 Right, hello everyone again. This is our fourth screencast end lecture for chemical kinetics. So in this session we're going to cover a bit more on the initial rates method. So the last screencast we covered kind of a basic idea of how to graph it and then the lecture we went through how to do it just fire equations not using any graphs or anything like that. So this I'm going to mostly cover that solution again step by step. So if you want to cover it again please watch ahead. If you're happy with it show feel free to skip this one and go on to the next bit. I'm also going to cover something on using Excel to make this solution. So if you're not too much of an advanced Excel user you might get some use out of that or you might not. It's optional, obviously it's not going to be examined but it is one of the more powerful tools we can really learn to use. So I'm going to introduce some ideas of using some functions and some shortcuts and just how to deal with it on a computer. So what we're really going to cover today we're going to have a look at the data that we've got. We're going to then kind of crunch down some equations. So what the first thing we're going to look at is how do we convert those rates laws into the log form of the equations that are really useful for the initial rates method and then we're going to throw those data together. Go into how to solve it for Excel and if you're just interested in the rate the rate law and the solutions at the end again click the YouTube links at the bottom if you want that. And once again my pen is not very happy so here it is it's back now. So we have two things we have A and B and they will go to C doesn't matter what they are this is just kind of the generic thing for now and the rate at time zero the initial rate the very first thing is equal to a rate constant multiplied by the concentration of A at time zero multiplied by the concentration of B at time zero and these are raised to two powers A and B here. Now you might see n or m or o x and y it doesn't matter these are just two numbers and we're going to find out what those numbers are. So we can see from this sort of schematic graph when it's got a huge initial concentration it will go down quickly and then our third experiment then our fourth experiment second and third experiments. So we've been given three experiments with three different rate constants or at least three different rates that we've managed to figure out four time equals zero. So notice the fact that these curve that means that the rate actually slows down as the reaction proceeds that's because the rate is proportional to concentration so we're not solving the rate constant which is well at least we're not yet going to solve the rate constant which is constant across the reaction we are solving the rate. So this is our data we make one run where we have 2.3 and 3.1 is our relative concentrations and we get the initial rate as 5.25 and then a second run with this data and a third one. Now the important thing to note here is that we have two runs where our concentration of B has been kept the same. This now means these are directly comparable with each other. So we've been given two rates and we notice that oh that's roughly gone up by well we can do it eyeball and just say well 42 to 170 that's wow four times even though we've roughly doubled the concentration of A here so we can work out a proportional difference between these two concentrations and a proportional distance there and get an estimate for A but now we're going to do it a bit more mathematically rigorously something that will be far more extensible if you have a more complicated system and a lot more data points so this is going to be a bit taxing but don't worry about it we'll take it slow we've already done this in the lecture so this should be a recap. First thing I want to do is make sure that all of these are in the actual numbers I've multiplied in by these I should have deleted this from the table but evidently I've forgotten about it so these are the actual row numbers I've missed off a couple of decimal places it turns out they are not too important if you go follow the status through yourself do it in excel keep as many significant figures as you can right so just to kind of demonstrate an idea here we're going to take the logarithms of each of these values and put them in the table now I've kept the same color coding scheme so all the values that are in red all belong to one experimental the values in amber or in another experiment and all the green ones are in another experiment as well so we can keep track of what goes over through this coloring scheme if you can't quite follow the labels so here are the log forms again in this and we want to take the rate low and take some logs of it again this is a really common feature so get you so either pressing this on your calculator or typing equals ln into excel when we come to it so that rate goes to log of the rate and then because these are multiplied together they split up so we covered this in the last lecture and these exponents now come down here so we've got three equations that are effectively linear now that means they can be added and subtracted so what we want to do is basically start adding and subtracting them so we've got these two data points here where we kept b constant so we're going to just focus on number two and three for now here they are rates two and rate three's equation when we take logs of them these are exactly the same thing remember we've just given them different labels so this is the concentration for experiment two and experiment three and so on and we're going to subtract them so this looks really long but