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Lecture 22. Chemical Kinetics Pt. 1.

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Lecture 22. Chemical Kinetics Pt. 1.
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UCI Chem 1C General Chemistry (Spring 2013) Lec 22. General Chemistry -- Chemical Kinetics -- Part 1 Instructor: Ramesh D. Arasasingham, Ph.D. Description: 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. Index of Topics: 0:00:00 Change in Free Energy Review 0:01:40 Intro to Chemical Kinetics 0:06:43 Defining Chemical Kinetics 0:09:57 Reaction Rate 0:15:02 Example of Reaction Rate 0:24:41 Average Rate of Concentration vs Time 0:34:13 Example of NO Gas Reaction Rate 0:40:08 Relationship Between Reaction Rates 0:47:57 Forward/Reverse Reactions
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OK How can I have everyone's attention please are there any questions before it began so today we are going to move on to the next chapter which is Chapter 14 in a textbook and will start looking at chemical kinetics are right and so you guys remember before we start talking like kinetics was toppled about the modern and that's because of the last quarter when we look at the we said 1 of the rules of human anatomy 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 use the term spontaneity to describe them and we said that would be amendments helps us explained the spontaneous direction of a reaction and went through the details of that and we said that for spontaneous reactions we said that we look at the minimum free energy and we calculate the changing free energy for reaction that signed comes out to be negative we know that spontaneous in the changes free energy which is delta G is positive we know that is not spontaneous but the reverse reactions spontaneous so let's take this
reaction that we're looking at here were looking at the combustion of methane giving you carbon-dioxide in water and if you calculate the changes free energy for that reaction we know that it comes out to be negative so that's a spontaneous reaction so we would represent less in graphical uniform of what we call the reaction coordinate which is up a lot of the free energy as a function of the progress of the reactor is a reaction progresses what changes it undergoes and the Modinomics regards remember we said that if you take delta G Delta Delta as we all call all state properties and we said state property always depends only on the initial and final states are right so we want to look at the altered gene then we plod the free energy as a function of the progress of the reaction In over here this is the free energy of the reactants and down here you have the the energy of the products into the difference between the free energy of reactants and products member products represent the final state the reactants represent initial state and will save Delta what Delta me he has moved from last quarter it's all a change and what the government and that's what this change me always the final minus the initial so well in the final state which is a part initial which of the reactants and so the difference between the free energy of products and reactants comes out to be negative and so we know that this reaction is spontaneous that know you as a Member repeatedly last quarter when things we said was that we talk about a spontaneous reaction it doesn't tell us anything about how fast the processes so spontaneous change can take place instantaneously an explosively for example all are a spontaneous change can be very very slow so slow that in our lifetime and we may not see a change all right so spontaneous change tells us the natural direction we know that there's a natural tendency that reaction to occur without any external influence however does not tell us anything about how fast the processes right could be very slow or it could be very fast now what determines how fast reactions how fast a wise reactions takes place of that task now falls within the domain of kinetics and that's what we're looking today so you want to look at this reaction quarters that have drawn but this is the initial stage and this is the final stage and that falls in the domain of the modern elements the and it's helps explain the spontaneous direction of reactions and we know that in the modern and it's probably interested is looking at initial and final states the building only at initial and final states recall that a state property and that depends on initial final states and not on pathway that's what it means only status state property and that the only domain we look at Delta GE the free energy change that reaction we can look at and that change with the heat is being released in that the action when the heat is absorbed in that reactions so gives us Delta H where is it gives us entropy change and also equilibrium constants of these are all the Madonna quantities and of 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 no 1 will want to looking at Connecticut and that falls in the middle of the year whichever highlighted in green and this falls in the domain of kinetics and this depends on pathway and the speed of the reactions of we wanted to explain why certain reactions takes place very rapidly and the other reactions that takes place so slow but in our lifetime we don't see any change now that falls within the domain of genetics of Caricom interest in looking at how fast reactions takes place and suddenly but is the pathway turns out how fast reaction takes place depends on the pathway and it takes a visitor will start looking at Connecticut and we wanted to find out what it means when we say kinetics chemical kinetics is the study is the study of how rapidly reactions proceed and so the details then along the way the
