Lecture 11. Mole and Molar Mass (no captions)
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Potma, Eric
UCI Chem 1P is a preparation go General Chemistry that covers: units of measurement, dimensional analysis, significant figures; elementary concepts of volume, mass, force, pressure, energy, density, temperature, heat, work; fundamentals of atomic and molecular structure; the mole concept, stoichiometry; properties of the states of matter; gas laws; solutions concentrations. Course may be offered online. Slides:
 Welcome back after a nice long session on Friday. Let me guide you through it. That's the score chart from last Friday. The knee was 56.2 standard deviation, which is basically a measure of the spread of the knee. It was 18.6, which means that this exam really cooled a lot of performances away from the chart. So it's a very broad distribution. For a teacher, this is great because I can beautifully expect a lot of performances. But a student in this report is not great, you all want to be right on close together and maybe somewhere more towards the 90s. So you may feel that 56 is not so good. Actually, completely fine. Completely on target. Last year, the performance was only 1 percentage point higher. So it was 57, now it's 56. That was very much average, I would say, for the years to come. Anything out of your board there. Let me say a few things. The exam was, like I said before, it was a little bit tight. It was part of the parcel of having only 50 minutes, including the ranging things. Again, other class, our new class, taking the same distribution exam. You cannot do it in another way, you cannot put your exam on the seat 400 percent. You don't have six hundred copies of several chairs, you simply cannot do that. So you have to move to the way you did it, takes a little time, takes a couple of minutes of your examination time. You know that. Many people told me that, and I said, I know that. And this is again part of this exam. This exam was tight, it was not very pleasant and comfortable. But on the other hand, you know, we still get a very good impression of what the performance of this class is. The second exam, you will see, will go a lot better. It is a little less intense. And it will feel more comfortable in the final, for me, relatively, I would say, now, even more time for you to take three questions. This is also kind of like sets the stage, because there are a couple of topics here that are important for you to be able to do these questions quickly. And so I definitely have had a lot of stuff here. I was trying to test you on several things, you sweep it all in, and this is the result. So not bad at all. We are on target. If you are on the low side of the mean, take this exam as an opportunity to see what parts of material need to be improved. So what is your personal weakness on the exam that means extra attention? You can hunt the office hours, you can go up and speak to your Twitter's, there's a special leader's Laura and Mike, who are very happy to help you out, ask them specific questions, take a human understanding, and ask for a specific answer. So again, you are in charge of your own success. You identify which parts of material are not easy to go with the use, and you act on it. Make sure that you get the information and be able to do the questions next time around. So I want to remind you, it's only 15% of your grade. This is for a particular reason. 15 makes up a lot. It really is not. The final is almost half of the grade. The final is really where it's all happening. The exam is really just a warming up exercise. Just to get started, so don't be demoralized, we didn't go so far for you. Actually, if you didn't go so well, it tells you which things you are going to go on. So it is more like an opportunity than an analyzing experience. Okay, yes? Do we get our grade too bad? Well, you can't approach the list first. Okay? It's actually on the slide. The grades of the old tests will not be curve. Only your cumulative grade will be curve. Your cumulative grade is two minutes, one final, and a homework together. That is your overall grade of this course. That will be curve. In my opinion, it doesn't make a lot of sense to curve individual exams. The much better measure of your performance is to look at your score. Your score is metric. It is a number that tells you how well you did. The maximum score is 100, and you have 50% of it means you get half right within a lot of time. That's what it means. Very good innovation with your performance. Don't do a riveting at the stage of your grade. It makes no sense. But it makes no sense to do that. Do that have an A or B. It makes no sense. At this stage of your grade, the only thing you should be concerned about is, do I understand that you're in? Okay? That is what you're in for. Worry about this riveting just till the better grade. Don't go telling your opponent what to do right now. It is just a waste of energy. Your exam will be available on the triple E page on Friday if everything goes right. So we have, as you noticed, we've rated everything on Friday. Very hard work. It's lost for educators and everything is done not manually. It's a very small thing. It's interesting how long you're in the same team. They are now currently in the coffee center. They're all being stamped and reproduced. And you'll see an idiot version in the real box. You're only in the airport when we're in town. This will take a couple of days. This is not really my control. It's not in the coffee center. Okay. You can contest your score if there is a genuine rated error. Don't come to me please with all kinds of arguments about why you should have more questions. That's not really the purpose of contesting your score. We have given questions, but it may be stuck to a very specific recipe for that. And we think the dollar can write a job. If your answer is correct, like you didn't get the points, you get your entire potential points. But if your answer is not correct, and someone in the margin has written something amazing, right, a little bit of an imagination, we cannot give you the answer points with that. Okay. So, if you guys do that, that's possible. Basically, I'm on the auto major. I'm just going to spend all my time with that. It's impossible. That's also not the purpose. I think you've graded very fairly. Okay, so the grading errors will be considered till... This is a Friday the 9th of November. So that means you get to return that on Friday, Monday and Friday, this Friday. And then you have one week time to talk to me. Talk to me. Send me an email. Okay, if you have a simple question, send me an email. I can do things right if you have a question. If you have specific questions, you can come to an office hours. Or you may even find it. Don't...the TAs are happy to discuss answers with you, but they cannot give you a question. They're only high to do that. Okay. All right. Let me quickly look at one question on the exam. It's about the can of Coca-Cola. This question, surprisingly, went not so well. Okay, most people were probably confused by this question. Let me go through it and just see who developed it in place. It says in doctor advices the patient not to consume more than this. Okay, so this is 85 grams. Okay, so I'm just quickly comparing the amount of what I have. This is 8.5 times 10 to the minus 2 kilograms, so it's 85 grams. Okay, so this patient should not consume more than 8 times the amount of sugar in an egg. Okay? Now, in one of these cans, there are 12 ounces of...sorry, this is 12 ounces. Okay? And it contains sugar at this concentration. So this is a volume. This is a volume. And this is a concentration, or a density. As you can see. This is gram of a liquid. This is mass of a volume. This is a density, and this is a volume. How many of these cans can this patient have? Alright? And the conversion here of ounces to milliliters is shown as well. So what do we need to calculate here? Well, what I need to calculate is, in the end, how many cans can the patient consume? What does that depend on? It depends on how much sugar is in there. Okay? 85 grams is the mass. So what I need to know is how many grams of sugar are in one can. Okay? I need to know how much sugar is in this can. It's a very simple thing. If your doctor tells you, you cannot eat so much sugar a day, and you see this on this...or probably... You want to know how much sugar is in this can. How many grams of sugar is in one of these cans? Right? How many grams of sugar is in one of these cans? Right? How many grams of sugar is in one of these cans? So that's a mass. Mass is volume times density. Do I have that information? That volume is not in milliliters or liters or whatever, but the conversion is right there. So what I do is this. Mass equals...this is the density, which I quickly convert from liters to milliliters. Okay? That's a factor of 1,000. If you can do that with a square meter in your hand, you can just write it out, because the difference between a milliliter and a liter is a factor of 1,000. Okay? So point 110 grams per milliliter times the volume. And the volume is right here, between parentheses. I want the answer in milliliters, so I use this conversion right here. 12 ounces, that's the volume, times this conversion factor. You see, the ounces will cross out, I get my answer in milliliters. So if you actually give this one here, you have your volume in milliliters, times this, milliliter, you get an answer in grams, 39 grams. 