 This is our 13th screencast and now we're really getting into the detail of topic 3, all the experimental methods So I'm going to use this one to go into a little bit more detail about these three methods So this is pressure conductivity and spectroscopy So if you paid attention to the last one, you'll recognize these as in situ measurements And I didn't really cover them in a lot of detail. I just said that they are possible now This is probably going to be a long and arduous screencast for which I do apologize If it makes you feel any better It's quite difficult for me to figure out and to put together as well There's quite a lot of detail in it. You can however just skip through some of it There's going to be a lot of derivations and equations So if you're happy with using equations, you can probably skip through the slides That'll be fine If you really want to go into the detail feel free to watch all of it or just skip to the part that you want I know more about again these links on the bottom are quite useful for just navigating around and maybe cutting through if I'm recapping things a bit too many times for you So let's just start with pressure Pressure, yeah, where do we start with pressure all the time? Ideal gas law pv equals nrt This is one of those equations that should be tattooed on the inside of your eyeballs by the end of your first term of being an undergraduate chemist And we can see that pressure is proportional to the number of molecules There are two here. There are count about five here So if we say that there's a change of number of moles in a reaction that is equal to Plus three. There are three moles appearing So our change in pressure is going to be proportional to that change in number of moles So it stands for reason in this case the pressure will increase. In fact, it will just over double You do have to scale that up Proportionately to the actual number of moles involved to get a real pressure out This is just kind of an ideal situation where we've got say two moles here and five here It reflects the story country perfectly But in this case, we're going to mostly focus on this other reaction here So I'm going to change it up for two no plus chlorine gas going to no cl Two of us. So we have three molecules on the side two molecules on the side So this stands to reason that the pressure is going to go down across this reaction So we're going to be interested in two values one pressure and another one dp by dt or the change of pressure And later we're going to break that pressure up into multiple values. So Pressure isn't just what we measure. It can also be terms of partial pressure So What's the first thing we know? Obviously the ideal gas law tells us pressure is proportional to the number of moles And that tells us something else. It means we can actually split pressure the total pressure that we measure That is would we stick a mammometer on here or any kind of device to measure pressure We can break that total pressure into two components in this case the pressure of no and the pressure of cl gas So here we've got two molecules of those. So two thirds of that pressure comes from No here now one third of the pressure comes from cl That's fun. That's how partial pressure works And so if we take a rate change of these pressures, we can get up an expression like this So this is kind of the advantage of mathematics We can just differentiate these and they all add up exactly the same Coffee being very important for doing this subject That's not the end of the story As we progress through the reaction react and start appearing So we actually need to add this on as well So a rate of change of no plus the rate of change of cl plus the rate of change of our product Is what contributes to the total pressure So you can see in this case Two out of two Of the pressure 100 percent of the pressure comes from the product But halfway through however, there's going to be a mixture This is only two for time equals zero the very start of our reaction And this is only true for time equals infinity Now I don't literally mean infinite time This is a placeholder for when the reaction has completed and everything has converted to products It may be an entirely hypothetical point. It may be the end of the reaction It may be actually in an hour's time rather than infinity, but there's just a bit of notation Don't get too bogged down by it So at any point in time This holds true all three components are Going together So this is our reaction to no plus cl2 goes to 2 No cl and we need to derive a rate for it. So the rate is as this equation says So let's just remember how we do this Our rate of change Of this is a given number Don't get confused. That's just kind of a number. This is also a number That's also a number and then we just need to equate them together and how do we do that? Well If they're disappearing as reactants, we have the negatives in if they're appearing as a product We put the positives in so remember that from the very first topic we were discussing And we also have to divide through by the stoichiometry because there's two Moles of NO disappearing for every mole of cl that's disappearing So NO is disappearing at twice the rate of cl or cl is disappearing At half the rate of NO So this is half the rate of this and the same holds true for that side And remember we can also add them up to get the total pressures Now this is not to say that rate is equal to this This is not true Like that is not equal this so in case you just get these two