Lecture 22. Chemical Kinetics Pt. 1.
CC Attribution - ShareAlike 3.0 USA:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this
Arasasingham, Ramesh D.
 UCI Chem 1C is the third and final quarter of General Chemistry series and covers the following topics: equilibria, aqueous acid-base equilibria, solubility equilibria, oxidation reduction reactions, electrochemistry; kinetics; special topics. 
 Okay, can I have everyone's attention please? Are there any questions before I begin? So today we are going to move on to the next chapter which is chapter 14 of your textbook and we will start looking at chemical kinetics. Alright? And so if you guys remember before we start talking about kinetics let's talk a little bit about thermodynamics. If you guys remember last quarter when we looked at thermodynamics we said one of the goals of thermodynamics was to account for the natural direction of reactions. Why is it that certain reactions have a certain tendency to occur on their own while others don't? And we used the term spontaneity to describe that and we said that thermodynamics helps us explain the spontaneous direction of a reaction. And we went through the details of that and we said that for spontaneous reactions we said that we look at the thermodynamic quantity free energy and when we calculate the change in free energy for a reaction if that sign comes out to be negative we know that it is spontaneous. If the change in free energy which is delta G is positive we know that it is not spontaneous that the reverse reaction is spontaneous. So let's take this reaction that we are looking at here. We are looking at the combustion of methane giving you carbon dioxide and water and if you calculate the change in free energy for that reaction we know that it comes out to be negative. Alright and so that's a spontaneous reaction. So we were to represent this graphically in the form of what we call the reaction coordinate which is a plot of the free energy as a function of the progress of the reaction. As the reaction progresses what changes it undergoes? And thermodynamics if you guys remember we said that if you take delta G, delta H, delta S we call all of these state properties and we said a state property always depends only on the initial and final states. So we want to look at delta G then we plot the free energy as a function of the progress of the reaction and over here this is the free energy of the reactants and down here you have the free energy of the products and so the difference between the free energy of reactants and products. Remember products represent the final state, the reactants represent the initial state and we say delta what does delta mean? You guys remember from last quarter? It's all a change and what does in thermodynamics what does change mean? Always the final minus the initial. So we're looking at the final state which is the product and the initial state which are the reactants and so the difference between the free energy products and reactants comes out to be negative and so we know that this reaction is spontaneous. Got it? Now if you guys remember repeatedly last quarter one of the things we said was that when we talk about a spontaneous reaction it doesn't tell us anything about how fast the process is. So a spontaneous change can take place instantaneously and explosively for example or a spontaneous change can be very very slow. So slow that in our lifetime we may not see a change. So spontaneous change tells us the natural direction. We know that there's a natural tendency for that reaction to occur without any external influence. However it does not tell us anything about how fast that process is. It could be very slow or it could be very fast. Now what determines how fast reactions, how fast or why reactions takes place so fast now falls within the domain of kinetics and that's what we're going to look at today. So if you want to look at this reaction coordinate that I've drawn that this is the initial state and this is the final state and that falls in the domain of thermodynamics. Thermodynamics helps us explain the spontaneous direction of reactions and we know that in thermodynamics what we're interested is looking at initial and final states. So if you're looking only at initial and final states we call that a state property and that depends on initial and final states and not on pathway. That's what it means when we say it's a state property. And in the thermodynamic domain we look at delta G, the free energy change for that reaction. We can look at enthalpy change where heat is being released in that reaction or where the heat is absorbed in that reaction so it gives us delta H. It gives us entropy change and also equilibrium constant. So these are all thermodynamic quantities and these are quantities that depend only on initial and final states and they fall within the domain of thermodynamics. And that's what we've looked at. Now we're going to move on to looking at kinetics and that falls in the middle here which I've highlighted in green. And this falls in the domain of kinetics and this depends on pathway and the speed of the reaction. So if we want to explain why certain reactions takes place very rapidly and there are other reactions that takes place so slow that in our lifetime we don't see any change, now that falls within the domain of kinetics. So kinetics we're interested in looking at how fast reactions takes place and secondly what is the pathway? It turns out how fast reaction takes place depends on the pathway that it takes. So today we're going to start looking at kinetics and if we want to define what it means when we say kinetics, chemical kinetics is the study of how rapidly reactions proceed and the detailed events along the way as the reactants transform to product. So if you want to define what chemical kinetics is, chemical kinetics is the study of how rapidly reactions proceed and of the detailed events along the way as reactants are converted to products or transform or as the reactants transform to products. So if you want to think about this, today we're going to do a lot of analogies about pathways and one way to look at it is you can consider kinetics as looking at a journey, all right? So in thermodynamics we're only interested, if you're considering a journey in thermodynamics we're only interested in the initial and final states. So it's like if you're taking a long trip it's as if you know where you originate and your destination and if you're only interested in where you start which is your origin and your ultimate destination that will be thermodynamics, you're interested in the initial and final states. In kinetics we're actually interested in the actual journey. What is the path where you take in that journey? What are the obstacles along the way that allows you to speed up and slow down as you proceed? So today we're going to look at the actual journey and that falls in the middle, okay? So if we're going to be interested in the journey and remember if you look at the definition for kinetics we're interested in how fast reactions takes place and the actual events that take place along the way. So we're going to start by looking at, first we'll look at some definitions and we're interested in looking at how fast a reaction proceeds. And so the term that we use to describe how fast, remember when you're driving a car what do you use to describe how fast a car proceeds in your journey? You use speed. In chemical kinetics the term that we use to describe the speed is rate, okay? So rate gives you the speed of a reaction. So we'll start by looking at what it means when we say rate. So we'll look at, we call this reaction rate and the reaction rate of a chemical reaction refers to the speed of the reaction. So from now on if we want to look at how fast a reaction proceeds or we call that the reaction rate, okay? And again remember the analogy is a journey. So if you are driving a car and you want to know how fast you're proceeding, remember the unit that we use to describe the speed of a vehicle is miles per hour. And so the way we calculate your speed is to look at the distance traveled divided by the time it took. That's what miles per hour. If you traveled 50 miles and it took you an hour that would be 50 miles per hour, alright? So just as you would when you're trying to figure out the speed of a vehicle it's always the distance traveled divided by the time lapsed. When we talk about chemical reactions and we want to take a look at rate we define rate as change in concentration as a function of change in time. So we define a quantity that we call average rate and the average rate is the average speed of a reaction and the average rate is always change in concentration of reactant or product, okay? Divided by change in time. Alright? So if we take a hypothetical reaction, let's say A going to be where the reactant is A and B is the product, then the average rate would be, if we're looking at the reactant it will be the change in concentration of A. Alright? Remember delta means change and we put the square brackets to indicate concentration and that divided by the change in time. So when we talk about rate it's