Chemistry: Approaching Chemical Equilibrium

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Let's suppose that an old man went out in a yard and a fence separated his yard from the yard of a little boy. A little boy was in the yard, and between the two yards was an apple tree that had dropped all of its apples into both yards. Well, let's suppose the little boy picked up an apple, lobbed it over to the old man's side. The old man didn't like that very much so he picked up his apple and lobbed it back. Well, of course, one thing led to another and before long both were hurling apples back and forth at each other as fast as they possibly could. And we could ask, "What happens to the number of apples in one yard compared to the other yard?" Maybe at first the number of apples in the little boy's side went down, simply because he was faster at picking them up and lobbing them over. But eventually we'd reach a point where the total number of apples on the little boy's side and the old man's side would reach a constant value. This would be an analogy to a chemical equilibrium that we've been discussing, where we reach a point where the forward rate of a reaction equals the back rate of the reaction.
Well, what would be the factors that determine where that equilibrium would lie? In other words, what determines the final ratio of apples in one yard compared to the other? It might be how fast the little boy is compared to the old man; how many years separate them; how mobile one is compared to the other; how big the yards are--we could think of a lot of reasons that might affect what that final equilibrium ratio is.
Well, what we want to ask now is, "What are the factors that determine a chemical equilibrium? What determines whether A and B are favored at equilibrium or C and D?" Remember, after all, an equilibrium is a balance point, and the equilibrium constant tells us numerically, quantitatively, what that balance point is. It tells us whether the reactants are favored at equilibrium or the products are favored at equilibrium. In other language, it tells us whether there are more reactants than products, or more products than reactants, once that equilibrium has been reached.
Well, in a chemical system there are two important principles that determine that equilibrium. One is that nature wants to get to the lowest possible chemical energy. And so reactions that release energy, that themselves then are going to lower potential energy, if you will, those reactions tend to be spontaneous, meaning they will run from reactants to products. But that's not the only factor affecting where an equilibrium lies. The other factor that we're going to need to worry about is the disorder, the relative disorder in particular, in the product side and the reactant side. Where is there more disorder? In going from reactants to products, is there in fact an increase in disorder or is there a decrease in disorder? Those are the two key components that are going to affect where that chemical equilibrium lies.
So let's explore this idea. Let's return to the Haber process, a very important industrial reaction combining nitrogen and hydrogen to make ammonia. Well, this reaction at room temperature is favored by 9 kilojoules per mole. In other words, when the reaction runs in the forward direction, energy is released. We can talk about the chemical energy on this side being less than the chemical energy here, and so again we could interpret this reaction going forward as nature wanting to generate a more chemically stable form, a more chemically stable species. And again, we get release of energy in that process.
Now, we can quantify exactly where that equilibrium lies with equilibrium constant. And if we talk about K[p], the partial pressure of products of the reactants taken to their respective powers, the value for K[p] is 5x10^5, indicating that products must be heavily favored at equilibrium. Well, that's all fine and good. That makes sense. That's consistent with our notion that nature wants to go to lower energy, and indeed that's the result as dictated by this equilibrium constant, which is again describing where that equilibrium lies. The problem from a practical standpoint is that this is an incredibly slow reaction, and at room temperature you'd have to wait your entire life for anything to happen. In fact, nothing would happen. Even when we add a catalyst, although that speeds up the rate of the reaction, it's still far too slow at room temperature to be useful. So let's heat it up. We know that increasing temperature increases the rates of the reactions. Maybe we can get to our equilibrium that way.
Well, if we go to 800 degrees, to pick a value, it turns out that the equilibrium constant now is 4x10^-5. What the heck is going on? Well, we've got a very low value now of K[p], much less than 1. That tells us physically that this equilibrium now favors the reactants, not the products anymore. So, yes, at 800 degrees we can get to equilibrium; the reaction runs forward. But the reaction runs backward as well, and the equilibrium--the balance point--favors now the reactants, not the products. So again, an equilibrium constant, describing again where that balance point is in a chemical reaction, is very sensitive to what the temperature is.
So what is it that causes the equilibrium now to shift in this direction, causes the reactants to be more favored at high temperatures and the products to be more favored at low temperatures? Well, although this gives off energy in this process, the other factor that we identified is the disorder. And look what happens in terms of disorder. We're going from four moles of gas to two moles of gas. In doing that, we're restricting the freedom of all of the atoms. We're forcing nitrogen to be in the same vicinity as three hydrogens, whereas here it's only tied to one nitrogen. So we're going from more particles to less particles, putting restrictions on these atoms that decreases the entropy, and so this forward reaction is not favored from a standpoint of disorder. There is more disorder over here. So what we're seeing is that high temperature favors disorder; real low temperature favors the chemical point of lowest stability, in other words, what the most chemically stable material is.