39 grams in one of these hands. Okay? You are almost right here to answer. This multiplication here of 1 to 3 numbers is basically the whole thing. All right? How many cans can you have? Okay, well, I have a maximum of 85. This is 39, so how many 39's are sitting at 85? 2.2. I can have 2.2 cans. That's it. That's the calculation. Okay, another issue is naming compounds. Naming compounds is something you can literally learn is a method, and to stick to the method, you will be fine. I saw a wide variety of very interesting, very intense. I'm going to give you a simple, some people say, this is sulfur fluoride, it's almost right, but not quite. This is hexafluoride. Okay? Sulfur hexafluoride. Oh, this is a nice one. I remember in one of the lectures, I say, be careful, about 20% of you guys are going to do this one wrong. Okay? Because you will say sulfuride, and it is sulfur fluoride. And you can hit it. I'm going to say 20%, about 15% of the folks did exactly this. Okay? So, you have to pay attention to it, because even people that's actually very interested in me, they put in 2-minus here, and I said, if I forgot, who's the 2-minus? They put in 2-minus here, and I said, oh, it's sulfur. This is solvent trioxide, it's a neutral compound. Okay, this one. Some folks said, disesium carbonate, this is an ionic compound. You never use this indicator, okay, this prefix. It is cesium carbonate. Ionic compounds do not have prefixes indicating the number of atoms. How about this one? A lot of folks said this, copper 1, selenide. But selenide is in the same family as oxide, right? It's in the same column, but this is 2-minus, I mean, the copper is 2. It has a charged 2-plus, oxidative state 2. This one, now what does this mean, guys? It's dissolved, and this is an H. What does it mean? Acid. Still, still, okay, a fraction of folks still call this ionic nitrate. Don't say the name, okay? This is nitrous acid. And this one, lastly, this is almost the same kind of situation as in this one, copper selenide. People call this barium, actually not the same situation, shavings iterations here, they think this is a type 2 metal. Barium is not, barium is 2-plus type 1, okay? It's in a second column, and those are type 1 metals. You never specify the oxidation state of type 1 metal. So, barium is 2 chloride, a disbarium chloride. Okay, keep your states in mind, keep practicing, and then we'll see if I've tried to find a concept on the UBU leadership. We have to move on, okay? We're going to chapter 3. So, we did already a quite big chunk of the material so far, and we're hopping into the next set of topics. So, what it is about. In chemistry, we deal with a lot of atoms. We need a material which is the whole of your hand, the solution, the sugar in your coffee, if not one molecule, there's too many. So, instead of talking just about one thing, we have collections of atoms, like collections of Ticke. But the problem is that these collections are rather large. Okay, so I'm just giving you an idea. This is one person, you can easily think of this, of this one person, just conceptualize it, there he is, one one guy. And then, we can even conceptualize this iteration here as counting about 300 million people. Even though here, there are people who say, look, there's a huge number, for some reason, our brain kind of understands that number. And we understand 300, that's about this. So, we kind of conceptualize it. Now, if you look at ions and molecules and atoms, the numbers are rather staggered. Okay, so this is one ionic hand, you can easily grasp it, this is just one sodium and one chlorine ion, they're together, nothing is wrong with it, easy to conceptualize. But what if you have one of these little chunks, one little grain of salt, tissue salt, already has one times 10 to the 19 ionic pairs. 10 to the 19 is a staggered number. Okay, that's huge. And this number here fades, prepares, to how many ions are in there. Our mind cannot poke in hand the magnitude of this number. You can try, but you don't, because you don't have the frame of reference. You're kind of lost on this number. And consequently, it's hard to do calculations and calculations with these numbers. So, it makes a lot of sense for chemists, and also for you, that you are as far in hands, you don't know yet, as you will. To have a different way of treating these large numbers. And you have to work this number, and that's the mole. What is it? It's a number. I can feel you excited. Okay? It is a number, that's it. That's all you have to know. We're not sorry. It makes funny numbers. I'm not sure if my M3 is very impressive, when you memorize this number, it's like my name. Oh really? That's great. So how many digits do you know? How many digits do you know? Four digits, or five, six? So, this number is big, right? It's big. It's 6, 4, 0, 2, 2 times 10 to the power of 23. And that's a very, very big number. But it is a number. I just want you to understand it's a number, like any other number. It has no units, right here, at the moment. So it's a number like 12 is a number, or 6 is a number, or 222 is a number, this is just a different number. It's a quantity of days. So how is it defined? What does it all come from? So it's defined, again, to your best rate of carbon. Definition is as follows. 12 grams of carbon-12, that is the isotope of carbon. Okay? Isotope 12 of carbon. Carbon-12. If you have 12 grams of only these atoms, then, the definition says, you have one more. Okay? If you stick to the definition, if you say that this is the definition, you can add what you have. And it turns out that this definition stipulates that you have this many. Right? So I'll tell you this moment here, 12 grams of carbon-12, that is your method, that is your new unit. Okay, you say, we're going to do it here, not how many of you have these things. Oh, I found this many atoms in there. And that's it. That's the definition. Nothing mysterious about it. It's a definition. Even if I'm a summer, so this is a pretty good definition, like A. Okay? So, again, I just want to re-emphasize that it is a number. People mix this up. People say the mole is so mysterious. Ah, just a number. Like a dozen is a number, you have to refer to comparison probably. But it's really true. Okay? You can have 12 atoms, or you can have this many atoms. In one case, you call it a dozen. In another case, you call it a mole. Now, I'm surprising that if I give you a question, and I replace every word mole with a word dozen, you have no problem with solving the question. But if I give you a word mole for dozen, you are completely clear. I'll give you a whole lot of people. Because you think the mole is hard to understand. It's not. It's just a number. Like a dozen is a number. Okay? So, in case you are confused by a question, and the word mole is nothing in your face, just secretly replace mole by the word dozen. And suddenly you think, oh, you just have to multiply two numbers. Okay? So let's look at a couple of consequences here. All right. So, if I have one mole of carbon C prime. Right? One mole of it. Well, then I have 12 grams. I have a very good definition. One mole of carbon C12 equals 12 grams. Because 12 grams of carbon C12 is one mole, is my definition. All right? So, the mass of carbon 12 is 12A mu, 12 atomic mass units. Okay? I mean, that's another definition. That's octagonal mass. So one mole times 10. So just substitute this here with that. Equals 12. Same line. But from this, I can just bring this guy to that side and put him to the following. One mole equals one gram per atomic mass unit. Atomic mass unit is a unit of mass. Gram is a unit of mass. So, in fact, it's dimensionless. It doesn't relate to a physical unit. It's just a quantity. Now, this is a very useful kind of conversion that you want, a relationship. Because I can do the following. I can take another