Lecture 11. Mole and Molar Mass (no captions)
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Molar volumeMagnetometerSeafloor spreadingEmission spectrumComputer animationLecture/Conference
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AreaLecture/ConferenceComputer animationDiagram
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BohriumTopicityStuffingAzo couplingSet (abstract data type)Medical historyLecture/Conference
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MashingBohriumWeaknessDeterrence (legal)CHARGE syndromeAreaElectronic cigaretteComputer animationDiagramLecture/Conference
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Grading (tumors)Grading (tumors)ErdrutschKlinisches ExperimentComputer animationLecture/Conference
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OreGrading (tumors)MagnetometerGrading (tumors)Sense DistrictAreaWaterfallPH indicatorComputer animationLecture/Conference
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OreGrading (tumors)Azo couplingBreed standardHardnessMan pageComputer animationLecture/Conference
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OreGrading (tumors)BeerElectronic cigaretteDeterrence (legal)Process (computing)Grading (tumors)Computer animationLecture/Conference
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Grading (tumors)OreGenomeBeerCalcium ammonium nitrateComputer animationLecture/Conference
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Coca-ColaKohlenhydratchemieTanningOptische AnalyseDarmstadtiumWine tasting descriptorsElectronic cigaretteWalkingNahtoderfahrungCalcium ammonium nitrateData conversionSunscreenChemical elementConcentrateDensityKohlenhydratchemieComputer animation
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TanningCoca-ColaKohlenhydratchemieOptische AnalyseSingulettzustandCalculus (medicine)Calcium ammonium nitrateLecture/ConferenceComputer animation
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SulfurCycloalkaneWine tasting descriptorsOxideChemical compoundMan pageSulfurSchwefelhexafluoridSchwefeltrioxidLecture/ConferenceComputer animation
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SulfurOxideWine tasting descriptorsCycloalkaneCarbonateHydroxybuttersäure <gamma->HydrogenNitriteAcidCiclopiroxolaminChemical compoundSchwefeltrioxidBarium chlorideBariumCaesiumIonenbindungCopperSetzen <Verfahrenstechnik>MetalAtomOxideAmmoniaSelenideCarbonateAcidProcess (computing)Ice frontLecture/ConferenceComputer animation
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Stop codonZeitverschiebungMedical historyMoleculeKohlenhydratchemieAtomLecture/ConferenceComputer animation
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AtomCollectingGesundheitsstörungComputer animationLecture/Conference
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PolyurethaneAtomIonenbindungMoleculeSodiumChlorineSaltCalculus (medicine)Sense DistrictAgricultureComputer animation
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AtomBohriumPharmacyComputer animationLecture/Conference
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AtomCarbon (fiber)Kohlenstoff-14WursthülleFarmerChemical formulaMedical historyKlinisches ExperimentComputer animationLecture/Conference
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AluminiumChemical elementAtomSample (material)Carbon (fiber)AtomValence (chemistry)TitaniumZincChemical elementBlock (periodic table)Data conversionWursthülleAzo couplingMolekulargewichtsbestimmungPotassiumHuman body temperatureAluminiumContainment buildingWaterfallThermoformingElectronic cigarettePaste (rheology)Action potentialNatural competenceChemical experimentLecture/ConferenceComputer animation
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AtomSample (material)TitaniumData conversionCarbon dioxideSea levelCalculus (medicine)SauerstoffatomAmount of substanceAtomSunscreenSample (material)MoleculeMedical historyChemical experimentLecture/ConferenceComputer animation
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AtomSample (material)Carbon dioxideMoleculeDrainage divideSauerstoffatomLecture/ConferenceComputer animation
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AtomMoleculeBase (chemistry)Lecture/Conference
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AtomSample (material)Molar volumeEthanolEnolAspirinNitrosamineSauerstoffatomVitaminAcidDarmstadtiumStuffingPressureWursthülleAluminiumTool steelElectronic cigaretteGrowth mediumActivity (UML)ScurvySauerstoffatomAmount of substanceSunscreenMoleculeChemical structureSystemic therapyWine tasting descriptorsAtomCarbon (fiber)WalkingChemistrySingulettzustandData conversionEstranCalculus (medicine)EthanolHydrogenMolekulargewichtsbestimmungCarbon dioxideVerdampfungswärmeCarbonChemical formulaVitaminAscorbic acidComputer animation
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AtomVitaminSauerstoffatomMolar volumeAcidDarmstadtiumCatalytic converterData conversionMedical historyTrauma (medicine)Amount of substanceSauerstoffatomGene expressionMoleculeAcidElectronic cigaretteChemical experimentComputer animation
