In some of the earlier concept development studies, and in earlier lectures, we began to study the process of phase equilibrium. By which, two different phases of matter could coexist. For example, liquid water in equilibrium with gaseous water. And we begin to understand the conditions under which this could occur, by analyzing what we call dynamic equilibrium. Having the rate at which water or liquid turns into gas, or evaporation at an equal rate with the process by which gas turns into liquid or condensation. Earlier, we suspected that chemical reactions might also come to equilibrium. To analyze that, in the previous two concept studies, we had developed a full understanding of the rates of chemical processes in which govern them. In this concept development study, we're now going to come to understand how reactions come to equilibrium. And we're going to begin by simply observing that equilibrium. How might we do that? Well, one way we might do it, is to consider what happens during the course of a chemical reaction and measure how many products it produced. Here's a simple chemical reaction: hydrogen gas reacts with chlorine gas to produce hydrogen chloride gas. Turns out if we react 1 mol of hydrogen with 1 mol of chlorine, and then measure the amount of hydrogen chloride which is produced, it gives us essentially exactly 2 mols. That's exactly what we would've expected by the stoichiometric coefficients here. 1 mol plus 1 mol should give us 2 mols. And in fact, 1 mol plus 1 mol does give us 2 mols. And that suggests, in fact, that the stoichiometry is doing exactly what we would expect it to do. But let's consider a second chemical reaction, very similar to the first one. Hydrogen plus iodine, both now again gas, giving us hydrogen iodide gas. In this particular case, again, if we take one mol of hydrogen, and one mol of iodine we notice we don't get two mols of hydrogen chloride. We get 1.72 mols of hydrogen iodide. Not consistent with the stoichiometry. That suggests actually that the reaction is essentially not gone to completion. We did not get all of the hydrogen iodide out that we might have expected would occur. Let's think about how that might have occurred in terms of the dynamics, or the reaction kinetics, such as we discovered or discussed in the previous slide. Let's imagine that what we are calculating here is the number of mols of either H2 or I2 or H2, or I'm sorry HI, as a function of time. In this particular reaction, we're starting off with one mol of both H2 and I2. And we know as the reaction proceeds, were going to start to lose both H2 and I2. But one of the things we can tell, is that we must not consume all of the H2 and I2 and it doesn't go to zero. In fact, it kind of plateaus at some level or another. This is for the H2 or for the I2 that curve, two curves are right on top of each other. For the HI, what we would discover is, in fact, we rise rapidly, but, eventually also hit a plateau, indicating two things. One, we didn't achieve the 2.0 mols of HI that we might have expected, we stopped short of that. Therefore, the reaction didn't go to completion. Furthermore, what we observe at these later times here, is that the conditions of the reaction system, the number of mols of reactants and the number of mols of products, are no longer changing. And we would be really justified in referring to that as equilibrium in the same way that we refer to equilibrium in the case of phase equilibrium. That, of course then, produces this question, why is it that a reaction does not go to completion? Why would not not occur? And the answer has to be that the system goes to equilibrium. But, we do not get the stoic yet, stoichiometric the amount of the product we predicted, because, in fact, the reactions gone to equilibrium. And why would the reaction go to equilibrium? Let's consider then a specific case here. A really simple example on how this might occur. Thinking about N2O4 decomposing to become, N2, N02, I'm sorry, combining decomposing to become two NO2 molecules. Let's image that, rather than just starting off with a specific amount of material one, that we're going to vary the amount of the reactant that we have here. So, here's our reactant and were going to vary the initial concentration of the N2O4. And then what we will do in the same way that over here we were looking at the concentrations of the products and the reactants. The difference here is were going to vary the amount of the reactants, for this particular reaction, and see how we expect re-reaction to come to equilibrium. We may expect that the graph will look something like this. Again, we might plot the concentration of each of the materials. I'd just write that as concentration of, a versus time. If we start off with only into 04, perhaps we might, have this amount of material here. We observed some decrease in the amount of N2O4. We observe an even more rapid appearance of the NO2. But these two, then again come to equilibrium. And the question is, what are the equilibrium concentrations of NO2 and of N2O4? And then we'll vary this initial condition. Let's see what this results actually look like when we do that. Here is the data. Remember, on the y, on the x axis here, we have plotted the initial amount of the N2O4, that's the starting point here. What we plotted on the y axis are two different things. The concentration of the NO2, and the concentration of the N2O4. Notice we get two very different curves here. One of them, the concentration of the N2O4, fairly uniformly increases as we increase the initial amount of N2O4. Seems like it makes sense. But we might have thought that the concentration of the NO2 would likewise increase in a simple linear fashion. And it does not. Instead, initially it rises more rapidly but then it