element, let's say aluminum. Okay? One mole times the mass of aluminum. Okay? So let's say one mole of aluminum atoms. The mass of aluminum atoms should be supposed to go here. What is the mass of aluminum atoms? Well, in A and U, I know what it is. It's right here. 26.98, but all of us want to hear it today. The average mass of aluminum atoms is right here. That is the number in the bureaucrat. Okay? If I multiply that by one mole, look, one mole is this. So I put it right here. I see A and U are crossed out. And they get an answering branch. In other words, this is 26.98 branch. All right? So one of the lines says, if I have one mole of an atom, I get my mass expressed in grams. Okay? The average mass of the atom is now expressed in grams as opposed to A and U. So every time you take one mole of these atoms, that means a whole bunch of them, they get them. Then the mass of that will be equal to the molar mass of that element, but this A and U replaced by grams. Okay? So on the other hand, we look at the bureaucrat table. This is what we just did. We have an element. We take exactly one mole of that element. It turns out its mass is equal to its atomic mass in grams. And it holds for every other element. Fantastic. You take one mole of it, you get this mass, which is the number in the bureaucrat table, which is the bureaucrat table that says A and U. And if you take one mole of these elements, you get that number in grams. Zin, say hey. You take one mole of same atoms, you get this mass, and the number in the bureaucrat table are now expressed in grams. And it holds for any other element. It doesn't matter which one. Okay? Because now I can just say one mole of all these elements and I know how much they weigh expressed in grams. What the masses express in grams. Okay, so let's do an exercise here. Let's take this block of titanium, a small little cube of titanium, and let's assume that this little tiny cube is 3 grams. Okay? And I'm going to ask myself a question. Okay, I have 3 grams of titanium. How many titanium atoms are in there? That's what I want to know. How many titanium atoms are in there? So I have to do a conversion. I have something in grams. I want something in number of atoms. How do we do that conversion? Well, one way to do that is this. I have grams. I know how much one mole of titanium is. But it is not that there are grams. Okay? I can make a conversion factor. One mole of titanium equals this many grams. And I can use this as a unit factor. Okay? A conversion factor in my calculation. So what I do is I start with listing this number in grams. I'm going to synthesize, out of here, a conversion factor. I want to go to quantity, number. Mole is a quantity. So I put mole on top and this at the bottom. And there is mole location. You see, grams will strike out. And I get now the number of moles of the tinny that are in three grams. Okay? This is it. 0.0626 moles of the tinny. So how many atoms are there in this cube? Well, this many. Okay? This is the quality. This many. But the quantity is expressed in moles. And I want it in real number now. So how do you do that? This is a mole. I just multiply by what the mole is. Just like I said, there are this many dozen titanium atoms. You would multiply by 12. So I multiply this at 6.0, 2, 2, 5, 10, and 20. Okay? So I get a number multiplied by what the mole is. That is a mole. This number is a mole. And then I get the normal atoms. 3.7 times 7.2 times. Again, this number is rather staggering. That's why we typically don't really bother about really calculating normal atoms and we stay on the level of the moles. Because those numbers are much easier to work with. That's the purpose of the mole. To make calculations easier and more manageable. Okay. Two quick examples. A sample of CO2 has 1.4 times 7 to the third moles of oxygen atoms. Not a question if how many moles of CO2 molecules are present? Okay? So what is the question about? Well, this question is about this. What is given is how many oxygen atoms you have. Not how many molecules of CO2 are present. Okay? I know how many oxygen atoms I have, but from it I can determine how many CO2 I have. So it's a relation. It's the same as saying you have two eyes. You all have two eyes. So in this room there are 600 eyes. How many people are there? 300. For each person it's two eyes. It's the same here. Each molecule has two oxygen atoms. Right? So for each molecule there are two oxygen atoms. So what I want to do is just take that number and divide that by two. Then I get this number, and that means I have this many CO2 molecules. And this is another situation where the different words can see diffusion. If I say molecule and methodus, you tend to think that this is going to be a very complicated calculation. But if I say eyes and people, no way to understand. So mathematically this is a job. Right? So just conceptually you have to give the same meaning. Don't be afraid of the number of atoms. Or how many atoms there are in certain molecules. It's just a calculation. It's just like two eyes of a person is a calculation. The sooner you can convince yourself that this is all straightforward, the faster you will get the answer. Okay. How many moles of H atoms are present in this molecule? If I have 2.88 moles of H. Okay, again, 2.88 moles is a quantity of molecules. Alright? What I want to know is how many H atoms I have. The quantity of H atoms. So what I see here, I have a molecule. It contains Cs and Hs. It contains six Hs. So for each one molecule I have six hydrogens. So how many hydrogens do I have? Well, I take this number, which is the number, a quantity, and I multiply it by six, 17.3 moles of H atoms. That's it. I just have to multiply this number by six. You can see it. Very easy, seems. And these simple exercises just for you to get used to where as molecules happens in, don't be afraid of doing these calculations. Yes? What about the part of the universe? What happens to it? What happens to it? Do you not have it? Well, I mean, you know, that's the same as saying, if I tell you that there are 600 eyes in the audience, how many people are there? Okay? That your question would be, but how long is that? How many noses are there? Right? I said, well, it's here on the nose. Right? Because each molecule has one target. Sorry, that means there's just the same number of particles that there are on the nose. The question was about oxygen, and how many molecules do you have? Eyes and people. But of course, people, I hope, are noses. Actually, people have many noses. If you are, you have to lie. They're all noses. This here is where the only particles are. Okay, now, what holds for atoms also holds for molecules as a whole. What does that mean? That means the following. I can determine not only how much or what the mass is of one mole of an atom, I can also determine what is the mass of one mole of a particular molecule. Right? So, for instance, let's take this one. It seems to age 6, power. That's ethanol. If I have one mole of ethanol, what would its mass be? How do you calculate that? Well, what you have to do is, you can see what's in it. One molecule of ethanol has two carbons, six hydrogryms, and one oxygen. Right? If I have one mole of ethanol, what means I have one times two moles of carbon, six moles of hydrogen, and one mole of oxygen. So that's what I have to calculate. Here we go. The mass of two moles of carbon equals two times the mass of one mole, which is this, 12 grams. Six moles of hydrogen is six times the mass of one mole of hydrogen, which is 1.00 grams. And one mole of oxygen is just the mass of oxygen, one mole of it, which is 16 grams, or 515.99. Okay, so what you have to do is, you have to do these notifications, and then add them up. Okay? The answer is 46.07. That is the molar mass of ethanol. So that means that if you have one mole of ethanol, a quantity, a certain quantity of ethanol, you will have, if you put the same on your balance, you will say this is 46.07 grams. Okay? So we say 46.07 is the molar mass of ethanol. Okay, so we do the ethanol here, right? What do you want? Asteroid. Asteroid is a cool molecule. If you feel generally the same, it's a very simple, but it's a small molecule, not to be speaking. Okay? Here is the mass structure, your favorite very good molecule. And here is the chemical formula. Chemical formula is in this regard very important. If you want to calculate the molar mass. Okay? That's 9, sorry, it has 9 carbons, 8 hydrogen, and 4 oxygenated. So what I want to do here, the first step I want to do, even before worrying about this question here, I want to know what is the molar mass of this compound. So what I do with this again, 9 moles of carbon, that means 9 moles, 9 times the mass of 1 mole of carbon, that's 9 times 12.01, that's this number right here. 8 moles of hydrogen, 8 times the molar mass of hydrogen, which is 0, sorry, 1.008, the multiplication you find this. And then 4 moles of oxygen, because it's 4, there's a 4 here, the thing's got 4 is right there. 