reactants transformed into the products right so if you want to find a chemical kinetics this commitment is the study of how rapidly reactions proceed in a detailed events along the way as reactants are converted to products transformed or as the reactors transformed to products To be wording about this today we're going to do a lot of analogies about pathways and 1 way to look at it is you inconsiderate kinetics and was looking at journey all right so intimate and that makes were only interested look view concerning the journey in the modern were only interested in initial and final states so it's like you're taking a launcher it's as if you know where you originate and your destination and the only interested in where you start which is your at an annual ultimate destination that we don't interesting additional final states kinetics were actually interested in the actual journey what is the path we have taken that during 1 of those obstacles along the way that allows you to speed up and slow down as you proceed said today with look at the actual journey and that falls in the middle of so it was going to be interested in the journey and women look at the definition of the kinetics of wages and how fast reactions takes place and the actual events that take place along the way so let us start by looking at 1st look at some definitions and we're interested in looking at how fast the reaction proceeds and so that turn that we use to describe how fast remember it when you're driving a car what you used to describe how fast the car proceeds in a general news speed is in chemical kinetics the term that we used to describe the speed is waiting OK so great gives you used the speed of a reaction that will start looking at what it means when we say it right so will look at what we call this reaction rate and the reaction rate but the chemical reaction refers to it's speed been all of the reactions from
now onwards if we want to look at how fast the reaction proceeds or we call that the reaction rate of case and again member of the analogy is a journey so if you are driving the car and you want to know how fast you proceeding remember the unit that we use to describe the speed of a vehicle is mph and so on the way we calculated the speed is to look at the distance traveled divided by the time it took that's what mph traveled 50 miles and it took you an hour that would be 50 miles per hour right so just as you were when you were trying to figure out the speed of a vehicle it's always the distance traveled divided by the time lapse when we talk about chemical reactions in 1 take a look at we defined rated as changing concentration as a function of changing times so we define a quantity that would call average rate at the
average rate is the average speed of reaction and the average rate is always changed invention in concentration of reactant or product 10 divided by change in time alright so if we take a hypothetical reaction let's say going to be where the reactant is and b the product there the average rate would be we're looking at the reactant it will be the change in concentration of the programmer Delta means change and would put the square brackets indicate concentration and that divided by the change in time so when we talk about rape it's always changing concentration divided by the changing times are right so remember we said Delta represents changes always initial statement the final stage that means the final concentration of Asia minus the initial concentration of gate that's Delta Delta is always remember final minus initialed the final state minus the initial state and so on here we are looking at the final concentrations minus initial concentration divided by the final time give minus the initial time right t yr lower case the 1st time India points to finalize plans the initial and the Union for a it would always be memo looking at concentration so that will be moles per liter divided by sex sold the unit of time that using connect fixes always seconds so sold the unit turns out to be currently there percentage OK so when we want everyone to look at how fast the reaction proceeds then the term that we use to describe the speed at that reaction is Wait reaction rate and reactionary is defined as the changing concentration of either the reactor the products divided by the change in time and scintillating ever-changing concentration you for concentration multiple leaders In the unit 4 times is seconds all right and therefore the speed of the reaction of the reaction rate is always molds for leader of such again now let's take a specific reaction and then look at this in in greater detail myself if I wanted to determine the speed of a reaction than I would have to experimentally measure the change in concentrations as a function of changing times so let's take an example where we're looking at let's say the reactions were looking at is this let's say we're looking at 2 2 gas going to 2 NO plus so we're looking at
