 Pretty easy for a theorist to calculate. They can calculate the energy of an isolated K plus ion in a vacuum, an isolated Cl minus ion in a vacuum. And if you tell them the crystal structure and that there are so many distances, then this is the kind of problem a theorist loves. Wow, how am I going to sum up all those positive repulsions out to infinity, and then all the attractions and figure the total energy of attraction of that crystal. And then compare it with the isolated ions. And our solution then was to try to come up with some reactions using Hess's law, to come up with some reactions that we can measure quite easily and that total up to the one that we want to get. So we just play a game of figuring out what we can measure for this reaction that we can't easily carry out in the lab. And what we're going to do is we're going to do it by stages. We're going to first take the atoms and then we're going to move an electron off one and on to the other. And we're going to keep track of all the energy in all these processes. And then we're going to total it up and see what we can get. Now the problem here is that some of these energies are rather large. And so although we can get a number, the number may not be as good as we would like because when you have to add and subtract large numbers, you lose precision. I get on the scale, I get a pretty good number. I put a submarine on a scale and then the submarine plus me and subtract and I can be plus or minus 1,000 pounds depending whether the tide was going in or out and a bunch of other stuff. And so we have to worry about that here because some of these numbers are going to be big. The first thing we're going to do is we're going to decompose the salt into its element because that's the heat of formation. That's the enthalpy of formation of potassium chloride. We can certainly measure that. That's in tables. The delta H of formation is in all kinds of tables for all kinds of simple compounds. So we can get a good number for that and because we're going backwards, it's minus the heat of formation. So we make potassium metal in the standard state and a half a mole of chlorine, molecular chlorine gas, again in the standard state. And then we have to take the potassium in the standard state and we have to turn it into potassium vapor. And I've mislabeled this but I'll fix it. This should be delta H of sublimation, not vaporization because I didn't start with a liquid, potassium solid at the standard state. And then we have to make a single chlorine atom out of molecular chlorine. So we take half a mole of Cl2 and make a whole mole of Cl dot. Chlorine atoms, far, far more reactive than just molecular chlorine. In fact, the Air Force had a program on ultra high energy fuels. You may know that in the space shuttle, they use various kinds of propellants, for example, hydrogen and oxygen can be used and you get a lot of thrust out of that. But in theory, if you could have instead of a tank of hydrogen and instead of a tank of oxygen as the diatomics, if you had a tank of H dot and a tank of O dot, it would weigh the same and you would get much, much, much more thrust. The problem is how do you stop the recombining and going back to the more stable form while you're waiting on the launch pad? And if that's a very energetic process, then your rocket just catches fire sitting there. So it's easier said than done. But anyway, there has been some work on that. Then we take the potassium metal in the gas phase and we ping an electron off it. And that's the ionization energy of potassium and that can be measured quite well. It's a fairly big number because as you can imagine, to take an electron off the atom is not quite so easy. But anyway, that's called the ionization energy and it can be measured quite well. And then we have to take chlorine and we have to add an electron to the atomic chlorine and it loves that, boy, it loves to get an electron and complete that octet. That's quite energetic and that can also be measured. That's the electron affinity of the chlorine atom. And now if we just take all these, the delta H's that we've got, we know that if we add the chemical equations, we just add the delta H's because delta H is a state function and it doesn't matter how we get to the final state, including by an imaginary path like this one. So we cancel out everything that appears on both sides and we end up with the reaction that we want. KCl as a solid going to K plus in the gas phase and Cl minus in the gas phase and then we just add up delta H1 plus 2 plus 3 plus 4 plus 5 and we get a number. And then we can compare the number with the theorists and then argue about who's right or who's wrong. The experimentalist says to the theorist, hey, you better make your calculation more accurate. You made some approximations there. You better go back and do it right and the theorist says to the experimentalist, you better do that experiment more carefully. I don't really believe that number you're getting there and until they come into registration, somebody's wrong or something's not taken into account. Sometimes there's something not taken into account and you make a discovery. So science, when everything agrees, is quite boring. When it's exciting is when you have two sides and both think they're right and then something doesn't agree and the question is what's out of whack? And that means that you're going to make a new discovery probably once you figure out what's going on. Okay. The lattice enthalpy I figured should have something to do with the melting point of these salts. They all melt at very high temperature but potassium chloride, if you heat it up enough, will melt into a liquid like ice melts into water. Be a nice clear liquid has essentially no vapor pressure because it boils at