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# Lecture 24. Chemical Kinetics Pt. 3.

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#### Automatisierte Medienanalyse

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OK I was going and start if I could have everyone's attention please their I want to make 1 quick announcement and that is I want to remind everybody that there are borders points for completing the so if you guys want the beginning of a quarter I said that there was 1 during the 2nd week of classes and I hope that you completely image from the 9th week of classes and the last hard to complete 2 earned those bonus points is to complete the teaching evaluations as well completely surveys are right you complete all that you will get the bonus points so please take the time to complete it and I would appreciate it if you would comment on the online homework and you sapling before and using wireless Wasyliszyn listen up on you can comment on what that would be great alright alright so you guys remember the last time we started looking at what we call the integrated weight-loss case as we will see later on it's important for us to figure out the rape laws that corresponds to a reaction we will see later on that we can use that to obtain information about halfway all right but before we start looking at pathways 1 understand what it means when we say the rate of reaction and we said the only way you can establish the rape is to carry out experiments in being there look at rate With his concentration all look at concentrations versus time are and we said that even tho we will look at how we can use the rate of reaction and the concentration of the reactant to figure out the Brady law on the order of the reaction but was unfortunately actually executing them in the laboratory becomes harder because measuring rate accurately of precisely sometimes is difficult and so we have a different approach will we look at concentrations versus time and we drive a mathematical equation that describes the concentration versus time dependence and
last time we derive expression for the 1st quarter of reactions to here just 1 reactor and for a first-order reaction we said general forward with the reaction turns out to be line -minus Alinghi's 0 equals minus and so if we rearrange that equation into a form that gives us while calls and experts say we can see that we end up with a straight line with a negative slope said you plot the natural log of the concentration of your react as a function of time and you have a straight line which is with negative slope it means that that the is first-order so what do you do so this is much the last can essentially what you do In that different time intervals you measure the concentrations of no remember the concentration of is the amount on reacted alright so as the reaction progresses the concentration of these is the amount that's left on reacted located and so different time intervals you can measure the concentration of being at the beginning .period equals 0 . it will be a 0 and you just mentioned the conservation at different times and now you can't take the natural law that they and you make a graph in the Intergraph turns out to be be a straight line the negatives slower than you know it's first-order right you don't end up with a straight line graph for the slow it means it's not restored parity .period status but it looks something different then you know there's no 1st will begin now having said that I know of this fine in new terms that would look at and this term is called half life so the half-life is the time it takes for the concentration of reactant 8 to fall to have its original value so if violinist applied instead of plodding natural log if I wanted just plot the concentration of me as a function of time all right and so if there s whereas the initial concentration then we know that indicators like cats instead of plodding natural log indeed versus time you just plug concentration versus time this is what it would look like the plot OK now have collided with the time it takes for the original concentration to be happy so it's exactly half of the year In the exactly half of that this would be we have the original concentration and we call that the time it takes is called the pact subsequent have indicate the half-light so the half-life is the time it takes for the regional concentration to be happy but not right take this concentration which is half the amount and look at the time it takes for it to be halved that would be now the concentration would be at a quarter review started with NBS it would be 2 where this is 1 to have and then this is the other team have and City have to have instituted case now he wanted to take the poor amount and the time it takes for the quarter amounted to become 1 eh would be that and that is 3 or treaty halves and that becomes the 0 . 8 and so this would be but the the time will be the same located my plot looks like this is a little longer but in reality it is 2 days for the 1st half life but take another 2 days the 2nd half life so the 2nd half life would be 4 days In the 3rd half-life would be 6 days duration so it's the time it takes for the regional concentration to be happy arrange :colon have so wanted to write an equation for Half-Life we can say at half alive we know that the concentration of game is half the original concentration and now becomes tedious because recall that the time it takes for that is half life and quality so they go back to the original equation that would July for the first-order reaction we know Ellen L a Over a 0 equals minus 18 and we know that half-life this becomes L ln a is now equal to the and that would be over at 8 0 0 equals minus Q t hat tease have of sentiment during his employers in this tournament that and this will become the half-life a so you can see the regional concentrations would cancel out there for LAN one-half equals a minus t hat as a negative sign here and to get the latest sign and we take the inverse of That's so if I take Ellen have mathematics is the same as negative Ellen to equals case 10 right and so now the reader is that turned 50 hostages the half-life and so if I rearrange that equation team have but this is not a sign there as well so the 2 men signs get rid of each of the TV have equals element to Over the rate constant King Illinois to is 0 . 6 9 3 1 divided by case so they're half-life is it's . 6 9 3 1 divided by the rate constant and that's what make so if you want a capital with a first-order reaction has 1 reactant anyways calculate what is the half-life rebel what is what is the definition of half-life the time it takes for the regional concentration started to be happy a pair still like this in a problem so he returned to this problem OK so turn to them so here is an example of applying what just learned in a problem what is the rate constant for the 1st quarter the composition of any 205 at 25 degrees Celsius in the half-life eventual fight at that temperature is given came so they tell us it is that it is first-order itself .period detect that what is your
