Lecture 23. Chemical Kinetics Pt. 2.
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Lecture 23. Chemical Kinetics Pt. 2.
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Lecture 23. Chemical Kinetics Pt. 2.

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23

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26

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2013

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English

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Abstract 
UCI Chem 1C General Chemistry (Spring 2013) Lec 23. General Chemistry  Chemical Kinetics  Part 2 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 acidbase equilibria, solubility equilibria, oxidation reduction reactions, electrochemistry; kinetics; special topics. Index of Topics: 0:00:00 Review on Rates 0:04:02 Kinetic Rate Laws 0:08:57 Example Using N2O5 0:15:53 Determining Rate Law and Order for Reaction 0:28:16 Determing Rate Expression and Value of the Constant 0:42:56 Measuring Rate of Chemical Reaction with Graphs

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OK can I have a lot of attention to itself let's go and start before I got here I wanted to find out how do you guys have any questions so we have moved on to looking at chemical kinetics Indian Guides remember last time we talked about the fact that we studied chemical kinetics we have 2 important goal 1 and we need to figure out how fast reactions to see and the 2nd goal of Connecticut is to figure out the reaction pathways to say reactions have we are interested in looking at is the detailed events that take place as reactants the products so interested in looking at how fast reactions proceed and secondly for interested in looking at and was not looking at both of these in detail but to begin with the focus on how fast reactions proceed and we said would talk about how fast reactions proceed term that we use is great and the last time we talked about the fact that you can talk about great in terms of average rates or you can talk about in terms of instantaneous race and we said that it is much more useful to us To referred to rein in terms of instantaneous rate and from now onwards when we use the term wait while we refer to is the instantaneous rate and then at the end of the class talked about the fact that most reactions of reversible and reaction is reversible and that means that there is a great associated with the forward reactions and there's a rate associated with the reverse reactions of the 2 rates forward and reverse and so looking at a reversible reaction the overall net weight that we measured experimentally is exactly the forward to the difference between the forward rate and the reverse again but to keep things simple From now on we will consider the fall would bring only immigrant pretend as to the forward rate is the only 1 that exists our right in reality of a forward rate anniversary but to keep things simple we're just going to focus on the forward rate OK so that last time we talked about the great we talked about the units for a united stand with means we talk about reaction rates OK now we're going to look at the in more detail about the look at the relationship between really and concentration right so To keep things easy for you I just made some short notes and he's not available class website this kind of highlights the important thing is that I want you to remember as you study this topic so
03:19
today I to look at the dependence of great on concentration and this looks at the relationship between the rate of reaction In the concentration and the concentration that we look at is the concentration of the reactor arrived so it turns out that the rate of a chemical reaction in Roma were focusing on the board reaction to the rate of a chemical reaction the forward direction nearly always depends on the concentration of 1 or more of the the reactants so if you're looking at a forward reaction and how fast that reaction proceeds will depend on the concentration of the reactants right here we 1 reactant it would depend on that continent that 1 reactor here to reactants of more than it would depend on the concentrations of all of the reactor so that the 1st thing to members the rate depends on the concentration of the reactor case and if you want a mathematically described his relationship in the form of an equation and recalled that the rate expression for the race locked so I'm going to take the same reaction is going write down so if we take the reaction where are reacted with only 1 reactant and this reactor and 2 products are to be announced equation is that 1 reactant going to products and I reacted as 88 and that lower case is is the coefficient that consequences so the rate of this reaction is going to depend on the concentration of income at the rate it always depends on the concentration of the reactor alright so it I want mathematically state this then I would say that the relationship is described as great the a constant K now member I want you to always make sure this is low KState not capital came when he was capital what is happening here represent the equipment constant OK so this is located here and remember the rate depends on the concentration of the reactor and raise 2 of power and which is a number on case and that she is here it's called the rate constants let's look the age of constant and that is called the rate constant this amid concentration of ETA and this and here is called the border but this with respect to that reactor rights and order where respect to them the reactor and this relationship you right in this format where use every equal the constant times the concentration raised the power and this relationship is what is called the raid law or expression so this is similar to the law mass actually does remember when right there chemical equilibrium expression awaits the products concentration of products may the provision is called the Loch mass action here the relationship between rage and concentrations of power the reactant is always call the race all right so that continuity is and some of the same name is written here so it's always a great equals came concentration of reactant rates that power