thousands of degrees Celsius and it can be a dandy way to move heat around. Molten salts are being explored as ways of storing heat, moving heat and so forth because they have very high heat capacities because moving these ions apart takes a lot of energy. The problem is you have to keep them quite hot or they solidify and if they solidify in your piping system then you're in trouble suddenly and so there's a trade-off. You usually don't want too high a melting point molten salt and I plotted some that I found here as a scatterplot and I plotted the lattice enthalpy on one axis and then the melting point. We had things like sodium fluoride and so forth. I didn't label them all but it looks like there's more, you know, there's kind of a trend, the correlation is weak. If these results were in biology and not chemistry, this would be proof positive of something or other, okay, that eating sugar gives you diabetes. These plots tend to look like this. But for a chemist we'd love to see things better. We'd like to take something else into account. Maybe these have different crystal structures and maybe if we took the crystal structure into account some way which has to do with the melting point then maybe these would start lining up better and then we'd have a better idea of what the true forces and energies in play actually were. But you can see we've got a range here and there's some correlation but it's definitely not something to write home about. Okay, there are also tables of trying to keep track of the energy it would take to break each kind of common bond that occurs in chemicals. And the way that's been done is that we get a library of representative compounds and we try to measure how much energy it takes to break each bond and they're slightly different because if we have something else there it may depend. If we have a carbon and there's a hydrogen hook to it, that carbon-hydrogen bond it takes a certain amount of energy to bust it apart into H dot and the carbon with a free electron on it. And the energy it actually takes depends on what else is hooked to the carbon. Is there an oxygen on it? Is there a nitrogen on it? Is there a fluorine on it? So on. But we can get a representative idea by just taking a bunch of compounds and then averaging. And so here's what we might do for methane. We can do these kinds of reactions. Usually this is done with a laser in a molecular beam or something like that but in any case we can do it and we can get an estimate of the energy and we have a certain amount of energy to break one CH bond in methane and make the methyl radical free radical and then H atom not molecular hydrogen. And then if we take this guy, we can knock another H off and make this guy, he's like an angry B CH2. You can't let these hit anything or touch anything because they react like that. Bingo. So you do this in a vacuum with a beam coming through and you shoot a laser and you see how much energy it takes to get the products which you measure separately, usually in a mass spectrometer. And then you take the methylene CH2 and you make a methine CH and another hydrogen and then you finally pluck off the hydrogen of the methine and you get carbon in the gas phase and hydrogen in the gas phase and you total up these four which are not the same but they're fairly close. They aren't totally different. The first one and the last one may be different. The others may be quite similar and then the average that we get is for this the average what we call the average strength of a CH bond in methane would be atom all up and divide by 4. And so these are extremely useful because if you have a table of mean bond enthalpies as long as you've got the kind of bond you're looking for then you can just add up the energy to bust all the bonds and then add up the energy to make all the bonds and you can get an estimate for the enthalpy of any chemical reaction you like. You don't need to know the heat of formation or anything but it's only an estimate because these are approximate. These numbers move around and this has been done. You take a bunch of them and you don't just take methane but you take ethane and propane and some other ones and it requires a little bit, yes. No, that's the average for one CH bond, okay, averaged over methane but when they give you a quote in a table for a CH bond they haven't just done methane, they've done a whole bunch of things. And what I was about to say is it requires some judgment when you're making the table what compounds you measure to put in the average, right? Just like anything. What do you count or what do you not count? For the census do you count people who are homeless or not, things like that. And if you know you're going to miss people do you try to estimate as well as you can who you've missed because they're sleeping under a bridge or do you just say no? Sleeping under a bridge you don't count. You don't get any services. Same thing here and I don't know exactly what they've included in the library because they usually fail to say but the current mean value that they get just to break one CH bond is 412 kilojoules per mole for a carbon hydrogen bond. That's the currently accepted value I think. And lots of bonds are listed so lots of them are there, they have mean bond enthalpies but you have to pay attention to the kind of bond. A carbon oxygen single bond requires a lot less energy to break it than a carbon oxygen double bond. And so they will in the table try to tell you what kind of bond they're talking about and you have to make sure when you look at your compounds that you're breaking and making the right bonds or you get the wrong estimate. And as I said if we know these bond enthalpies, these estimates then we can estimate delta H for any reaction and we don't have to do anything