# Gibbs Free Energy

by Jared Rovny

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00:01 There's one last thing we need to understand when a reaction goes forward, which is that while we do want to minimize the energy in a reaction, in other words, reactions are more favorable if they can minimize the energy.

00:16 So another way to say this is we have two hydrogens and one oxygen, they will want to bind together because that's a minimum energy setup for them to be in.

00:26 But there's also this competing effect which is that systems also want to maximize their entropy.

00:32 So these are the two things that we've talked about, so we can try to play them against each other and see which one will win out, if you will, for a given reaction.

00:40 So for example, in this reaction where we have two hydrogens and one oxygen going to be a water molecule, not only is there a change in enthalpy for that situation, there's also a change in the entropy for that situation.

00:53 So comparing these two we come up with a quantity called the Gibbs free energy.

00:57 The idea of the Gibbs free energy is that we're talking about how much energy is sort of free to allow a reaction to go forward.

01:06 We might naively think that all we require is that the change in the energy be negative, and we would say, well, that is a favorable reaction.

01:14 Things want to act so that the energy is minimized.

01:17 For example, if I lift some objects near and let go, it falls towards its minimum energy and atoms and molecules would do the same thing.

01:25 But we have to include this competing effect, the fact that the entropy also wants to be maximized.

01:31 So the Gibbs free energy is a way for us to quantify how much energy, if you will, is free to cause reactions to go forward.

01:40 So this will tell us whether a reaction can occur spontaneously or not.

01:44 This Gibbs free energy is represented with a letter G and the change in the Gibbs free energy for a given reaction will again not include the change in the enthalpy for that reaction which is related as we saw to the energy, but has the enthalpy minus the entropy for your reaction.

02:03 In other words, if the reaction is going to be a great change in the entropy, then this reaction is more favorable because things want to maximize their entropy.

02:12 There's a minus sign there because again, the energy and the entropy are playing against each other.

02:17 One of them the system wants to minimize and the other one the system wants to maximize.

02:21 And we also have a unit of the temperature here, because the entropy is not related to the energy or the enthalpy directly; it actually has a unit of temperature.

02:31 In other words, the disorder of your system and how we measure the disorder of the system relative to the energy or the enthalpy of the system has to do with what temperature that system is at.

02:42 The units in this, don't forget what each letter here is since we've introduced many letters up to this point, are simply the delta G which is representing our Gibbs free energy, telling us whether our reaction is spontaneous or not.

02:54 We have delta H, which is the enthalpy change of our reaction which we just saw how to find just by going from the total reaction to its component and back to the products of your reaction.

03:06 We have delta S, which is how the entropy of your system is changing.

03:10 And then of course we have T, which is representing the temperature of your system.

03:15 In order to know whether the reaction is going to go forward on its own even when there is enough energy to cause the sytem to go forward.

03:23 We compare it to the entropy using Gibbs free energy and see whether the Gibbs free energy is negative or positive.

03:32 You can really think about this somewhat intuitively by looking at the Gibbs free energy, and seeing if it is less than zero.

03:39 If it is a more negative number, that means the enthalpy was a small number and the temperature times the change in entropy was also a small number.

03:50 In other words, the more smaller, the more negative both of these numbers are the enthalpy and the change in the entropy, the more likely is the more favorable that your reaction is because this will mean it has a lot of energy change going forth and it also has a great increase in the entropy or likelihood for it to happen.

04:07 And so if this Gibbs free energy ends up being a negative number, so we can see how the competition plays out, if it's a negative number, the reaction can occur on its own spontaneously.

04:17 On the other hand, if the Gibbs free energy is positive, we would say, it is a nonspontaneous reaction, it will not just occur very easily or quickly on its own.

04:26 It's also, finally, important to know that the spontaneity of a reaction whether it can occur on its own is not the same thing as to whether the reaction will occur quickly.

04:37 So what we're saying is that while the reaction may be favorable, it might have a negative Gibbs free energy and will want to occur, it doesn't mean that it will occur quickly even if it could occur spontaneously.

04:48 So be careful as we're comparing the rates of reaction to the favorabilty of reactions.

04:54 On the one hand we have how quickly how a reaction occurs; on the other hand, we simply have wether it can occur spontaneously on its own or not.

05:03 All these variables that we've just introduced in this course with the energy and the enthalpy as well as the energy and the entropy altogether really with the Gibbs free energy can be very confusing especially the first time we see it.

05:17 When we're putting them all together in many different equations and justifying one way we'd use them, for giving reactions.

05:22 So I highly recommend you go over many example problems using the entropy, the enthalpy, and the energy in their different forms and see how they work together.

05:32 Having laid these groundwork and this foundation, we have one more topic to cover with thermodynamics before we finish our course on physics.

05:39 And that's for next time.

05:40 Thanks for listening.

The lecture Gibbs Free Energy by Jared Rovny is from the course Thermodynamics and Thermochemistry.

### Included Quiz Questions

1. ΔG = ΔH - TΔS
2. ΔG = ΔG = ΔH/T - ΔS
3. ΔG = ΔS - ΔH/T
4. ΔG = ΔH + TΔS
5. ΔG = ΔH/T + ΔS
1. ΔG = -10 kJ
2. ΔG = 0
3. ΔG = 10 kJ
4. ΔG = 100 kJ
5. ΔG = 50 kJ
1. Minimize energy and maximize entropy
2. Maximize energy and maximize entropy
3. Minimize energy and minimize entropy
4. Minimize entropy and maximize energy
5. Maximize entropy and maximize enthalpy
1. ΔG = -1.25 kJ < 0, hence the reaction is spontaneous
2. ΔG = 1.25 kJ > 0, hence the reaction is not spontaneous
3. ΔG = 0, hence the reaction is in equilibrium
4. ΔG = -1.25 kJ < 0, hence the reaction is not spontaneous
5. ΔG = 1.25 kJ > 0, hence the reaction is spontaneous

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