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# Gibbs Free Energy and Spontaneity : Intuition behind why spontaneity is driven by enthalpy, entropy and temperature. Introduction to Gibbs free energy.

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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.

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