equations or expressions mixed up They are not entirely related one is telling us what the rate is equal to so how do these relate to each other This one is telling us what do they all add to to get the observed pressure the total pressure of the entire system. That's Less to do with equating two rates. We still have to do a little bit of fiddling about to get that equal to it And that's kind of what we're going to do so assume for a moment that's six numbers in Our rate of change of the partial pressure of NO here reactant is minus 60 Pascals per second Now I've picked the sr units there of Pascals for pressure You might see other ones atmospheres for instance They're pretty equivalent but about a percent out is atmospheres are very good one at this you mean atmospheric pressure Tor you often see on memometers and pressure gauges It's a very Americanized you know from what I can tell and there's also millimeters of mercury Which is something you might see in weather prediction for some reason It comes from memometers that would actually a pressure would be able to move mercury by a certain number of millimeters And obviously time I'm using us per seconds, but you might see per minute and per hour Even per day if it's a really really long election But the important thing really is don't get too bogged down by units If possible try to convert them into these standard ones. It just makes things a lot easier for you So Pascals per second So if we want to insert this into this expression We can start figuring out that the rate of change of these must be related to it. So we have say a half That's minus a half will bring this down from here and times the this value, which we have a value for It's minus 60 and I'll be really in all and put the units in those on Pascals per second And that is equal to minus This will bring that down. We'll just focus on this one for now And so we can actually work out this value. Remember, this is just a number And we can figure it out So how we're going to deal with that as well first The negatives will cancel out And then Well, we can this is just a very simple sum. It's a half times minus 60 watts minus 30 Pascals per second. There we go d pcl 2 of d t Okay, so we can actually start working out what the In principle the rate of change of each individual component can be we can do the same for um the product as well But I'll skip over doing that and just say these are the answers. So If this is minus 60, this one is minus 30. That's plus 60 Now think about that actually Gels with our intuition as well because This is disappearing at twice the rate of that. So it should be double the number There you go 60 is twice 30 or more specifically minus 60 is double minus 30 And this is appearing uh with kind of a one-to-one Here, so this is appearing At the exact same rate as this because that would nice a one-to-one correspondence there So it is plus 60 Pascals per second Now our total pressure Is a combination of all three pressures or the rate of change of pressure Is equal to the rates of these so we could add all of these together. That's minus 60 minus 30 plus 60 Pascals per second And I'm sure you can add that up and you realize that cancels that cancels minus 30 Pascals per second. So the rate of change of this reaction should be minus 30 Pascals per second maybe add a particular point. So that may be an initial rate for instance So Let's just kind of review how the pressure works here. Remember, there's a direct correspondence between pressure and molecules It's not mass. It is The number of molecules pv equals nrt doesn't say anything about mass or anything like that. It's all the ideal conditions at least it's all about the discrete entities the number of molecules So when you can get that relationship in your head pressure becomes great to follow reaction rates by so We also need to remember partial rates partial pressures and kind of partial rates of reaction. So Our total pressure is equal to the components inside. So Remember that can be as many as possible atmospheric pressure. For instance, it's 70 nitrogen it's like 0.7 atmospheres into 0.3 atmospheres of oxygen ish and then kind of rounding errors is argon and Carbon dioxide or water vapor and so on. So those are like partial pressures. They would all add up to atmospheric pressure And so the rate of change of these can add up exactly the same way. So once we can get a rate of change The individual components we can get a total pressure or we can work backwards if we want Now let's go to conductivity conductivity as I said works if something is Splitting off into charges or charges are coming together and getting rid of So let's have a look at this reaction. For instance, if we stuck an electrode in here positive and a negative Oh Well, those are fairly initial molecules that you don't carry a charge. They're a little bit poorer Maybe there'll be a small amount of conductance in there. You're not going to be conductivity measurement But you stuck those electrodes in this Well, there's h plus there's cl minus. Are you going to get a lot of conductivity there? The electrons are going to go I'm going to love that Yeah that Set a range and set and fly all over the place. I think I'll like that you can get a high conductivity measurement And so What do we need to know about this reaction? We need to know its rate. So this rate Um, it's going to be a second order reaction ish So there are going to be two components to it Raise to a certain power because we don't really know the