always change in concentration divided by the change in time. Alright? So remember we said delta represents change and it's always the initial state minus the final state. That means the final concentration of A minus the initial concentration of A, that's delta. Delta is always, remember, final minus initial, the final state minus the initial state. And so here we're looking at the final concentration minus the initial concentration divided by the final time minus the initial time. Alright? T is lowercase t refers to time and therefore it's t final minus t initial. And the unit for rate would always be, remember we're looking at concentration so that will be moles per liter divided by second. So the unit of time that we use in connectix is always seconds. So the unit turns out to be moles per liter per second. Okay? So if we want to look at how fast a reaction proceeds then the term that we use to describe the speed of that reaction is rate, reaction rate. And reaction rate is defined as the change in concentration of either the reactant or product divided by the change in time. And since we're looking at the change in concentration, the unit for concentration is moles per liter and the unit for time is seconds. Alright? And therefore the speed of a reaction of the reaction rate is always moles per liter per second. Okay? Now let's take a specific reaction and look at this in greater detail. So if I wanted to determine the speed of a reaction then I would have to experimentally measure the change in concentration as a function of change in time. So let's take an example where we're looking at, let's say the reaction we're looking at is this. Let's say we're looking at 2 NO2 gas going to 2 NO plus O2 gas. So we're looking at this specific example of a reaction and we want to experimentally measure the reaction rate. Alright? And if we were to do that then we pick either reactant or product and let's say we pick this reactant. And at different time intervals you would measure the concentration of NO2. Alright? Now since the reaction is proceeding in the forward direction would you expect the concentration of the reactant to increase or decrease as the reaction progresses? You would expect it to decrease. So if I were to measure this in the laboratory and you were carrying out an experiment then I would make a table of time t and the unit would be in seconds and over here I would look at the concentration of NO2 and it would be moles per liter. So if I were looking at time t as a function of concentration and let's say we're measuring this in increments of 50 seconds. So I would measure the concentration at t equals 0. Alright? And the concentration of t equals 0 would be 0.0100. And remember what is the term that we use to describe the concentration at time 0? What do we call that? Initial concentration. So we call, so this would be the initial concentration. It's obvious. And that would refer to NO2 at t equals 0. So that would be NO2 subscript 0 to indicate that that's at t equals 0. Then we make a measurement at 50, 100, 150 and let's say 200 seconds. And if you were to carry that in the laboratory this would come out to be 0079. This would be 0065, 0055 and this would be 0048. So we measure the concentrations at different time intervals. So now we want to figure out what the speed of the reaction is. So we can say it turns out that if I wanted to calculate the average speed or rate of this reaction it's going to depend on the time span that I pick. So I could calculate an average rate from 0 to 200 seconds. But what we're going to do, or 0 to 100. So what I'm going to do is for convenience we're going to look at what is the speed of this reaction at every 50 second increments. So if I wanted to calculate the average rate I can say the average rate during the first 50 seconds. So let's look at the average rate during the first 50 seconds. But by definition we know that average rate is the change in concentration of NO2 as a function of change in time. Which is the final concentration minus the initial concentration. So it would be the concentration of NO2 final minus NO2 initial divided by T final minus T initial which is we're looking at the first 50 seconds. So the final concentration would be 0.0079 minus 0.110 and this is in moles per liter divided by 50 minus 0 and that would be in seconds. So we're looking at the average rate. So we're looking at the change in concentration during the first 50 seconds divided by the change in time. So if I were to write that down this would come out to be negative because we're taking a small number and subtracting a big number from it. So this comes out to be negative and it comes out to be negative 4.2 times 10 to the negative 5 moles per liter per second. And so we end up with a negative sign. Now all of you recognize that we're looking at rate or speed and it turns out speed does not have a sign. The analogy is you can be driving your car at 50 miles per hour in the forward direction and what would your speed be? 50 miles per hour. If you put your car in reverse and go backwards at 50 miles per hour what is your speed? It's still 50 miles per hour. That's the speed at which you're traveling. So speed does not have direction. Do you understand? Or sign. And so in order to get rid of this sign, this negative sign, what we do is move the negative sign over here. And the reason we're doing that is because we all understand that speed has no sign. There's no negative or positive. And so to get rid of this negative sign we bring it over here and we say now that this equals 4.2 times 10 to the negative 5 moles per liter per second. And the negative sign on the other side just reminds us that this is a reactant because when reactants are consumed their concentration decreases. And therefore when you calculate delta for reactants you will always end up with a negative sign. So we move the negative sign to the other side and the negative sign here is just a reminder to us that we're looking at reactants because reactants will always be consumed in a reaction. Okay? So this is for the first 50 seconds. Now if I calculate the average rate during the second 50 seconds and if you already carry out the same calculation we'll end up with negative delta NO2 divided by delta T would equal 2.8 times 10 to the negative 5 moles per liter per second. Alright? And if I were to do the same thing for the third 50 seconds and I could keep going on. So we'll stop with the third one. If I calculate the average rate during the third 50 seconds now this would also be negative delta NO2 divided by delta T would equal 2.0 times 10 to the negative 5 moles per liter per second. So now compare the speeds during the first 50 seconds with the second 50 seconds and the third 50 seconds and what does that tell you about the speed of the overall reaction? It's actually slowing down. Alright? So as the reaction progresses you can see that it's actually slowing down. Alright? And so that's important to remember because when you look at how fast reactions proceed and when you look at reaction rates all reactions are the fastest when they begin. Alright? And as the reaction progresses they slow down. Alright? Until they reach equilibrium. Okay? Now one of the things you'll notice is that when we're looking at average rate, average rate is not a really useful quantity. Why? Average rate will depend on the time increment that you picked. We just so happen to pick 50 seconds as our increment. Alright? If I had picked 100 seconds as our increment then I would end up with different speeds. Do you understand that? Different rates. If I had picked 200 seconds I would end up with a different increment. Okay? Now even though we use the average rate, I want you to keep in mind that average rates are not very useful, the problem being that the average rate that you calculate will depend on the time span that you pick. And if you pick different time spans then your rates are going to be different. Okay? Now if you want to represent this graphically, the same thing that we just looked at, we can represent this in the form of a graph and so if I were to represent this graphically I would plot concentration versus time. So remember, I'm going to put a concentration of NO2 on one side. Alright? And this would be in units of moles per liter or molarity. And we're looking at time and in kinetics the unit for time that we use is seconds. And remember we started with, this would be 0.0100 molar. That's the concentration that we started with. And as the reaction proceeds we know the concentration decreases and it will decrease in that way financially and then it will flatten out. And why does concentration flatten out? It never goes to completion. It stops short and it flattens out. And why does that concentration of the reactant flatten out? You guys remember, it has achieved equilibrium. Okay? When equilibrium is established it will flatten out and it will never go to zero because it establishes equilibrium for that. Because it doesn't go to completion, it establishes equilibrium. So in this graph if I wanted to, so this would be my initial concentration of NO2, the point at which I start. Okay? And remember