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# Gibbs free energy and spontaneity

## Video transcript

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 it's 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 yield 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 say our change in enthalpy is less than zero we know that this is exothermic why is that well 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 this is so we're releasing heat or energy so plus energy and we learned a last video I think newsies is the last video or a couple of video goes go we call this an exothermic reaction exothermic exothermic and then if you have a reaction on the other that that needs energy so let's say you have a plus B plus some energy plus some energy yield C then what does that mean well that means that we the the system absorbed energy the amount of energy you absorbed 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 endothermic endothermic you're absorbing heat now if we wanted to figure out whether a reaction just happens by itself whether it's spontaneous it seems like this change in enthalpy is a good candidate I 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 had to somehow add energy into the system my my gut tells me that this maybe isn't spontaneous let's let's see if we can but but there's a little part of me that says well you know what if what if the particles are running around really fast and they have a lot of kinetic energy that can be used to kind Ram these particles together maybe all of a sudden this would be spontaneous so maybe maybe enthalpy by itself wouldn't completely describe what's going to happen so in order to get a little intuition and maybe build up our intuition to 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 zero that tends to make me think it might be spontaneous but what if what if our Delta s what if our what if we actually become what if our entropy goes down what if things 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 just on the on their own just don't become a kind of go to the the macro state that has fewer microstates 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 there you know it seems like entropy matters somewhat and then there's the idea of temperature because I already talked about when I when I talked about energy here it's 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 that 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 become does it take on more states or fewer States does it become more or less ordered and then there's temperature there's temperature which is you know it's average kinetic energy there's temperature so let's just think about a whole bunch of situation so let's think of the first case let's think of the situation where our Delta H is less than zero and our and our entropy and our entropy is greater than zero I mean my gut already tells me that this is going to happen this is a situation where we're going to be more in tropic after the reaction so Edie you know one way of looking at entropy could have 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 to have this C 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 a more well I won't say stable or not but let's say that when these guys bump into each other when these guys bump into each other you end up with this let's say I'm and I'm making things up on the fly maybe this 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 off all by himself so we went from having two molecules to having three molecules we we have more disorder more entropy this can obviously take on more states and I'm telling you that Delta H is less than zero so by doing this these guys are all and Moore's there their electrons are in a more or 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 then become more stable they release energy so you have plus and then 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 plus some energy so it seems pretty obvious to me that this reaction is going to move it's 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 enthalpy 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 this to me I kind of have the intuition that regardless of what the temperature is we're going to favor the this forward reaction so I would say that this is probably spontaneous spontaneous spontaneous now what happens let's let's do something that's maybe a little less intuitive what happens if my Delta H is less than zero but let's say I lose entropy and this seems you know it would second law of thermodynamics says 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 maybe they form this character and and when they do that there 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 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 what seems like let's 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 slow and remember I'm not talking about when I talk about spontaneity I'm not fond I wrote spond TS this is spontaneous spontaneous Spontini another thermodynamic it's it's a fun word anyway it's spontaneous but when we have low temperature these the point I was making before I notice that I spelled its pontius was that when I talk about spawn today spontaneity I'm just talking about whether the reactions just going to happen on its own I'm not talking about how fast the rate of the reaction that's a key thing to know you know this is this going to happen I don't care if it takes it you know a million years for the thing that happen I just want to know is it going to happen on its own so if the temperature is slow these guys might be mean really creeping along you know barely bumping you to 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 a kind of a hand wavy rough intuition of things but because this will release energy and it'll go to a lower potential states the electrons kind of configure themselves when they get near each other and enter into this state and they'll 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 in the other direction so it seems like this would be spontaneous if the temperature is low so let me write that spontaneous spontaneous spontaneous if the temperature is low now what happens if the temperature is high 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 we're just talking about particular molecules were talking about entire systems but what happens here if the if the if the temperature of our system is high so let's take of the situation where the temperature is high now all of a sudden so on this side you know people are going to be knocking knocking into each other super fast you know if this guy bumps into this guy super fast it you know it's it's you can almost view it as a as a as a as a as a car collision well even better this could be car collisions if these were each individual cars and you know the atoms are 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 they if two cars run into each other fast enough all that screws and the glue and the welding won't matter there's 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 this side of the reaction these guys are just going to blow each other apart to this side and these guys since these guys are 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 you can kind is that that the the the counteracting force or the contracting inclination for their electrons to get more stable configured won't matter it's like you know imagine trying to screw drive you know attach a tire to something while you're while you're you know while you're running past the car you kind of have to do it you know even though that's more well maybe the analogy is getting weak here but I think you get the idea that if the temperature is 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 is that if the temperature is high enough I mean you know maybe say oh that's not high but what if it's super high temperatures if a super high temperatures and 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 he'll knock this guy into its constituent particles if it's if there's enough kinetic energy so here I get the idea that'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 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 zero 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 zero it tells me that it's going to be spontaneous spontaneous so we know that positive entropy positive entropy will make is is something good for spontaneity we saw that in every situation here if we have more states it's always a good thing it's going to likely to make something spontaneous now we want our whole expression to be negative if if it's spontaneous right so positive entropy should make my whole expression more negative so maybe we should subtract entropy so 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 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 temperature when when temperature is high spontaneity matters a lot I sorry 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 in tropic when temperature is low and then maybe they'll drift close to each other and they might and then the the the 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 if this my claim or my intuition based on everything we've experimented so far is that if this expression is less than zero we should be dealing with a spontaneous reaction spontaneous reaction and it does let's see if it gels with everything we say here if the temperature is high so this was this reaction right here was exothermic in the rightwards direction when we go to the right four more of these molecules to these fewer ones I told you it's exothermic now at low temperatures I my gut told me hey this should be spontaneous these guys going to drift close to each other and get into this more stable configuration and that makes sense that temperatures this term isn't going to matter much and you can imagine the extreme at Absolute Zero 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 zero 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 so this there if the temperature is high enough this direction won't be spontaneous and that this equation tells us this and then if we go to the if we go to the kind of the positive entropy positive enthalpy oh sorry negative enthalpy positive entropy so we're releasing energy so this is negative and our entropy is increasing our entropy we're getting more disorder 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 in tropic and we're releasing energy that should definitely be spontaneous in this equation also speaks to that so so far I feel pretty good about this equation and 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 our some of our fundamental formulas for entropy and and things like that but this is the formula for whether something is spontaneous and what I want to do this video just give you the intuition why this formula kind of makes sense and this quantity right here is called Delta G or change in Gibbs free energy and this is what does predict whether reaction is spontaneous so in the next video I'll actually apply this formula a couple of times and then the few videos after that we'll do a little bit more of how you can actually get this from some of our our basic thermodynamic principles
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