it does actually make sense for where this is coming from we've simply taken one and subtracted it from the other so as you can see the section involving rate number two here has come down rate number three all of those parts have been brought in together and just it's it's adding and subtracting it takes a little while to keep on top of it and it will take a while to write out manually but that's them there and if we get rid of that just so we can see we can see things start to cancel out our log k's well those values are going to be identical because k is a constant no matter what we do to the reaction apart from change the temperature and because the concentration of b was the same in those two experiments these two also cancel out so all the log b concentrations are identical this gets us a nifty little formula which is as a function of two rates which we know the answer to two concentrations which we know and then a and this is the value that we are interested in so we are going to solve for just that one value for now and now if we mess around with log rooms a little bit logs when you subtract them from each other to effectively the equivalent of dividing by or you can because we calculated these log values and put them on the lower table just use this equation this one might be a slightly simpler that one might be slightly simpler whichever way you want they are two ways of representing the exact same thing we are trying to solve for here at the end of the day so here's our data for just the values um not the log version so i'm going to do it this way rate two over weight three equals a log a two over a three so the values from say one two and three need to go into the right place and when you crunch those down you end up with a value of 2.0170 um so that roughly rounds off to about two so our value of a up here is two that's its second order with respect to a that was sort of in line with the initial guesstimate as well so we're doing quite well what about our next bit uh well we've now got a value of a and we've got go back to our three equations here rate one rate two the log values are just inputted into this table and what you can see is that now we've got a series of equations where we have values of b that we want to find out values of a which we now know and concentrations that we also know so you can do a similar kind of processes before um if you want to solve the equations individually that's possibly just about valid but you want to be able to cancel out this log k because you don't yet know what the rate constant is so if we take rate one and two these two equations and subtract them once more exactly the same logic as before uh here we go we're subtracting two things the two logs here come down and so on oh right not recolour this one properly that should be right uh and there you go you can see that they come down they subtract only the log k's um cancel out this time because those are the only ones that are the same but because we know a we can now calculate this we can now also calculate that those are values that are known those are values that are known and as a result if we start plugging in the other values that we've got b works out as one so we can actually throw those numbers in i'm not going to do it manually we'll cover a bit in the excel bit soon uh so microsoft excel you've probably played with some spreadsheets before let's uh have a look at it so hopefully my face in the top right corner shouldn't be overlapping with this too much so let's have a look at what i've done i'm gonna take out these for a bit first of all i've put my rate up here i've just gone into the equation editor and written it down so this is i'm constantly reminded of it and i've also formatted it all nicely if you haven't used it before you want to be highlighting up here and when you right click you want to go to format cells and you use superscript unfortunately excel doesn't have a shortcut for putting things into superscripts and subscripts it's a bit annoying unfortunately but all the data is in here i color coded it as i had before so that's our initial data first things first we want to get it into the absolute numbers we don't want it in that standard form so what i've put into these cells is equals 10 now if you want to write things linear it is the upper hat key it's shift 6 on my laptop it should be similar on everyone else's to the minus 4 that gets us 0.001 and then the same for here to the minus 5 here if i add a couple more just more places you can see here and to the minus 4 there so what i want to do is well you would multiply that value by this value now i'm going to do a little bit of an excel trick that you should really learn i'm going to hit the f4 key and what you'll see is these dollar signs appear in front of the numbers in the column and i sometimes call these strings because sometimes in older programming languages dollar signs got used for declaring string variables so what i want to do is actually delete one of these now you can actually press an f4 again and cycle through them but it's easier to delete so what this is going to do is whenever i start dragging the cell around it's going to keep 13 constant so if i drag this across and go back to this one what i've done is i've multiplied now this cell by that cell fantastic now what i want to do is pull the box around and drag down and if i click this button and go fill without formatting it keeps a bit of formatting that i preset there before so you can have that in manually if you like it's entirely up to you but what you'll find is that because we've kept number 13 constant here it is always going to multiply the right one down here now you could