we're measuring this in 50 second increments. So this will be zero seconds. This will be 50. Let's say that's 100. That's 150. That's 200. So if you were doing this in the laboratory and carrying out an experiment then the easiest way to figure out what the average speed is during the first 50 seconds is to draw a tangential line. So I'm interested in figuring out the average rate during the first 50 seconds. And so I can draw a tangential line that links the two. And if I calculate, so this would be 10 theta. And if I wanted to calculate the average rate for this, my average rate would equal the change in concentration of NO2 over change in time. And remember we put a negative sign in front of that to remind us that it is being consumed. So the slope comes out to be a negative slope. All right? Actually no. All right? And so you can take the slope of that and that will give you the average rate. And if you want to do the same thing for the second 50 seconds you would take the slope of that line and that would give you the rate at the second 50 seconds. And as you can recognize that as you go down the slope decreases and that tells you that the rate of the reaction slows down. So if you wanted to do this graphically in the laboratory and you wanted to calculate average rate you can figure out the slope that corresponds to the time elapsed. But as I said before average rate is not a useful quantity because it means that the average rate will depend on the time span that you pick and that could vary from person to person. So we need something more precise or allows us to look at it in terms of not having this variable in time span. And what we're going to use is what we call instantaneous time and instantaneous rate. And an instantaneous rate gives you the rate at an instant in time. All right? So we're going to, so a more useful quantity is the instantaneous rate. All right? The instantaneous rate gives the rate of a reaction in a particular moment in time. All right? So the way to look at instantaneous rate is if we were to decrease delta t and make it smaller and smaller and smaller and smaller and smaller to a point where it's just an instant a moment in time, a fractional second before and a fractional second after an instant in time and that's given as the instantaneous rate. So if you want to look at instantaneous rate, an instantaneous rate would be the rate at any given instant in time. All right? And it represents the rate, which is the change in time as a fractional second before that dot and a fractional second after that dot. Do you understand that? And that gives you the rate, what we call an instantaneous rate. And graphically, the way you figure out an instantaneous rate is to draw a slope or a tangential line that just runs to that one point like that. And if I calculate the slope that corresponds to that, what I get is now instantaneous rate. This would be the change in concentration of NO2 over change in delta t. But now this corresponds to the delta t is now a fraction of a, you know, you take that point, it's a fraction of a second before and a fraction of a second afterwards and that gives you the instantaneous rate. Does that make sense to everybody? So rather than calculate the slope based on a 50 second increment here, now the slope just touches that one single point and we find the tangential slope that goes to that one single point and that gives us instantaneous rate. So now you can see that when you look at instantaneous rate, now we don't have this variation in the time span, it's no longer 50 seconds, 100 seconds, 200 seconds, which depends on who is looking at what. And so the average rate would depend on the time span. Now when we go to instantaneous rate, you can see now it makes it independent of that. And therefore from now onwards, when we talk about rate, we will always look at instantaneous rate. We will not have that rate at any given instant in time. Now once again, if you take instantaneous rate and if you look at any point in this graph, if I take this point and I look at that, can you see that this slope would be greater? So as you keep, as the reaction progresses, you can see that the slope decreases and therefore once again, you can see that even if you look at instantaneous rate, you can see that the speed of the reaction slows as the reaction progresses. So if I look at instantaneous rate, where do you think the reaction would be the fastest? At t equals zero, can everybody see that? When t equals zero, the instant the reaction starts, that's when the reaction is the fastest. And so from now onwards, you need to know that the initial concentration, at the point at which you have the initial concentrations, at the point zero, at t equals zero, this is when the slope would be the greatest. So if you look at the slope of this graph, it would be like that. So the reaction is the fastest at t equals zero. And so the initial rate, so we call this initial rate, and the initial rate is always the fastest. And in any reaction, the instant the reaction starts reacting, that is at t equals zero, that would be when the reaction is the fastest. And then from that point onwards, the reaction slows down. And as the reaction progresses, you'll see that the rate of the reaction slows down. So now let's go back to that reaction that we looked at. So we looked at the reaction of 2N02 gas going to 2N02 gas plus O2 gas. And if we wanted to represent this reaction in the form of a graph, we said if we're looking at a reactant, the concentration of the reactant always decreases as the reaction progresses. Now we can also give rates in terms of products. Remember we said the definition is what? The rate of a reaction is the change in concentration of reactant or product as a function of time. So we can also look at the speed of this reaction or the rate of this reaction in terms of products. So if we were to plot a concentration versus time plot, so now we're looking at concentration versus time. Here the unit is always moles per liter, time is always seconds, and let's say on this scale, this represents 0.0100 molar. And if I'm looking at reactant, I said the concentration of the reactant would decrease and this represents the concentration of NO2. Now if instead I'm looking at products, now what happens is the instant the reaction starts, we have no products. So if I'm looking at NO, we know the instant we start, we have only reactants and zero products. But as the reaction progresses, now what's going to happen to the concentration of NO? Is it going to go up or is it going to go down? It's going to increase. So if I wanted to represent that, then I know that my products are going to increase and it would increase like that. And so this represents the concentration of NO, the product. Now if you look at the stoichiometry, you can see that for every two moles of reactant that's consumed, how many moles of this product is formed? Two. All right? So we know that in terms of moles, two moles is consumed and two moles are formed. So if we look at concentration, because they're all together, can you ever see the volume would be the same? So if I had one liter volume, then you can see that you have two moles per liter and as two moles per liter is consumed, two moles per liter of product would be formed. So the change in concentration as the amount that's consumed will always be the amount that's being formed on this side. And can you ever see on the other side when we look at oxygen, for every two moles of NO2 that's consumed, only one mole of oxygen is being formed. So only half as much oxygen is being formed. So if I take this, and if I take this to be 0.0050, which is exactly half of that, now if I take oxygen, oxygen, this would represent oxygen. Can you ever see that, the concentration change in terms of oxygen? Because for every two moles of reactant that's used up, only half as much oxygen is produced. All right? So if I want to talk about rate in terms of NO2, we said that this is the change in concentration of NO2 and we put a negative sign in front to remind us that NO2 is being consumed, we say change in concentration of NO2 divided by delta T. If I'm talking about rate in terms of NO, now I no longer need to put the negative sign in front because it's not being consumed, it is being formed. So usually we don't put a sign in front, we just leave it blank because we know it's positive. But just for you to begin with, just to remind you, I'm going to put this positive sign because now when we look at NO, we know that NO is being formed. And so that's why, because it's not being consumed, its concentration actually increases. So when you take final minus initial, you'll always end up with something that's positive because your final concentration will be much higher than your initial concentration. And if we're looking at, and these refer to instantaneous rate, okay? And if we're looking at rate in terms of O2, then it'll be, once again I'm going to put a positive sign, we don't usually put a sign in front of that, but this is just to remind you the contrast between this. You have a change in concentration of O2 as a function of change in time. Does that make sense