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SauerstoffatomVitaminAtomMolar volumeAcidMoleculeSauerstoffatomPeriodateAmount of substanceElectronic cigaretteCalculus (medicine)ScurvyLecture/ConferenceComputer animation
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ChlorideMolar volumeAtomGene expressionSample (material)Protein domainMoleculeAtomSet (abstract data type)AreaProcess (computing)TiermodellSauerstoffatomWaterFireWaterfallCarbon monoxideErdrutschMolar volumeGene expressionMolekulargewichtsbestimmungAmount of substanceKohlenstoff-14Chemical formulaCarbon (fiber)WalkingLeadSunscreenData conversionCalculus (medicine)Multiprotein complexIronLecture/ConferenceComputer animation
Transcript: English(auto-generated)
00:07
Welcome back after a nice long session on Friday. Let me dive right into it. That's the score chart from last Friday. The mean was
00:25
56.2 standard deviation, which is basically a measure of the spread all around the mean was 80.6, which means that this exam really pulled a lot of performances away from each other. So it's a very broad distribution. For a teacher, this is great, because I
00:45
can beautifully see a spectrum of performances. For a student, this, of course, is not right. You don't want to be kind of close together and maybe somewhere more towards the nanny mark. So you may feel that 56 is not so good, but actually completely fine.
01:08
Completely on target. Last year, the performance was only one percentage point higher, so it was 57. Now it's 56. So
01:21
that's very much average, I would say, from year to year. So this is not anything out of your ordinary area. Let me say a few things. The exam was, like I said before we started, and this goes a little bit tight, this is part and parcel of having only 50 minutes, including arranging things, getting the other class, our new class in, taking the seat,
01:44
distributing the exam. You cannot do it in another way. You cannot put the exam on the seat beforehand, because it is allocated seating. You don't have 600 copies of chair over chairs. You simply can't do that. So we have to move it the way we did it. It takes a little bit of time. So we have to move it the way we did it. It takes a little bit of time. So we have to move it the way we did it. It takes a little bit of time. It takes a couple of minutes of your examination time, and you know that. Many people told me that, and I
02:06
said, well, 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, we still get a very good impression of what the performance of this class is.
02:25
The second midterm, you will see, will go a lot better. It is a little less intense, and you will feel more comfortable, and the final will be relatively, I would say, easy, but more time for you to take your questions.
02:42
This midterm 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 you will be able to do them quickly. And so, that part of the exam has a lot of stuff here. I was trying to test you on several things, and this is the result.
03:03
So not bad at all, we are on target. If you are on the low side of the meeting, take this exam as an opportunity to see what parts of the material need to be improved on. So what is your personal weakness on the exam that needs extra attention? You can come to office hours, you can come to the office,
03:26
you can speak through Twitter, the discussion leaders, Laura and Mike, they are very happy to help you out. Ask them specific questions, things you don't understand, and ask for a specific answer. So again, you are in charge of your own success, you identify which parts of the material are not easy to use,
03:45
and you act on it. Make sure that you get that 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 ways out of that block, it really is not. The final is almost half of your grade. The final is really where it's all happened. This
04:08
exam is really just a warming up exercise. Just to get started, so don't be demoralized if it didn't go so well for you. Actually, if it didn't go so well, it tells you which things you are going to want. So it's a good thing.
04:22
It is more like an opportunity than a penalizing experience. Yes. Let me go through the list first. It's actually on the slide. The grade of all the tests will not be curbed. Only your cumulative grade will be curbed. Your cumulative grade is
04:43
two mentors, one final, and a homework. Together, that is your overall grade of this course. That will be curbed. In my opinion, it doesn't make a lot of sense to curve individual exams. A much better measure of your performance is to look at
05:00
your score. Your score is a metric. It is a number that tells you how well you did it. The maximum score is 100, and if you have 50%, it means you get half right within the allotted time. That's what it means. A very good indication of your performance. Don't do a arithmetic at this stage of the day. It makes no sense. It makes no sense to do that. Do that kind of thing.