go through and do that manually and do it nine times but imagine your data set is a lot bigger imagine doing it nine times 20 times 100 times this sort of thing is really powerful and useful and excel it's worth getting to grips with right so now the next table i want to do i want to hit the logs now in all the previous ones i didn't use those log numbers but here we'll do the exact same thing again i want to introduce a formula now so there's equals and this is a really easy one l n you can just about do it if you type in lowercase as well but excel just kind of defaults to uppercase for these functions so l n i'm going to open your bracket stick your number in there close the bracket this version of it might even complete that automatically without the bracket yeah it does uh so now if i've taken a log of that i can also drag across and there we go there we go up now i've put these equations in via equation editor and they get in the way unfortunately anyway we've now got the log numbers uh and everything so that was done quite relatively speedily if you just drag and drop down of course uh and it saves uh you having to do this now i've seen people who really don't understand computers type in things like log to forward stick into a calculator and then manually type it into excel and they've done that for dozens upon dozens of data points seriously don't do that just drag and drop uh to fill in your multiple cells and learn how to use these string values or the the dollar signs to help make absolute references learn how to do that use it apply it it is the 21st century now we should be doing this by default uh and now i've added in the other equations that i want and this is telling me the values i want to calculate so now i'm going to teach you a little bit of an excel trick uh so it's called named ranges and i use this a lot because it simplifies things down uh so what i'm going to do is i'm going to pick these rates these are the rates that i know and i'm going to right click it and i'm going to go to define name then i'm going to call it rate and now i click okay but i've already done this in advance so if i go up into the top left here and click rate it highlights those three cells and i've done the same for these three as well i've called it a concentration if i click that it highlights it be concentration highlights less so that comes entirely from highlighting a range right clicking and going to define them this is really really useful so that means now if i wanted to or maybe you'd be used to doing some and then dragging down okay as you can see it actually automatically recognizes that as a conch so if i just type that in there you go that's my named range if i want to do average i would just write b these values aren't really useful to us for kinetics but you know it's a nice shortcut for using the same cells over and over again you don't have to go out and select them you just give them a name it's really useful later on in kinetics i'll show you how to do some simulations and if you name your rate constant cell for instance it becomes really easy so we have an experimental number we have a rate a conch and b conch now i want to take down certain values as given by these equations now again this is a really long winded thing for excel for a data set this small but if you're doing it on much more extensive data with a lot of data points this will this method will be invaluable and it is something called index so i'm going to type in an equal sign down here and i'm going to type index so this says that it returns the value or reference of the cell at the intersection of a particular roller column in a given range that sounds a bit long-winded and wordy so let's open a bracket and have a look where it's after now it's asking for an array or a named range of data we already have some i'm going to call it rate there we go i don't need to go and find the cells i know that the rate cells contain this and i want to pick the row number and i have three one two or three now i could just type that number in but i'm going to instead select that this cell so d 37 where i've got a number two in it and i've done the same on the bottom row and as you can see i've filled in the rest i'm still always referencing that cell for the number and the index changes between rate the a concentration and the b concentration so if we have a look the rate number two 0.0042 right down here 0.0042 so it is actually extracted this value down and brought it to us now the reason i'm doing it this way is because i want number two and number three out i've given number two and number two here so that's just at three there we go now why i've dragged down from the above cells all these numbers again this is the long-winded weird way of doing it but if your data set is much bigger this will be invaluable to you you won't have to then go hunting for the numbers manually you just need to know where it is in your array um so if we have an array of just three it seems really trivial but if you've got an array of a hundred rate constants believe me you want to do this so we've picked number two number three and here they are now we want to find the log of rate two over rate three so all i need to do is find ln of rate two divided by this cell now if i want to show off a lot i could just type in instead of these helper cells i could just type in the index function and bring them out but i don't want to do that it's a bit pointless uh and we also want the value of log a two divided by a three uh also another cool thing about this is if you preset up an excel spreadsheet like this and you have all the functions in you can reuse it again and again so if you are doing