 We have homework to do this Friday at 11. No homework next week. The week, the Tuesday after that we have an exam. The problems that everybody missed on the first exam will be making an on-core appearance. So don't miss them again. You see the same kind of problem? You know exactly how to do it. Fast, not slowly. Quickly. Draw two curves. Done. Next problem. Calculate the unit cell. Done. Next problem. Okay? And I will be most interested in the ones where I felt people didn't get it. Like for example, the enrichment of helium from natural gas. A lot of people miss that. Make sure you learn how to do it and know how to do it. So that you can figure that out. Okay? It's not hard, but you have to actually make an effort to learn how to do it. That's all. Not difficult, but you have to learn how. If you've never done a cartwheel, then you won't want to watch the first one somebody tries. But after they practice a while, they look pretty good. And after they practice a lot, they can't even tell you how they do them. You actually talk with somebody who's a pro at something they sometimes can't tell you how they do it. Ask Michael Jordan how he does that acrobatic move. And he says, yeah, I'm at the top of the key and I see an opening and then it's in. No memory of how it occurred. A person like that's not a very good coach, unfortunately, because you do need somebody who remembers what it's like to not know. I pretend very hard to do that, but sometimes it's hard to pretend. But if I go too quickly, just ask a question. I don't mind clarifying things. I may think something's obvious. You may think everybody else thinks it's obvious. It isn't obvious until you know the answer. Now, there is a very important characteristic to have during an exam, and that is mind control. That can be practiced as well. I think it's worthwhile for us to take one minute and we will practice it. Here's what we're going to do. It sounds easy. We're just going to close our eyes, breathe naturally. And when we breathe in, we're going to mentally count one. When we breathe out again, we count two. When we breathe in again, we count three. And when we breathe out again, we count four. And then we keep repeating, one, two, three, four. Ready? Let's try it for a minute. Okay, that's a good way to prepare for an exam. Most people can't control their thoughts at all, and they don't even know they're not controlling them. One, two, God, this is a wasted time. What happened? You find yourself thinking about something else, listening to somebody coughing. What happened to three and four? Then you have to come back, and then you may be able to stick there for a minute and then something else. I've got to go shopping. Where did that come from? You notice that you don't know where those thoughts are coming from, and they're distracting. And the more distracting thoughts you have come in when you're trying to solve a problem, let's see, p plus a n squared over b squared. Jesus, I'm going to flop. What happened to the problem? It's possible to be in a low-grade panic for two hours during a final and never get anything done because you're undermining yourself all the time with thoughts of failure or triumph, but not thoughts or self-doubt. I should have studied harder. I'm no good. I knew this problem was going to be here. There's three thoughts that did not help you solve the problem and wasted time. If you want your life to go by just in the wink of an eye, spend all your time thinking. Be preoccupied. The more time you do that, the more the day will just disappear into nothing. The more time you spend in the 1, 2, 3, 4 mode, the longer your life will be. And if you watch those distracting thoughts come up, then you'll dismiss them during the exam and get back focusing on what's important, which is just how do I solve this problem here? Okay. Let's talk about thermal chemistry, work heat enthalpy, and heat capacity today by a lot on our plates. Work and heat have algebraic signs. Both can be positive or negative, and both work and heat refer to the system, which is that part of the universe that we've mentally carved out to study. And the rest of it, we call the surroundings and we aren't quite as interested in the surroundings. Just like a person who owns property is interested in the property up to the fence line and then not quite as interested in the millions of acres beyond that they don't own. If the work, W, is positive, that means the system increases in energy. The system increases in energy. That means, for example, a gas is compressed. We have to do the work to increase the energy of the system. If W is negative, the system decreases in energy and the gas expands. If we have a system like a power plant where we're using the system to produce energy, we want the system to do negative work so that we get the work and we get to use it. So the energy of the system goes down and we get the energy to drive our car or do something else with it. And if we have expansion against a constant external pressure, then the work is just minus the external pressure times the change in volume. So if the change in volume is positive then the work is negative. That means the system expanded and so its energy is less. And if we have a reversible expansion that means that the external pressure is always essentially the same as the internal pressure so that it expands ever, ever so slowly and that means