We've spent a lot of time in the previous lectures studying phase equilibrium. Comparing for example, the rates of evaporation or the rates of condensation. We want to move this over to begin to study chemical reactions. It's fairly clear that we're going to have to understand the rates of which chemical reactions take place. And that will be the focus of the study this week, particularly from concept development studies 20 and 21. In this first concept development study, we're just going to focus on, how do we measure and quantify the rates of chemical reactions? We're going to begin with a simple chemical reaction actually studied here at Rice by my colleague Bruce Wiseman. This is the decomposition of the molecule C60O3, an oxygenated form of the Buckminster Fullergreen molecule. In which the three oxygens give way to a single oxygen, as the two oxygens in a O2 molecule depart. Imagine that we wanted to know how fast this particular chemical reaction were taking place. Then one of the things that we might do, is to measure how much C60O3 was present at any given time. And measure the rate of the disappearance of that material. One way to do this for example, would be to measure a solution and how much a the C60O3 absorbed light. using Beer's Law, we can relate the concentration of the C60O3. To the color of the light the amount of absorbence of the light that there is. When this is done, we actually observe the following graph. Here what we've observed is the absorbence, but the absorbence is in fact proportional to the amount of C60O3 which is present. Notice, we have also studied this as a function of time. We're watching the passage of time in minutes. So, amongst the things that we are looking at is, how fast is this material disappearing? So, we're asking the question, based upon this measurement as a function of time, how fast is this chemical reaction? We could study it in a variety of ways, but one of the ways to look at this, might be to ask, how much of the C60 has disappeared after five minutes? And you'll notice quite a lot has disappeared over that first five minute period. Notice that over the next five minute period, the amount which has disappeared is less. And over the next five-minute period, the amount of C60O3, which has disappeared, is even less. That suggests that the amount of material which is disappearing, over a unit period of time depends upon how much material there actually is. How would we want to then measure how fast the reaction is? Well, a natural way to understand the rates of a process, if we were for example measuring the amount of C60O3 versus time. And observing that the graph seems to decrease something like this. Then we might want to know by how much has the amount gone down for a given period of time. And then we might imagine that the slope of this graph, which is the change in the concentration of the C60O3 versus time. Or alternatively, if we were to do this more precisely, we would do this with calculus. And take the derivative of the C60O3 concentration with time, but we could measure it as just simple, a simple slope as well. And when we do that then, we would define the rate of the reaction here, as being the slope of this curve as a function of time. Which could be estimated by simply taking finite amounts of time and finite amounts of concentration change, and taking the ratio of those two. That means that at each particular point along this graph, I could measure for example, the slope of the graph here. Or the slope of the graph here, or the slope of the graph here. And then we could actually plot the slope as a function of time. What if we then in fact take the slope and plot it as a function of time? We actually wind up with this graph. Graph looks a lot alike, so let's call attention to some of the differences here. Notice that what we have plotted on the Y axis here, is no longer the concentration of C60O3 as as a function of time. But rather the rate of change of C60O3 as a function of time. So in contrast to the previous graph that we examined, we are now actually looking at the change in the amount of C60O3 as a function of time. And what's interesting is that, that curve looks a lot like the previous curve. This downward decrease that we observe here, looks a lot like the decrease on the previous slide, which I'm going to click back to now. Notice the similarities between these two graphs. I've highlighted them back over here on the chart. What that suggests pretty strongly, is that the rate at which things are happening, is proportional to the amount of the material that we have. That the reaction is slowing down as it's proceeding. The rate is slower for these lower concentrations as a function of time, and faster early on in the reaction where the rates are much higher. And furthermore, that the reaction rate seems to be proportional to the concentration. That suggests what we ought to do is plot the C60 versus the rate or the rate versus the C60 and that's actually what's been done on this graph. We plotted the rate, defined before by the slope here versus the actual C60 concentration. In other words, what we have done is to take the Y axis from this graph and plot versus the Y axis for this graph. And what's fascinating about these results, is that we wind up with a rather beautiful straight line relationship that actually passes through the origin. What that tells us is that the rate on the Y axis is proportional to the concentration on the X axis. We could write this then as the rate defined above is proportional to, we're going to call the proportionality constant K. It is proportional to the concentration of the C60O3. And that in fact then begins to describe, as given in this equation here. The dependence of the reaction rate on the concentrations of the materials. It's a very simple relationship in fact as we can see. This is simple proportionality between these two. That is in fact then a really interesting result. It turns out to be a general not a general result, but an example of a general result. By which the rate at which reactions take place, is a function of the concentration of the materials which are reacting. In this particular case, the relationship is a simple one. Notice although it's not really obvious that it's there, that there is a exponent of one on that C60 up there and so there's a first power relationship. Not in all cases do we see a first power relationship. In fact, in the general case, if we have sort of a general chemical reaction of A and B reacting in some stoichiometric proportions to give C and D. We wind up with a rate relationship, between the rate of the reaction and the concentrations of the two reactants, A and B. Remember what we've got here. Here's reactant A and reactant B. Here's the concentration of reactant A and concentration of reactant B. And the rate at which this reaction now takes place in a general case, depends upon two exponents here. Notice these exponents here n and m, which may or may not be one or for that matter zero or two, or a variety of other different possibilities. In fact, n and m are usually integers almost always integers, not in 100% of cases. But there isn't a simple way in fact to predict those experimental values of n and m. For more general reactions, we're going to have to have some means by which we can do the kind of analysis that we have done here. To determine the rate law for the C60O3 decomposition for a variety of other kinds of reactions. We're going to come up with a general way to do that in the next lecture.