Now, if this still doesn't make a lot of sense to you, let's go ahead and look at a simple analogy which at least gets to this general notion. Let's suppose that there is a temple someplace and in this temple is a secret room. And in the middle of the room is a pit containing extremely deadly snakes. These snakes are all hanging out at the bottom of the pit. It's very cold; they don't have a lot of energy. This is the low point of energy. They all eventually fall into the pit and they just hang out in this pit. Well, we could talk about--if we're really anal about it, we could talk about this being an equilibrium between one state and another state, the state of being in the pit or the state of being out of the pit. And we could talk about an equilibrium between those two states. And we can say, okay, at low temperature the equilibrium favors heavily being at the bottom of the pit. Okay, good enough.
Now we can ask, "What happens if we increase the temperature?" Let's say we increase the temperature. The snakes, being reptiles, get more energy as we raise the temperature. They're now capable of getting out of the pit to some degree, and a new equilibrium will be reached. And in our new equilibrium, we have many more snakes outside than we did at the low temperature, so our equilibrium has shifted to some new position as we change our temperature. The question is, "Where is that new position?" What is now the ratio of snakes in the pit compared to snakes out of the pit? Remember, that would be an equilibrium constant, if you will--reactants over products, ratio of one state compared to another state.
My point here is that we have a new relationship that much more favors, now, snakes in this state--snakes being outside the pit--compared to at that other temperature. As we increase temperature, the fact that there is more disorder--there is more room for the snakes to wander around; there are more random positions that the snakes can be in, in the bigger room than in this little pit here--that's what is driving this reaction now, if you will. That's what is causing the snakes to move out. Not that the snakes have some predetermined plan to get out of the pit; they're dumb as posts. It's just that there's a lot more room out here, and so the random chances of a snake being found out here are higher now than down here, as long as there is enough random energy--in this case, the temperature has warmed up in the room--that they can get out and get back here.
So again the point is that at low temperature, the lowest point of chemical energy is the dominant factor determining where an equilibrium lies. We saw at low temperatures again all the snakes drop down to the pit, the point of lowest energy. At very, very high temperatures, the dominant factor becomes the entropy; where is there more disorder? In the case of the analogy, there was more disorder out here in the room than down in the pit. Chemical reactions behave in a similar fashion.
If we go back to the Haber process, again there is more disorder over here, but there's lower chemical energy here--more stability, I should say. At low temperatures, the products are favored at equilibrium. At high temperatures, the reactants are favored at equilibrium. Simply put, there are more reactants than products at high temperatures, whereas at low temperatures there are more products than reactants.
Other examples of reactions that fall into this general category would be the polymerization of ethylene. Now ethylene, you'll recall, is a carbon-carbon double bond and then we've got some hydrogens on it. This is just a hydrocarbon. Ethylene polymerizes--it reacts with other ethylenes, many other ethylenes--to create polyethylene, literally meaning a polymer of ethylene, and this is just a long hydrocarbon. A polyethylene is used in manufacturing of milk bottles, of dishes, of bumpers--all kinds of different plastics are in fact polyethylene. So this is of course a very important industrial process. This is a reaction, which readily happens because this is chemically more stable than the ethylenes. What we're doing is creating new carbon-carbon single bonds, sigma bonds more correctly, at the expense of breaking the weaker pi bonds. If that doesn't make a lot of sense to you, you may want to review chemical bonding. So this is a chemically better place to be for this system. The equilibrium favors polyethylene as long as we're at low temperature.
But if we raise our temperature too high, then the reverse reaction becomes dominant. And in fact this is a process called cracking, where long hydrocarbons are broken down into small alkynians. And this is also a very important industrial process because you can take crude oil, which has these long hydrocarbon chains, and crack these long hydrocarbons to make much more useful alkynes; they're also called oliphants. So both the back reaction and the forward reaction are really important. And how you control which happens is simply by changing temperature. That causes that balance to change, whether the reactants are favored or the products are favored.
Another example. This is an organic reaction where we're combining--the details of which right now are not important but what we're doing is combining two molecules of the same type together to make one. This is an example of a cycloaddition reaction. Big name. We'll talk much more about this later. The important point I want you to see now is just that we're combining two to make one. We're decreasing the disorder, but what we're doing that's favorable is making a chemically more stable substance. This is yet another example of a reaction that at low temperatures favors the product, and at high temperatures favors the reactant.
Now, last of all, let me just point out that not all reactions fall in this category. You certainly are going to find reactions that have the products favored both in terms of entropy and in terms of enthalpy--meaning they're chemically more stable and they have more disorder--and then you'll find the reverse. You'll have reactions where the reactants are favored both in terms of entropy and enthalpy. And depending on what system you have, that determines again the equilibrium constant for the chemical reaction.
So let's just summarize then. The equilibrium constant is crucial in defining the balance point, and therefore telling us whether reactants are favored or products are favored, and by how much they are favored. What determines that balance point, what determines that equilibrium constant, will be the enthalpy of the reaction and the entropy of reaction. Ultimately we'll want to quantify those numbers and tie them in explicitly with a chemical formula, with a relationship to the equilibrium constant, because that will allow us to actually calculate the position of the equilibrium.
Now, at this stage we're just going to return to the general notion of an equilibrium constant and how it tells us in what direction a reaction runs.
Chemical Equilibrium
Using Equilibirum Constants
Approaching Chemical Equilibruim Page [1 of 3]