and that's quite powerful because we may want to get an estimate about whether something's even worth considering. If the estimate's so far off that it's not going to work the way we want it to then we try to look for something else and so we've saved a ton of time because rather than combusting the thing and measuring it and then saying gee that's no good I'm going to need a tank as big as a freighter on that car if I use that fuel. We can do that just sitting at our desks. And conceptually all we're doing is we start with reactants. We convert them all into atoms. We bust every bond and then we take the atoms and we reassemble them into the new guys. Obviously atoms are conserved in a chemical reaction. That's why we balance the chemical reactions. And then if we got more energy out than what we used to break it apart the reaction is exothermic. If these are more stable these bonds are stronger then we're going to get heat out. When it makes a strong bond it shakes everything else out as heat. That's what happens. And then as I said we just recombine these we make the new bonds and then we tally it up and we see if the reaction is going to be exothermic or endothermic. And let's try this. Let's take a simple combustion reaction and try this. Okay. My example will be ethanol. The ill-fated ethanol push which was great for farmers who are growing corn and terrible for everybody else. One lesson from that debacle is that you should not burn food. Burning food is a bad idea. If you're going to make a campfire you don't throw all the chili con carne and spaghetti and stuff into the fire even though it'll burn. You throw wood into the fire which you can't eat and then you cook the other stuff. But what we are effectively doing by converting a lot of corn into ethanol to use as fuel is we were diverting corn from food and there was civil unrest in Mexico right away because the price of corn tortilla is surged. And if you want people to get angry make them hungry. That works. Remember the French Revolution? It's what happens. We have to watch out for stuff like that. Okay. So let's estimate. Well the first thing you have to do is balance it. And complete combustion always means CO2 and H2O. And if the fuel has nitrogen in it you have to be careful. You're going to get NOx of some type, NO2 and you have to kind of know what conditions you're operating under in that case. We take ethanol, CH3, CH2OH and we need to have two moles of CO2 because we've got two carbons so we have to have a two there. And we have to have let's see three that's six so we have three moles of H2O and then we just figure out the O2 after the fact to make it work. The O2 doesn't matter for the enthalpy of formation because the enthalpy of formation of O2 is zero. But for this thing we need to look up the strength of an O2 bond because we have to break three O2 bonds and then we have to reassemble them into CO2 and H2O. And therefore in this case it counts and we have to look it up. If you don't know the structure of something that has a name, ethanol or toluene, then you have to look it up and you have to get not just the molecular formula like this but you have to get it in a way that you can see how many of each kind of bond you've got. And therefore you have to know the structure of what it is that you're reacting. You can't just know the name or the formula. You need to know really the structure of it. This one is pretty much the way I've written it. There's three hydrogens on this carbon. The two carbons are then hooked together. There's two hydrogens on this carbon and then this carbon is hooked to an oxygen and then finally the oxygen is hooked to one hydrogen in ethanol. And therefore if we total it up we've got one, two, three, four, five CH bonds, one CC bond, one CO single bond and one OH which has to be a single bond. And then the oxygen gives three OO double bonds which we have to look up. That takes energy to break them apart. And then the products have four CO double bonds but carbon dioxide is kind of a special case. So if you look in the table carbon dioxide will be set aside separately because the CO bonds and carbon dioxide are especially strong. They tend to be a little bit more than other CO things in formaldehyde for example. We have four of those and then here we've got two OH single bonds for each of those and so we've got. And if you're doing this on an exam any bonds that are the same that you're making and breaking. If I have six OH single bonds here and five here then yeah, I can cancel five of them because I'm going to count them the same when I look them up so I don't need to, you know, whatever I can cancel out before I actually start adding and subtracting numbers makes it faster. The more stuff that cancels the luckier I am. And there if you do that then you'll figure out what you get and the easiest way to see what's going on is to draw an energy level diagram. I start with the reactants here. Ethanol and molecular oxygen and it takes energy to atomize them all into atoms because I'm breaking bonds and that always takes energy. And then I get a ton of energy back when I make these guys and therefore this is going down. This is exothermic like crazy using these atoms to make these stable molecules. And then the difference between this one going up and this one going down is what I want which is my estimate for delta H for this combustion reaction and that's just how I do it. It turns out then that in this case it's the reactants minus the products because these are all positive numbers breaking bonds. They're all listed as positive numbers in the table. And you have to be careful about that because usually it's you take the final state minus the initial state and this looks like it's backwards but I usually draw this. I draw an energy