to everybody? So you can give rate in terms of reactants or products. If it is products, it's the change in concentration of products divided by the change in time. And when we talk about instantaneous rate, it's a change in fractional change in time. All right? An instant before and an instant after the particular point in that graph that we're interested in looking at. Okay? Now, if you want to look at the relationship between the three speeds, because remember the speeds can be different or they could be the same. All right? So relationship between the three would be that if I take the speed of NO2, can everybody see this will be the same as the change in concentration of NO over delta T? Because for every two moles that's used up, two moles is being formed. So we know that for every two moles of the reactant that's being consumed per one liter, you're going to get the same amount of NO being formed for that instantaneous rate and therefore they should equal each other. But remember, oxygen will be half as much. So if I wanted to make oxygen which is half as much equal to this, what do I need to do to oxygen? Can everybody see? I'll need to multiply it by two. All right? So if I wanted to make this equal to the concentration of the speed or the rate of oxygen, I will have to say this equals two times the change in concentration of O2 over delta T. Also, can everybody see that this is a negative sign because it's being consumed? And remember I said before that's a negative slope. If you were to look at the other side, it would be a positive slope as they keep increasing and therefore you can see that this would be positive and this would be positive. So I can write the same thing and say or I could say that this is negative one half delta NO2 over delta T equals positive one half delta NO over delta T which equals delta O2 over delta T. So if we're comparing the instantaneous rate at the same instant in time between the reactant that's being consumed and the products that are being formed, can everybody see that that would be the relationship? So it turns out depending on the balanced equation, if you pick one, let's say initial at T equals zero what the rates are, this is the relationship between them. Or let's say five seconds into the reaction, if I want to look at the relationship between the instantaneous rate between the three, that would give me the rate. The relationship. So if I wanted to look at this in the general form, so for the general reaction, and I look at the general form of the reaction and let's say we're looking at A plus B reacting to give you C plus D, alright, then the general form of the reaction would be, if you're looking at the relationship between the rates of reactants and products, this is a reactant so it's going to have a negative sign. One over A is the coefficient, change in concentration of A versus change in time. This is a reactant so it's going to have a negative sign. One over B, the coefficient of the balanced equation, would give you delta change in concentration over change in time. Now we're looking at products, so it would be one over C, delta change in concentration of C divided by delta T, and if I take D, it would be one over D change in concentration of D over delta T. So for any general form of the reaction, if you want to look at the relationship between the relative rates of reactants and products, you turn to the balanced equation. So let's take a quick example. Now if you were asked to plot a concentration versus time graph and show what it looks like for this reaction. So we're going to look at the reaction 2 and 205 giving you 4 and O2 gas plus O2 gas. So for any given reaction now you should be able to plot a concentration versus time graph for reactants and products and then show the relationship between the relative rates of the reactants and products. So if I wanted to plot this, then what I would do is I will plot concentration versus time. Let's say this is all of moles per liter, this should be in seconds. Now can everybody see that the reaction, the sort of the relationship is 2, 4, 1. So on this scale, if this is one molar, this is two molar, this is three molar, and this is four molar, we can see that let's say that because the stoichiometry is 2 to 4 to 1, we know that to begin with N2O5 would decay like that. So let's say that the concentration of N2O5 is 2 molar. So this would represent the concentration of N2O5. Now for every two moles that's consumed, you're going to get 4 moles of NO2 so that you have to end up with twice as many. So that means that this would represent NO2, the relative change of NO2. You just have to make sure that the ratio is this is twice as much. Now what about oxygen? So that means if this is two molar, this is four molar, then this has to be one. So you can see that this would represent the concentration of O2. If you were to plot a concentration versus time plot for this particular reaction, this is how the profile should look like as you look at the relationship between reactants and products. Reactants will be consumed, their concentration needs to decrease. Products will be formed, their concentration needs to increase. Now if I want to look at the relationship between the relative rates of these, our reactant is N2O5 so there's a negative sign, a negative one-half change in concentration of N2O5 divided by change in time equals the products which is one-quarter change in concentration of NO2 over delta T. And over here, this would be change in concentration of O2 divided by delta T. You see that, that would be the relationship between the three. Now one of the assumptions that we make in all of this is as all of you know, all chemical reactions, the majority of chemical reactions are reversible. And one of the assumptions that we're going to make when we look at these reactions is that the reactions go only in one direction. Both reactions are reversible. So if I take this reaction of NO2, 2NO2 going to 2NO plus O2, we know that this reaction is reversible. So that means there's a forward reaction and that would be 2NO2 going to 2NO plus O2. There's also a reverse reaction where we're looking at 2NO giving you 2NO plus oxygen giving you 2NO2. So this is what we call the forward rate and this is the reverse rate. And in reality, when we do experiments, what we actually measure is the net rate, which is always the net rate equals forward rate minus reverse rate. And in reality, this is what we measure, what is measured experimentally. All right? However, from now onwards, we're just going to always ignore the reverse reactions. So for convenience, we will consider only forward rates. All right? So from now onwards, I just want you to keep in mind that it gets more complicated if you have to take into account the reverse rate as well. Can you tell me only in one instance will the reverse rate be zero? When is the reverse rate zero? Initial. When t equals zero, can everybody see that the reverse rate will be zero because there are no products to react to give you reactants. All right? And so if you take the t equals zero, initial concentration, the initial rate will always be the forward rate only. Got it? So next time, we'll look at this in greater detail.
 Okay, can I have everyone's attention please?  Are there any questions before I begin?  So today we are going to move on to the next chapter which is chapter 14 of your textbook  and we will start looking at chemical kinetics.  Alright?  And so if you guys remember before we start talking about kinetics let's talk a little  bit about thermodynamics.  If you guys remember last quarter when we looked at thermodynamics we said one of the  goals of thermodynamics was to account for the natural direction of reactions.  Why is it that certain reactions have a certain tendency to occur on their own while others  don't?  And we used the term spontaneity to describe that and we said that thermodynamics helps  us explain the spontaneous direction of a reaction.  And we went through the details of that and we said that for spontaneous reactions we  said that we look at the thermodynamic quantity free energy and when we calculate the change  in free energy for a reaction if that sign comes out to be negative we know that it is  spontaneous.  If the change in free energy which is delta G is positive we know that it is not spontaneous  that the reverse reaction is spontaneous.  So let's take this reaction that we are looking at here.  We are looking at the combustion of methane giving you carbon dioxide and water and if  you calculate the change in free energy for that reaction we know that it comes out to  be negative.  Alright and so that's a spontaneous reaction.  So we were to represent this graphically in the form of what we call the reaction coordinate  which is a plot of the free energy as a function of the progress of the reaction.  As the reaction progresses what changes it undergoes?  And thermodynamics if you guys remember we said that if you take delta G, delta H, delta  S we call all of these state properties and we said a state property always depends only  on the initial and final states.  