# Converting Between Moles, Atoms, and Molecules

In this video, we're going to learn how to convert back and forth between

### moles

and the number of#### atoms

or### molecules

we have. Now when we do conversions like this,#### atoms

and### molecules

are sometimes both referred to as particles. A particle is just a word for any individual thing so a particle could be a jellybean or a coin or a paperclip or an atom or a molecule. So we'll work through problems like this where we have to go from### moles

to#### atoms

or where we have to go from#### atoms

and convert back to### moles

. Okay, so here's our first question. For each one of these problems I'm going to do it two ways. First I'm going to show you how to think through it in kind of a simple, straightforward way so you can really understand what you're doing. Then, I'm going to show you how to use conversion factors. I think conversion factors don't always make a lot of sense and I know that a lot of students are confused by them. But teachers and textbooks tend to really like conversion factors so it's important to know how to solve questions like this using conversion factors too. Okay, so how many#### atoms

are in 5.5### moles

of#### atoms

? We're talking about### moles

and#### atoms

here so let's just refresh our memory about### moles

, okay? Mole is like a dozen but there are 12 things in a dozen and six-hundred-and-two hexillion things in a mole. We often abbreviate this super long number with all these zeros, 602 hexillion, as 6.02 times 10 to the 23rd (6.02x10^23).### Moles

...can be a little bit tricky at first and so I want to keep talking about the similarity to dozens as we work through this first problem, okay? We want to know how many

#### atoms

are in 5.5### moles

of#### atoms

but to get a handle on how to think through this, let's first think about how we would do this kind of problem if we were talking about dozens instead of### moles

. So what instead of 5.5### moles

, we were talking about 5.5 dozen? Well this math is probably pretty straight forward. There are 12 things in a dozen so if you figure out many#### atoms

are in 5.5 dozen, we take 5.5 and then multiply it by 12 which is the number of things in one dozen, and that would tell us how many#### atoms

or how many things are in 5.5 dozen. Okay? But we're not talking about dozens here, we're talking about### moles

. So instead of multiplying this by 12, the number of things in a dozen, we're going to take 5.5 and we're going to multiply it by 602 hexillion which is the number of things in one mole. Now this big number here is a real pain with all these zeros and if you're actually going to do this math chances are you're not going to want to use this long version here, you want to use the shorter version in scientific notation. So let's take this big number, 602 hexillion, and write it in a more manageable of 6.02 x 10^23. This is the same number as 602 hexillion but it's just an abbreviate version. Okay, so you've written this out. Chances are you're going to use a...scientific calculator or a graphing calculator to solve this problem so here's how you can type it in: 5.5*(6.02E23). This E23 is usually how we do exponents in a scientific calculator. The E is "ten to the exponent" and the 23 here is the exponent. Plug this in to the calculator and we're going to get this as the final answer. There are two things that I need to do to this answer. The first thing I need to do is take this out of calculator scientific notation and put it in to "normal person" scientific notation. So I'm going to write 3.311 and E24 is 10 to the 24 (10^24). So now it's in regular person's scientific notation but the next thing we have to do is take in to account significant figures. We'll look at the numbers that went in to this to figure out how to round it correctly, okay? There are two significant figures in 5.5 and there are three significant figures in 6.02 so we're going to round this number to the lower number of significant figures, we're going to round it to two. We're going to take 3, and this 3, and then look at the 1 to figure out whether to round up or keep it the same. It's a 1, it's lower than 5 so we keep it the same. We'll do 3.3 time 10 to the 24th (3.3 x 10^24) and what we're solving for here is

#### atoms

. This is our final answer. Now, so many people see a number like this 3.3 x 10^24 and they don't think of it as a real number so please keep in mind that this number is...just a shorthand for this super super long number with all these zeros. This is three-heptillion-three-hundred-hexillion