order, but we're going to guess And we notice the h2o is the solvent. So it's h2o everywhere And therefore first order approximation applies. So go back and Make sure you can understand the first order approximation to see what's going on here. We're saying that k obs is equal to k times h2o And it doesn't really matter what that power is raised to this is kind of constant across the reaction. So k obs is a nice little Not fair flipped a little bit too hard and sent itself ahead k obs is a good Um approximation. So this is going to probably go back first order. Maybe I don't think there's a good theoretical reason this m would be different Uh than one. So it's probably going to be first order. So let's go ahead and see what we can do with it. So We need to figure out the concentration of this And that is our starting product. We want to get a rate based on that trouble is conductivities measuring these products Oh, okay. That's a bit of a problem because remember that rate is really Equal to k times any reagent we can't stick a product in there And get a rate out the rates constants is always times a reagent But we can work it out. We can just say that That starting concentration at time equals zero It's that little label down there We just subtract from that. What does it turn into it? Well Breaks apart and it turns into one of these and Then produces one of these so if we said Oh, well, we take the That reactant And we subtract that cl minus from it Um, then we get the reactant at time t But unfortunately Conductivity will measure these positive ions as well. So we need to add them together and half So Half of these and it gets us this so try and satisfy yourself it might take a while to visualize it Satisfy yourself that this is true So we get that equation on the top here. There we go for any time t. We have The initial concentration subtract this but again Conductivities on a measuring the These are charged ions. So what we want is we want to subtract And get rid of this So we want to work out that in terms of Ions as well. So we do it on this equation here And that is equal to the timing at the end plus These at the end so it's as if it's entirely converted to these Ions the concentrations And thankfully at the very end we can say that this is zero It's entirely converted the reaction has gone to completion So we can get an expression for That reaction at time zero and it is equal to Half of cl plus h plus or in fact it is equal to The entire concentration of cl minus because it has converted from one to At least one of the other So we can substitute those in and get an expression like this So just to show you where these are all going to I've kind of Added some colors in here to help track it. You can see that we've got Well that comes down to here This Substitutes for this so it comes down to here and therefore we Get an expression for all this concentration at any particular time just in terms Of what those ions are those charged species a great bit of mathematics that helps us deal with conductivity measurements So there it is again at the top and we are also now interested in conductivity so conductivity is measured This Greek letter kappa we're not going to go into too much detail about how we get to it or what it's measured in We just need to know it's proportional to these concentrations so we Can kind of directly substitute this in because we know if they're directly proportional their rate of change the same so if we do d k d kappa by dt for instance that should be kind of the equivalent of any kind of charged species by dt as well actually i'll just take that as an h plus Or maybe I will actually I will draw it as an h plus There you go So if they're proportional their rates of change should be the same So we can actually start directly substituting values for k kappa Into these equations and this is how we do it So at time infinity at the end of the reaction We have the conductivity at the very end and then we subtract It for any arbitrary time t So there's an expression for what the concentration of the reactant is in terms of just its conductivity measurement That's great. So you can see how this tracks through here. We Add this into We substitute this for Kappa and it comes into here and we can actually do the same. We replace that t for infinity and do the same for this side So clear some of this off so you can see it a little easier. Thank you So now we've got the rate is equal to k obs times this we can actually substitute this in to here now So what you can see is we're now just swapping out Our concentration of our reactant for this conductivity measurement So k obs times the two differences in conductivity Raised to a particular power m because when we don't know the order of the reaction yet, although it's probably going to be first so There it is again just at the top and we're not going to integrate this now So this is a little bit of a tricky integration to do It's going to involve a standard integral, but I'll just show you how we get to it one of the ways of kind of thinking about integration is Think of these as individual values. You can move around it just like Just like normal numbers really so in principle you can bring that to this side And then it would integrate and you couldn't well we're going to integrate with respect to kappa So we need this on that side. And so what we end up with is one over There's some written that's One over that k ops D t so that's come over to that side. This has come over to that side And then we