that we can just use the internal pressure. The reason we like reversible expansions and reversible things is that they're simple to figure out. It's not that we're ever going to do them. It's they're simple to figure out and they tell you the best you can possibly do. You're always going to be worse than that. And so if the best you can possibly do is not good enough you've got to do something else. That's very important to know what that limit is. So reversibility again we've gone over this but a reversible process is one that can be reversed by just changing an infinitesimal amount of pressure if it's reversible then it starts to contract again. I put a little bit extra pressure on so it's essentially matched. The beauty of calculus is that you can have something differ by such a small amount that it's essentially zero but it's not. It means that you can do an integral and integrals as I will show you are easier to do than some. The reversibility is always extremely slow and in principle it's infinitely slow so we can't possibly do anything reversibly because we can't wait that long. Time is money. More importantly we all live for a certain amount of time. That's why very few people plan a white oak because if it takes 400 years to mature you have to really think way far ahead beyond the grave to plant it. Most people plan a tree like a eucalyptus that grows like crazy and doesn't live as long so that it'll be big in their lifetime. That's why we need some kind of programs where people look further ahead to the future for the common good and just plan things like that so that future generations can enjoy it. Heat, same thing. If Q is positive then heat flows into the system and increases its energy. That kind of process is called endothermic. It absorbs heat from the environment it's going to feel cold. It's going to be a kind of reaction that tends to get cold and then absorbs heat from the environment to warm back up. There aren't too many favorable reactions that do that and for example, if you dissolve ammonium nitrate in water it gets cold, still dissolves. I think early chemists thought that every favorable reaction that would just occur on its own produced heat and that's broadly true. Many of them do like burning gasoline or wood or many things but some don't and so that theory that it was just down to heat was wrong. If Q is negative then heat flows out of the system and the process is exothermic and that's the kind of thing that we use to create power. We run exothermic reactions and then we use the heat in some kind of a heat engine to produce work. For example, the spinoturbine and generate electricity. We burn coal. We produce heat. We produce steam. We produce work. We produce electricity and we produce a ton of CO2 unfortunately. Nobody thought that was bad when the industrial revolution started. Heat can only be transferred reversibly if you have two things at the same temperature or within DT. Once two things are at different temperatures if you bring them into thermal contact it's over. You've just lost because the heat goes from the hot body to the cold body and then you can't get it back. You can't do you can't magically separate heat by just waving a magic wand but you certainly can take boiling water and ice and you can mix them together at water at some intermediate temperature. That'll happen naturally and you can see microscopically how that happens because the boiling water hits the ice and then knocks the water molecules out of the ice and then they're all there and they all settle down to the same speed because they're all hitting each other. That's all that can happen. It's the most likely thing. It's very unlikely for part of the water to suddenly stop moving and freeze into ice and transfer its energy magically to a bunch of other water that's moving fast and suddenly boiling. That's extremely unlikely and so we don't ever see that happening although many of the greatest frauds in science have been to propose a machine that essentially does that separates heat into two parts a cold part and a hot part and then you run something with the hot part so you have a submarine you're going along you're just taking seawater you chunk out ice cubes out the back and then you create steam and then you power the propellers of the submarine and you go along through the ocean for free using the waste heat in the ocean to power this up. Won't ever work. First of all, heat flow if they're essentially at the same temperature is also slow. Okay. Remember we had that piston and we pulled the masses off we had four and we slid them off when we got work and if we slid them off more slowly we got more work and if we made them into grains of sand and just flicked them off then we'd end up with the most sand piled up the highest and we'd get the most work. And here if we have four masses then initially we pull a mass off and the pressure goes down from six to four and therefore it expands until it hits this curve which is the PV curve remember if it's a constant temperature PV is a constant because it's NRT and then we pull another mass off and it drops to two let's say and then it goes out to here and we pull another one off let's say it drops to one it goes out to here we capture then the stuff in the pink we get the work in the pink and we lose the work in the yellow and so we say gee if we wanted to capture this thing we'd have to drop