So we want to look at delta G then we plot the free energy as a function of the progress  of the reaction and over here this is the free energy of the reactants and down here  you have the free energy of the products and so the difference between the free energy  of reactants and products.  Remember products represent the final state, the reactants represent the initial state  and we say delta what does delta mean?  You guys remember from last quarter?  It's all a change and what does in thermodynamics what does change mean?  Always the final minus the initial.  So we're looking at the final state which is the product and the initial state which are  the reactants and so the difference between the free energy products and reactants comes  out to be negative and so we know that this reaction is spontaneous.  Got it?  Now if you guys remember repeatedly last quarter one of the things we said was that when we  talk about a spontaneous reaction it doesn't tell us anything about how fast the process  is.  So a spontaneous change can take place instantaneously and explosively for example or a spontaneous  change can be very very slow.  So slow that in our lifetime we may not see a change.  So spontaneous change tells us the natural direction.  We know that there's a natural tendency for that reaction to occur without any external  influence.  However it does not tell us anything about how fast that process is.  It could be very slow or it could be very fast.  Now what determines how fast reactions, how fast or why reactions takes place so fast  now falls within the domain of kinetics and that's what we're going to look at today.  So if you want to look at this reaction coordinate that I've drawn that this is the initial state  and this is the final state and that falls in the domain of thermodynamics.  Thermodynamics helps us explain the spontaneous direction of reactions and we know that in  thermodynamics what we're interested is looking at initial and final states.  So if you're looking only at initial and final states we call that a state property and that  depends on initial and final states and not on pathway.  That's what it means when we say it's a state property.  And in the thermodynamic domain we look at delta G, the free energy change for that reaction.  We can look at enthalpy change where heat is being released in that reaction or where  the heat is absorbed in that reaction so it gives us delta H. It gives us entropy change  and also equilibrium constant.  So these are all thermodynamic quantities and these are quantities that depend only  on initial and final states and they fall within the domain of thermodynamics.  And that's what we've looked at.  Now we're going to move on to looking at kinetics and that falls in the middle here which I've  highlighted in green.  And this falls in the domain of kinetics and this depends on pathway and the speed of the  reaction.  So if we want to explain why certain reactions takes place very rapidly and there are other  reactions that takes place so slow that in our lifetime we don't see any change, now that  falls within the domain of kinetics.  So kinetics we're interested in looking at how fast reactions takes place and secondly  what is the pathway?  It turns out how fast reaction takes place depends on the pathway that it takes.  So today we're going to start looking at kinetics and if we want to define what it means when  we say kinetics, chemical kinetics is the study of how rapidly  reactions proceed and the detailed events  along the way as the reactants transform to product.  So if you want to define what chemical kinetics is, chemical kinetics is the study of how  rapidly reactions proceed and of the detailed events along the way as reactants are converted  to products or transform or as the reactants transform to products.  So if you want to think about this, today we're going to do a lot of analogies about  pathways and one way to look at it is you can consider kinetics as looking at a journey,  all right?  So in thermodynamics we're only interested, if you're considering a journey in thermodynamics  we're only interested in the initial and final states.  So it's like if you're taking a long trip it's as if you know where you originate and  your destination and if you're only interested in where you start which is your origin and  your ultimate destination that will be thermodynamics, you're interested in the initial and final  states.  In kinetics we're actually interested in the actual journey.  What is the path where you take in that journey?  What are the obstacles along the way that allows you to speed up and slow down as you  proceed?  So today we're going to look at the actual journey and that falls in the middle, okay?  So if we're going to be interested in the journey and remember if you look at the definition  for kinetics we're interested in how fast reactions takes place and the actual events  that take place along the way.  So we're going to start by looking at, first we'll look at some definitions and we're  interested in looking at how fast a reaction proceeds.  And so the term that we use to describe how fast, remember when you're driving a car what  do you use to describe how fast a car proceeds in your journey?  You use speed.  In chemical kinetics the term that we use to describe the speed is rate, okay?  So rate gives you the speed of a reaction.  So we'll start by looking at what it means when we say rate.  So we'll look at, we call this reaction rate and the reaction rate of a chemical reaction  refers to the speed of the reaction.  So from now on if we want to look at how fast a reaction proceeds or we call that the reaction  rate, okay?  And again remember the analogy is a journey.  So if you are driving a car and you want to know how fast you're proceeding, remember  the unit that we use to describe the speed of a vehicle is miles per hour.  And so the way we calculate your speed is to look at the distance traveled divided by  the time it took.  That's what miles per hour.  If you traveled 50 miles and it took you an hour that would be 50 miles per hour, alright?  So just as you would when you're trying to figure out the speed of a vehicle it's always  the distance traveled divided by the time lapsed.  When we talk about chemical reactions and we want to take a look at rate we define rate  as change in concentration as a function of change in time.  So we define a quantity that we call average rate and the average rate is the average speed  of a reaction and the average rate is always change in concentration of reactant or product,  okay?  Divided by change in time.  Alright?  So if we take a hypothetical reaction, let's say A going to be where the reactant is A  and B is the product, then the average rate would be, if we're looking at the reactant  it will be the change in concentration of A. Alright?  Remember delta means change and we put the square brackets to indicate concentration and  that divided by the change in time.  So when we talk about rate it's always change in concentration divided by the change in  time.  Alright?  So remember we said delta represents change and it's always the initial state minus the  final state.  That means the final concentration of A minus the initial concentration of A, that's delta.  Delta is always, remember, final minus initial, the final state minus the initial state.  And so here we're looking at the final concentration minus the initial concentration divided by  the final time minus the initial time.  Alright?  T is lowercase t refers to time and therefore it's t final minus t initial.  And the unit for rate would always be, remember we're looking at concentration so that will  be moles per liter divided by second.  So the unit of time that we use in connectix is always seconds.  So the unit turns out to be moles per liter per second.  Okay?  So if we want to look at how fast a reaction proceeds then the term that we use to describe  the speed of that reaction is rate, reaction rate.  And reaction rate is defined as the change in concentration of either the reactant or  product divided by the change in time.  And since we're looking at the change in concentration, the unit for concentration is moles per liter  and the unit for time is seconds.  Alright?  And therefore the speed of a reaction of the reaction rate is always moles per liter per  second.  Okay?  Now let's take a specific reaction and look at this in greater detail.  So if I wanted to determine the speed of a reaction then I would have to experimentally  measure the change in concentration as a function of change in time.  So let's take an example where we're looking at, let's say the reaction we're looking at  is this.  Let's say we're looking at 2 NO2 gas going to 2 NO plus O2 gas.  So we're looking at this specific example of a reaction and we want to experimentally  measure the reaction rate.  Alright?  And if we were to do that then we pick either reactant or product and let's say we pick  this reactant.  And at different time intervals you would measure the concentration of NO2.  Alright?  Now since the reaction is proceeding in the forward direction would you expect the concentration  of the reactant to increase or decrease as the reaction progresses?  