4 moles of oxygen, 4 times the molar mass of oxygen, which is about 16, they get 64 is contributed by the oxygen. Put a line here and add one. 1 mole of acid is 180.60. So, if I had 1 mole of acid, this would be its mass. Let's look at this number here. I don't know how many moles are in this mass. This mass is much smaller than this mass. Why do I say that? Because if you look at how many moles it is, it is definitely much smaller than 1 mole. So if your n is going to be larger than 1 mole, you get something wrong. I have to find an answer for 50 milligrams of acid, and I know it's going to be a number much smaller than 1. You guys have to stress it a number of moles. So what do I do? I write down again the quantity, which is 50 grams, sorry, 50 milligrams expressing grams, 0.050 grams. Why do I do that? Well, because this is defined in grams, not milligrams, so I'll rewrite this in terms of grams. Then the conversion. Where do you want to go to? To moles. Where do you want to move away from? I want to move away from grams. So put gram at the bottom, moles on top, like this. This gram will cross out, and this calculation gives me a number expressed in moles. This is my unit factor, like we did with the conversions all the way. Okay? 2.8 times 10 to the right score. That is the answer. So this question is converting a quantity expressed in a mass, milligrams, into a quantity, which is moles, and you can use this unit factor to do that. Okay? Vitamin C, another very cool molecule. Here it is. Vitamin C is nothing but a sorbic acid. And here's the structure. Again, relatively small molecules are quite similar to gestication or even calc. If you don't have this thing, if you don't ingest it, your body can't eat it, as you're going to get it to redness and fruits, and you're actually pushing your unit system. This molecule has 6 carbons, 8 hydrogens, and 6 oxygens. So knowing this, those subscripts tell me exactly what the molar mass is going to be. Because we're going to do 6 times the molar mass of carbon, 8 times the molar mass of hydrogen, and 6 times the molar mass of oxygen. Okay? There it is. 6 times 12, 8 times 1, 1, 0, 0, 8, 6 times 16, and the total is going to be 176.12. That is the molar mass of vitamin C. Okay, that's it. What is the question? How many oxygen atoms are there in 5.3 micrograms of vitamin C? This is a number expressed in grams. So I have something in grams, micrograms, a mass unit, as a convertible to a quantity unit. So it's a conversion property. I'm going to need this. I'm going to need this as a conversion factor. They want the answer in oxygen atoms, the number of atoms, not the number of moles. So I have to do extra conversion and multiply it in the end to get what the mole is. So let's get that one out. What I do is I'm going to write this, write it. Okay? It's roughly arranged. 5.3 times center minus 6 grams, because the microgram is 10 to the minus 6. I want to convert this from gram to number of moles first. That means I take the scene here, put mole on top and this thing at the bottom. Grams will cross out. So I get 9 number now expressed in terms of number of moles. I find 3.0 times 10 to the minus 8 moles to sort of ask for minus. This is 2 significant figures, so I have 2 significant figures right here. Is this a final answer? No, it's not, because they want to have a number of oxygen atoms, okay, not in moles of the molecule. There's two things I have to do. First, I have to determine how many oxygen atoms there are for each molecule, that's 6. And then I have to convert that to number and multiply it back with the mole, with the mole number. So let's do that. This is the number of moles of vitamin C molecules. This is what one mole is. So I do this multiplication and get a total number of molecules. 1.8 times 10 to the 16 molecules of vitamin C. Again, replace this, not by the mole number, but by the number of dozen. The right thing to do automatically, now even thinking, you would say, oh, if this many dozen, okay, that's just like a number of times 4. Same here, just multiplying with the mole number. I'll cover God's concept, but I do not like the problem. Okay, this is the number of molecules. Each molecule has 6 oxygen atoms, so the number of oxygen atoms is 6 times this. This number of times 6 is going to give me my number of oxygen atoms. 1.1 times 10 to the 17 oxygen atoms. Make sure you really understand this, and you're very comfortable with calculation. And discriminate number of molecules from number of atoms in the molecule. The molecule can have multiple atoms in it, but that's not going to be bigger than that. Okay, another one. How many moles of lead for chloride are present in this many grams of it? Another conversion, from grams to moles, to one step conversion, if you know the molar mass of lead chloride, you can directly calculate how many moles there are in this mass. What do you do? The molar mass, if you calculate it first, comes to the clear table, one lead atom. This is the molar mass of lead. Okay, 4 times the molar mass of chlorine, that is the molar mass of chlorine, 4 times that, we add just the whole thing up, 0.49 from the zero grams per mole. Each mole you have 249 grams. This is my conversion factor. I'm going to write down this number, okay? This is another way to say it. The number of moles is nothing but the mass divided by the molar mass. It's not going to memorize it as the same trick. Basically, you take your mass, which is this number, you multiply by conversion factor, but always this number appears at the bottom, and on top is one mole. In other words, it's mass divided by the molar mass. That's a quick way to remember this. So, 5, 4, 4, 0 grams divided by that number equals 15.6. That's the number of moles. This formula here is exactly the same calculation we did on the previous slide. You take the rest in gram, you multiply by the new factor, molar mass at the bottom, this is one. So you just do it together, you get mass over molar mass. That's what it is. It's the same calculation, sourced together in one experiment. Number of moles equals mass over molar mass. Okay. Another one, very quick. Another sample, iron. And this is monoxide, sorry, carbon monoxide. It's found to contain, oops, I'm sorry, this is a complex, okay? It's a complex of iron and carbon monoxide. It contains this many grams of oxygen atoms. How many grams of carbon atoms are present? This is interesting. I have to convert a number of oxygen to a number of carbon atoms. Okay? Especially as a scientific notation. So, I know the number of oxygen, what is the number of carbon atoms? Well, it's one to one, actually. Okay? The number of oxygen atoms is basically the gram divided by the molar mass. That is a quantity. So 1.94 times 10 to the minus 5 grams, that is the mass quantity, divided by the molar mass, gives me the number of moles. Okay? 1.21 times 10 to the minus 6 moles. So what I did, I took the formula from the last slide, N and VA, number of moles, equals mass over molar mass. Mass over molar mass gives me a quantity, especially more. This is how many oxygen I have, and that is the same as carbon molecules. Okay? In other words, I have exactly the same number here as carbon. 1.21 times 10 to the minus 6. The only thing you have to do here is to convert a mass quantity into a mole quantity. That's it. You do that by this expression. What time is it? Um... Oh, look at this. I can do one step more, because what they ask is, not how many atoms you have, but what is the mass of those atoms. So once you have the number of atoms, you multiply it by the molar mass. Okay? So what I find is this many moles, this is the molar mass. The number of moles times the molar mass gives you the mass. Okay? So let me read it again. This is number of atoms. Okay? Number of moles. This is what one mole weighs. What the mass is of one mole. So let's say 2 dozen eggs, okay? One dozen eggs, five grams, so you multiply it by numbers. You're exactly the same thing. You have a number of moles, molar mass, you multiply it to, okay, the answer in grams. Okay, okay. That's it, and I'll see you on Wednesday.