integrate them. So we're integrating an expression like this now if we assume first order kinetics There's m equals to one we can just ignore it and get rid of it And it gets us this expression which we need to do from a standard integral. So here's What the integration expression looks like but that actually then calculates to this So we get it from a standard. I'm not going to bother deriving this if you really really want to look this up I'm sure there's math help out there online or on youtube. Someone will derive this somewhere. It's a bit intense probably so This is what we've got it's a log logarithmic value of The different measurements we can do that's the conductivity at the end of the reaction Conductivity at a particular time and that is equal to minus k ops times t Which is what you kind of expect from a Sort of a first order reaction anywhere. It is the rate constant times time So that means if we plot a log of this conductivity measurement Versus time we should get a straight line and look here's some data here's the conduct since going up Fragedly over time we plot a log of that. There we go Straight down. So there should be We get the gradient how does k So that gets us our rate constant from this data. So what we're trying to show here Is that we don't necessarily need to plot Concentration here. We can just find something that concentration is directly proportional to So pressure is the same conductivity is the same and when we move to spectroscopy and we'll see that absorbance can be used as the same thing as well So this does not necessarily need to be concentration if it is directly proportional to it So let's just review all this Conductivity that measurement of conductivity kappa value Is related to the concentration of ions. So concentration Is pretty much proportional to conductivity. We can use it in kinetics measurements So we can fiddle with some equations to derivations Back there. I'm going to review them all so we can get concentrations just in terms of those ions. So You have an h plus and c l minus for instance that something's broken out in two Doesn't matter what it is So that means we can then replace this with conductivity That's pretty good, isn't it? So we can use conductivity at time zero or any particular arbitrary time and Time equals infinity at the end of the reaction to start plugging values in to get wheel numbers And we assume first order kinetics a plot of that Value there the log of conductivity at two different times the difference between them versus time should be linear Okay, so first order kinetics Remember something will be like a curve and then when you log it That's just making this x and y graph Hb negative right. So the spectroscopy we're going to look at this reaction that I'm bromeing This hydrogen going to to hbr. So well Let's just write out a quick rate of question. You should be able to do this yourself as well. That's going to be d br2 by dt And it's going to be negative because that is disappearing and it's going to be equal to Well negative of h2 because it is disappearing dt and it's going to be equal to positive of d hbr by dt But half because remember this two of these are appearing So that's going to be double the rate of any of these Incidentally if you were to add those together At them instead, uh, you would Equal to dh I had writing dh br by dt those rates should be added together and they become equal So what's happening on a macroscopic level that's Um What's happening in terms of maths and individual molecules and the macroscopic level we're seeing a changing color because bromeing If you've ever seen it before it's a very bright red brownie gas. It's very volatile Certainly an interesting one to see in the lab because the students you open the Top it starts smoking at you. It's very very volatile and very darkly intensely colored So if you start reacting that that color is going to go away. We're going to go from this dark brownish Vessel to quite a almost transparent one So over time that color is going to change So if we want to measure that color say with spectroscopy, we find a point on the spectrum where bromine Very much intensely absorbs and then it will reduce it will go down and down and down So pretty much like this It's a beautifully cheesy powerpoint animation there You can see that all the bromines are disappearing and converting to hbr And the intensity of that light is increasing The wavelength isn't just the intensity. So we're not shifting a peak in Frequency space where they're just the intensity is changing And this comes down to something called the beer Lambert law We do call it the beer Lambert law I think Americans call it the beer law and Europeans call it the Lambert law or the Lambert law Which kind of tells you everything you need to know about scientific culture across countries But we like to compromise the corner the beer Lambert law And it says this the intensity of the light coming through Divided by the intensity that starts with is equal to 10 raised to the power of e see now And now I keep saying e it's not it's Epsilon Greek letters that's an emissivity coefficient or an absorption coefficient It's just a measure of how strongly molecule absorbs C is the concentration And l is the path length So that path length is how far is the sample? That there is a lot more justification about this from the microscopic level, but we don't need to worry about it just now Basically saying absorption will increase if You have more sample to that the light passes through