You would expect it to decrease.  So if I were to measure this in the laboratory and you were carrying out an experiment then  I would make a table of time t and the unit would be in seconds and over here I would  look at the concentration of NO2 and it would be moles per liter.  So if I were looking at time t as a function of concentration and let's say we're measuring  this in increments of 50 seconds.  So I would measure the concentration at t equals 0.  Alright?  And the concentration of t equals 0 would be 0.0100.  And remember what is the term that we use to describe the concentration at time 0?  What do we call that?  Initial concentration.  So we call, so this would be the initial concentration.  It's obvious.  And that would refer to NO2 at t equals 0.  So that would be NO2 subscript 0 to indicate that that's at t equals 0.  Then we make a measurement at 50, 100, 150 and let's say 200 seconds.  And if you were to carry that in the laboratory this would come out to be 0079.  This would be 0065, 0055 and this would be 0048.  So we measure the concentrations at different time intervals.  So now we want to figure out what the speed of the reaction is.  So we can say it turns out that if I wanted to calculate the average speed or rate of  this reaction it's going to depend on the time span that I pick.  So I could calculate an average rate from 0 to 200 seconds.  But what we're going to do, or 0 to 100.  So what I'm going to do is for convenience we're going to look at what is the speed of  this reaction at every 50 second increments.  So if I wanted to calculate the average rate I can say the average rate during the first  50 seconds.  So let's look at the average rate during the first 50 seconds.  But by definition we know that average rate is the change in concentration of NO2 as a  function of change in time.  Which is the final concentration minus the initial concentration.  So it would be the concentration of NO2 final minus NO2 initial divided by T final minus  T initial which is we're looking at the first 50 seconds.  So the final concentration would be 0.0079 minus 0.110 and this is in moles per liter  divided by 50 minus 0 and that would be in seconds.  So we're looking at the average rate.  So we're looking at the change in concentration during the first 50 seconds divided by the  change in time.  So if I were to write that down this would come out to be negative because we're taking  a small number and subtracting a big number from it.  So this comes out to be negative and it comes out to be negative 4.2 times 10 to the negative  5 moles per liter per second.  And so we end up with a negative sign.  Now all of you recognize that we're looking at rate or speed and it turns out speed does  not have a sign.  The analogy is you can be driving your car at 50 miles per hour in the forward direction  and what would your speed be?  50 miles per hour.  If you put your car in reverse and go backwards at 50 miles per hour what is your speed?  It's still 50 miles per hour.  That's the speed at which you're traveling.  So speed does not have direction.  Do you understand?  Or sign.  And so in order to get rid of this sign, this negative sign, what we do is move the negative  sign over here.  And the reason we're doing that is because we all understand that speed has no sign.  There's no negative or positive.  And so to get rid of this negative sign we bring it over here and we say now that this  equals 4.2 times 10 to the negative 5 moles per liter per second.  And the negative sign on the other side just reminds us that this is a reactant because  when reactants are consumed their concentration decreases.  And therefore when you calculate delta for reactants you will always end up with a negative  sign.  So we move the negative sign to the other side and the negative sign here is just a reminder  to us that we're looking at reactants because reactants will always be consumed in a reaction.  Okay?  So this is for the first 50 seconds.  Now if I calculate the average rate during the second 50 seconds and if you already carry  out the same calculation we'll end up with negative delta NO2 divided by delta T would  equal 2.8 times 10 to the negative 5 moles per liter per second.  Alright?  And if I were to do the same thing for the third 50 seconds and I could keep going on.  So we'll stop with the third one.  If I calculate the average rate during the third 50 seconds now this would also be negative  delta NO2 divided by delta T would equal 2.0 times 10 to the negative 5 moles per liter  per second.  So now compare the speeds during the first 50 seconds with the second 50 seconds and the  third 50 seconds and what does that tell you about the speed of the overall reaction?  It's actually slowing down.  Alright?  So as the reaction progresses you can see that it's actually slowing down.  Alright?  And so that's important to remember because when you look at how fast reactions proceed  and when you look at reaction rates all reactions are the fastest when they begin.  Alright?  And as the reaction progresses they slow down.  Alright?  Until they reach equilibrium.  Okay?  Now one of the things you'll notice is that when we're looking at average rate, average  rate is not a really useful quantity.  Why?  Average rate will depend on the time increment that you picked.  We just so happen to pick 50 seconds as our increment.  Alright?  If I had picked 100 seconds as our increment then I would end up with different speeds.  Do you understand that?  Different rates.  If I had picked 200 seconds I would end up with a different increment.  Okay?  Now even though we use the average rate, I want you to keep in mind that average rates  are not very useful, the problem being that the average rate that you calculate will depend  on the time span that you pick.  And if you pick different time spans then your rates are going to be different.  Okay?  Now if you want to represent this graphically, the same thing that we just looked at, we  can represent this in the form of a graph and so if I were to represent this graphically  I would plot concentration versus time.  So remember, I'm going to put a concentration of NO2 on one side.  Alright?  And this would be in units of moles per liter or molarity.  And we're looking at time and in kinetics the unit for time that we use is seconds.  And remember we started with, this would be 0.0100 molar.  That's the concentration that we started with.  And as the reaction proceeds we know the concentration decreases and it will decrease in that way  financially and then it will flatten out.  And why does concentration flatten out?  It never goes to completion.  It stops short and it flattens out.  And why does that concentration of the reactant flatten out?  You guys remember, it has achieved equilibrium.  Okay?  When equilibrium is established it will flatten out and it will never go to zero because it  establishes equilibrium for that.  Because it doesn't go to completion, it establishes equilibrium.  So in this graph if I wanted to, so this would be my initial concentration of NO2, the point  at which I start.  Okay?  And remember we're measuring this in 50 second increments.  So this will be zero seconds.  This will be 50.  Let's say that's 100.  That's 150.  That's 200.  So if you were doing this in the laboratory and carrying out an experiment then the easiest  way to figure out what the average speed is during the first 50 seconds is to draw a tangential  line.  So I'm interested in figuring out the average rate during the first 50 seconds.  And so I can draw a tangential line that links the two.  And if I calculate, so this would be 10 theta.  And if I wanted to calculate the average rate for this, my average rate would equal the  change in concentration of NO2 over change in time.  And remember we put a negative sign in front of that to remind us that it is being consumed.  So the slope comes out to be a negative slope.  All right?  Actually no.  All right?  And so you can take the slope of that and that will give you the average rate.  And if you want to do the same thing for the second 50 seconds you would take the slope  of that line and that would give you the rate at the second 50 seconds.  And as you can recognize that as you go down the slope decreases and that tells you that  the rate of the reaction slows down.  So if you wanted to do this graphically in the laboratory and you wanted to calculate  average rate you can figure out the slope that corresponds to the time elapsed.  But as I said before average rate is not a useful quantity because it means that the  average rate will depend on the time span that you pick and that could vary from person  to person.  So we need something more precise or allows us to look at it in terms of not having this  variable in time span.  And what we're going to use is what we call instantaneous time and instantaneous rate.  And an instantaneous rate gives you the rate at an instant in time.  All right?  So we're going to, so a more useful quantity is the instantaneous rate.  All right?  The instantaneous rate gives the rate of a reaction in a particular moment in time.  All right?  