it down maybe to five and then it would go to here and we'd carve out a little bit bigger rectangle and then if we did it even more slowly we'd go like this and then finally we'd get this curve and this curve is if the external pressure is just the pressure of the gas at all times and ironically this the area under this curve is a lot easier to calculate than adding up these squares especially if there's a lot of squares that gets tedious to do the formulas for sums are tedious the formulas for integrals are not so this would be the sum I take off mass I adjust the pressure and I have to add up each change in volume times the pressure that was in effect at that at that time and if this is hundreds of things I have to add these up maybe with a spreadsheet on a computer but if we match it at all times so that we get the area under the curve then this sum magically turns into an integral and even though the integral is intimidating when you don't know what it means exactly the integral is much easier to do than the sum and that's why chemists love reversible processes because they can just slap an integral do it easily figure out what the most they can get is and then see if that's going to be good enough and then you're not going to get that so you have to work on what the efficiency is so we'll give an example here the integrals look intimidating in fact I quite clearly remember when I was 5 or 6 because I was still on the east coast my father had a book that had all these things and I was absolutely fascinated by that book and what those could possibly mean and when would I learn what they meant would I learn that in kindergarten and my dad said no you won't learn it in kindergarten but you'll eventually learn it sadly you may have heard Maurice Sendot who wrote for the wild things are no but anyway I can show you how to do them there's a trick Maurice Sendot died he had a stroke I think on Friday and died at age 83 that's another thing I clearly remember as a child is reading that book and then I thought there are monsters because they're in the book so you have to be careful just because you can imagine something doesn't mean it's true it doesn't mean it exists and even if you think it doesn't mean it exists you have to verify these things so here's an example here's a sum 1 over n squared to infinity 1 plus 1 fourth plus a 9 plus a 16 plus a 25th and the answer the question is rather what is that what is that total to exactly so I can't just do it on a spreadsheet because it's got an infinite number of terms so I need to stand back and use the power of the human mind and the beauty is you can sum infinite numbers of things okay computer can't by comparison though the integral is pretty easy the integral from 1 to infinity of 1 over x squared when you learn how to do them is minus 1 over x evaluated at x equals infinity minus 1 over x evaluated at x equals 1 the 2 minus signs go away so the area under this curve is 1 this is going to be bigger than that obviously because this is outside the curve before the rectangles were inside the curve now they're outside the curve in a more advanced math class you will learn in fact that that integral is pi squared over 6 so you have to know something about Fourier series but that's actually quite simple to calculate and that's what it turns out to be so it's about 1.64 something which is a number that doesn't look like anything if you start totaling it you can't guess what it is by the number okay, if the final volume is bigger than the initial volume that works negative because the system has lowered its internal energy and supplied us with work in the surroundings and if we know the gas equation of state then we can figure out exactly what the reversible work is so if the pressure external pressure is just the internal pressure I know what p is it's nRT over v nR and T are constants there's nothing else here but v and dv so I have minus nRT dv over v and that's the the antiderivative of 1 over v is natural log formula here minus nRT natural log v final over v initial I want you to see these but I'm not going to require you to do funky integrals on exams this is not a math course on the other hand you mustn't be intimidated by things just because you don't understand them now I found out recently that the Wright brothers knew nothing basically nothing about fluid mechanics they just tried stuff and in fact in the history of engineering often times the engineers are ahead of the scientists because they're just trying stuff and then they see what works and then scientists come back and say well that means there's lift on the upper wing and you should maybe adjust the wings like this and they should have this kind of curve on them and so forth and so on you don't have to understand it but you don't have to understand how it works to fly you just have to be willing to get in there I don't know who had accident just because you can get off the ground doesn't mean you're going to stay level and interestingly for the longest time the wings looked like this they came out on big jets they came out like this and then suddenly the wings started coming out like this and there's this little thing on the end going up and that turns out to give you much better gas mileage so you can actually model that and some bright guy said hey if we just put this little thing scoop on the end we're going to get much better mileage