In this video, we're going to learn how to solve problems like these, where we have to convert back and forth between grams and moles. What is a mass in grams of 4.30 moles of aluminum? from some other countries might pronounce this aluminium.
So in this problem, we're talking about grams and moles. So the first thing we want to ask is what is the molar mass of aluminum? The molar mass is going to tell us how much one mole of aluminum weighs in grams.
So to figure this out, we look up aluminum on the periodic table, and we check out this number here. This number tells us that the molar mass of aluminum is 26.98 grams per mole, which means that one mole of aluminum weighs 26.98 grams. Now that we have this information, I first want to show you how we can solve this problem by just kind of thinking through it.
We're looking for the mass in grams of 4.3 moles of aluminum. Basically what do 4.3 moles of aluminum weigh? This is basically a multiplication problem. Let me show you what I mean.
Looking at this information here, we can say that if we had 1 mole of aluminum, it would weigh 26.98 grams. okay how much would two moles of aluminum weigh what we take 26.98 which is how much one mole weighs and we multiply it by two okay and we get this answer how much would three moles weigh we take 26.98 which is how much one mole weighs and we multiply it by three and get this answer okay you get the idea right now in this problem we're talking about how much four point Once again, we know that this is how much 1 mole weighs. We don't have just 1 mole, we have 4.30 moles. So let's take this number and multiply it by 4.30.
That is going to give us 116 rounded to 3 significant figures. I haven't worried about significant figures for the numbers up here. So basically, all I'm doing here is just thinking through the problem, keeping in mind mind that the molar mass tells me how much one mole weighs. And all I have to do is just multiply how much one mole weighs by however many moles I have. To kind of sum up what I'm doing here, I could write this simple rule that says that when we're going from moles to grams, moles to grams, what we want to do is multiply moles by the molar mass.
Okay, here's how we think through it. Now I want to show you how we can can solve the same problem with conversion factors because a lot of times teachers and textbooks use conversion factors instead of this kind of like thinking through it method. Okay, so here we're starting with 4.30 moles of aluminum.
We get that from the problem here. Now let's write some conversion factors. I want to take this and I want to multiply it by a conversion factor that's going to get rid of moles and is going to convert moles into grams.
So write. conversion factors we often want to look at some sort of an equation or equivalence or relationship okay so I can take this information about the molar mass and I can write it sort of as an equation here as a relationship right which is basically saying that if we have one mole of aluminum well that means we have 26.98 grams of aluminum check it out we have the equal sign and something on either side this is like a perfect example of the sort of relationship that we can write a conversion factor with okay there are two conversion factors we can write with this relationship. The first is going to have this on top and this on the bottom.
One mole of aluminum over 26.98 grams of aluminum. Or we can flip it. We can do this on the top and this on the bottom.
On the top, 26.98 grams of aluminum. And then on the bottom is going to be one mole of aluminum. Both of these conversion factors are going to be on the bottom.
factors are totally cool, they're totally fine but we only want to use one of them. And the one that we're going to want to use is the one that gets rid of moles of aluminum from up here. It's on the top here.
So in order to cancel out moles of aluminum is going to be on the bottom of the conversion factor that we want to use. It's on the top here but it's on the bottom here so this is the conversion factor we want to use. So get rid of this one for now, bring this over and now we have moles of aluminum on the top, cancels out, moles of aluminum on the bottom. We're left with grams of aluminum which is exactly what we want.
Okay, so now the math that we do is this times this divided by 1. which is going to give us 116 grams of aluminum rounded to three significant figures because there are three significant figures in here and we don't worry about the number of significant figures in one here. And check this out, the math that we're doing 4.30 times 26.98 is exactly the same math that we did when we were just thinking through it right because dividing something by one mole, dividing something by one doesn't change its value. So whether you do the thinking through it method or you do the conversion factor method you're doing the exact same math right you're just taking the moles and you're multiplying them by the molar mass and this tells us how much 4.30 moles of aluminum would weigh how many moles in 127.5 grams of sodium chloride NaCl as before we're talking about moles and grams so the first thing I want to ask is how much does one mole of sodium chloride weigh in grams?
This is just another way of saying what is the molar mass of sodium chloride. To figure this out, I look at the formula and I look at the elements that make it up. Okay, I've got Na and I've got Cl here.
So I look them up on the periodic table. Sodium and chlorine and these numbers here are the molar masses of the two different elements. Now I want to add Add these up, okay?
I look at the chemical formula here, and this tells me that I have one sodium atom. So I'm going to do 1 times 22.99, which is the molar mass of sodium. And then I have one Cl, so I'm going to do 1 times 35.45, which is the molar mass of chlorine.
Add these together, and I get 58.44, which tells me that the molar mass of NaCl, sodium chloride, is 58.44 grams. grams per mole or it means that one mole of sodium chloride weighs 58.44 grams. That is how much one mole of sodium chloride weighs.
Okay, so we have a certain amount of grams of sodium chloride and we want to know how many moles is that. Here's how we'd think through it, okay? Based on this information here about the molar mass, we know that if we had 58.44 grams that would be...
1 mole. Okay but we don't have 58.44 grams we have 127.5 grams. Okay this is more than just 1 mole. The question that we want to ask is how many 58.44s are there in 127.5? In other words how many times does 58.44 go into 127.5?
This is a division problem okay. We're going to do 127.5. 7.5 divided by the molar mass.
We're going to find out how many of these are in this. And that's going to tell us how many moles we have. When we do the math, rounding to four significant figures, we get 2.182 moles. We can sum up what I did here by saying that when we're converting from grams to moles, we take grams and we divide by the molar mass.
So that's what I'm doing here. Taking the grams and dividing. dividing by the molar mass to see how many molar masses fit in the number of grams that we have. Now for the conversion factor approach. I'm starting here with 127.5 grams of sodium chloride and I want to multiply this by conversion factor that will get rid of gram sodium chloride and will take me to moles of sodium chloride.
So to do that I'll take this information about the molar mass and I'll rewrite it. as an equivalence or a relationship like this. Okay, I got one thing on either side of the equal sign, which makes it really easy to turn this into a conversion factor. Here are the two conversion factors that I can write with.
Okay, one has moles on the top and this on the bottom. The other has grams on the top and moles on the bottom. The one that I want to use here is a conversion factor that is going to cancel out gram sodium chloride, which is on the top here.
So I want it to be on the bottom over here. I'm going to use this. this one. So now I've got gram sodium chloride on the top, gram sodium chloride on the bottom, they cancel out, leaves me with moles of sodium chloride.
And the math that I'll do is this times this divided by this and get 2.182 moles sodium chloride. And check out that the final answer is rounded to four significant figures because there are four here and there are four here. And I don't worry about the one here because it's part of the deficit. Now I just want to point out the math I'm doing here is exactly the same as the math in the think it through method. I take 127.5 and multiplying it by 1 doesn't change it at all.
So I'm still just doing 127.5 divided by 58.44 which is exactly the math that I did up here which just shows that when we're going from grams to moles we take the grams and we divide by the molar mass. So that was kind of a quick introduction on going between grams and moles. If you want some more practice problems, check out the video Converting Between Grams and Moles Part 2.