 Welcome back after a nice long session on Friday.  Let me guide you through it.  That's the score chart from last Friday.  The knee was 56.2 standard deviation, which is basically a measure of the spread of the knee.  It was 18.6, which means that this exam really cooled a lot of performances away from the chart.  So it's a very broad distribution.  For a teacher, this is great because I can beautifully expect a lot of performances.  But a student in this report is not great, you all want to be right on close together and maybe somewhere more towards the 90s.  So you may feel that 56 is not so good.  Actually, completely fine.  Completely on target.  Last year, the performance was only 1 percentage point higher.  So it was 57, now it's 56.  That was very much average, I would say, for the years to come.  Anything out of your board there.  Let me say a few things.  The exam was, like I said before, it was a little bit tight.  It was part of the parcel of having only 50 minutes, including the ranging things.  Again, other class, our new class, taking the same distribution exam.  You cannot do it in another way, you cannot put your exam on the seat 400 percent.  You don't have six hundred copies of several chairs, you simply cannot do that.  So you have to move to the way you did it, takes a little time, takes a couple of minutes of your examination time.  You know that.  Many people told me that, and I said, I know that.  And this is again part of this exam. This exam was tight, it was not very pleasant and comfortable.  But on the other hand, you know, we still get a very good impression of what the performance of this class is.  The second exam, you will see, will go a lot better.  It is a little less intense.  And it will feel more comfortable in the final, for me, relatively, I would say, now, even more time for you to take three questions.  This is also kind of like sets the stage, because there are a couple of topics here that are important for you to be able to do these questions quickly.  And so I definitely have had a lot of stuff here. I was trying to test you on several things, you sweep it all in, and this is the result.  So not bad at all.  We are on target.  If you are on the low side of the mean, take this exam as an opportunity to see what parts of material need to be improved.  So what is your personal weakness on the exam that means extra attention?  You can hunt the office hours, you can go up and speak to your Twitter's, there's a special leader's Laura and Mike,  who are very happy to help you out, ask them specific questions, take a human understanding, and ask for a specific answer.  So again, you are in charge of your own success.  You identify which parts of material are not easy to go with the use, and you act on it.  Make sure that you get the information and be able to do the questions next time around.  So I want to remind you, it's only 15% of your grade.  This is for a particular reason. 15 makes up a lot. It really is not.  The final is almost half of the grade. The final is really where it's all happening.  The exam is really just a warming up exercise.  Just to get started, so don't be demoralized, we didn't go so far for you.  Actually, if you didn't go so well, it tells you which things you are going to go on.  So it is more like an opportunity than an analyzing experience.  Okay, yes?  Do we get our grade too bad?  Well, you can't approach the list first. Okay? It's actually on the slide.  The grades of the old tests will not be curve.  Only your cumulative grade will be curve.  Your cumulative grade is two minutes, one final, and a homework together.  That is your overall grade of this course. That will be curve.  In my opinion, it doesn't make a lot of sense to curve individual exams.  The much better measure of your performance is to look at your score.  Your score is metric. It is a number that tells you how well you did.  The maximum score is 100, and you have 50% of it means you get half right within a lot of time.  That's what it means.  Very good innovation with your performance.  Don't do a riveting at the stage of your grade. It makes no sense.  But it makes no sense to do that.  Do that have an A or B. It makes no sense.  At this stage of your grade, the only thing you should be concerned about is, do I understand that you're in?  Okay? That is what you're in for.  Worry about this riveting just till the better grade.  Don't go telling your opponent what to do right now.  It is just a waste of energy.  Your exam will be available on the triple E page on Friday if everything goes right.  So we have, as you noticed, we've rated everything on Friday.  Very hard work.  It's lost for educators and everything is done not manually.  It's a very small thing.  It's interesting how long you're in the same team.  They are now currently in the coffee center.  They're all being stamped and reproduced.  And you'll see an idiot version in the real box.  You're only in the airport when we're in town.  This will take a couple of days.  This is not really my control.  It's not in the coffee center.  Okay.  You can contest your score if there is a genuine rated error.  Don't come to me please with all kinds of arguments about why you should have more questions.  That's not really the purpose of contesting your score.  We have given questions, but it may be stuck to a very specific recipe for that.  And we think the dollar can write a job.  If your answer is correct, like you didn't get the points, you get your entire potential points.  But if your answer is not correct, and someone in the margin has written something amazing, right,  a little bit of an imagination, we cannot give you the answer points with that.  Okay.  So, if you guys do that, that's possible.  Basically, I'm on the auto major.  I'm just going to spend all my time with that.  It's impossible.  That's also not the purpose.  I think you've graded very fairly.  Okay, so the grading errors will be considered till...  This is a Friday the 9th of November.  So that means you get to return that on Friday, Monday and Friday, this Friday.  And then you have one week time to talk to me.  Talk to me.  Send me an email.  Okay, if you have a simple question, send me an email.  I can do things right if you have a question.  If you have specific questions, you can come to an office hours.  Or you may even find it.  Don't...the TAs are happy to discuss answers with you, but they cannot give you a question.  They're only high to do that.  Okay.  All right.  Let me quickly look at one question on the exam.  It's about the can of Coca-Cola.  This question, surprisingly, went not so well.  Okay, most people were probably confused by this question.  Let me go through it and just see who developed it in place.  It says in doctor advices the patient not to consume more than this.  Okay, so this is 85 grams.  Okay, so I'm just quickly comparing the amount of what I have.  This is 8.5 times 10 to the minus 2 kilograms, so it's 85 grams.  Okay, so this patient should not consume more than 8 times the amount of sugar in an egg.  Okay?  Now, in one of these cans, there are 12 ounces of...sorry, this is 12 ounces.  Okay?  And it contains sugar at this concentration.  So this is a volume.  This is a volume.  And this is a concentration, or a density.  As you can see.  This is gram of a liquid.  This is mass of a volume.  This is a density, and this is a volume.  How many of these cans can this patient have?  Alright?  And the conversion here of ounces to milliliters is shown as well.  So what do we need to calculate here?  Well, what I need to calculate is, in the end, how many cans can the patient consume?  What does that depend on?  It depends on how much sugar is in there.  Okay?  85 grams is the mass.  So what I need to know is how many grams of sugar are in one can.  Okay?  I need to know how much sugar is in this can.  It's a very simple thing.  If your doctor tells you, you cannot eat so much sugar a day,  and you see this on this...or probably...  You want to know how much sugar is in this can.  How many grams of sugar is in one of these cans?  Right?  How many grams of sugar is in one of these cans?  Right?  How many grams of sugar is in one of these cans?  So that's a mass.  Mass is volume times density.  Do I have that information?  That volume is not in milliliters or liters or whatever,  but the conversion is right there.  So what I do is this.  Mass equals...this is the density,  which I quickly convert from liters to milliliters.  Okay?  That's a factor of 1,000.  If you can do that with a square meter in your hand,  you can just write it out,  because the difference between a milliliter and a liter is a factor of 1,000.  Okay?  So point 110 grams per milliliter times the volume.  And the volume is right here, between parentheses.  I want the answer in milliliters,  so I use this conversion right here.  12 ounces, that's the volume,  times this conversion factor.  