So the way to look at instantaneous rate is if we were to decrease delta t and make it  smaller and smaller and smaller and smaller and smaller to a point where it's just an  instant a moment in time, a fractional second before and a fractional second after an instant  in time and that's given as the instantaneous rate.  So if you want to look at instantaneous rate, an instantaneous rate would be the rate at  any given instant in time.  All right?  And it represents the rate, which is the change in time as a fractional second before that  dot and a fractional second after that dot.  Do you understand that?  And that gives you the rate, what we call an instantaneous rate.  And graphically, the way you figure out an instantaneous rate is to draw a slope or a  tangential line that just runs to that one point like that.  And if I calculate the slope that corresponds to that, what I get is now instantaneous rate.  This would be the change in concentration of NO2 over change in delta t.  But now this corresponds to the delta t is now a fraction of a, you know, you take that  point, it's a fraction of a second before and a fraction of a second afterwards and  that gives you the instantaneous rate.  Does that make sense to everybody?  So rather than calculate the slope based on a 50 second increment here, now the slope  just touches that one single point and we find the tangential slope that goes to that  one single point and that gives us instantaneous rate.  So now you can see that when you look at instantaneous rate, now we don't have this variation in  the time span, it's no longer 50 seconds, 100 seconds, 200 seconds, which depends on  who is looking at what.  And so the average rate would depend on the time span.  Now when we go to instantaneous rate, you can see now it makes it independent of that.  And therefore from now onwards, when we talk about rate, we will always look at instantaneous  rate.  We will not have that rate at any given instant in time.  Now once again, if you take instantaneous rate and if you look at any point in this graph,  if I take this point and I look at that, can you see that this slope would be greater?  So as you keep, as the reaction progresses, you can see that the slope decreases and therefore  once again, you can see that even if you look at instantaneous rate, you can see that the  speed of the reaction slows as the reaction progresses.  So if I look at instantaneous rate, where do you think the reaction would be the fastest?  At t equals zero, can everybody see that?  When t equals zero, the instant the reaction starts, that's when the reaction is the fastest.  And so from now onwards, you need to know that the initial concentration, at the point  at which you have the initial concentrations, at the point zero, at t equals zero, this  is when the slope would be the greatest.  So if you look at the slope of this graph, it would be like that.  So the reaction is the fastest at t equals zero.  And so the initial rate, so we call this initial rate, and the initial rate is always the fastest.  And in any reaction, the instant the reaction starts reacting, that is at t equals zero,  that would be when the reaction is the fastest.  And then from that point onwards, the reaction slows down.  And as the reaction progresses, you'll see that the rate of the reaction slows down.  So now let's go back to that reaction that we looked at.  So we looked at the reaction of 2N02 gas going to 2N02 gas plus O2 gas.  And if we wanted to represent this reaction in the form of a graph, we said if we're looking  at a reactant, the concentration of the reactant always decreases as the reaction progresses.  Now we can also give rates in terms of products.  Remember we said the definition is what?  The rate of a reaction is the change in concentration of reactant or product as a function of time.  So we can also look at the speed of this reaction or the rate of this reaction in terms of products.  So if we were to plot a concentration versus time plot, so now we're looking at concentration  versus time.  Here the unit is always moles per liter, time is always seconds, and let's say on this scale,  this represents 0.0100 molar.  And if I'm looking at reactant, I said the concentration of the reactant would decrease  and this represents the concentration of NO2.  Now if instead I'm looking at products, now what happens is the instant the reaction starts,  we have no products.  So if I'm looking at NO, we know the instant we start, we have only reactants and zero  products.  But as the reaction progresses, now what's going to happen to the concentration of NO?  Is it going to go up or is it going to go down?  It's going to increase.  So if I wanted to represent that, then I know that my products are going to increase and  it would increase like that.  And so this represents the concentration of NO, the product.  Now if you look at the stoichiometry, you can see that for every two moles of reactant  that's consumed, how many moles of this product is formed?  Two.  All right?  So we know that in terms of moles, two moles is consumed and two moles are formed.  So if we look at concentration, because they're all together, can you ever see the volume  would be the same?  So if I had one liter volume, then you can see that you have two moles per liter and  as two moles per liter is consumed, two moles per liter of product would be formed.  So the change in concentration as the amount that's consumed will always be the amount  that's being formed on this side.  And can you ever see on the other side when we look at oxygen, for every two moles of NO2  that's consumed, only one mole of oxygen is being formed.  So only half as much oxygen is being formed.  So if I take this, and if I take this to be 0.0050, which is exactly half of that, now  if I take oxygen, oxygen, this would represent oxygen.  Can you ever see that, the concentration change in terms of oxygen?  Because for every two moles of reactant that's used up, only half as much oxygen is produced.  All right?  So if I want to talk about rate in terms of NO2, we said that this is the change in concentration  of NO2 and we put a negative sign in front to remind us that NO2 is being consumed, we  say change in concentration of NO2 divided by delta T.  If I'm talking about rate in terms of NO, now I no longer need to put the negative sign  in front because it's not being consumed, it is being formed.  So usually we don't put a sign in front, we just leave it blank because we know it's  positive.  But just for you to begin with, just to remind you, I'm going to put this positive sign because  now when we look at NO, we know that NO is being formed.  And so that's why, because it's not being consumed, its concentration actually increases.  So when you take final minus initial, you'll always end up with something that's positive  because your final concentration will be much higher than your initial concentration.  And if we're looking at, and these refer to instantaneous rate, okay?  And if we're looking at rate in terms of O2, then it'll be, once again I'm going to put  a positive sign, we don't usually put a sign in front of that, but this is just to remind  you the contrast between this.  You have a change in concentration of O2 as a function of change in time.  Does that make sense to everybody?  So you can give rate in terms of reactants or products.  If it is products, it's the change in concentration of products divided by the change in time.  And when we talk about instantaneous rate, it's a change in fractional change in time.  All right?  An instant before and an instant after the particular point in that graph that we're  interested in looking at.  Okay?  Now, if you want to look at the relationship between the three speeds, because remember  the speeds can be different or they could be the same.  All right?  So relationship between the three would be that if I take the speed of NO2, can everybody  see this will be the same as the change in concentration of NO over delta T?  Because for every two moles that's used up, two moles is being formed.  So we know that for every two moles of the reactant that's being consumed per one liter,  you're going to get the same amount of NO being formed for that instantaneous rate and  therefore they should equal each other.  But remember, oxygen will be half as much.  So if I wanted to make oxygen which is half as much equal to this, what do I need to do  to oxygen?  Can everybody see?  I'll need to multiply it by two.  All right?  So if I wanted to make this equal to the concentration of the speed or the rate of oxygen, I will  have to say this equals two times the change in concentration of O2 over delta T.  Also, can everybody see that this is a negative sign because it's being consumed?  And remember I said before that's a negative slope.  If you were to look at the other side, it would be a positive slope as they keep increasing  and therefore you can see that this would be positive and this would be positive.  So I can write the same thing and say or I could say that this is negative one half delta  NO2 over delta T equals positive one half delta NO over delta T which equals delta O2  over delta T.  