07:07
and went case of rate constant and this series of constant and it is the order of the reacted respect to that reactor and this is the power to which the concentration is wary of case the power in the rate expression has no direct relationship to the questions in the balance equation :colon so this number and has no relationship to the court coefficient it's a number that we determined experimentally so there is no way In the hands for anyone to look at a balanced equation and say but that value and would come out to be as an accessory to the original where there you or I can look at a balanced equation and say what that value and is going to turn out to be the only way to determine the value of and is to experiment and later I'll show you how to figure it out OK this valuable then can be a whole number of or a fractional number all right so let's see if and it's called order appeared so in some reactions the value of and comes out to be 1 when the value of and comes out to be 1 of the its 1st order member that Indians order the reactions are right and therefore when any equals 1 would call it the 1st order so where it holds water the rent laws as this great recalls they raised to the power was honestly when something is raised to the power lines you don't need to stay as 1 of the leading blank you know there is to the power line of so so if you take this example of this reaction went into all 5 coasted to an 0 2 1st half an hour 2 it turns out experiment we know this is 1st order so the rate of being raped equals a constant here which is the rate constant times that constantly there's only 1 reactor and that when reacting power 1 so we knew right away that law like that we call that a 1st order rate gridlock all right because order and is wanted and comes out to be 1 of the great is written where in equals 1 the other reactors were intended to when I managed to win the lies administrative equals came into the power to and we call them reaction 2nd order in take an example this is an example of a reaction that has only 1 reactant in differing equals came the concentration of the reactant brings the power to and that would be the rate for 2nd order reactions are right and this is a reaction when it when 1 the reactor the order turns out to be too it be 2nd water tanks the sometimes the major when an equals 0 the writ large international rate equals the 88 raised to the power of 0 right and you know that it is raised the power 0 you know that's going to be 1 and so the rate will be so when it was a reluctant Venus and recalled its arrangement will be looking because they raised about 0 turns out to be 1 and therefore that means rate equals the rate constant so the rate equals the rate constant then we call that is you reaction to an accessory say could be 0 in any equals 0 it's Tulsa order it any holes won its 1st order if any was to it's 2nd order and so on and so forth usually a common ones 0 1 and 2 right and lastly in the history the a fractional numbers have intake In this reaction you can see the rate constant comes to 1 and a half right so here the rate equals concentration raises the power of a fractional number this week we have asked for 1 . 5 and therefore that is the order with respect that we reactor so but less than a year to remember here is for you remember is that the lesson from all this is that the reaction order is an expression of the property that cannot be predicted from the chemical equation it has to to be deduced from experiment are so every reaction that you look at the relationship between the concentration of the reactant are right and the rate is called the rape and the weight loss is always with the same form rate equals a constant care which is the rate constant times the concentration of the reactor and raised to the power of the enemy and that and is called the order of the reaction arise so what happens if you have more than 1 reacted so so you have more than 1 reactant illustrate an example of a
12:28
reaction where you have more than 1 reactant so the reactions with 2 or more reactants the realized given by certain elements that we have a hypothetical general foreman equation where you have been with the policy of the EU can have any number of reactants going to products in the race laws
12:47
written as rate equals once again the rate constant now we have to react and certainly a race to the power of a number the race the power of
13:00