You see, the ounces will cross out,  I get my answer in milliliters.  So if you actually give this one here,  you have your volume in milliliters, times this,  milliliter, you get an answer in grams, 39 grams.  39 grams in one of these hands.  Okay?  You are almost right here to answer.  This multiplication here of 1 to 3 numbers  is basically the whole thing.  All right?  How many cans can you have?  Okay, well, I have a maximum of 85.  This is 39, so how many 39's are sitting at 85?  2.2.  I can have 2.2 cans.  That's it.  That's the calculation.  Okay, another issue is naming compounds.  Naming compounds is something you can literally learn  is a method, and to stick to the method, you will be fine.  I saw a wide variety of very interesting, very intense.  I'm going to give you a simple, some people say,  this is sulfur fluoride, it's almost right, but not quite.  This is hexafluoride.  Okay?  Sulfur hexafluoride.  Oh, this is a nice one.  I remember in one of the lectures, I say,  be careful, about 20% of you guys are going to do this one wrong.  Okay?  Because you will say sulfuride, and it is sulfur fluoride.  And you can hit it.  I'm going to say 20%, about 15% of the folks did exactly this.  Okay?  So, you have to pay attention to it, because even people  that's actually very interested in me, they put in 2-minus here,  and I said, if I forgot, who's the 2-minus?  They put in 2-minus here, and I said, oh, it's sulfur.  This is solvent trioxide, it's a neutral compound.  Okay, this one.  Some folks said, disesium carbonate, this is an ionic compound.  You never use this indicator, okay, this prefix.  It is cesium carbonate.  Ionic compounds do not have prefixes  indicating the number of atoms.  How about this one?  A lot of folks said this, copper 1, selenide.  But selenide is in the same family as oxide, right?  It's in the same column, but this is 2-minus,  I mean, the copper is 2.  It has a charged 2-plus, oxidative state 2.  This one, now what does this mean, guys?  It's dissolved, and this is an H.  What does it mean?  Acid. Still, still, okay, a fraction of folks still call this ionic nitrate.  Don't say the name, okay?  This is nitrous acid.  And this one, lastly, this is almost the same kind of situation  as in this one, copper selenide.  People call this barium, actually not the same situation,  shavings iterations here, they think this is a type 2 metal.  Barium is not, barium is 2-plus type 1, okay?  It's in a second column, and those are type 1 metals.  You never specify the oxidation state of type 1 metal.  So, barium is 2 chloride, a disbarium chloride.  Okay, keep your states in mind, keep practicing,  and then we'll see if I've tried to find a concept on the UBU leadership.  We have to move on, okay?  We're going to chapter 3.  So, we did already a quite big chunk of the material so far,  and we're hopping into the next set of topics.  So, what it is about.  In chemistry, we deal with a lot of atoms.  We need a material which is the whole of your hand,  the solution, the sugar in your coffee,  if not one molecule, there's too many.  So, instead of talking just about one thing,  we have collections of atoms, like collections of Ticke.  But the problem is that these collections are rather large.  Okay, so I'm just giving you an idea.  This is one person, you can easily think of this,  of this one person, just conceptualize it, there he is, one one guy.  And then, we can even conceptualize this iteration here  as counting about 300 million people.  Even though here, there are people who say,  look, there's a huge number, for some reason,  our brain kind of understands that number.  And we understand 300, that's about this.  So, we kind of conceptualize it.  Now, if you look at ions and molecules and atoms,  the numbers are rather staggered.  Okay, so this is one ionic hand,  you can easily grasp it, this is just one sodium  and one chlorine ion, they're together,  nothing is wrong with it, easy to conceptualize.  But what if you have one of these little chunks,  one little grain of salt, tissue salt,  already has one times 10 to the 19 ionic pairs.  10 to the 19 is a staggered number.  Okay, that's huge.  And this number here fades, prepares,  to how many ions are in there.  Our mind cannot poke in hand the magnitude of this number.  You can try, but you don't,  because you don't have the frame of reference.  You're kind of lost on this number.  And consequently, it's hard to do calculations  and calculations with these numbers.  So, it makes a lot of sense for chemists,  and also for you, that you are as far in hands,  you don't know yet, as you will.  To have a different way of treating these large numbers.  And you have to work this number, and that's the mole.  What is it?  It's a number.  I can feel you excited.  Okay?  It is a number, that's it.  That's all you have to know.  We're not sorry.  It makes funny numbers.  I'm not sure if my M3 is very impressive,  when you memorize this number, it's like my name.  Oh really?  That's great.  So how many digits do you know?  How many digits do you know?  Four digits, or five, six?  So, this number is big, right?  It's big.  It's 6, 4, 0, 2, 2 times 10 to the power of 23.  And that's a very, very big number.  But it is a number.  I just want you to understand it's a number, like any other number.  It has no units, right here, at the moment.  So it's a number like 12 is a number, or 6 is a number,  or 222 is a number, this is just a different number.  It's a quantity of days.  So how is it defined?  What does it all come from?  So it's defined, again, to your best rate of carbon.  Definition is as follows.  12 grams of carbon-12, that is the isotope of carbon.  Okay?  Isotope 12 of carbon.  Carbon-12.  If you have 12 grams of only these atoms,  then, the definition says, you have one more.  Okay?  If you stick to the definition, if you say that this is the definition,  you can add what you have.  And it turns out that this definition stipulates that you have this many.  Right?  So I'll tell you this moment here, 12 grams of carbon-12,  that is your method, that is your new unit.  Okay, you say, we're going to do it here,  not how many of you have these things.  Oh, I found this many atoms in there.  And that's it.  That's the definition.  Nothing mysterious about it.  It's a definition.  Even if I'm a summer, so this is a pretty good definition, like A.  Okay?  So, again, I just want to re-emphasize that it is a number.  People mix this up.  People say the mole is so mysterious.  Ah, just a number.  Like a dozen is a number, you have to refer to comparison probably.  But it's really true.  Okay?  You can have 12 atoms, or you can have this many atoms.  In one case, you call it a dozen.  In another case, you call it a mole.  Now, I'm surprising that if I give you a question,  and I replace every word mole with a word dozen,  you have no problem with solving the question.  But if I give you a word mole for dozen,  you are completely clear.  I'll give you a whole lot of people.  Because you think the mole is hard to understand.  It's not.  It's just a number.  Like a dozen is a number.  Okay?  So, in case you are confused by a question,  and the word mole is nothing in your face,  just secretly replace mole by the word dozen.  And suddenly you think, oh, you just have to multiply two numbers.  Okay?  So let's look at a couple of consequences here.  All right.  So, if I have one mole of carbon C prime.  Right?  One mole of it.  Well, then I have 12 grams.  I have a very good definition.  One mole of carbon C12 equals 12 grams.  Because 12 grams of carbon C12 is one mole,  is my definition.  All right?  So, the mass of carbon 12 is 12A mu,  12 atomic mass units.  Okay?  I mean, that's another definition.  That's octagonal mass.  So one mole times 10.  So just substitute this here with that.  Equals 12.  Same line.  But from this, I can just bring this guy to that side  and put him to the following.  One mole equals one gram per atomic mass unit.  Atomic mass unit is a unit of mass.  Gram is a unit of mass.  So, in fact, it's dimensionless.  It doesn't relate to a physical unit.  It's just a quantity.  Now, this is a very useful kind of conversion that you want,  a relationship.  Because I can do the following.  I can take another element, let's say aluminum.  Okay?  One mole times the mass of aluminum.  Okay?  So let's say one mole of aluminum atoms.  The mass of aluminum atoms should be supposed to go here.  What is the mass of aluminum atoms?  Well, in A and U, I know what it is.  It's right here.  26.98, but all of us want to hear it today.  The average mass of aluminum atoms is right here.  