remember so far would derive expression only for 1st orders of this is the 1st order
reactions and we know that is the half-life for this is TV have equality 4 . 0 3 times 10 to the 4 seconds they want to know what is the rate constants that reaction right so so I know that the only relationship between these 2 that we looked at thus far is that's the have articles . 6 9 3 1 divided by I know what this is this is a number this where to find it so you can see case he was . 6 9 3 1 over have and therefore Katie calls . 6 9 3 1 divided by the half-life adjust .period 4 . 0 3 times 10 to the power for 2 seconds and so on if you put that in calculating work that out it comes out to be 1 . 7 2 times 10 to the negative 5 and you can see that the unit is Pesek Lemaire case rate constant and the unit for a constant varies depending on where they what the order that reaction answers 1st order and you can see that's the unit for the rate constant so that's pretty straightforward there have calculated that now for the 2nd part of the under the same conditions 1 percentage of 5 molecules will not have reacted after 1 day all right so what they're asking is when the team is 1 them they want now what is the Percent I'm reacted so we figure out Percent under the act the case so if you want a cup the dissent and reacted now we have to make use of our integrated great law and we know the integrated rape law is Alan 88 divided by 8 0 0 equals minus K. T right for the 1st part we calculated time is 1 day they want to have percentage on reacted to never received this would mean the racial 1 reacted member AEA is always the amount on reacted and says that the amount of reactor it I want have a percentage of what is essentially the amount of reactive divided by what you started with without the toll which is the words of concentration times 1 the possess times 100 to see survivors find the ratio and multiplied by 100 that will give me the Percent on reactor all right so bold and do it this remember figure out what this ratio is so we can say talent Over P. 0 which is due regional concentration or in this case I should put the actual numbers which is Ellen into all 5 the original concentration and 205 equals -minus Now I know my case is 1 . 7 2 times that to negative 5 per 2nd at times time member in Connecticut's What is a unit that we use times 2nd so they give us 1 day so that means I need to convert that 2 seconds so you know that there are 24 hours in a day a 60 minutes an hour and 60 seconds in a minute or so hours announcer consulate minutes and minutes of cancer this is Pesek and and 2nd Council becomes a unit was squandered and so I know that LAN in 205 5 were the original concentration and 205 equals if you take it figure that term out comes to 1 . 4 9 case 3 6 24 hours an exact number of 60 Minutes is an exact number 60 seconds an exact number so we end up with a number that is treating figures all right now I do is taking the inverse long to get rid of the this lot survive take in response on this side and to take English log on that side so what I end up with is 205 divided by the regional concentration into a fight and I take the English flag of that that comes out 2 . 2 3 now remember and taking the inverse logs so if I'm keeping track of Siegfried that I have a tree six-figure number when I go from here to here only count the decimals also goes to 2 significant figures all right and then now that I have figured this out now percentage and reacted would be and 205 divided by by in 205 the original concentration times 100 which 23 per cent all right Solidarity's just taken the value that I counted multiplied by 100 negative said so that means in 1 23 % is left on reactive in resolving a problem you have to ring the question carefully because if they asked to 4 % reactor the person that actually reacted 77 % so when you carry out online homework sometimes the last few for to calculate the person under reacted sometimes lasted calculates the facility reacted and so if political prisoners on reacted you know that some of the has reacted Zaklady literally at the sold-out shows a little at a 1st reaction now reading in the same thing that we've done for the 1st order and we will look at what happens with the 2nd order reactions to limit driving expression for the 2nd order reactions and so if you have a case where just 1 reactant anybody 2nd order we know that the general form at the rate of the rate equals the rate constant cancer a concentration of Asia now his 2nd order is raised to the power to arrive I hope took time to review the stuff that we covered last Friday because this is going to be a little looked at a so all of you know this is the general form of the rate law we know at 2nd order and we know that rate equals K times it to the power to but since the to write an integrated rate along with a new replaces rape law the return with change in concentration incremental change in concentration of 8 as a function of incremental change in time
