Converting Between Grams and Moles

In this video we are going to learn how to solve problems like these where we have to convert between

grams

and

moles

what is the mass in

grams

of 4.30

moles

of aluminum. People in other countries might pronounce "aluminum," so in this problem we are talking about grams and moles, so the first thing we want to ask is what is the molar mass of aluminum. The molar mass will tell us how much one mole of aluminum weighs in grams, so to calculate this we look up. aluminum on the periodic table and we review this number here, okay, this number tells us that the molar mass of aluminum is twenty-six point nine eight grams per mole, which means that one mole of aluminum weighs 26 point nine eight grams now that we have this . information First I want to show you how we can solve this problem, but just thinking about it, we are looking for the mass in grams of four point three moles of aluminum, basically what four point three moles of aluminum weigh.

This is basically a multiplication problem let me show you what I mean okay, look at this information here okay, we can say that if we had one mole of aluminum it would weigh twenty-six point nine eight grams okay, how much would two moles of aluminum weigh what we took twenty? six point nine eight, which is what one mole weighs and we would multiply it by two, well, and we get this answer, how much would three moles be? We take twenty-six point nine eight, which is what a mole weighs and we would multiply it. say it for three and get this answer.

Well, you get the idea. In this problem we are talking about how much 4.30 moles are. 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 four three zero, which will give us 116 rounded to three significant figures. I haven't worried about the significant figures of the numbers here, well basically all I'm doing here is thinking. solve the problem keeping in mind that molar mass tells me how much a mole weighs and all I have to do is multiply how much a mole weighs by the number of moles I have to summarize what I'm doing here.

Write down the simple rule that says that when we go from moles to grams, from moles to grams, what we want to do is multiply the moles by the molar mass. Well, that's how we think about it now. I want to show you how we can solve the same. problem with conversion factors because many times teachers and textbooks use conversion factors instead of thinking about the method. Well, here we start with 4.30 moles of aluminum, we get it from the problem. Now let's write down some conversion factors. I want to take this and I want to multiply it by a conversion factor that will remove the moles and convert the moles to grams.

Well, to write conversion factors, we often want to see some type of equation, equivalence, or relationship. Okay, so I can take this molar mass information and I can write it as an equation here as a ratio, which basically says if we have one mole of aluminum, that means we have twenty-six point nine eight grams of aluminum, check it out, we have the sign equal and something on each side. This is like a perfect example of the type of relationship with which we can write a conversion factor. Okay, there are two conversion factors that we can write with this relationship.

Okay, the first one is going to have this on top and this on the bottom, okay, one mole of aluminum over twenty-six point nine, eight grams of aluminum, okay, or we can flip it over, we can do this on the top and this on the bottom, okay, so at the top twenty six point nine. eight grams of aluminum and then at the bottom there will be one mole of aluminum. Well, both conversion factors are great, they're totally fine, but we only want to use one of them and the one we're going to want. use is the one that removes the moles of aluminum from up here, here it is at the top, so to cancel out the moles of aluminum it will be at the bottom of the conversion factor that we want to use, okay, it is at the top . here, but it's at the bottom, so this is the conversion factor we want to use.

Okay, get rid of this one for now. Bring this in and now we have moles of aluminum at the top, cancel out the moles of aluminum at the bottom and we're left with grams of aluminum, which is exactly what we want. Okay, now the calculations we do is we multiply this divided by one, which is going to give us 116 grams of aluminum rounded to three significant figures because there are three significant figures here. and we don't worry about the number of significant figures in one here and look at this, the calculations that we're doing 4.30 times twenty-six point nine eight are exactly the same calculations that we did when we were just thinking about it correctly. because dividing something by a mole dividing something by one doesn't change its value, so whether you do the think through method or you do the conversion factor method, you're doing the exact same calculations, you're just taking the moles and we're doing them. multiplying by the molar mass and this tells us how much 4.30 moles of aluminum would weigh how many moles are there in 127 point five grams of sodium chloride NaCl as before, we are talking about moles and grams, so the first thing I want to ask is how much does it weigh? one mole of sodium chloride in grams.

This is just another way of saying what the molar mass of sodium chloride is. To figure this out, I look at the formula and look at the elements that make it up. I have na and I have 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 them up well I look at the chemical formula here and this tells me I have a sodium atom , so I'm going to multiply one by twenty-two point nine nine, which is the molar mass of sodium and then I have a CL, so I'm going to multiply one by thirty-five point four five. which is the molar mass of chlorine, let's add them together and I get fifty-eight point four four, which tells me that the molar mass of sodium chloride NaCl is fifty-eight point four four grams per mole or it means that one mole of sodium chloride weighs fifty eight. point four four grams, that's how much one mole of sodium chloride weighs.

Okay, so we have a certain number of grams of sodium chloride and we want to know how many moles that is. That's how we think about it. Okay, based on this information here about the molar. mass we know that if we had 58 point four four grams it would be one mole, okay, but we don't have fifty-eight point four four grams, we have one hundred twenty-seven point five grams, okay, this is more than just one mole, the question is What What we want to ask is how many fifty-eight point four four are there in 127 point five. In other words, how many times does 58.4 four fit into 120 seven point five?

This is a division problem. Well, let's do one hundred and twenty-seven. point five divided by the molar mass we are going to find out how many of these are in this and that will tell us how many moles we have when we do the calculations rounding to four significant figures we get two point one eight two moles We can summarize what I did here by saying that when we convert from grams to moles we take grams and divide them by the molar mass, so that's what I'm doing here taking the grams and dividing them by the molar mass to see how many molar masses fit into the number of grams we have now for the approach of Conversion factor.

I'm starting here with one hundred twenty-seven point five grams of sodium chloride and I want to multiply this by the conversion factor that will remove the grams of sodium. chloride and it will take me to moles of sodium chloride, so to do that I'm going to take this molar mass information and rewrite it as an equivalence or a relationship like this. Well, I have one thing on each side of the equal sign. which makes it really easy to convert this into a conversion factor, here are the two conversion factors that I can write with it, okay, one has moles on the top and this one on the bottom, the other one has grams on the top and moles at the bottom.

What I want to use here is a conversion factor that will cancel out the grams of sodium chloride that are at the top here, so I want it to be down here. I'm going to use this one, so now I have gram sodium chloride at the top gram sodium chloride at the bottom cancel out, leaving me with moles of sodium chloride and the calculations I'll do are this multiplied by this and get to point one eight two moles of sodium chloride and verify 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 definition now I just want to point out the calculations What I'm doing here is exactly the same as math in the think it through method.

I take one twenty-seven point five and multiplying it by one doesn't change at all, so I'm still doing one twenty-seven point five divided by fifty eight point four four. which is exactly the calculation I did up here, which shows that when we go from grams to moles, we take the grams and divide them by the molar mass, so that was kind of a quick primer on how to go from grams to moles, if you will. some more practice problems, watch the video on

converting

between grams and moles, part two