05:22
It makes no sense. At this stage of the day, the only thing you should be concerned about is do I understand the derivative? That is what you are here for. Worry about this derivative just till the very very end. Don't go and tell your friends about the derivative right now. It is just a waste of energy.
05:43
Your exam will be available on the triple E page on Friday, if everything goes right. So we have as you noticed, we graded everything on Friday. Right hard work, lost by the indicators and everything. Everything is done manually.
06:01
A very small team of people. People are staying home on your exam, you all see. They are now currently in the copy standard, they are all being scanned and reproduced in the OCR version in the real box. So you are only in the OCR version of your exam. This will take a couple of days. This is not within my control, this will get done on the copy standards.
06:25
Okay. You can contest your score if there is a genuine graded error. Don't come to me, please, with all kinds of arguments about why you should have more partial credit. That is not the purpose of contesting your score.
06:44
We have given partial credit, we have stuck to a very specific recipe for that, and we think we have done a great job. If your answer is correct, like you didn't get the points, you get you're entitled to get extra points.
07:01
But if your answer is not correct, then somewhere in the margins you have written something that may be right, a little bit of imagination, we cannot give you extra points for that. So if you guys do that, I'll be out of my job. I'm going to spend all my time on that. It's impossible. That's also not the purpose. I think you can grade it very privately.
07:24
Okay, so the grading errors will be considered till this is Friday the 9th of November. So it means you get your exam back on Friday, normally on Friday, this Friday, and then you have one week time to talk to me send me an email, okay? If you have a simple question, send me an email. I can
07:44
do things right for a question. If you have specific questions, you can come to my office hours. The TAs are happy to discuss answers with you, and they cannot give you partial credit. Only I can do that. All right. Let me quickly look at one question on the exam that's about the can of Coca-Cola.
08:09
This question surprisingly went not so well. Most people were probably confused by this question. Let me go through it and just see put these elements in place.
08:22
It says a doctor advises a patient not to consume more than this. Okay? So this is 85 grams. So I'm just quickly converting the magnitude of what I had. This is 8.5 times 10 to the minus 2, kilograms, and it's 85 grams.
08:41
So this patient should not consume more than 8.5 grams of sugar in a day. Now in one of these cans, there are twelve ounces of sorry, this is twelve ounces, and it contains sugar at this concentration. So this is a volume. This is a volume. And this a concentration, or density, as you can see. This is
09:06
a gram of a liter. This is mass of a volume. And this is a density and this is a volume. the volume how many of these cans can this patient have? And the conversion here ounces to milliliters is shown as well. So
09:21
what do we need to calculate here? Well, what we need to calculate is, in the end, how many cans can the patient consume? Why does that depend on? It depends on how much sugar is in there. 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
09:43
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 almost, you want to know how much sugar is in this. How many grams of sugar is in one of these cans? How do you calculate that? So that's the mass mass is volume times density. Do I have that information? Yes. There is the density, there's your volume.
10:05
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't do that
10:23
quickly in your head, you can just write it out, because the difference between a milliliter and a liter is a factor of 1,000. So 0.110 grams per milliliter times the volume. And the volume is right here, between parentheses. I want
10:44
the answer in milliliters, so I use this conversion factor. 12 ounces, that's the volume, times this conversion factor You see this answer will cross out, I get my answer in milliliters. So if you execute 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 cans.
11:09
You are almost right here with the answer. This multiplication here of one, two, three numbers is basically the whole thing.
11:22
How many cans can you have? Okay, well, I have a maximum of 85, this is 39, so how many 39s are sitting at 85? 2.2. I can have 2.2 cans. That's it. That's the calculation.
11:42
Okay. Another issue is naming compounds. Naming compounds is something you can literally work. It's a method, and you stick to the method and you will be fine. I'm going to give you several.
12:01
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?
12:24
Because you will say sulfide, and it is sulfur trioxide. And again, I'm going to say 20%, but about 15% of the folks did exactly this. Okay? So you have to pay attention to that. Because even people, that's actually very interesting to me, they put a 2- here. As if I
12:45
forgot how many times I did that. They put a 2- here and they said, oh, it's sulfide. This is sulfur trioxide. It's a neutral compound. Okay. This one. Some folks said
13:01
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.
