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we're going to explore Gibbs free energy a little bit in this video in particular its usefulness in determining whether a reaction is going to be spontaneous or not which is super useful in chemistry and biology and it was defined by Josiah Willard Gibbs and what we see here we see this famous formula which is going to help us predict spontaneity and it says that the change in Gibbs free energy is equal to the change and this H here is enthalpy so this is a change in enthalpy which you could view as heat content especially because this formula applies if we're dealing with constant pressure and temperature so that's a change in enthalpy minus temperature times change in entropy change in entropy so s is entropy and it seems like this bizarre formula that's that's hard to really understand but as we'll see it makes a lot of intuitive sense that Gibbs free Gibbs Josiah Willard Gibbs he defined this to think about well how much enthalpy is going to be useful for actually doing work how much is free to do useful things but in this video we're going to think about it in the context of how we can use change in Gibbs free energy to predict whether a reaction is going to spontaneously happen whether it's going to be spontaneous and to get straight to the punchline if Delta G if Delta G is less than zero our reaction is going to be spontaneous it's going to be spontaneous it's going to happen assuming that things are able to interact in the right way it's going to be it's going to be spontaneous now let's think a little bit about why that makes sense if this expression over here is negative our reaction is going to be spontaneous so let's think about all of the different scenarios so in this scenario over here if our change in enthalpy is less than zero and our entropy increases our enthalpy decreases so this means we're going to release we're going to release energy here we're going to release enthalpy and you could think about this as so let's see we're going to release energy so release I'll just write this is a release of enthalpy over here I end up with less end than I started with but entropy increases disorder increases the number of states that my system can take on increases well this makes a lot of sense this makes a lot of sense that this is going to happen spontaneously regardless of what the temperature is I have these two molecules they are about to bump into each other and when they get close to each other there are electrons maybe you say hey way there's a better configuration here where we can go into lower energy states where we can release energy and in doing so these these different constituents can part ways and so you actually have more constituents they've parted ways you've had energy released entropy increases it makes a lot of sense that this is a natural thing that would actually occur so this over here this is spontaneous Delta G Delta G is not just Delta Delta G is less than zero so this one over here I'm going to make all the spontaneous ones I'm going to I'm going to square them off in this green color now what about this one down here this one down here Delta H is greater than zero so your enthalpy for this reaction needs to increase and your entropy is going to decrease so that's you know you can imagine these two atoms or maybe these molecules that get close to each other but their electrons say hey no no in order for us to bond we would have to get to a higher energy state we would require some energy and the disorder is going to go down this isn't going to happen and so of course and this is a combination if Delta H is greater than zero and if this is less than zero then this entire term is going to be positive and so Delta G is going to be greater than zero so here Delta G is going to be greater than zero and hopefully it makes some intuitive sense that this is not going to be spontaneous so this one this one does not this one does not happen now over here we have some permutations of Delta H s and Delta s is and whether they're spontaneous depends on the temperature so over here if we're dealing our Delta H is less than zero so we're going to have a release of energy here but our enter pre decreases what's going to happen well if the temperature is low these things will be able to gently get close to each other and their electrons are going to be able to interact maybe they get to a lower energy State they can release energy and they were they're releasing energy and the electrons will spontaneously do this but the entropy has gone down but this can actually happen because the temperature the temperature here the temperature here is low and some of you might be saying wait doesn't that violate the second law of thermodynamics and you have to remember the tantrum the entropy if you're just thinking about this part of the system yes that goes down but you have an it you have heat being released and that heat is going to make is going to add entropy to the rest of the system so still the law of second the second law of thermodynamics holds the the entropy in the universe is going to increase because of this released heat but if you just look at the constituents here the entropy went down so this is going to be this right over here is going to be spontaneous as well and we always want to go back to the formula if if this is negative and this is negative well this is going to be a positive term but if T is low enough this term isn't going to be matter T is you can view it as the waiting factor on entropy so if T is low the entropy doesn't matter as much then enthalpy really takes over so in this situation delta g we're assuming T is low enough to make Delta G to make Delta G negative and this is going to be spontaneous now if you took that same scenario but you had a high temperature well now you have these same two molecules let's say that these are the Mount maybe this is this one's a purple one right over here you have the same two molecules here hey you could they could get to a more kind of they could release energy but over over here you're saying well look they could and the the change in enthalpy is negative but they're buzzing past each other so fast that they're not going to have a chance their electrons aren't going to have a chance to actually interact in the right way for the reaction to actually go on and so this is a situation where it won't be spontaneous because they're just going to buzz past each other they're not going to have a chance to interact properly and so you can imagine if T is high if T is high this term is going to matter a lot and so the fact that entropy is negative is going to make this whole thing positive and this is going to be more positive than this is going to be negative and so this is a situation where our Delta G is greater than zero so once again not spontaneous and everything I'm doing is just to get an intuition for why this formula for Gibbs free energy makes sense and remember this is true under constant pressure and temperature but it's a reason these are reasonable assumptions if we're dealing with you know things that a test-tube or if we're dealing with a lot of biological systems now let's go over here so RN we are our change in enthalpy is positive and our entropy and our entropy would increase if these react but our temperature is low so if these reacted maybe they would bust apart and do something they would do something like this but they're they're not going to they're not going to do that because when these things bump into each other they're like a you know on all of our electrons are nice there are nice little stable configurations here I don't see any reason to react even though if we did react we were able to increase the entropy hey no reason to react here and if you look at these different variables if this is positive if this is positive even if this is positive as T is low this isn't going to be able to overwhelm that and so you have a delta g that is greater than zero not spontaneous but if you took the same scenario and you say okay let's let's up the temperature here let's set up the average kinetic energy then these things are going to be able to slam into each other and even though even though the electrons would essentially require some energy to get to to really form these bonds this can happen because because you have all of this disorder being created you have these more states and it's less likely to go the other way because well what are the odds of these things just getting together in the exact right configuration to get back into these this lower number of molecules and once again you look at these variables here even if Delta H is greater than zero even if this is positive if Delta s is greater than zero and T is high this thing is going to become especially with the negative sign here this is going to overwhelm the enthalpy and that the change in enthalpy and make the whole expression negative so over here Delta G is going to be less than zero and this is going to be spontaneous so hopefully this gives you some intuition for the formula for Gibbs free energy and once again you have to caveat it's under it assumes and pressure and temperature but it is useful for thinking about whether a reaction is spontaneous and as you look at biological or chemical systems you will see the Delta G's for the reactions and so you'll say oh it's a negative Delta G that's going to be a spontaneous reaction it's a zero Delta GA that's going to be an equilibrium or you could say okay it's a positive Delta G that's not going to be spontaneous

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