level diagram and I see which is which and then I figure out what I'm going to get for the entire thing that's the easiest way to do it. Okay. Some comments. These are only estimates. They can be maybe plus or minus 10% in some cases so you can't trust them too closely but they'll give you an idea. And they may not ever predict subtle things. For example, remember we had those two cis and trans dichloroethylene and we decided that the transform would be more stable because there would be steric repulsion between the big balloon like chlorine atom. But if I do it this way then because both of them have exactly the same number of bonds then they're predicted to be equally stable. It takes exactly the same amount of energy to break apart cis dichloroethylene as it does to take apart trans dichloroethylene because I just count the number of bonds. I got one CC double bond, two CCL single bonds, two CH single bonds and they're both the same but they're predicted to be exactly the same and that shows you that this approach is never going to tell you some subtle thing about structural isomers based on this because it's not accurate enough to ever possibly do that. The reference state for these reactions is always the isolated atoms. Whatever you have as reactants, whatever you have as products, you're going up to a common denominator up here of isolated atoms. That's how you're figuring out what's going on. With enthalpy of formation, the common denominator is the elements in their standard states and because those things have actually been measured by somebody, those numbers are way better. Therefore if you have a choice, if you have all the enthalpy of formation of every chemical in a reaction you always do it that way because that's going to be far more accurate but you may not in some cases, you may not have the numbers you need. This thing we invented, the internal energy U plus PV is really of central importance in chemistry because we usually carry out reactions of constant pressure, not constant volume. Therefore we're interested in the heat evolved at constant pressure, not the heat absorbed or released at constant volume. Therefore there's hardly any mention of delta U except to introduce the idea of internal energy being the sum of heat plus work and then after that chemists rapidly move all the way over to delta H and that's it. That's all they talk about after that. Okay. Let's talk now about heat flow. If we add heat, let's say with a blow torch to a block of copper at constant pressure we will raise the temperature of the block of copper and if we pick another material for example aluminum then aluminum starting at the same temperature and receiving the same number of joules of heat will rise in temperature but not as much on a per gram basis. If I take 10 grams of copper and I put in so many joules of heat the temperature goes up so many degrees. If I take 10 grams of aluminum and do the same thing the temperature goes up but not quite as much and you'll notice that if you buy expensive cookware the bottom of the pot is copper often, right? And then the sides of the pot are aluminum or something else and if you want to place in hell where the coals are warming, hang all those pots up so that everybody who walks into your house can see them all the time and then you spend all your time polishing the copper which always tarnishes so that it looks beautiful and you can see your face in it. If you want an even worse chore go over to Newport Beach where a guy has a solid copper garage. Of course what you're supposed to do with copper if you have a copper roof is you're supposed to let it turn green like the Statue of Liberty. You're supposed to let it get a patina so you get copper sulfate, copper oxide and then it just sits there and that's what you're supposed to do but if you're stubborn and you say no, you know, I like the look of shiny copper then what you have to do is every week you have to get out there and polish it with polish because oxygen will react or you have to coat it with plastic but then or some varnish but then it's not quite as appealing as just the bare metal and I run by that house every other week or so and I'm absolutely amazed. He must have an army of people polishing that garage because it's always very, very impressive. A little green around the edges but nothing worse than that. That's a very bad idea to set up a lifestyle like that unless you can afford to have someone else do the work. Okay, so if we measure the temperature rise per gram we get something called the specific heat. The specific heat has units of joules per gram per centigrade and the specific heat of aluminum is larger than that of copper therefore the bottom of the pan will rise in temperature more quickly if it's aluminum I won't be wasting my gas flame heating up the whole pot I'll heat up the bottom and then start cooking whatever's in there right away more rapidly. Also copper conducts heat extremely well. That's another issue. If I take these two blocks and they're at different temperatures and I want them to come to the same temperature all I have to do is bring them into thermal contact usually that means you bring them so they touch or they're very near each other so they're both heating up air but in any case eventually if you bring them close and in thermal contact they will come to a joint temperature and it'll be in between where the two started. If you sit down on a metal chair in a stadium let's say that's been baking in the sun sometimes the first thing you do is sit down and you get up again because it's so hot it's actually burning your butt off but if you sit in a plastic chair that's been out in the sun it doesn't seem so hot the question is what's going on and I think I mentioned this last time but if you toast