13:22
But selenide is it's in the same family as oxide, right? It's in the same column. So this is 2 minus, I mean the copper is 2. It has a charged 2+. Oxidation state 2. This one, now what does this mean, guys? It dissolves. And this is an
13:45
H. What does it mean? It's an acid. Still, still, okay, a fraction of folks still call this hydrogen nitride. Okay? Don't do it again. Okay? This is nitrous acid.
14:01
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, same situations here they think this is a type 2 metal. Barium is not. Barium is 2+, type 1. Okay? It's in the second column, and those are type 1 metals.
14:25
You never specify the oxidation state of the type 1 metal. So this is not barium 2 chloride, it is barium chloride. Okay. Keep these things in mind, keep practicing, and then we'll see when the final comes along. We have to move on. Okay? We're going to chapter 3.
14:57
Okay. So what is this about?
15:06
In chemistry, we deal with a lot of atoms. We need a material which is available in your hand, the solution, the sugar in your coffee, it's not one molecule. It's many.
15:21
So instead of talking just about one thing, we talk about collections of atoms, like collections of people. But the problem is that these collections are rather large. Okay? So I guess you get the idea. This is one person, you can easily think of this of this one person, you just conceptualize it, there he is, one guy, and then you can even conceptualize this situation here
15:47
that's concentrated about 390 people. Even though here you know people is a huge number, for some reason our brain kind of understands that number. and you understand 300, it's about this. You kind of conceptualize it. Now, if you look at
16:07
an ion and molecules and atoms, the numbers are rather staggered. Okay? So this is one ion a can, you can easily grasp it, this is just one sodium and one chlorine ion there together, nothing is wrong with it, easy to conceptualize, but what if you have one of these little chunks?
16:27
one little brain of salt, a tissue of salt already has 1 x 1019 ion pairs in it. 1019 is a staggering number. It's huge. This number here fades, compared to how many eyes are in there.
16:48
Our mind cannot comprehend the magnitude of this number. You can try, but you don't. because you don't have a frame of reference. You're kind of lost by this number. And consequently, it's hard to do calculations and manipulations with these numbers.
17:05
So it makes a lot of sense for chemists, and also for you, since you are aspiring chemists. You don't know any chemists. You will. to have a different way of treating these large numbers. And you have heard this number, and that's the law.
17:24
What is it? It's a number. I can feel the excitement. It is a number. That's it. That's all you have to know.
17:41
It makes a funny number. It makes a funny number. Oh really? That's great. How many digits do you know? You know how many digits do you know? Four digits, or five, six?
18:00
So this number is big, right? It's big. It's 6.022 times 10 to the 23rd. And that's a very, very big number. But it is a number. I'm just wanting 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 220 is a number. This is just a different number. It's a quantity of things.
18:29
So how does that define? Where does that come from? Well it's defined, again, through our best friend, the carbon atom. The definition is false.
18:40
12 grams of carbon 12 that is the isotope of carbon. Isotope 12 of carbon. Carbon 12. If you have 12 grams of only these atoms, then the definition says you have one mole.
19:00
So if you stick to the definition, if you say this is the definition, you can count what you have. And it turns out that this definition stipulates that you have this many. So if I tell you this more would be here, this is the definition. If you take 12 grams of carbon 12, that is your method. That is your new unit. Okay? You say you have
19:21
it here, now how do you measure these things? Oh, I count this many atoms in there. And that's it. That's the definition. Nothing mysterious about it. It's just a definition. You have to define it somewhere, so this is a pretty good definition, like any. So again, I just want to re-emphasize it is a number, people mix this up. People make the moles look mysterious. Ah! Just a number.
19:44
Like a dozen is a number, you've heard it comparison probably, but it's really true. 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 it's surprising that if I give you a question, and I replace every word mole with the word dozen, you have no problem solving the question.
20:06
I think I put the word mole for dozen, you are completely confused. Because you think the mole is hard to understand, but it's not. It's really just a number, like a dozen is a number.
20:22
So in case you are confused by a question, and the word mole is not even in the 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.
20:41
All right. So if I have one mole of carbon C12. One mole of it. Well, then I have 12 grams. I guess that's basically the definition. One mole of carbon C12 equals 12 grams. Because 12 grams of carbon C12 is one mole.
21:05
So the mass of carbon C12 is 12 amu. 12 atomic mass units. Okay? That's another definition. That's how atomic mass units are defined. So one mole times this, we just substitute this here for that, equals 12. Same line.
