Calculating number of water molecules in a bottle

by Patrick Ford
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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.