Gibbs Free Energy - Online Tutor, Practice Problems & Exam Prep

The Gibbs free energy (ΔG) determines the spontaneity of a reaction, influenced by enthalpy (ΔH), entropy (ΔS), and temperature (T). ΔH reflects bond energies, where negative values indicate exothermic reactions and positive values signify endothermic processes. ΔS measures disorder; positive ΔS favors spontaneity. Temperature amplifies the effect of ΔS on ΔG. In multi-step reactions, ΔG is the sum of individual steps, with the highest activation energy indicating the rate-determining step. Transition states are high-energy, transient states, while intermediates are stable enough to be isolated.

Breaking down the different terms of the Gibbs Free Energy equation.

We know that the thermodynamics or spontaneity of a reaction is directly related to the Gibbs free energy. So, it's going to be really important that we understand how to break down the Gibbs free energy equation and know how to use it. All right. So in this video, I'm going to describe every term and help you guys see how it relates to reactions.

The first thing, going all the way back, Gibbs free energy, or ΔG, is going to predict the favorability of the reaction. Remember that another word for favorability is spontaneity. It's comprised of 3 terms: ΔH, ΔS, and T. I want to go through each one, one at a time, and talk about what they mean.

ΔH is the enthalpy. Enthalpy can get confusing because ΔH and ΔG are often the same. Many times, if you have a negative enthalpy, you'll also have a negative spontaneity, and many students get confused, thinking that they're actually the same thing. They're not. ΔH is just one component of the spontaneity, but we also have to take into account the temperature and ΔS. So let me start right there.

What is the enthalpy? It's simply the sum of the bond association energies for the reaction. What that means is I'm going to be making bonds, I'm going to be breaking bonds. All of those actions require that I'm putting in energy or I'm receiving some energy. When I add all those together, whatever my final number is, that's my enthalpy. And later on we're going to learn how to actually add and subtract that stuff. But for right now, I'm just trying to tell you guys the big picture.

If something has a negative enthalpy, a negative ΔH, that's what happens when you make bonds. When you make bonds, you are getting some energy back. Why? Because I already taught you guys, I showed you in the free energy diagram how you could gain energy by putting two atoms together. That's what we call exothermic. Exothermic doesn't always mean that the reaction is favored. Remember, favorability has to do with exergonic or endergonic, but it is one component of it.

Well, what if your enthalpy is positive? If it's positive, that means I’m breaking bonds because it requires energy to break bonds. Once you break bonds, that’s going to be endothermic because of the fact that it requires that I'm putting energy into the system to make those atoms separate.

Now let's talk about one that's actually a little more difficult to understand: the entropy, ΔS. Entropy is a measure of disorder in the system. This can seem very confusing because it's like, how does the system know how disordered it is? I'm going to explain this in more depth later when I actually talk about entropy all on its own. But for right now, I just want you guys to know what the signs mean. If it's negative entropy, that means that I'm going to a more ordered state. Entropy means how disordered something is, so the opposite of disordered is ordered. If it's positive, that means it’s more disordered. A state always wants to be in its most disordered arrangement possible, so that's going to be a good thing. So, when ΔS is positive, that means my reaction is going to be a little more favored. Hopefully, you guys understand that negative means ordered, positive means disordered, and positive is the one that is actually favored.

Finally, we have our last variable, which is temperature, and note where temperature is in the equation. Temperature is going to be a coefficient of ΔS. What that means is that as temperature goes up, it's going to amplify the effect of entropy on my overall favorability. As I increase the temperature of my reaction, the entropy of the reaction is going to matter a whole lot more in determining the overall fate of my reaction, whether it's going to be favored or not. On the other hand, as I reduce my temperature down to 0 Kelvin or absolute zero, it's going to mean that my entropy becomes less and less important. Eventually, as you approach absolute zero, entropy doesn't matter at all anymore because there's actually no more movement, and all that matters is the heats of dissociation. That's kind of theoretical, but I hope that makes sense to you guys. We're going to be learning and talking about that more later when we discuss entropy all on its own.