this specific example of a reaction and want experimentally measure the reaction rate are right and he wouldn't do that then we take in the reacted or product analysts say we picked this reactor and at different times into roles you would measure the concentration of a note to right now since the reaction is proceeding in the forward direction would you expect the concentration of the reactant to increase or decrease as reaction progresses you expected to decrease so if I were to measure this in the laboratory and will carry out experiment that I would make a table of time 2 and the unit will be in seconds and over here I would look at a concentration of N O 2 all right and it would be moles per liter case Alabama looking at time t as a function of concentration and let's say we're measuring this in increments of 50 2nd solved I would measure the concentration act equals 0 hour ride and the concentration of people 0 really . 0 1 0 0 and you know what is the term that we use to describe the concentration at times 0 what we call that initial concentrations of recall so this would be the initial concentration it's obvious and that would refer to and 2 AT T equals 0 so that would be in order to use subscript 0 to indicate that that's equals 0 then will make a measurement at 50 100 to 150 and that's the 200 seconds and if you were a character in the laboratory this will come out to be 0 0 79 this be 0 0 6 5 0 0 find 5 and this would be 0 0 4 8 .period so we measure the concentrations at different times interrupts Sinaloa figure with the speed of the reactions and 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 picked out so I could happen average rate from 0 to 200 seconds all right but what they do or preserved 100 so I'm is for a convenient way to look at what is the speed of this reaction at every 50 second increments are right so that wanted account with the average rate I can say the average rate during the the 1st 15 all right so let's look at the average rate during the 1st 50 seconds and then by definition we now that average rate is a change in concentrations of NO 2 as a function of changing times which is the final concentration minus the initial concentrations of me the concentrations of NO 2 final -minus in 0 2 initial divided by the final minus t show which areas will get the 1st 50 seconds so the final concentration will be 0 . 0 0 7 9 minus 0 . 0 0 1 0 0 and same is in moles per liter divided by 50 miners 0 and that means 2nd case of looking at the average rate with the fighting will look the Chadian concentration the 1st 50 seconds divided by the changing times and 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 a negative and it comes out to be negative for . 2 times 10 to the negative 5 molds presently there per 2nd are right and so we end up with a negative side not all you recognize that we're looking at rate of speed and it turns out speed does not have a sign right it's the analogy is don't you can be driving your car at 50 mph the 4 directional just 50 mph the budget controversy angle backwards at 50 mph what is your speed it's still 50 mph that's the speed at which a so I'll speak this have directions you understand or science and so on In got to get rid of this sign this negative sign what we do know is moved the negative sign over here and the reason we're doing that is because we all understand that speed has no side there's no negative or positive alright and so to get rid of his negative side we bring it over here and say now that the equals 4 . 2 times tend to 5 moles per liter per 2nd all right and then sign on the other side just reminds us that this is a reactor because when reactants that consumed their concentration decreases and that's when you count the Delta for reactants you always end up with the native son obtained so we will then be assigned to the other side and the negative signs here is just a reminder to us that we're looking at reactants because reactants will always be consumed in reaction a so this is for the 1st 50 seconds nite I calculated the average rate during the 2nd 50 seconds and Italian carrier the same calculation will end up with negative Delta and want to divided by Delta T with equal 2 . 8 times tendinitis 5 moles Prince leader per 2nd right and thereby wouldn't do the same thing but that the 50 seconds and negative going on so will start the 3rd wants to buy calculated the average Ray during I need there 15 seconds now this would also be negative Delta In to divided by by Delta T the 2 . 0 times tend to negative 5 moles per liter Pesek so compared those speeds during the 1st 50 seconds with the 2nd 50 seconds and the 3rd 50 seconds and what does that tell you about the speed of the overall reaction it's actually slowing down our says the reaction progresses you can see that slowing down our right and so that's important to remember because when you look at how fast reactions proceed when you look at reaction rates all the actions of the fastest when they begin arrive and as a reaction progresses the slowdown all right until they reach equilibrium again not 1 of things you notice says there were looking at average rate average rate is not a really useful quantities wine the average rate will depend on the time increment that you pick we just so happened to pay 50 seconds as I increment all right if I had picked 100 seconds as I increment then I would end up at different speeds to resent at different rates might take 200 seconds I would end up with a different increment became so opulent we use the average rate I want 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 a different time spans the new rates and the different opinion not the 1 to represent this graphically the same thing that we just looked at me can represent us in the form of a grass and so if I would represent this graphically I would plot concentration versus time so when and the