out of our kerosene and then all the new planes have that now because there's no reason not to do it but they just have to so as long as we can solve for P the function of V we can do it so for example we can do a Van der Waals gas here I can isolate P and all this stuff's V and then I just turn this over and put an integral on it and in fact here's the secret integrals.com will solve any integral you give it you don't really need to memorize the antiderivatives the way I did as a kid that's one of the things I did I memorized all the tricks all the antiderivatives tan theta over 2 trig substitutions you name it so that I could do integrals quickly because if you couldn't do integrals quickly it's like having to look up every word in the dictionary when you're trying to read Shakespeare you can't get the flow of the play or anything because you're bogged down read what's the definition of this what's the definition of this you can't get any flow and if you're doing lots of problems in physical chemistry you can't see the problem if you waste too much time getting stuck with the integral so you just have to know the integral it's like running there's a certain pace at which it's comfortable to run if you run too fast you get tired out but if you deliberately try to run too slow then that's very awkward and that takes more energy than doing it in a more natural way now you can use Mathematica if you take Chem 5 which I recommend that you do you'll learn how to use it really unbelievably good software in my opinion okay I went to integrals.com and I handed it this and this is what it did I get a term that's like the other term but now it has this subtractive volume off for the NB and then I get an additional term which is due to the attractive part which has a different form and that would be the most work I could expect to get out of Van der Waals gas sometimes we have to use a different much more accurate equation of state to figure out the reversible work especially if it's at really high temperature and pressure you just have to look things up if you're really doing important work you just become familiar with the steam tables and you calculate what you can possibly get and whatever you calculate for reversible when you actually make a steam to try to get that work it's going to be less than 100% efficient okay if we make a small change in internal energy U and we can write a small change to make this a little delta if you find the D intimidating same thing and I use a funny Greek delta here because these are not really things you can integrate because those things don't correspond to an area under a curve if I have something that corresponds to an area under a curve then if I go to here and then I go back and then I go to here I get the same area under the curve because it's a good thing it totals up if I have something that doesn't correspond to an area under a curve it's like for example having a spiral if I have a two-dimensional surface and if I have a spiral so I go around and I come back and I'm up above where I was and then I go around again and then I'm up here then I can't tell that doesn't correspond to an area under a curve and that's like friction if I keep rubbing something it depends not where my hand starts and stops but it depends how many times I rub the thing how much energy gets dissipated as friction so friction which is heat alone is not something that's conserved if you minimize friction with oil you'll get much better work out of high friction then you just waste a ton of energy turning work into heat if we only do pressure volume work we know what the work is that's just the external pressure times whatever the change in volume was and if we say gee what if we do it at constant volume well constant volume means that dv is zero and that means that the change in internal energy at constant volume is just the change in heat at constant volume and if I integrate this becomes a delta u and this just becomes q the amount of heat added or subtracted at constant volume and this tells us that if we keep something at constant volume and we add or subtract heat that's just going to change the internal energy of our system constant volume is another idealization because most things when you heat them they expand very hard in the lab to keep things at constant volume so this is kind of interesting theoretically but practically not that useful since it's very hard to do the experiment on the other hand almost every chemistry reaction we do is at constant pressure because we usually have an Erlenmeyer we're swirling it around it's in the lab at one atmosphere of pressure and so that we do often and we're very much interested in the heat at constant pressure and that's called the enthalpy conduct most reactions on the bench at constant pressure and we need to figure out how to calculate the heat released we need to invent a state function so that we can keep track of it no matter how we did the reaction because we don't know what the reaction is and the trick is we make a new function u is a state function and pv is a state function because if we specify the state we specify p and v therefore h is a state function and then we take h and we just do a little calculus we take its derivative if you don't like just dh you can always say dh dx if you've done that and then at the end you can get rid of all the dx's but the derivative of h is the