21:24
From this I can just bring this guy to that side and conclude 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 is just a quantity.
21:48
Now this is a very useful kind of conversion that you want, or relationship, because I can do the following. I can take another element let's say aluminum one mole
22:00
times the mass of aluminum Okay? So let's say one mole of aluminum happens. The mass of aluminum happens should be supposed to go here. What is the mass of aluminum happens? Well, in amu, I know what it is. It's right here. 26.98. That follows from the periodic table. The average mass of aluminum atoms is right here. That is the number in the periodic table. Okay? If I
22:27
multiply that by one mole, look, one mole is this. So I put that right here. I see amu is the mass of aluminum atoms. across out, and it has an answer in grams. In other words, this is 26.98 grams. All right? So what does the line say?
22:44
The line 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 amu. So every time you take one mole of these atoms, that means a whole mass of aluminum atoms.
23:05
So I'm going to move on to them, the temperatures. Then the mass of that will be equal to the molar mass of that element. That is amu replaced by grams. So let's have a look at the periodic table. This is what we just did.
23:22
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. Potassium. You take one mole of that element, and it's equal to the mass of the atom. All of it, you get this mass, which is the number in the periodic table, which is the periodic
23:41
table that says amu. And if you take one mole of these elements, you get that number in grams. Zinc. Same thing. You take one mole of zinc atoms, you get this mass here, the number in the periodic table, are now expressed in grams. And it holds for any other element. It doesn't matter which one.
24:02
okay? That's right, because now I can just take one mole of all these elements and now how much they weigh expressed in grams. What the mass is expressed in grams. Okay. So let's do an exercise here
24:22
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. And I'm going to ask myself a question. Okay. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat. I have heat in 3 grams of titanium. How many titanium atoms are in there? That's what I always know. How many titanium
24:42
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? So one way to do that is this. I have grams, I know how much one mole of titanium is, but then it is not a very large. Okay. I can make a conversion pattern. What is the conversion pattern?
25:05
One mole of titanium equals this many grams. I can use this as a unit factor. 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
25:23
I want to go to quantity, number mole is a quantity so I put mole on top, and this is the bottom. And this is multiplication. You see, grams strike out and I get now the number of moles of the tinny that are in three grams. This is it.
25:43
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 yet the quantity is expressed in moles. And I want it in real numbers now. So how do you do that?
26:05
Well, this is the moles, I just multiply it by what the mole is. Just like if I said there are this many dozen titanium atoms, you would multiply by 5. So I multiply this by 6.022 times 10 to the 23rd. Okay? I take that number, multiply it by what the mole
26:25
is, that is a mole. This number is a mole. And then I get the number of atoms. 3.7 times 10 to the 23rd. Again, there's no number is rather separate. That's why we typically don't really bother about really calculating the amount of atoms, and we stay on the
26:43
level of the moles. Because those numbers are much easier to work with. That's the purpose of the moles. To make calculations easier and more manageable. Okay. Two quick examples. A sample of CO2 has 1.4 times 10 to the 3rd moles of oxygen atoms.
27:11
The other question is, how many moles of CO2 molecules are present? So what is this question about?
27:22
Well, this question is about this. What is given is how many oxygen atoms you have. Not how many molecules of CO2 you have. I know how many oxygen atoms I have, but from it I have to determine how many CO2 I have. So it's a relation. It's the same as saying
27:41
you have two ions. You all have two ions. So in this room, there are 600 ions. How many people are there? 300. So this person has two ions. It's the same here. Each molecule has two oxygens. So for each molecule, there are two oxygen atoms. So what I want to do is just take that number
28:03
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 a different word can seem diffusion. If I say molecule and atoms, you tend to think this is going to be a very complicated calculation, but if
28:27
I say eyes and people, nobody has an issue. So mathematically, this is a joke. But just conceptually, you have to give these things meaning. Don't be
28:40
afraid of the number of atoms, or how many atoms there are in a certain molecule. It's just accounting. It's just like two eyes on a molecule. This person is accounting. The sooner you get to the base of the cell, and this is all straightforward, the faster you will get to the end.