concentration of an old 2 on 1 side are right and this would be In units of moles per liter a malaria and we're looking at a time and in Connecticut the unit 4 times that is 2nd and where where we started where this would be . 0 1 0 0 more that's the
concentration of the stock and as the reaction proceeds we know all the concentration decreases and it will decrease in that way exponential and it will flatten out and widest concentration like no it never goes to completion it stopped short of any flattens out and why it is that the concentration of the reactor can flatten out because remember it has achieved equilibrium OK when equilibrium established the flat now out and it'll never go to 0 because it establishes equipment for that dozen good completion because establishes equilibrium so in this that if I wanted to so this would be this would be my my initial concentration of NO to the point at which I
stopped take and level measuring this in 50 second increments of this will be 0 seconds this'll be 50 let's invest 100 that's 150 that's 200 take so if you were doing this in the laboratory in carrying out an experiment than the easiest way to figure out what the average speed is during the 1st 50 seconds is to draw a tangential lines so it is an interested in figuring out that there the average rate in the 1st 50 seconds and so I can draw attendance a line that links the 2 and if I calculated so this will be 10 feet and if I wanted to capture the average rate for this might average rate would equal the change in concentration of N O 2 over change in time and member with a negative sign in front of that to remind us that it is being consumed so the smoke comes out to be a negative slope are actually on the public and so on you can take the slope of that and will give you the average rate and if you want to do the same thing but a 2nd 50 seconds it would take the slope Of that line and that would give you the rate at 2nd 2 seconds and as you can we recognize that as you go down the slope decreases in that tells you that the rate of the reaction to that case so if you want to do this graphically in the laboratory white account average rate you can figure out the slope that corresponds to the time lapse but as I said before average rate is not useful quantity because it means that the average rate will depend on on the time spent the people and that vary from person to person occasion we need something more something that is more precise form allows us to look at it in terms of not having this variable In time spent case and what what views is what we call instantaneous type and an instantaneous and instantaneous rate gives you the raid at an instant in time operates a woman so a more useful quantity here is the instantaneous rate of the instantaneous rate us the rate reaction In the particular for the moment in time all right so the way I look at instantaneous rate is if we decrease delta T and make it smaller and smaller and smaller and smaller and smaller too to a point where it's just an instant a moment in time of fractional 2nd before 2nd after an instant in time and ask given as the instantaneous rate so we want to look at instantaneous rate instantaneous rate I would be the range at any given instant in time identity represents that the the way in which the change in time as a fractional 2nd before that Dr. infractions 2nd after that .period your standard and that gives you the race what we call an instantaneous rate and graphically the way you figure out an instantaneous rate is to draw up a small quiet character line that just wants to that 1 .period like that arrange an invite calculated the slope that corresponds to that what I did is now instantaneous rate and this would be the change in concentration of N O 2 for a change in delta T but now this corresponds to the delta T he is now a fraction of it you know if you take that point it's a fraction of a 2nd before fractious 2nd afterward and that gives you the instantaneous rate design accessory so rather than calculate the slowly based on a 50 second increments here now we the slope this touches that 1 single point and we find potential slope that goes to that 1 single point and that gives us instantaneous rate so now you can see that we look at incentives right now we don't have this variation in time span it's no longer 50 seconds 100 seconds of 200 seconds which which depends on who is looking at 1 end to the average would depend on the time span now willingly to instantaneous rate you can see now it makes it independent of that are and therefore from now on roads we talk about rate we will always look at instantaneous rate we're looking at that rated at any given instant in time now once again if you take instantaneous rate and if you look at any point in this crap if I take this point and I look at that and
