know that things on their own just don't
kind of go to the macro state that has fewer micro
states, you know. An egg doesn't just put itself
together, and bounce, and kind of jump off the floor on its
own, although there's some probability it would happen. So it seems like entropy
matters somewhat. And then there's the idea
of temperature. Because I already talked about,
when I talked about energy here. I was like, well, you know, even
if this requires energy, maybe if the temperature is
high enough, maybe I could actually ram these particles
together in some way, and kind of create energy to go here. So let's think about--
so let's see. let's think about the
ingredients, and let's think about what the reactions would
look like depending on different combinations
of the ingredients. So the ingredients I'm going to
deal with-- delta H seems to definitely matter,
whether or not we absorb energy or not. We have delta S, our
change in entropy. Does the system take on more
states or fewer states? Does it become more
or less ordered? And then there's temperature,
which is average kinetic energy. So let's just think about a
whole bunch of situations. So let's think of
the first case. Let's think of the situation
where our delta H is less than 0, and our entropy is
greater than 0. I mean, my gut already
tells me that this is going to happen. This is a situation where
we're going to be more entropic after the reaction. So one way of looking
at entropy, you could more states. Maybe we have more particles. We've seen that entropy is
related to the number of particles we have. So this
could be a reaction where let's say we have this--
see, we want to have more particles. So let's say I have that guy. And say he's got one guy like
that there, and then I have another guy like this, and
let's say he's got a molecule like this. Let's say that a more-- well,
I won't say stable or not. But let's say that when these
guys bump into each other, you end up with this. And I'm making things
up on the fly. Maybe one of these molecules
bonds with this molecule, so you have one of the
dark blues. I'll draw all the dark blues. Bonds with this light blue
molecule, one of the dark blues bonds with the
magenta molecule. And maybe that brown
molecule just gets knocked off all by himself. So we went from having
two molecules to having three molecules. We have more disorder,
more entropy. This can obviously take
on more states. And I'm telling you that
delta H is less than 0. So by doing this, these guys,
their electrons are in a lower potential, or they're in a more
stable configuration. So when the electrons go from
their higher potential configurations over here, and
they become more stable, they release energy. So you have plus-- and then I
just know that, because I said from the beginning that
my change in enthalpy is less than 0. So plus some energy. So it seems pretty obvious to me
that this reaction is going to be spontaneous in this
rightward direction. Because there's no reason why--
first of all, it's much easier for two particles to
bump into each other just right to go in that direction
than it is for three particles-- if you just think of
it from a probability point of view-- for three particles to
get together just right and go in that direction. And even more, these guys
are more stable. Their electrons are in a
lower potential state. So there's no even kind of
enthalpic reason for them to move in this direction, or you
know, kind of a energy reason for them to move in
this direction. So this, to me, I kind of have
the intuition that regardless of what the temperature is,
we're going to favor this forward reaction. So I would say that this is
probably spontaneous. Now, what happens-- let's do
something that's maybe a little less intuitive. What happens if my delta
H is less than 0? But let's say I lose entropy. And this seems, you know, with
second law of thermodynamics, if the entropy of the
universe goes up. I'm just talking about
my system. But let's say I lose entropy. So that would be a situation
where I go from, let's say, two particles. Let's say I got that particle,
and then I have this particle. And then, if they bump into each
other just right, their electrons are going to be more
stable, and maybe they form this character. And when they do that, the
electrons can enter into lower potential states, and when they
do, the electrons release energy, so you have some
plus energy here. And we know that, because this
was the change in enthalpy was less than zero. We have lower energy in this
state than that one, and the difference is released
right here. Now will this reaction happen? Well, it seems like-- let's
introduce our temperature. What's going to happen
at low temperatures? At low temperatures, these guys
have a very low average kinetic energy. They're just drifting
around very slowly. And as they drift around
very slowly-- And remember, when I talk about spontaneity-- I wrote sponteous. This is spontaneous. Sponteous should be another
thermodynamic. It's a fun word. When I talk about spontaneity,
I'm just talking about whether the reaction is just going
to happen on its own. I'm not talking about
how fast, or the rate of the reaction. That's a key thing to know. You know, is this
going to happen. I don't care if it takes, you
know, a million years for the thing to happen. I just want to know, is it going
to happen on its own? So if the temperature is slow,
these guys might be really creeping along, barely bumping
into each other. But they will eventually
bump into each other. And when they do, they're just
drifting past each other. And when they drift past each
other, they will configure themselves in a way-- things
want to go to a lower potential state. I'm just trying to give you kind
of a hand-wavey, rough intuition of things. But because this will release
energy, and it will go to a lower potential state, the
electrons kind of configure themselves when they get near
each other, and enter into this state. And they release energy. And once the energy is gone, and
maybe it's in the form of heat or whatever it is, it's
hard to kind of get it back and go on in other direction. So it seems like this would
be spontaneous if the temperature is low. So let me write that. Spontaneous if the
temperate is low. Now what happens if the
temperature is high? Remember, these aren't the
only particles here. We have more. You know, I'll have another
guy like that, and another guy like that. And then this, on this
side, I'll have, you know, more particles. There's obviously not
just one particle. Then all of these macro
variables really make no sense, if we're just talking
about particular molecules. We're talking about
entire systems. But what happens here if
the temperature of our system is high? So let's think of a situation
where the temperature is high. Now all of a sudden-- so on the
side, people are going to be knocking into each other
super fast. You know, if this guy bumps into this guy super
fast, you can almost view it as a car collision. Well, even better, this could