raisin bread and then eat it while it's hot the raisins always seem a lot hotter to your tongue than the bread. The question is what's going on since these are presumably at the same temperature and the answer is that your heat receptors don't respond to temperature they respond to heat the molecules that are detecting if it's hot or cold and sending signals to your brain saying get your hand off there now or run if they're flames are responding to heat and so it depends how much heat gets transferred to you and it also depends how quickly it gets transferred to you because you have blood flow going through various parts and if the heat is transferred slowly your blood goes through and takes some of the heat and new blood goes through and the temperature locally doesn't go up that much and so you say well it's hot but I can eat it but if it's too much so it's starting to cook you that hot you either spit it out or you get up off the chair and so there are two issues as to what goes on. The first is you're responding to the total amount of heat not the temperature. Something that has tiny heat capacity that's extremely hot like a little spark from a sparkler that lands on your arm doesn't although it's extremely hot it doesn't have much heat content because it's a very tiny mass and therefore it tends to bounce off and not burn you even though it's extremely hot. And the other thing is it depends on the rate at which the heat is transferred as well and metals transfer heat extremely effectively so when you sit down you get a lot of heat coming in quickly and then you're off that thing and they have a high heat capacity so they can store a lot of heat when they go up a few degrees that a lot of heat's gone into that chair more than the plastic chair and then when you sit down and you're colder all that heat goes into you and then you get off a few proteins start coming undone on wound and you're off. Do you know what temperature it takes water to be at what temperature before you say no, no. Anybody got any idea? Because if you do you can stick a temperature in something before you get in. That's sometimes a good idea if you're in a hotel and you draw a bath and that's in Europe sometimes the water is boiling and you can if you your way of testing it as you put your foot in then when you struggle to get your foot out you can actually flip and fall and get hurt because it's burning your foot to that extent that you kind of panic and lose your balance. I think Princess Margaret did get scalded in the palace in England because the water was drawn that was too hot, not enough cold in and she just got in and then slipped and fell in the tub and then you have to get out and by then you're red and it was just way, way too hot. It turns out it's only 120 degrees. At 120 degrees you can put for example your foot if you've got an injury from plank tennis because I've done this you can put your foot in your leg up to your knee 50 Celsius that's it not even close to 100 Celsius, 50 Celsius in water that's it. If it's going to get any hotter you can't stand it you take it out but if it's that temperature you can leave it. They usually don't have it quite that hot but they liked it. They like to heat up joints that have problems then work the joint to get the flexibility back and then ice it right away to bring down the inflammation and if you do that regularly if you're an athlete you'll heal much more rapidly than if you just sit around and say ouch my elbow hurts so they do do that. Okay let's use the first law then to predict the joint temperature that two or more masses will reach at equilibrium. This is problem 39 then. Let's take aluminum and copper. Let's take 10 grams of aluminum initially at scalding temperature 50 degrees Celsius and 15 grams of copper initially at 20 degrees nice and cool and let's just bring them into thermal contact let's have them touch and let's assume that none of the other heat is lost. That's a big assumption because if you have hot things and you have air obviously the air going over it can cool things down and therefore you have to be extremely careful when you're measuring heat that you don't lose any heat. If you lose any heat to the air or some other place it's not accounted for and you get the wrong number. If we do this in an insulated container and no heat's lost to the surroundings the question is what joint temperature will they reach? The specific heat of aluminum metal is 0.9 joules per gram per degree Celsius and the specific heat of copper is only 0.385 joules per gram per degree Celsius. Well this is what's going to happen. We have the hot guy and the cold guy. They're initially at different temperatures and we bring them into thermal contact heat will flow from the hot guy to the cold guy. Okay? Heat always flows from hot to cold. And then finally they will come to some joint temperature. While they're, when they're at a joint temperature like this they're dead. We can't use them to do anything. When they're initially like this if instead of just bringing them into thermal contact we do something else like we use this guy to boil some water and make some steam and run a turbine and we use this guy to cool off the steam so that we get a pressure difference across the turbine so we can spin it then we can do some work. We can actually produce energy. Once we have things at different temperature it's like water behind a dam rather than just opening the dam and just letting it go out we can let the water go through and generate energy and it goes out and we bleed off something to do something we want to do. But in this case we're just going to waste the potential here to do work and we're just going to turn it into this average temperature. The question is what is the average temperature? Now the key