That is the number in the bureaucrat.  Okay?  If I multiply that by one mole, look, one mole is this.  So I put it right here.  I see A and U are crossed out.  And they get an answering branch.  In other words, this is 26.98 branch.  All right?  So one of the lines says, if I have one mole of an atom,  I get my mass expressed in grams.  Okay?  The average mass of the atom is now expressed in grams  as opposed to A and U.  So every time you take one mole of these atoms,  that means a whole bunch of them, they get them.  Then the mass of that will be equal to the molar mass  of that element, but this A and U replaced by grams.  Okay?  So on the other hand, we look at the bureaucrat table.  This is what we just did.  We have an element.  We take exactly one mole of that element.  It turns out its mass is equal to its atomic mass in grams.  And it holds for every other element.  Fantastic.  You take one mole of it, you get this mass,  which is the number in the bureaucrat table, which is the bureaucrat table that says A and U.  And if you take one mole of these elements,  you get that number in grams.  Zin, say hey.  You take one mole of same atoms, you get this mass,  and the number in the bureaucrat table are now expressed in grams.  And it holds for any other element.  It doesn't matter which one.  Okay?  Because now I can just say one mole of all these elements  and I know how much they weigh expressed in grams.  What the masses express in grams.  Okay, so let's do an exercise here.  Let's take this block of titanium, a small little cube of titanium,  and let's assume that this little tiny cube is 3 grams.  Okay?  And I'm going to ask myself a question.  Okay, I have 3 grams of titanium.  How many titanium atoms are in there?  That's what I want to know.  How many titanium atoms are in there?  So I have to do a conversion.  I have something in grams.  I want something in number of atoms.  How do we do that conversion?  Well, one way to do that is this.  I have grams.  I know how much one mole of titanium is.  But it is not that there are grams.  Okay?  I can make a conversion factor.  One mole of titanium equals this many grams.  And I can use this as a unit factor.  Okay?  A conversion factor in my calculation.  So what I do is I start with listing this number in grams.  I'm going to synthesize, out of here, a conversion factor.  I want to go to quantity, number.  Mole is a quantity.  So I put mole on top and this at the bottom.  And there is mole location.  You see, grams will strike out.  And I get now the number of moles of the tinny  that are in three grams.  Okay?  This is it.  0.0626 moles of the tinny.  So how many atoms are there in this cube?  Well, this many.  Okay?  This is the quality.  This many.  But the quantity is expressed in moles.  And I want it in real number now.  So how do you do that?  This is a mole.  I just multiply by what the mole is.  Just like I said, there are this many dozen titanium atoms.  You would multiply by 12.  So I multiply this at 6.0, 2, 2, 5, 10, and 20.  Okay?  So I get a number multiplied by what the mole is.  That is a mole.  This number is a mole.  And then I get the normal atoms.  3.7 times 7.2 times.  Again, this number is rather staggering.  That's why we typically don't really bother  about really calculating normal atoms  and we stay on the level of the moles.  Because those numbers are much easier to work with.  That's the purpose of the mole.  To make calculations easier and more manageable.  Okay.  Two quick examples.  A sample of CO2 has 1.4 times 7 to the third moles  of oxygen atoms.  Not a question if how many moles of CO2 molecules are present?  Okay?  So what is the question about?  Well, this question is about this.  What is given is how many oxygen atoms you have.  Not how many molecules of CO2 are present.  Okay?  I know how many oxygen atoms I have,  but from it I can determine how many CO2 I have.  So it's a relation.  It's the same as saying you have two eyes.  You all have two eyes.  So in this room there are 600 eyes.  How many people are there?  300.  For each person it's two eyes.  It's the same here.  Each molecule has two oxygen atoms.  Right?  So for each molecule there are two oxygen atoms.  So what I want to do is just take that number  and divide that by two.  Then I get this number,  and that means I have this many CO2 molecules.  And this is another situation  where the different words can see diffusion.  If I say molecule and methodus,  you tend to think that this is going to be a very complicated calculation.  But if I say eyes and people,  no way to understand.  So mathematically this is a job.  Right?  So just conceptually you have to give the same meaning.  Don't be afraid of the number of atoms.  Or how many atoms there are in certain molecules.  It's just a calculation.  It's just like two eyes of a person is a calculation.  The sooner you can convince yourself that this is all straightforward,  the faster you will get the answer.  Okay.  How many moles of H atoms are present in this molecule?  If I have 2.88 moles of H.  Okay, again, 2.88 moles is a quantity of molecules.  Alright?  What I want to know is how many H atoms I have.  The quantity of H atoms.  So what I see here, I have a molecule.  It contains Cs and Hs.  It contains six Hs.  So for each one molecule I have six hydrogens.  So how many hydrogens do I have?  Well, I take this number, which is the number, a quantity,  and I multiply it by six, 17.3 moles of H atoms.  That's it.  I just have to multiply this number by six.  You can see it.  Very easy, seems.  And these simple exercises just for you to get used to  where as molecules happens in, don't be afraid of doing these calculations.  Yes?  What about the part of the universe?  What happens to it?  What happens to it?  Do you not have it?  Well, I mean, you know, that's the same as saying,  if I tell you that there are 600 eyes in the audience,  how many people are there?  Okay?  That your question would be,  but how long is that?  How many noses are there?  Right?  I said, well, it's here on the nose.  Right?  Because each molecule has one target.  Sorry, that means there's just the same number of particles  that there are on the nose.  The question was about oxygen,  and how many molecules do you have?  Eyes and people.  But of course, people, I hope, are noses.  Actually, people have many noses.  If you are, you have to lie.  They're all noses.  This here is where the only particles are.  Okay, now, what holds for atoms also holds for molecules as a whole.  What does that mean?  That means the following.  I can determine not only how much or what the mass is  of one mole of an atom,  I can also determine what is the mass of one mole  of a particular molecule.  Right?  So, for instance, let's take this one.  It seems to age 6, power.  That's ethanol.  If I have one mole of ethanol,  what would its mass be?  How do you calculate that?  Well, what you have to do is, you can see what's in it.  One molecule of ethanol has two carbons,  six hydrogryms, and one oxygen.  Right?  If I have one mole of ethanol,  what means I have one times two moles of carbon,  six moles of hydrogen,  and one mole of oxygen.  So that's what I have to calculate.  Here we go.  The mass of two moles of carbon equals two times the mass of one mole,  which is this, 12 grams.  Six moles of hydrogen is six times the mass of one mole of hydrogen,  which is 1.00 grams.  And one mole of oxygen is just the mass of oxygen,  one mole of it, which is 16 grams,  or 515.99.  Okay, so what you have to do is,  you have to do these notifications,  and then add them up.  Okay?  The answer is 46.07.  That is the molar mass of ethanol.  So that means that if you have one mole of ethanol,  a quantity, a certain quantity of ethanol,  you will have, if you put the same on your balance,  you will say this is 46.07 grams.  Okay?  So we say 46.07 is the molar mass of ethanol.  Okay, so we do the ethanol here, right?  What do you want?  Asteroid.  Asteroid is a cool molecule.  If you feel generally the same,  it's a very simple, but it's a small molecule,  not to be speaking.  Okay?  Here is the mass structure,  your favorite very good molecule.  And here is the chemical formula.  Chemical formula is in this regard very important.  If you want to calculate the molar mass.  Okay?  That's 9, sorry, it has 9 carbons, 8 hydrogen,  and 4 oxygenated.  So what I want to do here,  the first step I want to do,  even before worrying about this question here,  I want to know what is the molar mass of this compound.  