be car collision. If these were each individual
cars, and the atoms were the components of the cars, if
they're like smashing into each other, even though they
want to be attached to each other, they have screws and
whatever else that are holding it together-- if two cars run
into each other fast enough, all that screws and the glue and
the welding won't matter. They're just going
to blow apart. So high kinetic energy--
let me draw that. So if they have high kinetic
energy, my gut tells me that on the side of the reaction,
these guys are just going to blow each other apart
to this side. And these guys, since these guys
also have high kinetic energy, they're going to be
moving so fast past each other, and they're going to
ricochet off of each other so fast, that the counteracting
force, or the contracting inclination for their electrons
to get more stably configured, won't matter. It's like, imagine trying to
attach a tire to something while you're running
past the car. You kind of have to do it-- even
though that's a more-- well, maybe the analogy
is getting weak, here. But I think you get the idea
that if the temperature's really high, it seems less
likely that these guys are going to kind of drift near each
other just right to be able to attach to each other,
and their electrons to get more stable, and to do this
whole exothermic thing. So my sense is that if the
temperature is high enough-- I mean, you know, maybe say, oh,
that's not high enough. But what if it's super
high temperatures? If it's super high temperatures,
then maybe even this guy will bump into that. Instead of forming that, he'll
knock this other blue guy off, and then he'll be over here. I should do the blue
guy in blue. And maybe he'll knock this
guy into his constituent particles, if there's enough
kinetic energy. So here I get the idea that
it's not spontaneous. And even more, the reverse
reaction, if the temperature is high enough, is probably
going to be spontaneous. If the temperature is high
enough, these guys are going to react, are going to bump
into each other, and the reaction is going
to go that way. So temperature is high, you go
that way, temperature is low, you go that way. So let's see if we can put
everything together that we've seen so far and kind of come up
with a gut feeling of what a formula for spontaneity
would look like. So we could start
with enthalpy. So we already know that look, if
this is less than 0, we're probably dealing with something
that's spontaneous. Now let's say I want a whole
expression, where if the whole expression is less than 0, it
tells me that it's going to be spontaneous. So we know that positive entropy
is something good for spontaneity. We saw that in every
situation here. That if we have more states,
it's always a good thing. It's more likely to make
something spontaneous. Now, we want our whole
expression to be negative if it's spontaneous, right? So positive entropy should make
my whole expression more negative, so maybe we should
subtract entropy. Right? If this is positive, then
my whole expression will be more negative. Which tells me, hey, this
is spontaneous. So if this is negative, we're
releasing energy. And then if this is positive,
we're getting more disordered, so this whole thing
will be negative. So that seems good. Now what if entropy
is negative? If entropy is negative, this
also kind of speaks to the idea that if entropy is
negative, it kind of makes the reaction a little less
spontaneous. Right? In this situation, entropy
was negative. We went from more
disorder to less disorder, or fewer particles. And what did we say? When temperature is high,
entropy matters a lot. When temperature is high, this
less entropic state, they ram into each other, and they'll
become more entropic. When temperature is low, maybe
they'll drift close to each other, and then the enthalpy
part of the equation will matter more. So let's see if we
can weight that. So when temperature is high,
entropy matters. When temperature is low,
entropy doesn't matter. So what if we just scaled
entropy by temperature? What if I just took a
temperature variable here? Now, my claim, or my intuition,
based on everything we've experimented so far, is
that if this expression is less than 0, we should
be dealing with a spontaneous reaction. And let's see if it gels with
everything we say here. If the temperature is high--
so this reaction right here was exothermic, in the
rightwards direction. When we go to the right, from
more of these molecules to these fewer ones, I told
you it's exothermic. Now, at low temperatures, my gut
told me, hey, this should be spontaneous. These guys are going to drift
close to each other, and get into this more stable
configuration. And that makes sense. At low temperatures, this term
isn't going to matter much. You can imagine the extreme. At absolute 0, this term
is going to disappear. You can't quite reach
there, but it would become less and less. And this term dominates. Now, at high temperatures, all
of a sudden, this term is going to dominate. And if our delta S is less than
0, then this whole term is going to dominate and
become positive. Right? And even if this is negative,
we're subtracting. So our delta S is negative. We put a negative here. So this is going to
be a positive. So this positive, if the
temperature is high enough-- and remember, we're dealing with
Kelvin, so temperature can only be positive. If this is positive enough,
it will overwhelm any negative enthalpy. And so it won't be spontaneous
anymore. And so if the temperature is
high enough, this direction won't be spontaneous. And this equation
tells us this. And then if we go to the
negative enthalpy, positive entropy, so we're releasing
energy, so this is negative, and our entropy is increasing--
our entropy, we're getting more disordered--
then this becomes a negative as well. So our thing is definitely
going to be negative. And we already had the sense
that look, if this is negative and this is positive, we're
getting more entropic and we're releasing energy, that
should definitely be spontaneous. And this equation also
speaks to that. So so far, I feel pretty good
about this equation. And as you can imagine,
I didn't think of this out of the blue. This actually is the equation
that predicts spontaneity. And I'm going to show it to
you in a slightly more rigorous way in the future,
maybe going back to some of our fundamental formulas for
entropy and things like that. But this is the formula for
whether something is spontaneous. And what I wanted to do in this
video is just give you an intuition why this formula
kind of makes sense. And this quantity right here
is called the delta G, or change in Gibbs free energy. And this is what does predict
whether a reaction is spontaneous. So in the next video, I'll
actually apply this formula a couple of times. And then a few videos after
that, we'll do a little bit more of how you can actually
get this from some of our basic thermodynamic
principles.