you see that the slope it would be greater so as you keep as the reaction progress as you can see that the soul decreases and therefore once again you can see that in view of the instantaneous rate you can see that the speed of the reaction slows as the reaction progresses are so violent that instantaneous rate where you'd think the the reaction would be the fastest at equal 0 Aparecida that went to equals 0 the instant the reaction staff starts that's when the reaction is the fastest all right and so from now on would you need to know that the initial concentration at the point at which you have the initial concentrations of the . 0 at 2 equals 0 this is 1 the school would be the greatest so you look at the slope of this craft could be like that cake so the reaction is the fastest AT T equaled 0 or that and so the initial rate so we called the initial raid and initial raid it is always the fastest and in any reaction that instead the reaction stocks reacted that isn't equals 0 that would be when the reaction is the fastest in and from that point onwards the reaction slows down that came as a reaction progresses we'll see at the rate of the reaction slows down OK so no let's go back to that reaction that we looked at OK so we hear we looked at the reaction of 2 known to I'm going to to NO gas plus both to get our rights and we wanted to the represent this reaction in the form of a program we said we were looking at a reactor and the concentration of the reactant always decreases as reaction progresses now we can also give rates in terms of products are at levels said the definition is 1 of the rate of reaction is the change concentration of reactant all product as a function of time so we can also look at the speed of his reaction of the weight of this reaction in terms of products so there we were at a loss at concentration versus time so now we're looking at a concentration versus time here the union is always moles per liter times always seconds and let's say on this scale this represents . 0 1 0 0 Moeller and about looking at reactor and I said the concentration of the reactant would decrease and this represents a concentration of 1 or 2 now if instead of looking at products now what happens is that instant the
reaction starts we have no products Our writes about looking at NO we don't the instant we start we have only reactants and 0 products right but
as the reaction progresses now what's going to happen to the concentration of NO it's going to go up down it's going crazy alright so that water represent back then I know that I products are going to increase and it would increase like that the case and so this represents the concentration of power NO the program no look the story geometry you can see that for every 2 moles of reacted that's consumed how many malls of this product is formed 2 arrange so we know that in terms of malls to malls is consumed and 2 moles of form obtained so we look at concentration because there altogether never the volume would be the same so if I had 1 liter volume that I you can see that you have to multiple leader and as to multiple leader is consumed 2 most believe your product reform so the changes In concentration as the amount that's consumed will always be the amount has been formed on the side obtained but Tennessee on the other side of look at oxygen for every tools of NO 2 that consumed only 1 wall of oxygen is being forms only half as much oxygen is being formed to buy take theirs and by taking this to be . 0 0 5 0 which is exactly half of that now if I take oxygen oxygen this would represent oxygen the receipt of the concentration change in terms of oxygen because for every 2 moles of reacted that's used up only half as much oxygen is produced all right so if I want to talk about weight in terms of of the of N O 2 we said that this is the change in concentration of N O 2 and would put a negative sign in front to remind us that in 0 2 is being consumed we say changing conservation and 2 divided by Delta if I'm talking about greater in terms NO now I know longer need to push the negative sign in front because it's not being consumed is being formed so users will put a sign in front just blind because we know it's positive but just for you To begin with just to remind you I know but this positive signs because now we look at it and now we know that in all 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 always end up with something that's positive because a final concentration would be much higher than initial concentration obtained and were looking at and his referred instantaneous rate and we're looking at rates In terms of 0 2 then once again on a part of the positive side will it was a sign in front of that but this is just to remind you the contrast between this you have a change concentration 0 2 as a function of changing times does that make sense a ready so you can give me great in terms of reactants a products that its products is a change in concentration of products divided by the changing times and we talked about instantaneous rated it's a change in factual changing times are an instant before an instant after the political point that aircraft that was interested in looking at a case the everyone look at the relationship between the 3 speeds because members of the speeds can be different for they could be the same arrived so relationship between the 3 it was the for would be that invited the speed of NO to can ever see this will be the same as the changing concentration of NO we dealt such because for every 2 malls that's used to malls is being formed so we know that for an Reed to moles of the reacted that's the consumed per 1 liter Givens get the same amount of NO being formed for that team instantaneous rate and therefore they should equal each other but remember oxygen will be half as much it's about where make oxygen which is half as much equal to this 1 lady due to oxygen in resounding to multiplied by 2 all right so that I wanted to make a sequel to the concentration of at the speed of the rate of oxygen I will have to say this equals 2 times the change in concentration of 2 were dealt take also see that this is a negative sign because it's been consumed in reverse said before that slope we will look at the other side of