20. Heat and Temperature
Moles and Avogadro's Number
Moles & Avogadro's Number
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Hey guys. So a lot of times in our physical equations we usually use the mass of a material. So for example, our most important equation F equals M. A. We use the mass to calculate the force. But a lot of times in thermodynamics, you're gonna need to know the number of moles or the number of particles that make up a material, like a gas. So I'm going to introduce to you the moles and also avocados number in this video. And I'm also gonna show you a systematic way to convert between these three related ideas, the mass, the mole and the number of particles. If you've ever taken a chemistry class, you're probably familiar with the mole. But if not, I'm gonna go ahead and introduce it to you. So let's check this out. The mole, which is given by the letter Little end is really just the amount of material. It's an amount of stuff That is equal to a very specific number of particles. 6.02, 2 times 10 to the 23. This really big number here is known as α. God rose number has a special name. And we also give it the letter big end A for avocado. So a mole is really just a shortcut way of saying it's an amount that's equal to this many particles. It's kind of like if you said if you had a dozen donuts, that doesn't just means that you have 12. A mold just means that you have this many of whatever it is that you're talking about and it actually applies to any substance that you talk about. For example, if you have a mole of nitrogen, that just means 6.22 times 10 and 23 nitrogen atoms extravaganzas number. If you have a mole of H 20, it just means that you have an H and avocados number of H 20 molecules. If you have a mole of dollars, you'd be an extremely rich person because you would have an avocado is number of dollars. That's just, you know, a mole just means a shortcut of way of saying this many particles or whatever it is now, as we said before and a lot of our thermodynamics discussions and equations, we're gonna be talking about these sort of three related ideas, the mass, the mole and also the number of particles and specifically you're going to need to know how to convert between them. So unfortunately what happens is that a lot of these terms have sort of similar letters. The number of particles is given by big end. The number of moles is given by little end and the massive something is given by little em they're all sort of like they're sort of sort of similar. Now, fortunately the equations are very straightforward. So let's check this out if you wanted to connect to the number of particles to the number of moles, we're just gonna use this equation over here, Little N equals big end. The number of particles divided by a big address number. If you have some amount of particles, we want to figure out how many moles you just have to divided by this really, really big number here, the number of particles and it'll get you that many moles. So let's go ahead and check out our first example here. So we want to calculate how many moles are in this many carbon atoms. So what are we trying to do? We're trying to go from a number of moles which is Little N. And we were trying to get I'm sorry, we're trying to go from a number of particles Big N. And we're trying to get to the number of moles. So we're really just trying to go from here to here and therefore we're just going to use this equation. Alright, so let's do it. So we have Little N is equal to Big and over Salgado's number. So this is gonna be 8.33 times 10 to the 37. This is gonna be particles. And then we're gonna divide it by avocados, number 6.22 times 10 to the 23rd. The units for this are basically particles per mole. So what you see here is that the particles and over particles will cancel out and you're just left with moles. And if you go ahead and plug plug this into your calculator, you're gonna get 1.38 times 10 Times 10 to the 14. And this is how many moles of carbon atoms you have. And that's the answer. Right? So you just figure out in this flow chart here which two variables you're trying to connect and then use the equation. Let's check out the second example. We're trying to calculate how many grams of aluminum is in this many moles of aluminum. So here we're going from moles and now we want to calculate a gram which is a mass. So here in our flow chart, we're actually trying to go from here to here. So we're gonna need another equation to do this. And that equation is little M. The mass divided by big M. So this big M. Here is called the molar mass of a material. It's also known for those of you have taken chemistry as the atomic mass, which you can find in any periodic table. So, fortunately here, clutch, we have our own periodic table. You can find at the bottom of this page here. And if you go ahead and click on aluminum, what you're gonna get is that the atomic mass is 26.98. That's the molar mass. What that means is that there are that many grams per one mole of aluminum. All right. Now, one thing I want to mention here is that one way to kind of remember these equations is that little N is always equal to the two letters divided so big and over. Little big end over avocados number. there are two big ends and also little M over big M. That might be one way that you remember that. Right? So let's go ahead and use this equation here. If we have N equals little M. Divided by a big. Um but we want to calculate this little M. Here, that's the mass. So we rearrange this equation and we're gonna get em is equal to n times this is going to be big M. So the number of moles that we have is 2.35 and the molar mass of aluminum were given is 26.98. So this is 26.98 like this. And if you go ahead and work the sandwich, you're gonna get a mass of 63.4 and that's grams of aluminum. Alright, so that's the answer. That's 63.4 g. Let's check out the third one. Now we want to calculate how many particles are in 24 g of H 20. So here we are we have is we have a mass and we're actually trying to get actually really laid out this way. So we have a