Intermediates vs. Transition States

So it turns out that ΔG doesn't just describe a one-step reaction. It can also describe multi-step reactions. All right? If you have more than one step to go to completion, the ΔG would just be the sum of all the steps. All right? Now, what I want to do is I want to show you guys a really common example of a 2-step reaction and show you what kind of species that generates. It turns out that here I have my 2-step reaction shown. You guys don't know this reaction yet, so you don't need to actually understand it. But here is basically the free energy diagram and the reaction coordinate. What I start off with here is an alkyl fluoride. Okay? Then what I get is this transition state. Okay? See how it says TS? Transition state, where the Fluorine is being partially broken right now. Okay? So what that means is it's this like middle place where the Fluorine is like not fully dissociated, but it's also not fully associated. So it's like in the middle. Okay? Then what I get is this species where the fluorine is completely gone and now I'm missing the octet of this carbon. This is called a carbocation. This happens to be what we call an intermediate. Okay? Then we get is another transition state where now we're going to try to put a bromine on here because the end product is that you get an alkyl bromide. So now my bromine comes here and it's partially making a bond. That's another transition state. And then finally, we have the last product, which is my alkyl bromide. What I want to show you guys is the way that this actually relates to what transition states are and what intermediates are. Okay? Transition states are high, very energetic points of the reaction that cannot be isolated. Okay? What does that mean in terms of can't be isolated? It means that if I have a test tube and I tried to get a bunch of this thing inside of that test tube, it just wouldn't happen. And the reason is because it's a very, very high energy state. It's almost like if I was jumping into the air and falling back down, the transition state is me being up in the air. Does that actually mean that I could ever just exist in the air for any given period of time? Not really. That's just a period of time that I have to go through in order to get to my end destination, but it isn't actually something that you could isolate and just say, okay, I want to see just Johnny up in the air for like 5 minutes. That's not going to happen. Okay? Then an intermediate is actually something that is of a higher energy, but it can be isolated. Okay? It's a molecule that is simply at a higher energy state than normal, but it actually does can be isolated. So for example, that would be like me jumping onto a stool. Okay? Now I have greater potential energy. I'm a little bit I don't have I'm not quite as stable because now I have more potential energy, but I can stay there as long as I want. Okay? And that would be like this carbocation right here. This carbocation is not as stable as the beginning. As you can see, the energy for the carbocation is greater than the energy for my starting reagent, which is the alkyl fluoride, but it's still stable enough that it could be isolated and it could just exist there for any given period of time until I want to do something to it. Okay? So I just wanted to show you guys the difference between a transition state and an intermediate. A transition state is always going to be indicated by this little dagger sign at the top with brackets. Whenever you see that, that means that this is a transition state. An intermediate is usually not going to have any kind of notation like that at all. It would just look like that. The dotted line around it has nothing to do with it. I'm just saying it might be like a positive charge or whatever. Okay? Now how are you going to notice these on a free energy diagram? Because on a free energy diagram, these words that I gave you or these letters are not always going to be given to you. Just know that the transition states are the highest energy states possible, so those are going to be your highest points on the graph. Okay? So your transition states are always going to relate to the very highest energy points, the ones that you have to just pass through very quickly in order to get to the end. Okay? An intermediate is going to refer to any dip on the graph. Okay? Anytime that you have a dip that it's between 2 higher points, that's going to be an intermediate. Okay? Now notice that remember that we used to measure or we talked about how the rate of reaction had to do with the activation energy. But in this case, I actually have 2 different activation energies. I have the activation energy 1 that represents the amount of energy it takes to get first past my first transition state. Okay? But then I also have a second activation energy here, which represents the amount of energy it takes to get over my second transition state. Okay? So which of these is going to tell me what the rate of the reaction is? Are they both? Do I just add them up and then that's the rate? Trick question. Absolutely not. Okay? What we're going to do is we're just going to go with the highest activation energy. So whichever one that is, whether it's activation energy 1, 2, 3 or 10. Let's say this is a 10 step or whatever. You just go with the very highest activation energy and that is going to be your rate determining step or what we call our slow step. So this would be my slow step right here and what that means is that my rate determining step is going to be forming this intermediate right there. Why is that? Because notice that this activation energy is that high. This activation energy is tiny in comparison. So which one's going to have a greater effect on the overall rate of the reaction? This one right here. Okay? And it turns out that in order to get to the end, the most determining thing is just going to be how quickly can I go through the slow step? If I can make the slow step a little bit faster, that's good for my reaction in terms of rate. But it doesn't matter what I do to this activation energy. It's so small that it doesn't matter by comparison. I'm always going to be waiting for the first one to form before I do the second one anyway. Okay? So I hope that makes sense to you guys. I just want to show you guys the difference between a transition state and an intermediate. Once we get into actual reactions, this is going to matter a whole lot because we have to talk about that all the time in terms of what's a transition state and what's an intermediate. All right. So hopefully that makes sense. Let's go on to the next topic.