obviously If it has to pass through 10 molecules to get from a to b it'll absorb You know half as much if it had to pass through 20 molecules going from a to you know twice as far So multiplying those all together gets us that value so This is quite a useful law to remember Because it's the basis of most analytical spectroscopy certainly the best basis of most kinetic spectroscopy Watch that again I spent some time on this animation. I may as well show it twice as you can see it's converting the intensity of This is increasing so we want to say that absorption Is decreasing over this so we want to convert this to a linear equation because the sex potential one is not very good So what you can see is if you take logs of both these sides like this 10 logs specifically you get 10 on me You get log of this is equal to minus that absorption coefficient times concentration times the path length and we actually start defining This term called absorption As equal to negative of that log and this gets us What you usually see if you write down the BLM bit law, so that is again the BLM bit law uh As we as chemists are interested in it. Now if you look at some physics, especially spectroscopy the atmosphere They tend to use this version and Multiple components to it. Uh chemists were kind of mathematically illiterate creatures, aren't we? So we like this nice and straight version. This tells us that absorption is directly proportional to concentration So Any particular species x the the amount that that Absorption figure and we take the log of this as directly proportional to it So usually this is the number that a spectrometer spits out at this So if you're using an instrument you get absorption if you're trying to do it manually And work out light intensities. You've got to work out this and it's exponential Yeah But get a computer to do it for you. Basically the spectrometer will spit out a And then that is directly proportional to concentration. So if you're doing fairly straightforward kinetics once again A plot of absorption versus time will probably do something like this above we're doing that programming going to HBR Reaction the absorption is going to go down. We plot a log of that log of absorption versus time. It'll be a straight line. Brilliant So let's just kind of review this spectroscopy. It's been a long screencast. We're on 28 minutes. Pretty hell uh The method for spectroscopy the molecules individually absorb light So the absorption must change as a reaction proceeds We're really interested in kind of the macroscopic concentration of these. So those are proportional to each other And then there's the BLM below remember, this is another one of those Tattooed on your eyeballs equations. You need to know absorption is equal to a coefficient of extinction or absorption coefficient times the concentration times the path There's some interesting things about the units of this Since length and well length is in Obviously in kind of meters or it's a distance concentration is in something per Distance cubed those cancel out and You get distance minus cubed. Uh, so that has to be It's kind of the units that has distance squared in it, which is kind of weird. Um, what does that represent? We'll maybe cover that in a separate video Um, so only you can deal with the units of that. Yeah, should be fine Uh, so therefore absorption versus time can be used instead of concentration Potion of time you're likely to get a graph like this spat out of a spectrometer at you and you can use that data kind of roll instead of Trying to converge concentration directly So let's just review the whole thing now that we're hitting half an hour of video Pressure mostly the centers around the fact pp equals nrt On your eyeballs this equation Pressure is directly proportional to the number of moles so you need to remember Pressure and the fact that you can add then partial pressures together Once you can deal with that you can start substituting pressures and partial pressures for concentration and get kinetic data that way Conductivity this is obviously a little bit more complicated that derivation. I think was quite intense by some standards So those ions the charged ions are proportional to conductivity. So you need to do a little bit more But ultimately you can start taking conductivity measurements and substituting it so that conductivity there versus time is going to be proportional to your rate of reaction as well and absorption In spectroscopy that absorbs that a value and we have to remember that that is minus log of So these incident lights that's the actual intensity flight that you measure A is the number that a spectrometer will actually spit out at you because it's very convenient If you haven't built a spectrometer by the way you have to do that calculation yourself But A is the one that's proportional to Concentration you can once again use absorption versus time so that Kind of concludes our three main methods of in situ measurement So these are a couple of examples in a bit of intense detail, certainly Well, I hope it was useful for you if you sat through it Um, you don't need to obviously memorize all of this. These are just examples for how you go about it So certainly if you are not very strong with maths go through these derivations and try and figure them out yourself again links On this little table of contents and menu just underneath my face here that you can go back over them again Um, see you in lecture and we will do some problem solving on this kind of thing