mass and we want to get to the number of particles, remember that is big N. So in our diagram we're actually trying to go from this little M and we're trying to go all the way back to the number of particles. But in order to do that, we're gonna actually have to go through moles moles is kind of the bridge between these variables. So if you kind of think about this, if I'm trying to get from here to here and I actually have to first go through moles and then convert it to the number of particles. So that's what we're gonna do here. So in this first step we're just gonna use the equation and equals little M. Over big M. I want to calculate the number of moles. So I'm just gonna go ahead and plug in my mass and divided by the molar mass. I'm just gonna so this is going to be a little M. And that is gonna be a big M. So this is my mass which is 24 g. And this is my molar mass which I'm given is 18.2. So this is 18.2 like this. And if you go ahead and work this out, what you're gonna get is 1.33 moles. That's how many of that. So many moles of H. 20. That I have. The second step here is now I actually wanna go from moles to number of particles. And I'm actually gonna use the other equation. I'm gonna use my my N over N. A. Equation. So this is N equals and I have N over N. A. Now what I'm actually trying to do is calculate N. So I'm just gonna rearrange this equation. This is gonna be end is equal to little end times of a God rose number. So I have a little end. That's the number of moles. Right? That's that's 1.33. 1.33 times. And then I've got uh 6.22 times 10 to the 23rd. That's the number of particles let go and move. And I've got the number of particles is equal to 8.1 times 10 to the 23. And that's gonna be particles, Right? That's how many molecules or particles if you will of H20. That you will have. All right. So that's the answer. That's how you sort of navigate this flow chart here. Just figure out where you're trying to go what you're given and target variables. And use the right equation. Let me know if you guys have any questions
If the molar mass of hydrogen is 1.008 g/mol, what is the mass (in grams) of 2 hydrogen atoms?
3.35 × 10-24
1.69 × 10-24
Calculating number of water molecules in a bottle
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Hey guys, welcome back, let's get started here. We have the molar mass of water, which is 18 g per mole. But were asked to calculate this problem is how many molecules of H 20. We would find in a 1.5 liter bottle of water, like one that you would find at the store. So let's get started here. Which variable are we asked to solve for? Well, in our flow charts of particles, moles and mass or actually we're looking for n the number of particles or molecules. So really what I'm looking for is N of H 20. How many H 20 molecules? So in order to find out big N, I'm gonna have to use this first equation here. The one that relates moles 2, 2 particles by using avocados number. So this little end is going to be the number of H 20 molecules divided by avocados number. If you ever forget it, it's right here. 6.2 times 10 to the 23 power. So basically I'm gonna have to move this over to the other side. I've got N times Big End or that's that's avocados number, sorry. And that's going to be equal to the number of H 2 0 molecules. Now I know what this is. This is just a constant. What I don't have the O is the number of moles. All I'm told in this problem is that the molar mass is 18 g per mole. But remember that is a big M that's capital M. That's the molar mass and I'm only just told that this is a 1.5 liter bottle of water. I'm not told the number of moles. So I'm kind of stuck here, but it's okay because if I'm stuck in using, if I'm stuck for the number of moles, you can always get that by using the other equation. The one that relates mass two moles by using the molar mass. So basically that's what I have to you do. I have to come out of this equation to solve for N. That's N equals little M over big M. So really to find out the number of moles, I just need the number of the mass divided by the molar mass. Now I have the molar mass, that's just the 18 g per mole. But I don't have is the mass. All I'm told is the leaders. Remember that's just a unit of volume. Well, one thing you need to know, one conversion that's pretty useful to know is that one liter of water is equal to one kg of water. That's just the density thing. So it's just kind of want to put it here that this is only for water, but one leader is equal to one kg. So when it says a 1.5 bottle liter bottle of water. Really, what this means is that M is equal to 1.5 kg. And now we have with the mass is equal to so this little end is equal to 1.5 kg divided by this is gonna be g per mole. Now, just be very careful when you plug this into a calculator. You don't just go ahead and do this right now because we have kilograms and grams per mole. So we need to make the units agree with each other. Either we can convert this unit two kg per mole or we can just expand this out two g. Either one is uh is perfectly acceptable, I think one is a little bit easier. Just expanding the 1.5 kg. two g By moving the decimal place to the right. So 1.5 kg is 1500 divided by 18 g per mole. Which you'll see is that the g cancel out? And you're gonna get 83.3 moles. So that's how many moles that we're dealing with here. But that's not our final answer because remember we have to pop this back into this equation to solve for the number of particles. So basically you're going to take this and you just plug it back into for for this little end here like this. And what you're gonna get here is 83.3. This is going to be moles And you multiplied by avocados number. That's 6.0-2 Times 10 to the 23. Remember this is particles per one mole. So what happens is the moles will cancel and you'll just end up with the number of particles which is 5.2 times 10 to the 25th. And that's going to be uh particles or molecules, let's say, let's say molecules Of H 20. Alright, so that's it for this one, that's the final answer. Let me know if you have any questions.