I would put a negative sign in front because it's a reactant and a reactant is consumed in the reaction came so this equals kid he square all right now I'm going to put all the concentration turns on 1 side and take everything else to the other side and selected the negative signs here I can say this Over the years square equals kid times the 2 right now by integrated over the range of initial concentrations the limits I initial concentration to any concentration In over here that would be at times 0 2 any time t and to integrate the ad which in is 1 over at AA minus 1 over the initial concentration equals case team but so it's a sudden order reaction the greater rate law dependence of concentration on time comes out to be in this form OK so you need to know this equation I want to be these equations so you need to know whether the first-order what equation should be you need to know what the equation would be for a 2nd order reactions at now I want to be arranged this so that I can get it in the form of life for the next seat in other words to figure out which then you know what former this equation will give me a straight line graph I can say now that wonderful were being the cost to 18 plus 1 over his ears and is going to take this term over there so now this will turn out to be the Y axis now you can see that case is the slope time is the x-axis plus seed gives me that intersect so indicate you can see that it's positive and so this gives me a politcal so the general form this reacted by taking less and about phonograph of 1 school where as time this is the Y axis time is the excessive as you can see I end up with a straight line where right so if I were the plot the I would end up with a slow and slope will give me the rate constant and everybody can see but this is a slow that has a positive slope and intercept will be won over the initial concentration so what this means that that by would carry out an experiment the laboratory and so if I were to look at a different time intervals I have different concentrations of aiding and so when at time 0 this'll be the initial concentration and then let's say a 50 second increments of icons and that divided measure the concentration of right now I'm your Excel spreadsheet now you take the inverse of the game and you can put those values are right any bright plot 1 where a recessed time and if I end up with a straight line graph with a positive slope like that and then I know but that the 2nd order are right so you looking at the variation of concentration versus time and say you making a plot and if you make a plan of 1 busses times and you end up with a straight line for the past so that means its 2nd order if you don't get a straight line but if you take these values and take Ellen was this time it gives you a straight line What is that first-order odyssey that you the shape of the fall of the graft and you can figure out which a straight line and I will tell you it's a first-order reaction or 2nd reaction against no we can do the same thing that we did the 1st order and we can
know that the concentration of 88 equals half the original concentration we know all that time now becomes half-life OK so we've got equation was in order which is 1 away the minus 1 over the 0 he calls negative take we know I'd have to life of and replace all of this now this To where 0 when it started I'm doing this 2nd please bear with me I'm thinking about something else so we know that at half alive a concentration of 88 is a 0 divided by 2 and we know t equals T hat and we know for a 0 or reaction from 0 reaction we know this is concentration of aid -minus 0 equals negative came
to the best of 1 0 previously downward for the 2nd order obtained and sold by taking less and now I'm going to say at half life and replaced the terms I know that a equals a 0 divided by 2 minus the 0 equals minus Q t hat producers so now looking at half life and you can see that divide this is 1 this is half the price of tracked 1 from the other without Oleander which is negative is your divided by 2 equals negative Katie have so the negative signs of cancer decide and so on the have the Qualls should concentration divided by 2 kill "quotation mark all right so the great law because you have to divide his mathematically we only look at 3 comment orders the common ones and 0 first-order and 2nd order all right and so we derive the great loss for the 3 now regular class website reduced standing at home I want come summarize everything this way so there's a copy of this in the class website and so what we're looking at it as we looked at 0 my 1st 2nd order arrived the rate of Beaver 0 ordinary people's Kane for 1st radicals Cape Air Race Apollo 1 calls came in at least a part 2 the 2nd order take now the former the integrated that we do I just given here so equals minus Katie plus is 0 Delaney equals minus Katie plus Ellen is 0 4 1 0 the equals KTB was 1 0 with a 0 so this is the form of the integrated great that we do ride again now the plot needed to get a straight line because remember we going to determine whether reaction is 1st 2nd orders are orders based on which plot gives you a straight line so for for a 0 . 8 versus the with straight line the the negative small a case slope will be negative case here Allen for a first-order Ehrlich what did you a straight line graph with the negative slope and 1 0 Sistine will give you a positive slope for a 2nd or reactions so that's why we dropped 3 grass and figure out which 1 of these will give us a straight line again lastly the half-life equations that we derive is given here so a 0 orders this half-life for this is and half-life for 2nd order in that case you need to remember these equations ride on any you weren't enough examples like the whole work as well as the online homework division of practice so that now we should be able to know which equated to use to figure out the half-life of 0 order half-life 2nd order and half-life for first-order is unclear to begin with this handy with you dissertation on the wall is carrying out homework is good that table and you can look at the property equations and after a while it was so comfortable in that he no longer believed that table right now the problem is that up to this point we will look at that is only 1 reactor are right and is only 1 reactant then it's pretty straightforward what we had to figure out the order when you have more than 1 reactor alright so you during the next stage we have to come up with something more clever to figure out the integrated rape last you have more than 1 reactor now you guys remember previously when we looked at the rate versus concentration memory said we designed experiments so that we can cancel out 1 reactor in America we worked at problems last Friday we said want to go the the order the reaction is we actually designed experiment so that would keep the concentrations you know major rate at different concentrations but here than 1 reactant always keep the concentrations of 1 of those reacted the same sort the cancel out and change only the other alright likewise 1 means the integrated rape law we have to design experiments in a special way right so so obvious considered great weight loss the