a number and immediately reacted to the sea waves to the power of why and number otherwise are right and that would describe the rate lots so the only 2 the weightloss law would be the concentration of the 2 reactants each raised to the power a number of cases where on the border with respect to and the order with respect to be and if you that is the overall order right so it's a good example so really take this example of this reactant reacted with hydroxide to give you the age feel free to minus of age to it's when looking at his reaction now you were asked to write the raid along the 1st thing you would do is look at that equation forgot how many reactants there are there to react right there for the British law of the rate expression would you read it Of that reaction equals a constant came which is the rate constant times the concentration of each reactor raised to the power of a number so it turns out experimentally we figure out that this is the 1st order and hydroxide is 2nd order all right so that we used to say that this reaction is 1st order in age to appeal to minors and 2nd order in hydroxide in the overall order would be 1 the 1st 2 which has strained is there could and that's what we call there are a lot all right and I want to remind you this is very similar to the loss of mass action theory but we write down and equilibrium constant the walls of the concentrations raced to the part the petitions likewise in Connecticut's when we look at the Great all the rate expression it's always the rate this gives the relationship between Britain that reaction and the constitutions of reactants rate and the rate of the forward direction members were concerned about the rate the 4 directions the rate always will depend on the concentration of reactants and that gives the relationship so now I want to know how much I said we can't figure this out experimentally and so we can look at a balanced equation and just say what this order will turn out to be His order With respect to react and vary from reaction to reactions as I said before there is no way for us to look at in advance and saying what the author is going to be any all it figure out water is to figure it out experimentally rightful initially how we do it so it mathematical calculations and essentially what you can do so let's take this problem into the worksheet that I do not have the class cited political look at how 1 determines the rate for a reaction and how 1 determines the order became so here we are looking at a reaction and the 1st thing I want to look at us and if you look at the equation the balance equation that's provided to you can erase it Muslim 1 reactor all right so the weight loss can only depend on the concentration of that react a so the latter would do as you would do several different trials and at different concentrations of the reactant you can calculate the way that reaction remember how we calculate rates experimentally what you do is in the lab you would look at concentrations versus time alright you would make a plot and then you would pick an instantaneous times and you would take this long at that instant in time the attendant should slope and from that we can figure out what the Rangers right so we talk about the last time so we know what we have here is we're looking at that rate is at 3 different concentrations of the reactor so he is the 1st concentration and the corresponding rate is a 2nd concentration the corresponding rates and this is 3rd concentration and the corresponding rate right now we're going to use this data to figure out 1st the order of the reaction so the question is determined the order of the reaction and wife the rate expression so we started writing the general form of of the rape law can sell without figuring out where the water is evaporated general all of the read lot what would that look like to read equals member what is what is great about how the rate equals 1 the rate constant times the concentration of the reactant raised to the power I'm a number and that we need to establish so this is the general form of the rate lot now we have to figure out what that exactly a lot of again now you look at the experimental measurements can and see that we are measuring radiated we know the corresponding
18:18
concentrations but we don't know what the value of this constant is and we don't know what the value of this engines and ultimate goal is to figure those out this problem all right so we write general fall over the rate law because we know the rate of the reaction depends on the concentration of the reactor all right so if look at this equation we have to unknown and mathematical you have to wonder all of you recognize the need to equations to software Our writer Alan directly to announce we need to equations so and you will have the right to equations based on 2 sets of data so that the 1st set of data we know
19:00
that the rate equal Cape Times 8 races the power and so it out
19:06
1 of my greatest 7 . 5 times since the negative for per liter a 2nd salary the rate equals came times we know the concentration for that 1 . 0 0 5 0 Moeller raised to the power of and so that's 1 immigration and it was the 2nd question analysts say it when the raided is tends the negative 3 times since negative 3 moles per liter per 2nd equals the same constant but now my concentration is . 0 1 0 Moeller grace the power and that is too so not ultimately I got a figure out a way to use both of these equations because remember I have to and only have 2 equations that can solve that and figure out what the value and is an active forgot about the case and you can see that applies divide 1 equation by the others and usually it's best to keep the out simple it's always best to take a bigger numbers and by bigger number by a smaller number than viceversa version of the same answered that he would just keep them out simple so there's a bigger number scientists at 3 times 3 moles per liter 2nd equals came times 0 . 