derivative of u plus the derivative of the product u is this if it's reversible and the derivative of the product of p times v is the first times the derivative of the second plus the second times the derivative of the first and then the reversible work here is minus pdv so beautifully pdv goes away and we have the reversible heat and vdp and then if we say hey we don't let p change then what we find is that the change in this state function we made up which we're going to call enthalpy is the heat released or absorbed at constant pressure and that's very important because that's how we do chemistry reactions we usually do them at constant pressure you have to be a little bit careful if you have extreme situations in a car cylinder it's not constant pressure because you're pushing down and then it's expanding and so forth calculation is much more difficult than this but anyway this gives us an idea if we want to figure out what heat will be released or absorbed at constant pressure we could either do every possible chemical reaction or we could kind of have a system where we have certain numbers that we know and then we add and subtract things because it's a state function we don't have to know how it happened we add and subtract things and then we get what we want and the most important invention along these lines is called the enthalpy of formation it's the heat absorbed or released at constant pressure when you make one mole of a compound from elements in their standard states what the standard state is usually at 298.15 Kelvin but it's always at one atmosphere or one bar they've probably updated it now pressure and it's the most stable form of the element at one atmosphere pressure and usually 298 or sometimes they'll list another temperature and then that's what the standard state is at that temperature except for phosphorus where white phosphorus is the accepted standard even though that's not the standard form okay let's do a problem let's write down the correct reactions that refer to the enthalpy of formation for ammonia benzene and methane now we have to write some pretty improbable reactions but we don't care whether these reactions will go up in our lifetime we're just writing them down we first have to know what these trivial names mean ammonia is NH3 benzene is C6H6 which is a liquid and methane is CH4 gas we have to form each compound from the elements in their standard states and we have to balance the equation using fractions if necessary so that we get one mole of compound one mole when they say the enthalpy of formation is blah blah blah kilojoules per mole it's per mole of the compound not per mole of the reactant or something else and so here they are and I look them up if I take one half and two gas then I get one nitrogen and I take three halves and I get two gas I get three hydrogen then I can take these two elements and I can make ammonia and I can actually do this that's done on millions of tons scale and the enthalpy of formation it's exothermic it's minus 46.11 kilojoules per mole of ammonia for benzene I have to take six carbon atoms as graphite that's the standard form plus three molecules of molecular hydrogen and I get one mole of C6H6 liquid and it's plus 49 kilojoules per mole and if I make methane from graphite and hydrogen this reaction I certainly wouldn't want to wait around for it to happen I get minus 74.81 kilojoules per mole and it's kind of interesting that the enthalpy of formation of benzene is endothermic and you'll learn more about that in organic chemistry but benzene is kind of a special case in many ways okay, let's try to figure out how we could determine in the laboratory the standard enthalpy of formation of carbon monoxide carbon monoxide is poisonous and it's a gas and chemists tend not to like to deal with poisonous gases because gases have a bad habit of getting away from you and once they get out into the atmosphere they're very hard to get back the genie back into the bottle and they just prefer liquids by far but we have to deal with gases sometimes here's the literal reaction if we just look it up we take one half of a molecular oxygen plus C as graph carbon as graphite and we get one mole of carbon monoxide and it's exothermic to the tune of minus 110.53 kilojoules per mole we can't do this reaction in the lab because we can't ensure that when we burn the carbon we only get carbon monoxide because usually when you burn carbon you get carbon dioxide and how are we going to stop it adding two oxygens it does that very easily if it didn't we'd all die of carbon monoxide poisoning because every time we lit a fire we'd get tons of carbon monoxide coming up and it would kill us so usually it burns to give carbon dioxide and therefore we can't literally do this reaction we could do this reaction in the lab but we can't get it to go to this product we're stuffed we get carbon dioxide so what we do instead is we say hey this number whatever it is doesn't depend on how we made the mole of carbon monoxide because enthalpy is a state function we have to figure out a way to go around it so that we actually have two easy experiments and here are the two easy experiments first of all we burn graphite completely it's easy to burn something completely because you keep burning and burning and burning until it's all burned up that we can do we measure the heat and get CO2 and then we can get a canister of