Kendal Orenstein

**Rutger's University**

M.Ed., Columbia Teachers College

Kendal founded an academic coaching company in Washington D.C. and teaches in local area schools. In her spare time she loves to explore new places.

Share

**Gibbs Free Energy** is a concept invented to create a thermodynamic relationship between enthalpy and entropy. It is most frequently used with the equation *gibbs free energy = enthalpy - (entropy)(temperature).*

Alright so we're going to talk about Gibbs Free Energy and Gibbs Free Energy is talking about the spontaneity of a reaction. Is does a reaction occur without outside intervention or does it require some sort of outside help electricity or whatever it maybe to get the reaction going. Well Gibbs actually put together a combination of entropy and enthalpy function and made our new, an equation that actually tells us if something is spontaneous or not. Because it depends on enthalpy we would like that product to be low on energy, we also like things to be very messy and disorderly. We have to 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 the combination of enthalpy, entropy functions that determined the spontaneity of a process over the amount of energy that is left after the reaction takes place.

Okay so after this combination we can get the amount of energy that is actually released or gained during this reaction. Okay so our free energy out delta g is going to be the free energy it's measured in kilo joules or some sort of measurement of energy. So it can be kilo joules, joules, calories whatever it maybe. Enthalpy which is the amount of energy that is either gained or needed for the reaction to occur is also measured in kilo joules or we want to make sure that these 2 are the same if this is measured in joules this must also be measured in joules we make sure those are identical. Subtracted from the temperature the temperature should be in Kelvin but can also see it in degrees Celsius and then it's actually dependent on the units of entropy. Entropy is the measurement of disorder, how chaotic something is so or how messy something is. So that is going to be measured in kilo joules per Kelvin typically but these must be the same and then these must be the same units, before we can actually have, do the Mathematical equation to get the correct answer.

Okay so this is, 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 is 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 of reaction it doesn't matter what it is, we have out delta h is negative meaning it releases energy. We like that, we like it, it released 232 kilo joules 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 messing it, the universe likes to be the more disorderly. So this is good, so we have exothermic high disorder at 273 Kelvin that's fine let's keep the information. Does this, is this reaction going to be spontaneous? My guess is yes, yes this reaction will be spontaneous.

Okay 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 kilo joules minus to 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 kilo joules so it's 0.138 kilo joules per Kelvin. And so when I multiply this together I get a total of let's see negative 37.7 kilo joules. Negative 232 kilo joules minus 37.7 kilo joules is going to give me negative 194.3 kilo joules. 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'd like a negative delta g, so I'm going to 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.

Okay so we have to make sure delta g is negative, so a combination of enthalpy and entropy is going to give us a negative delta g awesome. So let's go over here to [IB] some data. So we already discovered if we have a negative enthalpy meaning we release energy and we increase disorder those are both good. Both positive things any time you have these 2 combinations no matter what the temperature is, it'll always be spontaneous, always be spontaneous. Let's say we have a positive delta h meaning we needed energy, we require energy for this reaction to occur and we decrease our entropy meaning we got things kind of 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, okay let's look at other combinations. So let's say endothermic meaning we require energy for this to happen but disorder was very high meaning we got lots or disorder.

Well that's when our temperature comes into play, so let's look at our formula again and let's say okay 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 so there's 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, to 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 this is going to change into a positive so the temperature is going to have to use very low for this reaction to occur. We want this number to be low so that negative overwrites 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. Okay so make sure we can remember these but we also, we should always probably check the answer to put this in the formula to see if it works, if it's spontaneous or not. Sometimes you might come across a question looks like this, we have cobalt plus sulfur plus oxygen gas giving me cobalt sulfate, cobalt 2 sulfate.

This is a combination of formation reaction where the compound or 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 an ordinary conditions or standard conditions that's it have a little superscript of the 0 up top and I'm saying it's exothermic it releases 888.3 kilo joules for every mol and it is also, it also is goes down in disorder. It goes from lots of products particles to 1 particle; we don't really like it very much. So it actually decreases in entropy, decreases in disorder. So at what temperature will this reaction be spontaneous? Well we have a negative delta h and a negative delta f, so we're going to say at lower temperatures it's spontaneous, at high temperatures it's not spontaneous. But what is low, 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 kilo joules per mol minus our temperature which we're going to find out times our delta s which is negative 118.0 kilo joules per Kelvin.

Okay 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 I'm I doing that? Sorry, I'm going to add 888.3 [IB] so then I have on this side I'm going to have 888.3 kilo joules per mol equals negative, actually it's going to be a positive because negative times a negative is a positive so equals positive 118.0 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 than this, this is the threshold anything lower than this it'll be spontaneous anything higher than this it'll be non-spontaneous. So this is a question you might come across and you might want to just always make it a 0 so we know whether it's going to be spontaneous or not. Okay that's Gibb's Free Energy in a nutshell.