simple reactions with only 1 reactor it turned out special approaches are required to with more complicated reactions right so let's say that we are looking at OK so if I want to write the losses looking at our 2 reactants and I wanted figure this out of the rape law as all of you can see rate equals King concentration it lets race the power and Times concentration of B Race to the power in OK so now we have designed this in a special way so that we can look at the rate of 1 at a time and the way we do that is to be set up the concentrations so that concentration is really small this is the order of 10 to read the other is 1 more 2nd you see the difference between the 2 reactants is about thousandfold right so we specially designed experiments so that the concentration of 1 reactant is kept small but give the order of 10 3 and the other is of the order a thousand times more like 1 and the reason is that the reaction takes place the small concentrations limiting reactant all right and so what's going to happen the smaller 1 is only going to react and relative to the smaller concentration the media concentration doesn't appear to change because remember limiting reactant is a thousand times more so the reaction takes place at nite at the scale of tend that 3 and a 1 although which is a thousand times more concentrated stays relatively unchanged for
the scale of the the reaction to receiver and so it happened that that we set it up so that we can take care is along with smaller concentration the is the 1 with the larger concentration so be concentration is much much greater than what happens because this is much much greater it appears relatively unchanged and so on what happens if as the reaction progresses the concentration of the does not change all that much so will approximated sale but as the reactor progresses the concentration will always be new regional concentration which is a constant our right to the door the rape Lowry said rate people came in a race to the power and the race apart and we can say now we can replace the concentration of the but the original concentration of the and can everybody see that this term does not change services a constant all right so because this is a constant and include this with the constant and I came up with the following which I call this is called the suit or a constant it's not the real rate constant but because this includes the rate constant escaped prime exactly the will rate constant which is this case times this constant which is the concentration of the do I see that it's essentially what I'm doing is by keeping 1 concentration with large I'm making it look like the W 1 reactor right because 1 concentration does not change and now what have would to do is carrier this experiment and I would take a different time into worlds I will look at concentration of the is not changed the constant so at equals 0 this'll be a 0 and all measure the concentration all right no I will take Ellen and I also plot 1 0 with a but and in this way I will see whether I am out which of these will give me a straight line wrapped so if this is experiment being over here this is experimenting and you can see now which which language a straight lines Illinois it is eliminated was this time to straighten what is at times its 1st order in our rights and the slope that I calculated this is where you wanna watch out this slope so let's say that I thought this out and I end up with the talent versus time would give be a negative slowly OK so these other points on that aircraft now the these make a crime which is the Sunil rate constant Our because of reduced this To look as the only 1 reactant right the rate constant is the single rate constant would just keep got it so now I have to repeat his experiment and do this all over again but now I have to to keep in concentration 1 more and the reverse of the nominating read the 1 that is small in concentrations are so now we consider a concentration is far greater than the and therefore now the 1 that will be constant would be the externalities conceded this term is constant all right so now this equation would users to rate equals kg double crime this is a different 1 K double crimes times be raised to the power and and so now once again have to repeat his experiment where the and now I'm looking at concentration of being so that this will be 0 this'll be the initial concentration of the to begin with a different time increments I will measure the different concentrations of the 0 now I will have to look at Elland be Weir says 1 over being "quotation mark but but and so you have to do to experiments and so on that returned to experiment the now I want to look at this this is the worst this time is that a straight line no this is 1 of the worst this time is that a straight line no but if I take Allen Lee was this time it gives me a straight line with the negative slope so what is what is it that water with respect to be 1st are right so now from this life and now this slope that I get so once again it just so happens that you had Ellen with this time gives you a straight line and so these points would be what you would call figure out and now I can see this slow would you make a double crime all right and we know then that is 1st first-order as well but I do not interest in a single rate constant analysis and keep climbed the their minds that interesting case novel crime need to figure out OK so now I have to get out of 1st order I think will pick any 1 of these schools and I that cheered crime equals the real rate constant times the original concentration of me Race to the Pole 1 that I know this number have got from there "quotation mark this if the original concentration which is 1 will have already figured out its 1st order a writer so now I can rearrange that and find out what the real rate constants that re-educate equals Cape Prime over initial concentration Over the region of Thrace the power line because its 1st order some accessories you can use the same equivocated novel prior management of the semantics 1 rate constantly see that you can use a kid line that so great constant experimentation or you can use a single rate constant from the seller disallowed this is not the
class that are right under your worksheets right and you can see that to different slopes that you will end up
with the same rate constants obtained .period different today
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