carbon monoxide that somebody's purified and we can burn that completely as well so now we have two reactions we burn graphite to get carbon dioxide and we burn carbon monoxide to get carbon dioxide and then all we have to do is add and subtract because we can measure the heat of both of these no problem if we reverse the second reaction and add it to the first we get this situation and then we can cancel out things that we don't need and we get the reaction we want and therefore if we just take this one here measure its heat we measure this one and we reverse it we'll get what we want and each reaction is pretty simple because we just burn it to completion and this really is the power of thermodynamics is that you can get something you can get a number for something that you want to get that is extremely difficult to actually measure accurately in the laboratory by measuring two things that are easy to measure accurately and then using the power of the state function to tell you the answer you want to get and what that means then is that if you look at the table of all these enthalpies of formation they all look like random numbers but in fact they're not because they all have to fit together like pieces of a puzzle because if I add and subtract this to that it has to be this number over here that's also in the table or something's wrong so they all have to be here's how they cancelled out initially initially to get this CO2 here I have a whole O2 and I have half an O2 here so when I cancel the half I put a half here and the CO2 goes away with the CO2 so it's out of our hair and so that's where I put the half in there that's how it disappeared and then the only things left are half an O2 and C graphite and then the only thing left on this side CO everything else is gone this is the one then that I want the enthalpy of formation is just a way to standardize the heat of reaction with respect to the elements but oftentimes the reactions that we would write down are just never going to actually happen in the lab for example you can look up the enthalpy of formation of glucose here's glucose in the open form circulating in your blood at about 80 milligrams per deciliter or much higher than that if your pancreas is giving up the ghost because you've eaten so much sugar glucose is highly regulated like sodium in your blood your body does not want a ton of glucose circulating in your blood glucose is fuel for energy but much like I fuel a car I put in gasoline in the tank and then if I say gee I want more energy so I think I'll start putting gasoline in the passenger compartment and all over the roof and everywhere else the car doesn't work well the reaction for glucose literally is to take graphite hydrogen and oxygen and get this and I assure you that you can never carry this out in the lab but you can write it down for the enthalpy of formation it doesn't matter whether you can actually carry the reaction out from the elements often you can once we know the enthalpy of formation we can figure out delta H for any reaction because we just decompose all the reactants into the elements and then just reassemble the elements into the new products and we've got numbers for every step if we want to react glucose with something we first take glucose and we turn it into carbon as graphite hydrogen as molecular hydrogen oxygen and then we take those and we assemble them back together into some other product and bingo we've got the enthalpy for that reaction for example here's an isomerization reaction this dichloroethylene the chlorines are on the same side once you've got a double bond it can't rotate anymore just like a flat plane sitting there floating around you got a single bond it can spin and they spin about 10 to the 13 times per second which is pretty fast these don't and therefore these two are different when the chlorines are across this has a different dipole moment than this this has a different boiling point than this this has a different human toxicity to your liver than this and so forth we call these isomers cis on the same side and trans is across across the tracks first decompose the cis isomer into the elements we make graphite hydrogen and chlorine and the energy to do this the heat will be minus delta H of formation because delta H of formation is starting with these three and getting this so if I reverse the reaction I reverse the sign of delta H reversing the products and the reactants and then I just take those same three and I reassemble them into the trans and I look up delta H of formation for the trans in the table and then delta H for that reaction which I can't do I can't go in there with a pair of tweezers and just go like this to every molecule I don't have that kind of control but I can still figure out what delta H for this hypothetical reaction would be from turning cis into trans it's minus delta H of formation for cis plus delta H of formation for trans and then I can figure out is that exothermic or endothermic will that release heat when I turn cis to trans or will it absorb heat when I turn cis to trans okay which isomer do you think without without knowing anything I realize you don't know anything I will post the slides so you can look at them which one do you think is more stable cis or trans whose lower down because the more stable one is the one will tend to get if one of them is valuable and the other one is not and the