the positive slope as they keep increasing and therefore you can see that this will be positive and this would be possible again so I can write the same thing and say or I could see that this is negative and one-half Delta N O 2 Over Delta T positive one-half Delta NO 4 over delta T which equals Delta too Over delta T compared the instantaneous rate at the same instant in time between the reacted that's being consumed and the products that have been formed can a that that would be the relationship a cake so it turns out depend on the balanced equation if you pick 1 lets initial x equals 0 what the rates are this is the relationship between them are at let's say 5 seconds into the reaction from 1 look at the really relationship between the instantaneous rate between the thing that give me the rate of care the relationship so if I wanted to look at this in the general form so that the general reaction
and the general Coleman the reaction and that's it we're looking at any must be reacting to give you see plus the RIA the general form of the reaction would be built the relationship between the rates of reactants and products this is a reactant and have a negative sign 1 or where a is the coefficient changing concentration of 80 process changing times this is a reactants it's contaminated signs 1 Overby question the past equation would give you Delta changing concentrations over changing times now looking at products so the 1 always see Delta changing concentration of C divided by Dr. T. inviting the of B 1 windy changing concentrations do call for Delta to suppress any general former the reaction if you want to look at the relationship between the relative rates of reactants and product returns to the balanced equation there so let's take a quick example Mountain View were asked to a concentration versus time grass and show what it looks like for this reaction so willing to look at the reaction to into all 5 giving you for NO to gas plumber "quotation mark to death all right so let's so for any given reaction are usually able to plot a concentration versus time Graf for reactants and products and show the relationship between the relative rates but the reactants and products of cases like wanted a lot less than what I would do is I will plot concentration versus time let's say this is as all of you know most believe there should be insects not can the reaction at the rear the solar relationship is to fall 1 OK so on this scale if this is 1 molar this is to Moeller this is 3 Moeller and this is formally we can see that lets say that because the stock geometries 2 2 4 2 1 we know that due to begin with into all 5 would decay like that this was a let's say that the concentration of into flight is to Mohler so this would represent a concentration of into a fight all right now every 2 that's consumed giving 4 walls of N O 2 so that it you have to end up at twice as many so that means that the US would represent an ode to the wrote change of NO 2 you just have to make sure that the ratio it this is twice as much obtain what about oxygen so that means this is to Mohler services for wear and this has to be 1 of Casey concede that this would represent the concentration of 0 0 2 so you would have a lot of concentration versus time slot for this particular reaction and this is how the profile should look like as you look at the relationship between reactants and products reactants will be consumed their concentrations decrease products reform the concentration needs to increase that I will look at the relationship between the relative rates of these are reactant is into all 5 so there's a negative sign and negative 1 one-half change in concentration into all 5 divided by changing times equals the products which is 1 quarter changing concentration in order to over delta T and over the air this would be change in concentration of both to divided by Delta T see that that would be the relationship between the 3 all right now 1 of the assumptions that make In all of this is all of you know all chemical reactions the majority of chemical reactions are reversible all right and when the assumptions that will make when we look at these reactions is that the reaction school wounding 1 direction are most of the actions of our are reversible so it might take this reaction don't 2 to N O 2 going to to end all plus 0 2 we know that this reaction is reversible indicated so that means there's a foreword reaction and that would be to N O 2 going to to NO possible to there's also a reverse reaction while we're looking at 2 NO giving you 2 and less oxygen giving it to In order to write so there what we call the fall would bring it and this is the reverse race OK and in reality when we do experiments will we actually measure is the net rate which is always the net weight equals forward rate -minus reversed rate right In reality this is what we measure what is measured experimentally of right however From now on words we're just always ignored the adverse reaction so for convenience we will consider only wearing rates are writer from now onwards I just want to keep in mind that gets more complicated if have to take into account the restraint as well here can you tell
me only 1 instance well the the 0 when reverse rate 0 initial went equal 0 commemorates the that the the reverse rate will be 0 because the final product to react to the new reactants right and so you take effect equals 0 initial concentration the initial rate will always be the forward rate only got so next time will look at this in greater detail the