So if we're comparing the instantaneous rate at the same instant in time between the reactant  that's being consumed and the products that are being formed, can everybody see that that  would be the relationship?  So it turns out depending on the balanced equation, if you pick one, let's say initial  at T equals zero what the rates are, this is the relationship between them.  Or let's say five seconds into the reaction, if I want to look at the relationship between  the instantaneous rate between the three, that would give me the rate.  The relationship.  So if I wanted to look at this in the general form, so for the general reaction, and I look  at the general form of the reaction and let's say we're looking at A plus B reacting to  give you C plus D, alright, then the general form of the reaction would be, if you're looking  at the relationship between the rates of reactants and products, this is a reactant so it's going  to have a negative sign.  One over A is the coefficient, change in concentration of A versus change in time.  This is a reactant so it's going to have a negative sign.  One over B, the coefficient of the balanced equation, would give you delta change in concentration  over change in time.  Now we're looking at products, so it would be one over C, delta change in concentration  of C divided by delta T, and if I take D, it would be one over D change in concentration  of D over delta T.  So for any general form of the reaction, if you want to look at the relationship between  the relative rates of reactants and products, you turn to the balanced equation.  So let's take a quick example.  Now if you were asked to plot a concentration versus time graph and show what it looks like  for this reaction.  So we're going to look at the reaction 2 and 205 giving you 4 and O2 gas plus O2 gas.  So for any given reaction now you should be able to plot a concentration versus time graph  for reactants and products and then show the relationship between the relative rates of  the reactants and products.  So if I wanted to plot this, then what I would do is I will plot concentration versus time.  Let's say this is all of moles per liter, this should be in seconds.  Now can everybody see that the reaction, the sort of the relationship is 2, 4, 1.  So on this scale, if this is one molar, this is two molar, this is three molar, and this  is four molar, we can see that let's say that because the stoichiometry is 2 to 4 to 1, we  know that to begin with N2O5 would decay like that.  So let's say that the concentration of N2O5 is 2 molar.  So this would represent the concentration of N2O5.  Now for every two moles that's consumed, you're going to get 4 moles of NO2 so that you have  to end up with twice as many.  So that means that this would represent NO2, the relative change of NO2.  You just have to make sure that the ratio is this is twice as much.  Now what about oxygen?  So that means if this is two molar, this is four molar, then this has to be one.  So you can see that this would represent the concentration of O2.  If you were to plot a concentration versus time plot for this particular reaction, this  is how the profile should look like as you look at the relationship between reactants  and products.  Reactants will be consumed, their concentration needs to decrease.  Products will be formed, their concentration needs to increase.  Now if I want to look at the relationship between the relative rates of these, our reactant  is N2O5 so there's a negative sign, a negative one-half change in concentration of N2O5  divided by change in time equals the products which is one-quarter change in concentration  of NO2 over delta T.  And over here, this would be change in concentration of O2 divided by delta T.  You see that, that would be the relationship between the three.  Now one of the assumptions that we make in all of this is as all of you know, all chemical  reactions, the majority of chemical reactions are reversible.  And one of the assumptions that we're going to make when we look at these reactions is  that the reactions go only in one direction.  Both reactions are reversible.  So if I take this reaction of NO2, 2NO2 going to 2NO plus O2, we know that this reaction  is reversible.  So that means there's a forward reaction and that would be 2NO2 going to 2NO plus O2.  There's also a reverse reaction where we're looking at 2NO giving you 2NO plus oxygen  giving you 2NO2.  So this is what we call the forward rate and this is the reverse rate.  And in reality, when we do experiments, what we actually measure is the net rate, which  is always the net rate equals forward rate minus reverse rate.  And in reality, this is what we measure, what is measured experimentally.  All right?  However, from now onwards, we're just going to always ignore the reverse reactions.  So for convenience, we will consider only forward rates.  All right?  So from now onwards, I just want you to keep in mind that it gets more complicated if you  have to take into account the reverse rate as well.  Can you tell me only in one instance will the reverse rate be zero?  When is the reverse rate zero?  Initial.  When t equals zero, can everybody see that the reverse rate will be zero because there  are no products to react to give you reactants.  All right?  And so if you take the t equals zero, initial concentration, the initial rate will always  be the forward rate only.  Got it?  So next time, we'll look at this in greater detail.
General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__0_239.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__240_287.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__288_335.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__336_383.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__384_527.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__528_587.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__588_647.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__648_707.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__708_767.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__768_815.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__816_935.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__936_1007.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1008_1055.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1056_1139.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1140_1259.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1260_1307.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1308_1367.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1368_1427.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1428_1499.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1500_1607.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1608_1667.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1668_1751.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1752_1799.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1800_1847.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1848_1955.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__1956_2003.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__2004_2063.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__2064_2111.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__2112_2171.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__2172_2219.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__2220_2315.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__2316_2399.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__2400_2483.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__2484_2759.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__2760_7319.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__7320_14243.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__14244_18575.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__18576_23159.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__23160_30479.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__30480_31883.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__31884_36623.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__36624_43115.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__43116_53627.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__53628_64187.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__64188_66143.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__66144_70319.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__70320_71855.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__71856_74903.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__74904_74951.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__74952_74999.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__75000_75047.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__75048_75095.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__75096_75479.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__75480_75659.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__75660_75707.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__75708_75923.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__75924_75971.png General_Chemistry_1C__Lecture_22__Chemical_Kinetics_Pt__1__75972_76047.png