some research that involves getting rate constants for about 50 different reactions well instead of going through this process 50 different times set it up have blank spaces for your data insert your data and get the program to solve it for you saves a lot of time this is kind of why i'm telling you the long winded versions now if you rearrange this equation to solve for here you essentially want that divided by that number 2.0174 which just so happens to be what i can't be going into this cell here and just as another function what i've done is the round function so we wanted to round it off type round open up what number do i want i want to round that one down so how many digits one there we go we've solved it is now two so if i were to at some point rerun three more experiments like this all i would need to do is copy my data that i get into here and there we go that's my rate law half solved already brilliant so now i've done the same thing down here but instead of well i could replace it with one and two and just see what happens but instead i've redone it exactly the same as worth using these index functions picked experiments one and two solved it down here using the exact same way of reference these cells to get logarithms in fact i could replace that two with that cell there we go same thing and then i wanted to divide those because that's them joining together and then once we divided them together we get one so that is i'll i'll try and stick this sheet upon canvas for you to read through and have a look at and that's kind of it for excel there's a couple of different functions in there that i think are really useful and i think it's really useful to see them used in context certainly for solving this you can do it manually if you want you don't have to do this i just think that it's useful to know so anyway that's our excel bit so now let's have a look at the solution our rate is k a squared times b we've got those numbers out so a came from that b came from one uh now we now have an equation so i'm going to just we have three rates for instance we want to find k there's a rate constant so we worked out this coefficient this coefficient we also have some data for these now so what we can do is sit through and divide through uh well rearrange that it's raised over a squared b there we go save you the hassle of doing that yourself solve that for three different rows of our table and there we go our k averages i've taken an average of all these three probably not need to do this repeatedly uh and we get 3.214 times 10 to the 8th so that's actually a really fast reaction as well so let's go through and just review what we did well our data we collected three experimental runs uh well at least three you probably want to get more for statistical reasons to make sure they're all right and at least two have an equal concentrations kind of a b because we want to compare them they can select so with our equations we take a log of the rate and log of the concentrations of both and of course for all the data we do the both sides of the rate law as well so that um so i keep writing k equals uh rate equals k times a b whatever we take a log of that and produces along equations and then if we subtract two equations we get to eliminate the identical components because we've remember we've got equal concentrations of b we can eliminate those and we get an equation which is a function of this exponent a so we get that now we subtract the two others and we get a function of the two other values that we need so if we plug the first exponent back in we can solve for the second one so once we've got data for a we can actually get b just by in fact three data points you might want a few more and depending on how rigorous you want to do it so in excel we did a bit of this this is extension so if you skipped it you'll have missed out remember use your column as headings and to keep things clear because if you're going to use excel to format a lot of data it's going to run away from you quite quick if you're talking about hundreds of data points you need to have a good handle on it so i've used color coding throughout this red green and yellow for the three different kinetic runs that we've done find that useful if you're not very good with color or you're slightly colorblind find another option maybe something higher contrast for instance don't forget to convert everything via real values so you want to multiply things by 10 to this power of five or power to minus four and so on and the log values ln and the other things i kind of went into the functions are index that is where you stick an array in here so that's your range of numbers and then which number so if i have five cells in here and i set this to five then one two three four it'll return this fifth value here which is pretty really useful it's pretty much one of the most useful functions in excel which no one uses unless you're really good with it so and finally our solution we get a and b which may not necessarily be perfect around numbers so just round it off to nearest whole or convenient fraction because yes sometimes the rate law is not whole numbers but for 99 percent of your purposes it definitely should be um most of the time it'll be right put these into your rate law so rate is equal to k times a to b to the one sulfur k so pretty simple yes we've taken about nearly half an hour to go through all of that but hopefully that is a nice convenient and encapsulation of the solution for this so after this we're going to go on to the sudo first order approximation and a little bit more of a convenient way of solving for k from some rate data but until then see you at the next lecture