So what I do with this again,  9 moles of carbon, that means 9 moles,  9 times the mass of 1 mole of carbon,  that's 9 times 12.01,  that's this number right here.  8 moles of hydrogen,  8 times the molar mass of hydrogen,  which is 0, sorry, 1.008,  the multiplication you find this.  And then 4 moles of oxygen,  because it's 4, there's a 4 here,  the thing's got 4 is right there.  4 moles of oxygen,  4 times the molar mass of oxygen,  which is about 16,  they get 64 is contributed by the oxygen.  Put a line here and add one.  1 mole of acid is 180.60.  So, if I had 1 mole of acid,  this would be its mass.  Let's look at this number here.  I don't know how many moles are in this mass.  This mass is much smaller than this mass.  Why do I say that?  Because if you look at how many moles it is,  it is definitely much smaller than 1 mole.  So if your n is going to be larger than 1 mole,  you get something wrong.  I have to find an answer for 50 milligrams of acid,  and I know it's going to be a number much smaller than 1.  You guys have to stress it a number of moles.  So what do I do?  I write down again the quantity,  which is 50 grams, sorry,  50 milligrams expressing grams,  0.050 grams.  Why do I do that?  Well, because this is defined in grams,  not milligrams,  so I'll rewrite this in terms of grams.  Then the conversion.  Where do you want to go to?  To moles.  Where do you want to move away from?  I want to move away from grams.  So put gram at the bottom,  moles on top, like this.  This gram will cross out,  and this calculation gives me a number expressed in moles.  This is my unit factor,  like we did with the conversions all the way.  Okay?  2.8 times 10 to the right score.  That is the answer.  So this question is converting a quantity expressed  in a mass, milligrams,  into a quantity, which is moles,  and you can use this unit factor to do that.  Okay?  Vitamin C, another very cool molecule.  Here it is.  Vitamin C is nothing but a sorbic acid.  And here's the structure.  Again, relatively small molecules are quite similar  to gestication or even calc.  If you don't have this thing,  if you don't ingest it,  your body can't eat it,  as you're going to get it to redness and fruits,  and you're actually pushing your unit system.  This molecule has 6 carbons, 8 hydrogens, and 6 oxygens.  So knowing this, those subscripts tell me exactly  what the molar mass is going to be.  Because we're going to do 6 times the molar mass of carbon,  8 times the molar mass of hydrogen,  and 6 times the molar mass of oxygen.  Okay?  There it is.  6 times 12, 8 times 1, 1, 0, 0, 8,  6 times 16,  and the total is going to be 176.12.  That is the molar mass of vitamin C.  Okay, that's it.  What is the question?  How many oxygen atoms are there in 5.3 micrograms of vitamin C?  This is a number expressed in grams.  So I have something in grams, micrograms,  a mass unit,  as a convertible to a quantity unit.  So it's a conversion property.  I'm going to need this.  I'm going to need this as a conversion factor.  They want the answer in oxygen atoms,  the number of atoms, not the number of moles.  So I have to do extra conversion and multiply it in the end  to get what the mole is.  So let's get that one out.  What I do is I'm going to write this, write it.  Okay?  It's roughly arranged.  5.3 times center minus 6 grams,  because the microgram is 10 to the minus 6.  I want to convert this from gram to number of moles first.  That means I take the scene here,  put mole on top and this thing at the bottom.  Grams will cross out.  So I get 9 number now expressed in terms of number of moles.  I find 3.0 times 10 to the minus 8 moles  to sort of ask for minus.  This is 2 significant figures, so I have 2 significant figures right here.  Is this a final answer?  No, it's not, because they want to have a number of oxygen atoms,  okay, not in moles of the molecule.  There's two things I have to do.  First, I have to determine how many oxygen atoms there are  for each molecule, that's 6.  And then I have to convert that to number  and multiply it back with the mole, with the mole number.  So let's do that.  This is the number of moles of vitamin C molecules.  This is what one mole is.  So I do this multiplication and get a total number of molecules.  1.8 times 10 to the 16 molecules of vitamin C.  Again, replace this, not by the mole number, but by the number of dozen.  The right thing to do automatically, now even thinking,  you would say, oh, if this many dozen, okay, that's just like a number of times 4.  Same here, just multiplying with the mole number.  I'll cover God's concept, but I do not like the problem.  Okay, this is the number of molecules.  Each molecule has 6 oxygen atoms, so the number of oxygen atoms is 6 times this.  This number of times 6 is going to give me my number of oxygen atoms.  1.1 times 10 to the 17 oxygen atoms.  Make sure you really understand this,  and you're very comfortable with calculation.  And discriminate number of molecules from number of atoms in the molecule.  The molecule can have multiple atoms in it,  but that's not going to be bigger than that.  Okay, another one.  How many moles of lead for chloride are present in this many grams of it?  Another conversion, from grams to moles,  to one step conversion,  if you know the molar mass of lead chloride,  you can directly calculate how many moles there are in this mass.  What do you do?  The molar mass, if you calculate it first,  comes to the clear table, one lead atom.  This is the molar mass of lead.  Okay, 4 times the molar mass of chlorine,  that is the molar mass of chlorine,  4 times that, we add just the whole thing up,  0.49 from the zero grams per mole.  Each mole you have 249 grams.  This is my conversion factor.  I'm going to write down this number, okay?  This is another way to say it.  The number of moles is nothing but the mass divided by the molar mass.  It's not going to memorize it as the same trick.  Basically, you take your mass, which is this number,  you multiply by conversion factor,  but always this number appears at the bottom,  and on top is one mole.  In other words, it's mass divided by the molar mass.  That's a quick way to remember this.  So, 5, 4, 4, 0 grams divided by that number equals 15.6.  That's the number of moles.  This formula here is exactly the same calculation  we did on the previous slide.  You take the rest in gram,  you multiply by the new factor,  molar mass at the bottom, this is one.  So you just do it together, you get mass over molar mass.  That's what it is.  It's the same calculation,  sourced together in one experiment.  Number of moles equals mass over molar mass.  Okay.  Another one, very quick.  Another sample, iron.  And this is monoxide, sorry, carbon monoxide.  It's found to contain, oops, I'm sorry,  this is a complex, okay?  It's a complex of iron and carbon monoxide.  It contains this many grams of oxygen atoms.  How many grams of carbon atoms are present?  This is interesting.  I have to convert a number of oxygen to a number of carbon atoms.  Okay?  Especially as a scientific notation.  So, I know the number of oxygen,  what is the number of carbon atoms?  Well, it's one to one, actually.  Okay?  The number of oxygen atoms is basically the gram  divided by the molar mass.  That is a quantity.  So 1.94 times 10 to the minus 5 grams,  that is the mass quantity,  divided by the molar mass,  gives me the number of moles.  Okay?  1.21 times 10 to the minus 6 moles.  So what I did, I took the formula from the last slide,  N and VA, number of moles,  equals mass over molar mass.  Mass over molar mass gives me a quantity,  especially more.  This is how many oxygen I have,  and that is the same as carbon molecules.  Okay?  In other words, I have exactly the same number  here as carbon.  1.21 times 10 to the minus 6.  The only thing you have to do here  is to convert a mass quantity  into a mole quantity.  That's it.  You do that by this expression.  What time is it?  Um...  Oh, look at this.  I can do one step more,  because what they ask is,  not how many atoms you have,  but what is the mass of those atoms.  So once you have the number of atoms,  you multiply it by the molar mass.  Okay?  So what I find is this many moles,  this is the molar mass.  The number of moles times the molar mass  gives you the mass.  Okay?  So let me read it again.  This is number of atoms.  Okay?  Number of moles.  This is what one mole weighs.  What the mass is of one mole.  So let's say 2 dozen eggs,  okay?  One dozen eggs,  five grams,  so you multiply it by numbers.  You're exactly the same thing.  You have a number of moles,  molar mass,  you multiply it to,  okay, the answer in grams.  Okay, okay.  That's it, and I'll see you on Wednesday.
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