Converting Between Grams and Moles (Part 1)

In this video we're going to learn how to solve problems like these: we're going to have to convert back and forth between grams and moles. What is a mass in grams of 4.30 moles of aluminum? People from other countries might pronounce this (phonetic spelling) ăl"yo͝omĭn'ēəm. So in this problem we're talking about grams and moles; so first thing we want to ask is what is the molar mass of aluminum? 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. Okay. 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. Okay. We're looking for the mass in grams of 4.3 moles of aluminum. Basically what 4.3 moles of aluminum weighs. This is basically a multiplication problem. Let me show you what I mean. Okay. Looking at the information here, okay, we can say that if we had one 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'd multiply it by 2. Okay, and we'd get this answer. How much would three moles weigh? We take 26.98 which is how much one mole weighs and we'd multiply it by three then get this answer. Okay, you get the idea right? Now in this problem we're talking about how much 4.30 moles weigh. Once again, we know that this is how much one mole weighs. We don't have just one mole, we have 4.30 moles. So let's take this number and multiply it by 4.30. That's going to give us 116 rounded three significant figures. I haven't worried about significant figures for the numbers up here. Okay. So basically, all I'm doing here is just thinking through the problem keeping in mind 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 can 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 you 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 the math. Okay, so here we're starting with 4.30 moles of aluminum. We get that from the problem. Now let's write some conversion factors. I want to take this and I want to multiply it by conversion factor. It's going to get rid of moles and it's going to convert moles into grams. Okay, to write conversion factors we often want to look at some sort of an equation, or equivalent, 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, as a relationship. Right which is basically saying that if we have one mole of aluminum well that mean we have 26.98 grams of aluminum. Check it out: we have equal sign in something on either side; this is like 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. Okay. The first is going to have this on top and this on the bottom. Okay. One mole of aluminum over 26.98 grams. of aluminum. Okay. Or we can flip it. We can do this on the top and this on the bottom. Okay. So on the top 26.98 grams of aluminum and then on the bottom it's going to be one mole of aluminum. Okay. Both these conversion factors are totally cool, they're totally fine. But, we only want to use one of them. And the one 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 we want to use. Okay. It's on the top here, but it's on the bottom here. So this is the conversion factor we want to use. Okay. So get rid of this one for now Bring this over, and now we have moles of aluminum on the top cancel out moles of aluminum on the bottom, and we're left with grams of aluminum, which is exactly what we want. Okay. So now the math that we do is this: this times this, decided by one which is going to give us 116 grams of aluminum rounded to the three significant figures, because there are three significant figures in here. And we don't worry about the 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 that 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 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 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 cholrine. And these number here are the molar masses of the two different elements. Now I want to add these up, okay? And look at the chemical formula here, and this tells me I have one sodium atom, so I'm going to do one times 22.99 (which is the molar mass of sodium) and I have one Cl (chlorine) so I'm going to do one 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 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 think through, okay? Based on this information here about the molar mass we know that if we had 58.44 grams that would be one mole. Okay, but we don't have 58.44 grams, we have 127.5 grams. Okay, this is more than just one mole. The question that we want to ask is how many 58.44 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 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 what I'm doing here: taking the grams and dividing by the molar mass to see how many molar masses fit into the number of grams that we have. Now for the conversion factor approach. I'm starting here with 127.5 grams of sodium chloride. I want to multiply this by conversion factor. It will get rid of grams of sodium chloride and will take me to moles of sodium chloride. So to do that I'll take this information about molar mass and I'll rewrite it as an equivalence or relationship like this, okay. I've 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 I can write, 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 the grams of 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 one. So now I've got grams of sodium chloride on the top, grams of sodium chloride on the bottom - they cancel out. That leaves me with moles of sodium chloride, and the math I'll do is...this times this divided by this...and get 2.182 moles of sodium chloride. And check out that the final answer is rounded to four significant figures because there are four here and there are four I don't worry about the one her because it's part of the definition. Now I just want to point out the math 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 introdcution on going between grams and moles. If you want some more practice problems, check out the video 'Converting Between Grams and Moles - Part 2'.