thing is that heat has an algebraic sign. It can be plus or minus and therefore you don't want to try to second guess who's heating up and who's cooling off. You can always do that if you're given two masses because you can assume the cold guy's heating up and you can assume the hot guy's cooling off and you're going to be 100% correct. But if you're given three masses like you might be given on the next exam then if you try to do it that way you may get into a muddle because you won't know if the third guy's going to heat up or cool off and then you're trying to guess the sign before you do it. Therefore you don't guess the sign. You just follow the rote procedure. The temperature is going to come out somewhere in between but the heat that's going to either flow from or to, I'm not going to try to guess, the aluminum depends on the specific heat times the mass of aluminum and then it's always the final temperature minus the initial temperature. That's all you have to remember. It's always final minus initial in thermodynamics anyway but that's all you have to remember. And I don't care whether this Q sub AL is plus or minus so many joules. I do not care. I'll figure that out later when I figure out whether T star is higher or lower than T aluminum, what I started with. Likewise for the copper I write exactly the same thing. The only thing that's different is I, well, everything could be different. The heat capacity is different than I have however many grams of copper I have and then the starting temperature is different but the ending temperature is the same. I've got numbers for this, this and this, this, this and this. I've got numbers for everything here except T star but I need an equation. I have one unknown T star and I need one equation and the equation is that because no heat is lost to the environment and I didn't run a chemical reaction to make any heat, the sum of the heats is zero because energy is conserved and I didn't add or subtract any energy. Therefore my equation is Q aluminum plus, plus the sum is conserved plus Q copper is zero. That'll mean that one of them turns out to be negative but I never write minus and I never try to say, oh, the heat's going here and this is heating up and this is cooling down. If I try to do that half the time I get it wrong. Okay, so let's do it. Here's our first law equation. Q aluminum plus Q copper is zero then I substitute in what I've got here and that should be equal to zero and then I just insert the numbers and in this case I don't bother converting to Kelvin. I could but it doesn't matter because a degree Kelvin and a degree Celsius are the same size and I therefore it's only the difference I'm measuring and that's going to be the same and if I want the answer in Celsius why convert to Kelvin, get the answer and then convert back to Celsius. That's just taking time and adding extra steps that can do nothing except make you more error prone. I have then 0.9 times 10 grams times T star minus 50 plus 0.385 times 15 grams times T star minus 20 equals zero. I put in the numbers so I have nine joules times T star over degree C. I write it this way. This may be unfamiliar to you but I write it this way to indicate that T star's got to be in degree C. Okay. Because only then will the units work out for me. That's the term here. This one's 450, nine times 50 and then this one's this term here and then this 115 is this last term there and I add it all up and I get 14.775 joules times T which has to be in degree C minus 565.5 joules equals zero and I can divide both sides by joules to get rid of the joules and I will find out that T star in degree C should be 38.274 which I'll just round to 38.3 and that's the answer. And now that I know T star, if I were asked okay, how much heat did the aluminum lose? How much heat did the copper gain? I could go back and figure it out because I have a formula up here for how much and I can figure out if the algebraic sign was plus or minus in each case. Okay. And that's how I would do it. Final minus initial, if it's more blocks it's a whole bunch of blocks but I've got to know the starting temperature of each block, I've got to know the heat capacity of each block, I've got to know the mass of each block and then I just have another term here with T star and some other numbers and it's all the same. It looks intimidating but it's all the same. No matter how many blocks you've got it's always the same. There's a lot of them, you're going to use a computer obviously to do it because it takes too long, yeah. I called the final temperature T star in this case just because it was the common temperature, the special temperature at equilibrium but I could have called it the final, I could have called it T final. Oh yes, I could say after the blocks were put together they came to this temperature, what temperature were the blocks initially but the answer is I have to give you the temperature of at least one of the blocks because there's an infinite number of combinations of hotter and hotter and hotter and colder and colder and colder that will all come to the same final temperature. I would have to give you the temperature of one block and the final temperature otherwise you couldn't get it. You need to know two out of three of them otherwise you can't figure it. Because if you have a really cold one and a really hot one they make the same temperature as well what if they just started at that temperature and went nowhere. That could be a solution too, they were always a T star so I'd have to know the temperature of one of the blocks. Okay, calorimetry is the business of measuring calories. It's interesting to me that they list calorie content on food and then you ask the man in the street or the woman in the street and they have no idea what a calorie