Here’s what students ask on this topic:

What is Gibbs free energy and how does it determine the spontaneity of a reaction?

Gibbs free energy (ΔG) is a thermodynamic quantity that predicts the spontaneity of a reaction. It is defined by the equation:

$\mathrm{\Delta G}=\mathrm{\Delta H}-T\mathrm{\Delta S}$

where ΔH is the enthalpy change, T is the temperature in Kelvin, and ΔS is the entropy change. A negative ΔG indicates a spontaneous reaction, while a positive ΔG means the reaction is non-spontaneous. ΔH reflects the heat absorbed or released, and ΔS measures the disorder. Temperature amplifies the effect of ΔS on ΔG, making it crucial in determining reaction spontaneity.

How do enthalpy (ΔH) and entropy (ΔS) affect Gibbs free energy (ΔG)?

Enthalpy (ΔH) and entropy (ΔS) are key components of Gibbs free energy (ΔG), defined by the equation:

$\mathrm{\Delta G}=\mathrm{\Delta H}-T\mathrm{\Delta S}$

ΔH represents the heat absorbed or released during a reaction. A negative ΔH (exothermic) contributes to a negative ΔG, favoring spontaneity. ΔS measures the disorder; a positive ΔS increases disorder and also contributes to a negative ΔG. Temperature (T) amplifies the effect of ΔS. Thus, both ΔH and ΔS, along with temperature, determine whether ΔG is negative (spontaneous) or positive (non-spontaneous).

What is the difference between a transition state and an intermediate in a reaction mechanism?

A transition state is a high-energy, transient state that occurs during a reaction, represented by a peak on a free energy diagram. It cannot be isolated because it exists only momentarily as reactants convert to products. An intermediate, on the other hand, is a relatively stable species that exists between transition states, represented by a dip on the diagram. Intermediates can be isolated and exist for a longer period compared to transition states. Understanding these concepts is crucial for analyzing reaction mechanisms and determining the rate-determining step.

How does temperature affect the Gibbs free energy of a reaction?

Temperature (T) plays a significant role in the Gibbs free energy (ΔG) equation:

$\mathrm{\Delta G}=\mathrm{\Delta H}-T\mathrm{\Delta S}$

As temperature increases, the term $T\mathrm{\Delta S}$ becomes more significant. If ΔS is positive, increasing temperature makes ΔG more negative, favoring spontaneity. Conversely, if ΔS is negative, increasing temperature makes ΔG more positive, reducing spontaneity. Thus, temperature can amplify the effect of entropy on the overall favorability of a reaction.

What is the rate-determining step in a multi-step reaction, and how is it identified?

The rate-determining step in a multi-step reaction is the slowest step, which has the highest activation energy. It dictates the overall reaction rate. On a free energy diagram, it is identified as the step with the highest peak (transition state) that must be overcome. This step requires the most energy to proceed, making it the bottleneck of the reaction. By focusing on this step, chemists can understand and potentially accelerate the overall reaction rate.