0 1 0 moles per liter race the power and divide that by 7 . 5 times and the negative for bowls preceded 2nd equals skate times . 0 0 5 0 0 moles per liter raised to the power all right to use the analogy and he would cancel out and so God is now in equation with 1 another and so if you take this into buying this would end up with this it was here both of these arrays to the power and it's about 2 . 5 I can see that this comes out to the tune and that means the power and and so then there is the I figured out what any standard In too so we know that this reaction is 2nd order all right by taking the data with no essentially what we're doing is experiment when measuring the rate and we're looking at is dependent on concentrations that would change the concentration of reactants and by doing this experiment in the latter we can figure out of the water of reaction it's so now I think about what the rate lot there's so migrated along would be in that raid equals the constant rate constants thanks a child raised to the power to so that answers the 1st part and this is how in the laboratory to determine what the order of the reaction is memories said we can't figure this out in advance we can't predetermine upstream could do but this order and would come out to be the only way to determine if it is to carry out their experiment you measure the rates at different concentrations and to figure out the rate of focus it's another we've figured out what the rate as we can move on to looking the 2nd part of the question so determine the order of the reactions like the rate lock so I asked Alexander Wright the rate law this is what you need to give you cannot give this because this is the general form with the generic equation and you have to find out the unique Laidlaw that corresponds to this reaction and we figured out that it is 2nd order never the 2nd part of that problem when asked to calculate the rate constant and give its unions so part B I need to figure out what Kate since I figured out the 2nd University I can just take any 1 of these equations now I know that the end is too and now I have only 1 unknown I can solve the case all right so I can say I know that great equalized times HIV rates the parties therefore if I take 1 set of data and I'll take the 1st set of data which is 7 . 5 times 10th in 84 balls the leader a 2nd it also times . 0 0 5 0 moles per liter square and therefore I we're this equation I can take a also 7 . 5 times tend to negative for malls procedure divided by by 2 . 0 0 5 0 moles per but since the so the malls square president square right and if you were to put the numbers into a calculator and work this out which would end up with is a 2 significant number so the theory now I'm dividing moles per liter per 2nd by Wall square police square cake it's abiding the malls you can see that 1 of these malls and 1 of those who have out you can see between these 2 181 members of the committee of 1 so that would end up with these leaders from all per 2nd all right and so the unit now turns out to be leaders from all 2nd economists see that the unit for the rate constant will vary depending on the order that reactions so there is no 1 standard unit for the rate constants like people constant them with an equipment constant the varies depending on the lot action likewise the units the rate constant will change depending on the water and so will say that unit for the rate constant will vary depending on the rate law on the rate expressions of Kate so you need to figure out the corporate units and sales that would be the rate constant and then to part c the parts tells us to our access to calculate the reaction for a concentration of equaled 2 . 0 2 Moeller OK so now we need to figure out the real another lowered the value of is now that we know what the value of any chance we change the concentration is you forgot the corresponding the rate paid so once again we go back to the equation and the region which we know is times H I take the power to now we learn that the rate that now we know what became a value is so that 30 times leader so per mole per times the concentration which is . 0 0 2 0 moles per liter squarely and said the pedantic calculator it comes out to be 1 . 2 times tend to negative for and you can see that the unit now works out to be more malls proeuro Pesek remember the unit for 88 is always concentration per time to you know that unit has come out to be changing concentrations multiple leader and changing times which is Pesek southernmost leader Recep right and you'll see that in unit's work so this is how I I don't know how to had the best carried out an experiments lab kinetics this is how you figure out what the order of the reaction is you know what the rates are so we didn't example problem where we had only 1 reactor right now what happens if you have more than 1 reactor and instead take an example of how you figure out the border relative will too multiple reactants let's example once again what use an equation that
27:49