is. Here's the scary thing, a calorie in chemistry is the amount that it takes to raise one gram of water one degree Celsius but a calorie in food is a kilocalorie in chemistry. They just call it a big C for calorie for food but it's actually kilocalorie. And so if you eat 2,500 kilocalories a day you're up around 10 megajoules, 10 million joules. That is a lot of running. If you think of a machine that's going to do that and that's why no matter how much you exercise if you eat poorly or unwisely you're going to end up as big as a house because that's that there's no way. If you run a marathon flat out you'll lose one, you know, less than a pound of fat and therefore if you, you know, if you run slowly it's going to be 35 miles. So if you're one pound too heavy that's 35 miles you've got to do and then not eat. And usually if you do 35 miles last time I checked the second people hit the tape, right? And then they eat much more than they did because now they're not only hungry but if you're tired and hungry then your defenses are really pretty low and then if there's Snickers bars around you go wild. So you have to be careful. Well the calorie values on food are also a little bit of a suspect because if we just burn food in a calorimeter we'll get a delta H but it won't be the same as if we eat it. Won't be exactly the same because for example if the food has fiber the cellulose in a bomb calorimeter will burn and produce heat but because our body can't metabolize cellulose for us it's zero calories. If you just eat cellulose you die. You feel pretty full but there's no calorie content and if you keep eating cellulose and nothing else you just drop dead and therefore they have to try to buck out how much fiber is in there, how much stuff is undigestible. The other thing is that if you eat certain kinds of molecules your body may elect not to burn them at all. If you're short of a certain amino acid and you eat that amino acid your body doesn't burn that up and say yeah let's just throw that in the furnace. It instead elects to use it to synthesize new protein and therefore it gets much more complicated than you think sometimes to figure out what's going to happen. Well even if you measure in a calorimeter it's really tricky because heat can always leak in. Heat can get in from anywhere. You have to be ever so careful if you're accounting for heat and big mistakes have been made by measuring reactions and not being careful enough to ensure that no heat got away or got in. The calorimeter itself usually has a carefully calibrated heat capacity and then if you measure a temperature change delta T then that can be converted into joules of heat that you produced by running the reaction. Now let's have a look. Let's burn some magnesium. Don't ever burn magnesium because you cannot put it out. Once it gets going it's extremely difficult. Burns extremely hot and quite heat and it's extremely difficult to put out. But suppose we put a small amount, a tenth of a gram about of solid magnesium and we burn it in oxygen in a constant volume bomb calorimeter and the calorimeter has a heat capacity of 3,024 joules per degree C. If we measure the temperature rise and I don't know how they got four digits but let's go with it. If the temperature rises 1.126 degrees Celsius then calculate the heat given off in the reaction and kilojoules per mole. You can already see one problem when you're doing this. Where do you measure the temperature? What if you have three temperature gauges in there and they all measure slightly different temperatures? Which one do you take or do you average them and so forth? It gets tricky because you have to be able to mix things fast and get the heat to equilibrate everywhere so you don't have any hot or cold spots. Okay, the constant volume heat we'll just call it Q sub V is given by the heat capacity of the bomb calorimeter and then the change in temperature. Therefore I know the heat that was produced. It's 3,405.024 joules. I don't believe all those digits of course but that's an intermediate result. I work out that the molar mass by looking it up of magnesium is 24.31 grams per mole and therefore I have 3,405 joules per .1375 grams. Convert it to kilojoules. Convert it to moles and I end up with 602 kilojoules per mole. Well I had a look and I looked up the enthalpy of formation of magnesium oxide and it's minus 601.24 kilojoules per mole which is pretty close. Of course the enthalpy refers to constant pressure and this bomb calorimeter was done at constant volume which is slightly different. We might get a more accurate answer by using a bit more magnesium and getting a slightly larger temperature change but we should never let the calorimeter change temperature a lot because the heat capacity of the calorimeter will be temperature dependent and if I let it change too much I may not know what it is anymore unless I have an equation for how the heat capacity varies with temperature. When you have gases involved the constant pressure molar heat capacity is larger than the constant volume heat capacity because if I heat something up at constant pressure and it's a gas it's a constant pressure it always expands and therefore it doesn't heat up as much so its heat capacity looks higher because instead of just sitting there and going up in temperature like crazy it expands a little bit and that it has to do work to do that that energy comes from somewhere and so it's not quite as hot and therefore in more advanced courses you'll see that the constant pressure molar heat capacity of a gas is equal to the constant volume molar heat capacity plus just the gas constant which comes from PV equals NRT basically. Okay, here's a case study. These guys are going to lift grease out of the economic mire that it's in. And they are raising