29:00
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. What I want to know is how many
29:20
H atoms I have. The quantity of H atoms. So what I see here, I have a molecule it contains C's and H's. It contains six H's. So for each one molecule, I have six hydrogens. So how many hydrogens do I have? Well, I take this number, which is a number, a quantity,
29:43
and I multiply that by 6, 17.3 moles of H atoms. That's it. I just have to multiply it. Very easy, it seems, and these simple exercises are just for you to get used to the words molecules, atoms, and
30:00
don't be afraid of doing this calculation. Yes. What happens to 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?
30:20
Then your question would be, how many noses are there? I say, well, there's 200 of those. Because each molecule has one carbon. Sorry, that means there's just the same number of atoms that there are molecules. The question was about oxygen and how many molecules we have. Eyes and people.
30:43
Of course, people might also have a nose, actually people have many molecules. They have two arms, they have two legs, they have all kinds of things. This CO2 has only carbon and oxygen. Okay. Now, what holds for atoms also holds for molecules as a whole. What does that mean? That means the following.
31:07
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. So, for instance, let's take this one.
31:24
C2H6R. What's ethanol? If I have one mole of ethanol, what would its mass be? How do you calculate that? What you have to do is you can see what's in it.
31:41
One molecule of ethanol has two carbons, six hydrogens, and one oxygen. If I have one mole of ethanol, that 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.
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The mass of two moles of carbon equals two times the mass of one mole, which is this. Twelve 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 one mole of hydrogen.
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And one mole of oxygen is 16 grams, or 15.999. Okay. So what you have to do is you have to do these multiplications, and then add them up. The answer is 26.07.
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That is the lower 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 this thing on your balance, you will say, is this 26.07?
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So we say, 46.07 is the lower mass of ethanol. Okay. So we can do this for any other molecule, right? Let's move on. After the full molecule, if you feel good and you think, it's a nice box, it's not very simple, but it's a small molecule.
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Here is the line structure, your favorite way to draw a molecule, and here is the chemical formula. The chemical formula is in this regard very important. If you want to calculate the mole mass.
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Okay? There's nine sorry, there's nine carbons, eight hydrogens, and four oxygens in it. 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 mole mass of this compound? So what I do is this again. Nine moles of carbon, that means nine moles, nine times
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the mass of one mole of carbon, that's nine times the mass of one mole of carbon. 12.011. That's this number right here. 8 moles of hydrogen, 8 times the moles of mass of hydrogen, which is 0. Sorry, 1.008.
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Do the multiplication and you find this. and then 4 moles of oxygen, because it's 4, there's a 4 here. That 4 is right there. 4 moles of oxygen 4 times the molar mass of oxygen, which is about 16, and you get 64. It's contributed by the oxygen. There's one line here and you add one. 1 mole of estrogen is 180.16. So if I had 1 mole of it, this would be its mass.
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Let's look at this number here. I want to know how many moles are in this mass. This mass is much smaller than this mass. Why do I say that? Because if
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you've captured how many moles it is, it is definitely much smaller than 1 mole. So if your answer is going to be larger than a mole, you get something wrong. I need to find an answer for 50 milligrams of aspirin, and I know it's going to be a number much smaller than 1 if I express it in a number of moles.
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So what do I do? I write down again the quantity, which is 50 grams, sorry, 50 milligrams, expressed in grams. 0.050 grams. Why do I do that? Well, because this is defined in grams, not in milligrams, so I rewrite this in terms of grams.
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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 I 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.
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This is my unit factor, like we did with the conversions all the way. 2.8x10-4. That is the answer. So this question is converting a quantity expressed in a mass unit, grams, milligrams, into a quantity unit, which is moles. And you can use this unit factor to do that.
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Okay? Vitamin C, another very cool molecule, here it is. Vitamin C is nothing but ascorbic acid. and here's the structure. Again, a relatively small molecule with quite some majestic implications for human health.
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If you don't have this thing, if you don't ingest it, your body can't hit it, as you can get to veggies and fruits, and you are actually producing your immune system. This molecule has six carbons, eight hydrogens, and six oxygens. So knowing this, no subscripts, tell me exactly what the molar mass is going to be.