actually slows down. It actually is not nearly as great. The consequence of these two factors together, is that the ratio. We'll notice here, the ratio of the product to the reactant, varies enormously. In fact, in this region here, the ratio of the product to the reactant is greater than one. By this region out here, the ratio of the product to the reactant is very, very much less than one. Apparently, the relationship between the amount of the reactant and the amount of product, varies enormously dependent upon the conditions of the reaction. That might not sound like equilibrium. But remember, in each of the experiments we run regardless of how much N204 we start off with, we wind up with constant amounts of NO2 and N204 as illustrated in this graph. How can we account for this result? To do that, we're going to analyze the data a little bit more carefully. We'll analyze it actually, by instead of plotting the N204 and the N02 against the initial concentration, we're going to plot the plot, the reactant concentration, against the product concentration. When we plot them against each other we can actually get a straight line. In this particular case, I won't go through the analysis here, we can get a straight line by taking the square root of the N2O4 concentration. That is the equilibrium into a full concentration, and plotting it versus the pressure of the NO2. This is a straight line, it's a wonderful straight line. It's a proportionality that goes through zero. And what that suggests to us, as is illustrated by this equation then, is, that the pressure of the product, is proportional to the square root of the pressure of the reactant. That's not at all an expected result, but it in fact, shows up empirically. We can rewrite this equation by squaring both sides of the equation, and moving the pressure to the other side of the equation. And we very simply then come up with the pressure of the products squared, divided by the pressure of the reactant, turns out to be a constant. It's not the same as that number c in the previous equation, it's actually the square of c, as we just consider a comparison of these two equations. Well, that's a really interesting result. In fact, it is our first illustration of something that we call an equilibrium constant. For the reaction N204, decomposing to become 2NO2, the pressure of the product squared divided by the pressure of the reactant always gives us the same number over and over again. This ratio is, in fact, a constant. Notice, there's an interesting form to that function. Consider the following facts. The product is in the numerator. The reactant is in the denominator. And furthermore, the exponent on the product and numerator is the same as the stoichiometric coefficient in the reaction. And the exponent in the denominator on the pro, on the reactant one, is the same as the stoichiometric coefficient on the reactant. Now, that might just be a happy coincidence. Turns out it's a general result. To show that, let's actually look at some additional experimental data. Here's another reaction. Nitrogen gas plus hydrogen gas produces ammonia, also a gas. If this previous result is general, we should be able to take the stoichiometric coefficient on the ammonia. And the stoichiometric coefficient on the hydrogen. And the stoichiometric coefficient on the nitrogen. And assemble this product of pressures, with the product in the numerator. And the reactance of the denominator. And see whether or not that's a constant. The constant is a function of what? Well, from what we did before, we varied the initial conditions, and looked to see, whether when we observed the constant pressures at equilibrium, whether or not this combination would, in fact, turn out to be constant. So let's do that. Here is the experimental data. We'll vary, for example, the volume in which the container is held. We'll vary initial conditions by varying the amount of nitrogen or hydrogen that we start off with. And then we will measure for each of those cases, the equilibrium pressures of the reactants and of the gases. Then we will assemble this strange product of the pressures and calculate it. And notice, it comes out to be essentially constant that we get that, in fact, this results in a constant. We could actually do this for a great many reactions. And if we do, what we'll discover is that as a general rule, we have something that is called the Law of Mass Action. Here's a very general kind of chemical reaction. a molecules of A plus b molecules of B react to give c molecules of C plus d molecules of D. That's complete, sort of a, a general way of writing any chemical reaction. Then the Law of Mass Action, observed experimentally as we have done here, for these two chemical reactions, says that this product of the pressures in which the pressures of the products are in the numerator and the pressures of the reactants are in the denominator, and each pressure is raised to its stoichiometric efficient as an exponent. For example, the pressure of c is raised to the integer c. The pressure of d is raised to the integer d. That when we assemble that particular accumulation of pressures, we discover that that's a constant over all. And in fact, we'll observe this for basically any chemical reaction. That is an absolutely beautiful result. It's a highly unexpected result. This is a strange thing to have put together. Stoichiometric coefficients are ratios of things that react with ratios of things that are produced. Why should those coefficients become exponents? Why are the products in the numerator and the reactants in the denominator? And why overall should that particular ratio always turn out to be the same number for a particular chemical reaction? We're going to analyze the reasons for that in the next lecture.