one that's not valuable is more stable I'm in trouble because I'm going to get a ton of stuff I don't want can be quite important to know well if you look at them they all have the same number of atoms stuck together because they are isomers that's essentially what isomers are and so the bonds are probably nearly of equal strength and I would guess they cancel out pretty much the big chlorine atoms and when we just draw these letters we aren't really drawing how big these are the big chlorine atoms are closer together on the cis because they are right across so they are like two big balloons annoying each other hey get out of here and they prefer to have more room and so if I rotate this one over to the trans where they are further apart that's going to be more stable and that's in fact true and unfortunately for chemists trans fat is more stable than the natural fat which is the cis isomer which is produced by plants if you look at fatty acids that are unsaturated that means they have a double bond plants always produce things where the carbon chain comes out on the same side of the double bond and they tend to be oils like corn oil soybean oil olive oil and what chemists did when there was a big worry that people were eating too much large is they said will produce a fat with a double bond it will be unsaturated and unfortunately it was the trans isomer which interestingly enough didn't spoil so if you put that fat into Twinkies they would be good for months and months and months because bacteria didn't like that fat either things that bacteria don't like are not good for us and things that kill bugs are not good to breathe and so what happened was a lot of health conscious people switched from butter to margarine and ate a ton of trans fat in the 70s and 80s and then they died of a heart attack and then the health authority said hey what is this trans fat does that promote heart disease and it turns out of course it promotes it like crazy worse than large worse than just saturated fat so it had a double bond but in fact because it was a cross it would stack up and trans fat is this vile solid material white and just terrible and you just throw it in and you make a ton of donuts or whatever with it and then people people tend not to eat fat on its own I've never seen anybody take a stick of butter and just go if you take fat and flour and sugar people go wild and they eat the same amount of fat but they don't realize it and so Shaka's rule is if the fat is solid at room temperature don't eat it at least not much if it's liquid you're probably better off let's talk about Hess's law it turns out our isomerization reaction is just a special case of Hess's law in fact Hess's law is nothing other than the enthalpy is a state function so the enthalpy of a reaction is always the sum of the enthalpies of formations of the products minus the reactants for example if I want to figure out the combustion of acetone here's acetone used in fingernail polish and all kinds of things that smell and I take acetone and I burn it it will burn with oxygen I'll get three moles of CO2 and three moles of H2O then I can ask okay what is delta H for this reaction and the answer is if I know delta H of formation of all these guys and this is an element so delta H of formation of an element in its standard state is always zero then I have these three that I have to look up on the table it's duck soup I just look them up and I have to multiply them by the numbers because delta H is for one mole and I made three moles so I'm going to get three times as much heat therefore the delta H the enthalpy of combustion is just three times whatever the enthalpy of formation of carbon dioxide is plus three times whatever it is for water those are the two products minus whatever the formation is for acetone and then O2 being an element the delta H of formation is zero so I didn't bother to put it in but I could put in delta H of formation of O2 and later put it in as zero and that's how you have to do it you just have to be sure that you include the threes here because it is per mole and you made three moles so it's three times as much and that's why you have to be able to balance chemical reactions because if you get the numbers wrong when you balance the reaction then you get the heat wrong then everything's wrong and not surprisingly the very first thing we teach you to do is to balance chemical equations okay let's talk about heat capacity think probably the last time I had raisin toast was in college but I do recall that the raisins are always hotter than the toast but everything's at the same temperature so why is it that the raisins always seem hotter or why is it that if I get in a steam room it's much hotter than a sauna at the same temperature has to do with the heat capacity and the heat capacity just measures if I put in so many joules of heat how much does the temperature go up I put in the same heat the different things the temperature goes up a different amount some things seem to have an ability to absorb heat without actually raising temperature all that much water for example is very good things like that are very good to cool stuff off because they absorb a ton of heat that's why we use water to put out the fire and whatever this proportionality constant is here this heat is called the heat capacity and if you do it at constant pressure it's the constant pressure heat