money for this project that is going to revolutionize power supplies. Here's their scheme. They're proposing to sell thermal power supplies and you can use them for whatever you want. You can heat, you can boil water, you can generate electricity and they tell you what they're using. The ingredients they use are high pressure hydrogen and powdered nickel. The first thing I would do is look up whether the formation of nickel hydride is exothermic because that might explain the heat that they're seeing. But the other thing you've got to be very careful about is that if you've got powdered nickel metal and hydrogen if you have a tiny leak and you let in oxygen you'll get an exothermic reaction like crazy and you'll be measuring all kinds of excess heat and you'll get really excited and you'll say, I've got this incredible power supply. It's way more than, right? And here's what they think they've done. They claim to have rediscovered low energy nuclear fusion. This is the kind of nuclear fusion that occurs only in the center of the sun or in an H-bomb. And they in their literature say that that's what they think is going on and that's why these power supplies are so great. And because they've patented all the intellectual property they're going to sell them worldwide and they're going to make a killing. And what they would like you to do is give them money so that they can get off the ground because they're a startup. And my question to you is whether or not you should invest because of course a lot of startups don't pan out and then you lose your money. The guys working there got paid and sometimes right before they go bankrupt they pay themselves a lot like they did at Lehman Brothers. So my question is could it be possible? Because we mustn't just dismiss it out of hand because it seems outlandish. But we have to ask could it be possible that they are seeing nuclear fusion in this device? Well let's look at their literature. Here's their description. This is freely available on the web so I don't think I'm doing anything too wrong. But anyway they show you this little picture. This is their pre-industrial prototype and they comprise single and multiple reactor so they use the R word configurations using nickel and hydrogen in an exothermic reaction to produce thermal energy in the kilowatt range providing safe and stable products. Now my question is how does it work? They have the answer, maybe this is hard to read down here, type of equipment according to Greek class, electric appliance, boiler, thermal source, chemically assisted low energy nuclear reaction. They just slip that in there. Now it's easier to see it. So there it is. Chemically assisted low energy nuclear reaction. Aha! The first thing you say is do you have any nuclear physicists on your scientific advisory board? No. Have you measured any gamma rays coming out of this thing? Because usually when you have nuclear reactions that's one of the site. No. Why do you think it's doing this? Because we looked at it after we ran it and the surface was really rugged and there were all these defects and looked like it had been blown up and so here's my conclusion on that investment. Unless they prove that that's what they're doing this is just a way to lose a ton of money. Okay? So this is just like the power enhancer thing but it's more sophisticated because it will produce thermal energy because nickel and hydrogen will react and if I leak oxygen in on the slide I'll get a big thing and then they come back and they put another tank of hydrogen and they recharge it with powdered nickel. But the question is how much energy does it take to make the powdered nickel and the tank of hydrogen? And what you'll probably find out is it takes a lot more than what you're getting out and they're just charging you an arm and a leg to recharge it once you buy the thing and then probably won't work. But we'll see, they might be able to prove that it does. Good luck. So here's my warning, many, many schemes sound plausible. Remember Alexander Pope, a little learning is a dangerous thing, drink deep or touch not the period in spring. There are shallow drafts intoxicate the brain while drinking largely sobers us again. So if you're an engineer and you understand their jargon and you don't understand that this is probably impossible, you might think it's a good venture. You might put some money in. Sometimes these things turn out to be correct but only if you let somebody independently verify it and sometimes very surprising things do turn out to be true and other things that seem self-evident to most people turn out to be false. That's why we've got science is to separate the wheat from the chaff and in every case we've got to do three things. We've got to repeat the experiment, not the same guy, a different lab, they repeat the experiment, they get the same result. It's repeatable. Second, we look for clues as to what's happening. If I'm getting a nuclear reaction I look for neutrons, I look for gamma rays, if I don't see any of those I don't believe it. And third, we never let anything except whatever the evidence is sway us. If we don't have any evidence for something then our default is to be skeptical always. We don't believe things without evidence because that way madness lies. Once you believe anything without evidence then I can just attach whatever else I want to that belief and I can extract money from you or do whatever I like. And so the default is if you're unsure you don't believe in it. Okay? All right. What we're going to do next Tuesday is work on some practice problems for the final and a little bit of Chapter 18. And then the Tuesday after that we're going to have the exam. So next week we're going to review practice, practice, practice. We're ahead slightly so we're okay.