has to react all right so you look at that now in looking at the reaction will be happy to an old reacting with a will to continue to an to bright and so in the laboratory what we're going to be looking at it now now we have to concentrations to look at and so we have to concentrations and the figure of the corresponding rate all right and so we have 3 sets of data and the way we do this keep the maps simple while the way we kind of reconstruct experiment in our particularly so that we can figure out the order the reaction is in the way we do that if you look at what we do know is we came 1 of the concentrations constants of you get in now and the the 1st 2 sets of data keep those 2 concentrations the same but only change other 2 and we figure out experimenting with the rates are all right that's what we do it now for the next set of experiments we looked he used to do the same and Training Institute you see them so we know as we collect data were if you have multiple reactants will keep 1 concentrations of the reactants the same all right and change the other 2 and that allows us to figure out the orders respected that and now the next time we do this we carried the other 2 reactants the concentration the same and change the others to do so once again to solve a problem this time we start by writing to the general form of the rape law OK secondly you help me right that's about right general form of this great loss I would start by by saying read equals 1 but we're right down next the key the ring constantly at Lord's history times my 1st reaction is 1 in no it's going to be raised to some voluntary number and now I have another reactor so many other reactant with people to raise to some opportunity and and ultimately I have to figure out what it is In 1 of of India's if I want to know what the rate locked in a bitter so now we have 3 sets of data so I can write 3 equations so I can say that the 1st equation will be rate is 2 . 8 times 10 the negatives sex part the the 2nd equals the constant care times the concentration of a would be 1 times 10 the 84 Moeller raises power and times 1 times 10 to negative for race power and that would be my 1st Data OK secondly I have the 2nd data which is 8 . 4 0 Konstantin 6 moles per liter per 2nd you also can times 1 times change the native for Grace Apollo and times 3 times 10 to negative for based upon and that would be equation to In the 3rd 1 would be 3 . 4 times 10 selected 5 malls spread leader of 2nd equals Cape Town's twotime Stenson it for smaller race apart and at times 3 times calculated for smaller trees power and all right now I'd go back to this general quality equation into the sea all we manage experiment is raped we know the concentration of and we know the concentration of in order to buy what we don't know what's going on is we don't know what it is and we don't know what cases In a related renounce algebraic Mohammadi places the need to software if you want to figure out the 3 announced need 3 algebraic equations assaulted 3 announced separate down the 3 equations right now we stand by let's state the equation to which is bigger than many equation 1 and divided equation to buy equation 1 all right so I take these students he would end up with is 8 . 4 times 10 negative 6 moles per liter per 2nd equals case times 1 times 10 negative for Moeller place the power and times 3 times 10th inning before the grace the power and the divide that migration 1 which is 2 . 8 times Internet's 6 moles per liter 2nd equals King times 1 time strengthening formula rates power and times 1 times 10 the negative for all power again when I divide 1 equation by the other is that the case will cancel out now by designs were keeping these 2 concentrations the same making you see the reason why we do that might keep the conservationists saying halted would cancel out as well all right so century I have eliminated 1 turned that equation now provided by the slightest up to read and over here I this this despite that and that 3 Race to the power of so now just very simply I know that and equals 1 some quickly figured out what the orders with respect to that by dividing 1 equation by the other and by design we always keep the concentration the same so the Council out of here now so I think it is not going to figure out the other 1 by designer keeping these 2 concentrations the same Sinaloa to do is to figure out there's an animated by mistake equation by that case so now that I know well and as I need to develop engines and so far that once again I always by dividing the bigger number by the smaller number in terms of rape and on take this equation and divide this equation by that date so I end up with it all of this some analysts say 3 . 4 times Stanton negative 5 moles per liter per 2nd equals the case all right times 2 times 10 to the negative for mall times 3
34:57
times since the negative not now figured out that this and is 1 2nd per the 1 they remind that his 1st order came when divide that by 8 . 4 Konstantin 86 moles per liter 2nd Cape Town's now messages after the 1 Stanford negative for smaller in this elite 3 times tend to negative for all the graces Apollo 1 so I can't guarantee cancel out by design now we take the 1 with the the other 2 concentrations of the same so that these jurors will cancel out so what I end up with is not listed divided by history and this town divided by this and both of these raised to the power of em 10 so the divide his fighters would end up with is for and over here I have to divided by 1 of which is to raised to the power and therefore I know and comes out to to be too all right so by dividing just algebra simple algebra and taking advantage of designing the experiment so that we always 1 of the concentration is the same and on the the there we can figure out what the order of the reaction so now we have the right along what is my real along my radio along that determined from experiment turns out to be that radiates the walls a constant capable his case my reacted and is an old and I know it's 2nd order in