capacity and if you do it per mole then it has units of joule per Kelvin it turns out that CP itself can depend on temperature it's not just a constant but it may change as you heat stuff up and if you want to do accurate work you have to take into account the temperature dependence of CP and in fact you can look it up in tables there are tables of the heat capacity of all kinds of things that just give you something like this I start with this equation and I integrate from the standard temperature which might be 298 I can look up delta H in the table at 298 and I can look up I can go to some other temperature let's say 1000 Kelvin where I want to run my chemical process and I can take the difference between the enthalpy state function of these two temperatures and that's just equal to the integral of CP of T DT so I need to know what the heat capacity is as a function of temperature and if you look it up in books they usually give you something like this they say the the heat capacity of water is A plus BT plus CT squared plus sometimes D over T or T2 and they give you numbers here and that means that you can shove in these numbers you can go to integral.com and you can just do the integral and you get an expression and then if you put in T final and T initial you get the change and what that lets you do is that lets you start at 298 Kelvin where you can look up enthalpy and then you calculate the enthalpy of a reaction at any temperature nobody has to help you you just do it and sometimes reactions are endothermic at one temperature and then they become exothermic at another temperature it just depends well we just do this trick for every reactant and every product and I just want you to see this for me but I want you to understand that you can calculate the enthalpy of any reaction at any temperature if you know the enthalpy of formation of the standard temperature and if you've measured the heat capacity of the materials over the temperature range of interest and if you haven't you can estimate the heat capacity so you can still get an estimate if we've got a flame we've got a welding torch and we've got a flame the usual assumption is the reactants come in at 298 Kelvin they react and then the excess heat heats up the products so it's the products the CO2 and the H2O or whatever the products are that are coming out of the flame then really hot and if I know the heat capacity of the product and I assume no heat is lost when I ignite the flame because it's burning so quickly then I can figure out how hot the flame can possibly get and that's very useful if I want to use the flame to for example make a welding torch there'll be certain kind of gases that I can combine spark it and I can get a torch and it's going to be really really hot so I can weld steel with it and there's going to be some other gas like liquid propane that if I use that in a welding torch it's not going to get hot enough to make a proper sealed actually melt the stuff and get it to weld together and therefore if I know how hot I have to get it and I have a choice of buying a canister of gas I buy the cheapest one that's going to do the job that's the one I have on the work site not one that goes to 3000 Kelvin that I don't need if I don't actually need that okay we won't have time to finish it but let's just set up the scenario we know we can write down delta H for reactions that we can't do and there's one special reaction that we can't do which is the lattice enthalpy of a crystal that is of a lot of theoretical interest and so we'd like to get a number for it because although we can't do the reaction it turns out theoretical chemists and physicists can calculate what it should be and they want to know if their calculation is right on the money agreeing with experiment or if their theory about how all the forces in that salt is wrong so we want to be able to supply them with a number and here's the lattice enthalpy it's a very simple reaction to write down we take a salt for example potassium chloride which is a solid and we vaporize it into the potassium ions and the chloride ions we just take the salt this big crystal has a unit cell and we just go poof and we make potassium ions and chloride ions as gas we can't do this reaction in the lab it's never going to work because they'll just they'll tend to stick together these have opposite charges but for a guy with a computer and time on his or her hands this thing is fun to calculate because when you calculate the attraction in the crystal you have to say gee there's a potassium here and a chloride here they attract and then hey there's another potassium on the corner they repel and there's another chloride here they attract and he attracts this guy and this is a great big puzzle to write down an endless fun and you take different amounts and you say how many potassium repulsions do I have to include here and people have worked out how to do that and it's quite interesting to get into the statistical mechanics of that and because we can't measure this in the lab and because theorists would like to know the number so they can compare with their calculation we instead have to find a bunch of reactions that we can measure in the lab and then we have to add them up to get the one that we're after so this is going to be our method we'll start on this next time we'll add what we're after we're going to need five different reactions