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Because we are 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. 6x12, 8x1.008, 6x16, and the total is going to be 176
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.12. That is the molar mass of vitamin C. Okay. That's it. What is the question here? How many oxygen atoms are there in 5.3 micrograms of vitamin C? This is a number expressed in
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grams. So I have something in grams, micrograms, a mass in it, as a converter into a quantity unit. So it's a conversion problem. I'm going to need this. I'm going to need this as a conversion pattern. They want the answer in oxygen atoms, the number of atoms, not the number of moles, so I have to do an extra conversion and multiply
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it in the end with what the mole is. So let's get that one by one. What I do is I'm going to write this right there. Okay? Express it in grams. 5.3 times 10 to the minus 6 grams, because the micro is 10 to the minus 6. I want
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to convert this from grams to number of moles first. That means I take this thing here, put moles on top, and this thing on top. The grams will cross out, and I get my number now expressed in terms of number of moles. I find 3.0 times
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10 to the minus 8 moles of assorted acid. This is two significant figures, so I have two significant figures right here. Is this the final answer? No, it's not. Because they want to have it in number of oxygen atoms, not in moles of the molecule.
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First, I have to determine how many oxygen atoms there are for each molecule. That's six. And then I have to convert that to number and multiply that 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
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this multiplication and get the 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 word dozen. And what you would do automatically,
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without even thinking, you would say, oh, if this many dozen, okay, that's just like this number times 4. Same here, just multiplying with the mole number. Or however you want to call it. Okay. This is the number of molecules, each molecule has 6 oxygens, so the number of oxygen atoms is 6 times this. This number times 6 is going to give me the number of oxygen atoms. 1.1 times 10 to
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the 17 oxygen atoms. Make sure you really understand this, and you are very comfortable with calculation like this.
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And discriminate number of molecules from number of atoms in the molecule. The molecule is going to have multiple atoms in it. So that number is going to be bigger than that. Okay. Another one. How many moles of lead? 4. are present in this many grams of it. Another conversion. From grams to moles. A one-step conversion. If you know the molar mass of
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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, go to the periodic table, one lead atom, this is the molar mass of one of lead, okay, 4 times the molar mass of lead.
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molar mass of chlorine, that is the molar mass of chlorine, 4 times that, we add this whole thing up, 349.00 grams per mole. For each mole, you have 249.00 grams.
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This is my conversion factor. I'm going to write down this number, okay, well, this is another way to say it, the number of moles is nothing but the mass divided by the molar mass. This is another way to memorize the same trick. Basically, you take your mass, which is this number, you multiply by the conversion factor,
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where always this number appears at the bottom, and the top is one mole. In other words, it's mass divided by the molar mass. That's the quick way to remember this. So 5, 4, 4, 0 grams divided by that number equals 15.6. That's the number of moles.
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So this formula here is exactly the same calculation we did on the previous slide. You take your mass in grams, you multiply by the new factor, molar top, molar mass at the bottom, this is one. So you switch it together, you get mass over molar mass. Right? That's what this is. It is
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the same calculation, switched together in one expression. Number of moles equals mass over molar mass. Another one, right quick?
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another sample, iron and this is monoxide, sorry, carbon monoxide. It's found to contain this is a complex, okay? This is a complex of iron and carbon monoxide. It contains this many grams of oxygen atoms. How
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many grams of carbon atoms are present? This is interesting. I have to convert a number of oxygen to the number of carbon atoms. Okay? Express your answer in scientific notation. So I know the number of oxygen, what is the number of carbon atoms? Well, it's one-to-one, actually.
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Number of oxygen atoms is is basically the gram divided by the molar mass. That is a quantity. So 1.94x10-5 grams, that is the mass quantity, divided by the molar mass gives me the number of moles.
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1.21x10-6 moles. So what I did, I took the formula from the last slide, and mVA, number of moles, equals mass over molar mass. Mass over molar mass gives me a quantity expressed in moles. This is how many oxygen I have, and that is the standing of the carbon molecules.
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Okay? In other words, I have exactly the same number here for carbon. 1.21x10-6. The only thing you have to do is convert a mass quantity into a mole quantity. That's it. And you do that by this expression. What time is it?
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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.
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So once you have the number of atoms, you multiply it by the molar mass. Okay? So what I find is this is moles, this is the molar mass. The number of moles times the molar mass gives you the mass. Okay? So let me re-correct again.
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This is number of carbon atoms, okay? Number of moles. This is what one mole weighs. What the mass of one mole. So let's say two dozen atoms, okay? One dozen weighs 5 grams, but you multiply it by numbers. Exactly the same thing. You have a number in moles,
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molar mass, and you multiply it so you get the answer in grams. Okey-dokey. That's it, and I'll see you on Wednesday.