an and firstorder in order to so you want to describe this great lines a 2nd order with respect to and all its 1st order with respect to all too and what is the overall order for this reaction to plus 1 3 francs so ultimately in many of these problems our ultimate goal it's still figure out this expression with what the order is and that gives us the rape law of expression OK now was the 2nd another 7 determine the rate long another 1 mistake can figure out the value of the rate constant so that the value rate constant you just think any 1 of these equations so let's take the first one where we want figure out rate constant so we know great equals times and allsquare times too so if I want to know where respirator constant is that this will be the rate divided by a concentration and squared times the concentration of people to which if you take the 1st set of data in the 2 . 8 Constantin it's 6 malls preliminary the 2nd divided by the concentration of NO which of the onetime strengthening before malls currently there hoping square in times the concentration of too which is 1 times 10 to the negative for Wallstreet leaders and so do the work carried out the answer comes out to be too the answer comes out to be of course were divided about myself the answer comes out to be 2 . 8 times 10 to the power 6 leader square per mole square per 2nd all right so what you need to do is look at that this'll be malls that this time Sicily malls Q per liter square Of the Prairie Newcastle units out and you can see once again that the unit of the rate constant varies depending on the orders so there's no 1 standard unit for the rate constant it's going very well and you figure out the appropriate you OK so it's very important because on an exam and you created not only on numerical answer but also on the unit so you have to make sure that you check to make sure cancel the units out and get the appropriate unit for the constant OK so many questions at this point so we looked at the effects of the chemical messengers 1 that when we talk about great member last summer to introduce you to the idea of what it means when we say the rate of reaction now that really understand what it means only saving rate now we know that the way it actually depends on the concentration of the reactor are right and the relationship between weight and the concentration the reactant is given by the rape law right and where many refer to a rape law it's got to parts to its history constant infighting water and so we have to figure that out and this is done experimentally there's no way in advance 1st to predict what the outcome is going to be so we can predict this in advance then you have to deal with experimental data and the only way to figure it out is to use experimental data into the type of problem that you will get Will in experiment this is the data that we obtained now from this data and figure out what the real lots and we 2 examples of how you figure out the weight loss all right what we have just 1 reacted had to figure out if 2 reactors have you figure it out you can know of while this is interesting and fun we want to call them when we deal with this is experimenting it's very difficult to measure the rate Rehman told the way you measure the rate of the reaction in 2 0 plot concentration versus ties and then take an instantaneous time and then draw attention line that goes to the point and figure out the schools of that line the create 9 trim experiment when you actually tried to do this in the light it's not that it's very difficult to do this precisely right it's who you know getting the right candidates aligned known just a slight twist continued and so it turns out when you are measuring rate as a function of concentration it's very very difficult to precisely measure the rate so wild and the calculations of pretty straight forward executing this in the lavatory becomes
42:01
difficult OK and so we need a slightly different approach so it turns out that we're trying to accomplish the same goal but now we want to take a slightly different approach right so instead of looking at memories so we looked at the dependence of weight on concentrations are right and we find in the wild it helps us understand the topic actually accomplishing measuring rates the lab is cumbersome and difficult all right so we need a different approach that makes it a lot easier for us to accomplish this Our right so we do instead of looking at rate versus concentration all we do is now what is much more easier for us to measure it just concentration versus time Our right so I take advantage of concentration versus time so to measure the rate of a chemical reaction we have to determine small changes in concentration occurring during a short time into all sometimes even difficult insufficiently precise experimental data for small changes because memory you have to pick up a point in they year to get and salt that runs to the point and sometimes that is difficult to do it again and alternative is to fit all the data over a longer time interval with an equation that expresses the concentration of the species U.S. future of time someone I mean by that so long as we figure out rain Is it a lot concentration where is the time and usually we look at it in terms of react so we will look at the concentration of 88 With this time in seconds and we said the like that said I wanted to figure out instantaneous so wanted to carry this out I would make measurements at different times into wells like that some major at different times