Gibbs Free Energy INSTRUCTOR: All right, so we're going to talk about Gibbs free energy. And Gibbs free energy is talking about the spontaneity of a reaction. Does a reaction occur without outside intervention, or does it require some sort of outside help-- electricity or whatever it may be-- to get the reaction going? Well, Gibbs actually put together a combination of entropy and enthalpy functions and made our new equation that actually tells us if something is spontaneous or not. Because we know it depends on enthalpy. We like the products to be lower energy. We also like things to be very messy and disorderly. We like to have high entropy and low enthalpy. So he put them together into this formula. So let's actually read what he said. What he did was he defined a combination of enthalpy-entropy function that determined the spontaneity of a process over the amount of energy that is left after the reaction takes place. So after this combination, we can get the amount of energy that is actually released or gained during this reaction. So our free energy, our delta G-- is going to be the free energy-- is measured in kilojoules, or some sort of measurement of energy. So it can be kilojoules, joules, calories, whatever it may be. Enthalpy, which is the amount of energy that's either gained or needed for the reaction to occur, is also measured in kilojoules, or we want to make sure that these two are the same. If this is measured in joules, this must also be measured in joules. We want to make sure those are identical. Subtract it from the temperature. The temperature should be in Kelvin, but you also see it in degrees Celsius. And then it's actually dependent on the units of entropy. Entropy is a measurement of disorder, how chaotic something is or how messy something is. So that is going to be measured in kilojoules per Kelvin, typically. But these must be the same. And then these must be the same units, before we can actually do the mathematical equation, to get the correct answer. OK, so the delta G is what's actually going to determine if something is spontaneous or not. It's a combination of all these things. And the sign of it's going to tell us if the reaction is spontaneous or not. So let's look at some information and determine together if something is spontaneous. So for this sum reaction-- it doesn't matter what it is-- we have our delta H is negative, meaning it releases energy. We like that. It released 232 kilojoules of energy. That's really, really good. We went from a high-energy system to a low-energy system. We like that. This is so far all good. Our disorder, our delta S value, is 138 joules per Kelvin. That's good too. We increase disorder. We like increasing disorder. We like messiness. The universe likes to be more disorderly, so this is good. So we have exothermic, high disorder, at 273 Kelvin. That's fine. This is a piece of information. Is reaction going to be spontaneous? My guess is yes, yes this will reaction will be spontaneous. OK, let's prove it to ourselves. Let's look at our formula again. Delta G equals delta H minus T delta S. And let's plug everything in. So our delta H is negative 232 kilojoules minus our temperature, which is 273 Kelvin, times our delta S, and this is in joules. I want to make sure these units are the same, so I'm going to change this to kilojoules. So it's 0.138 kilojoules, kilojoules per Kelvin. And so when I multiply these together, I get a total of negative 37.7 kilojoules. Negative 232 kilojoules minus 37.7 kilojoules is going to give me negative 194.3 kilojoules. This is my delta G. Notice my delta G is negative. I like that. Negative delta G is very, very good. That means the reaction is going to be spontaneous, which we already proved to ourselves before, just looking at the information. So we like a negative delta G. So I'm going write this up here, just to make sure we don't forget. Delta G is negative in order to be spontaneous. It must be negative, spontaneous reaction. OK, so we have to make sure our delta G is negative. So our combination of enthalpy and entropy is going to give us a negative delta G. Awesome. So let's go over here and decipher some data. So we already discovered, if we have a negative enthalpy, meaning we released energy, and we increase disorder, those are both good, both positive things. Any time you have these two combinations, no matter what the temperature is, it will always be spontaneous, always be spontaneous. Let's say we have a positive delta H, meaning we needed energy, required energy for this reaction to occur. And we decrease our entropy, meaning things became more orderly. We don't like that combination. No matter what the temperature is, it's not good. So we're going to say, this is never spontaneous OK, let's look at other combinations. So let's say it's endothermic, meaning we require energy for this to happen. But disorder was very high, meaning we got lots of disorder. Well, that's when our temperature comes into play. So let's look at our formula again. And let's say, OK, we have a positive delta H-- so this is positive-- minus a positive delta S. We want our overall equation to be negative, so this must be very high. We're going to want our temperature to be very high, because we want this number to be very large, because it has a negative sign in front of it. So we want our temperature to be very high. So at high temperatures, spontaneous, at low temperatures, non-spontaneous. And we probably would have to check it within the formula to make sure, just determine what is high and what is low. Let's look at this combination, a negative-- it's exothermic, which is good, but it also becomes more orderly, not good. So we're going to have to figure out which combination, what's going to happen to make it spontaneous. Let's look at this again. And we say our delta H is negative, which we like, minus a negative sign. So what's going to happen is it's going to change it to a positive. So the temperature is going to be very low for this reaction to occur. We want this number to be low, so the negative overrides, to make the overall combination of these guys negative. So we're going to say, at low temperatures, it is spontaneous. At high temperatures, it is non-spontaneous. So make sure we can remember these, but also, we should always probably check in the answer, in the formula to see if it works, if it's spontaneous or not. Sometimes you might come across a question that looks like this. We have cobalt plus sulfur plus oxygen gas giving my cobalt sulfate, cobalt 2 sulfate. This is a combination of formation reaction where the compound of substance is being formed by its elements. So this is a formation reaction, which is why my subscript F. And we're going to say it's at ordinary conditions, or standard conditions. That's why I have a little superscript with a 0 up top. And I'm saying it is exothermic. It releases 888.3 kilojoules for every mole. And it is also-- it also goes down in disorder. It goes from lots of particles to one particle. We don't really like that very much. So it actually decreases in entropy. It decreases in disorder. So at what temperature will this reaction be spontaneous? Well, we have a negative delta H and a negative delta S. So we're going to say at lower temperatures, it's spontaneous. At higher temperatures, it's not spontaneous. But what is low and what is high? Well, an easy way to check that is to see when delta G is going to be 0. When delta G is 0, delta H is going to be negative 888.3-- I forgot an 8-- kilojoules per mole, minus our temperature, which we're going to find out, times our delta S, which is negative 118.0 kilojoules per Kelvin. So then I want to isolate my T, so I'm going to divide both sides by negative 888.3. No, I'm not going to do that. Why am I doing that? Sorry. I'm going to add 888.3. I don't know where my math skills just went. So then on this side, I'm going to have 888.3 kilojoules per mole equals negative-- actually, it's going to be positive, because a negative times a negative is a positive-- so equals positive 118.0 times our temperature. And then divide both sides by 118.0, and let's figure out what that is. 7.53 Kelvin. This is when the reaction is going to be spontaneous. It's spontaneous at low temperatures. When the temperature gets higher then this-- this is the threshold-- anything lower than this, it will be spontaneous. Anything higher than this, it will be non-spontaneous. So this is a question you might come across, and you might want to just always make it 0 so we know when something is going to be spontaneous or not. OK, that is Gibbs free energy in a nutshell.