I measured the concentration of air so in what we measure is the amount that's left and reacted to the beginning we have initial concentration it reacts slowly there would be no comment these leftover than it would proceed at a different like the 1st 50 seconds we figure out how much it is and react than 100 seconds to figure out how much his left hand reacted and then at 150 seconds we figure out how much he is left reacted and you would end up with a lot like that but I wanted to go great I would have at the instant the reaction begins with initial I would have gotten into line to that and figure out what it is that's hard to do and what's more what's much more easier is to take this explained to the year that you see and come up with a mathematical equations drive a mathematical equation that actually did that describe this process right and would derive a mathematical equations that looks at the dependence of concentration was this time and gives us the whole dependents of their entire plot all right so we wanted to write a mathematical equation that describes lot so in order to do that we have to look at each 1 several will get a firstorder reaction and let's say women driving equation for a firstorder reaction and where you have only 1 reactor about the arrival of a mathematical expression that describes the whole process and describes the dependence of concentration was this time I will start with with the rape along and the original offered this would be rate equals all right ,comma the reactants do I have only 1 reactor and my reacted this it is 1st firstorder itself you know I put 1 there but I don't need to the oneyear because it's a firstorder reaction occasion Nelson's unwanted derived an equation that we take advantage of integrating the whole process under say that you right the rate memory is 1 Delta concentration of being divided identity member so instead of using delta and candidacy will be in small incremental changes so that instead of using dealt with this change and the use or Dad which represents small incremental changes and some of have small incremental changes in 88 as a function of small incremental changes in time so I'm representing break this way and member it's a reactor and the reactants consumed and to have negative sign front that that would equal chase times the concentration of the that now the relentless this equation so that now as saying that the small incremental change divided by by age equals negative keys do you teach rights and just put all concentration turns on 1 side and the time terms on the other side and members of incremental changes and I'm not going to integrate so there have explains the whole process where From when it begins so that so limits on I start with initial concentration of the 2 concentration of and over here many times French equals 0 . 2 In the accuracy and this process now essentially invite integrated that's what I end up with his talent the minus Allen is 0 the walls minus T you don't understand us all I'm interested is that you know what the final outcome it's right so if you have a daily integration idiomatic classes I call a wanted member the outcome of this equation turns out to be a variance or you can also be right in a sense that this is Allan the forward Ellen the 0 equals minus Q t know what this equation represents abstract integrated I'm looking at small incremental changes integrated and integrating it into the whole limits starting from initial concentration I to have the reacts at the constitution at time t this is what it would look like got now if I would write this I I would expect you to memorize this because it's a firstorder reaction and her firstorder reaction you need to know this is what it looks like a writer and this as well that our representatives in the form of a graph conceived by taking balanced gave minus the initial concentration of Ellen is 0 people's minus the 18 Bavaria is this :colon Labrador talent it is also minus the "quotation mark ln the 0 so I'm just taking is over there and now this is in the form of this where the y axes and is the it's negative slow times xaxis that will be the exact says this will be the slow plus which is the interest that all right in the form of life peoples was in Mexico City and so you can see my plot out but that would tell me is that if I fly Helen race's times I should end up with a straight line graph all right like this where the interests that would be the initial concentration that's out there and the slow when the call came and you can see it's a negative slope right so the final takehome message that I want to remember it as if it's a firstorder reaction would you do if you measure it method grab you look at concentration started at different times roles you forgot the concentration of 8 so this is a 88 at different time intervals and 0 this'll be the initial concentration in at different times roles you measure the concentration of a all right now you take you know units in itself you can repeat to Ellen Page and if you make a lot of Delaney versus time you end up with a straight line the negative slope what is that time especially the
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summit center everybody so now instead of measuring way it would have been used in the laboratory I would measure concentration versus time and takes the natural log of the concentration and draw graphs environment with the negative slope stabilization initial orders that army is 1st all right that a lot of the theater company in the last