#### atoms

. So 3.3x10^24 isn't some martian number, keep in mind that it's just a short hand version of this very long number here. And for some reason, if your teacher doesn't let you use a calculator and you have to do this out by hand, I have another video on doing mole calculations by hand instead of a calculator so you can check that out. Anyway this is how we do this problem using a simple, straightforward method. We multiply 5.5 by the number of things in one mole, plug it in to the calculator, and this is what you get. Now let's look at how we can solve the same problem using conversion factors instead. In this case we're going to be starting with this number here, 5.5### moles

and now we're going to want to multiply this by a conversion factor that's going to get rid of### moles

and that's going to give us#### atoms

. To write this conversion factor, we're going to think about### moles

, let's look at this definition up here. I want to rewrite this just as an equation with an equal sign, okay? So here we have one mole equals this much, I really haven't changed anything but I put the equal sign in here because we use relationships like this with one thing on either side of an equal sign. We use relationships like this to write conversion factors, okay? So here's how we'll take this relationship and write a conversion...factor. A conversion factor has both a top and a bottom and we take something on one side of the equation, one mole, and we can put it on the top of the conversion factor and the thing that is on the other side of the equal sign we'll put on the bottom. So I'll do 6.02 x 10^23 things here but we're talking about

#### atoms

and this conversion factor is just telling me that in one mole there is 6.02 x 10^23#### atoms

. But for every equation like this with an equal sign, there are two conversion factors we can write. We can write it like this or we can flip it, that's cool too. So I can also write 6.02 x 10^23#### atoms

on top with one mole on the bottom. Now both of these conversion factors are totally valid, which one do we want to use for this problem? We want to multiply this by a conversion factor that's going to get rid of### moles

and leave me with#### atoms

. So### moles

is on top here, I'm going to want to choose the version of this conversion factor that's going to give me### moles

on the bottom so they cancel out. So I'm going to use this one and then I have### moles

on the top here cancel out,### moles

on the bottom cancels out here, and that's going to leave me with#### atoms

. So what's the math I'm going to do? I'm going to do 5.5 times 6.02 x 10^23 divided by 1. You might realize that dividing this number by one doesn't really change anything so all the math we're really doing is 5.5 times 6.02 x 10^23 which is exactly what we did up here. So...you can just type this in to your calculator and get this as your answer. Or you can decide that you want to put this whole conversion factor in and you can type it in like this: 5.5*(6.02E23/1). Whichever one that you type in you are going to get the same number here which in regular person scientific notation is going to look like this and we round it using sig figs to get this number here. Now, once again, don't forget that 3.3 x 10^24 is just an abbreviated version of this very long number of

#### atoms

, okay? So that is how we go from### moles

to#### atoms

. Now let's look at how to do problems from the other direction from#### atoms

or### molecules

to number of### moles

. How many### moles

is 4.6 x 10^24 Sulfur#### atoms

? Okay, check out this number. I just want to remind you that this isn't some weird martian number, this is just a shorthanded abbreviation for this very long number with a whole bunch of zeros. As we did before, instead of jumping right in to### moles

, let's do this common sense approach where we think about what we would do if instead of### moles

we were talking about dozen. If we want to know how many dozen this big number were, we'd recognize is that there are 12 things in a dozen and so we would divide this number by 12. There are 12 things in a dozen, we want to know how many times 12 goes in to this number, okay? So we're going to be dividing by the number of things in a dozen. But as before, we aren't talking about dozen, we're talking about### moles

. So...instead of dividing by the number of things in a dozen, we want to find out how many

### moles

this is so we are going to divide by the number of things in one mole. So we're going to divide by 602 hexillion. As before, you're probably not going to want to use these giant versions of each number with all these zeros. So this is where the scientific notation come handy, let's rewrite this in scientific notation. We're going to do 4.6 times 10 to the 24 divided by 6.02 times 10 to the 23 (4.6 x 10^24)/(6.02 x 10^23). Put this in to the calculator and you'll want to type it in like this. We'll replace the 10^24 with E24 or 10^23 with E23, hit return and we're going to get a number like this. Now it's not in scientific notation so we don't have to worry about that but we are going to want to round this with significant figures. There are two significant figures here, three significant figures here, so we're going to round this to two significant figures. We're going to take 7 and the 6 and look next door to see if we round up or keep it the same and it's a 4 so we keep it the same and we're solving here for### moles

so it will be 7.6### moles

of Sulfur#### atoms

are in this super huge number of Sulfur#### atoms

. I'm just going to slip this in right here and now let's see how we use conversion factors to solve this same problem, okay? Here we're going to be solving 4.6 times 10 to the 24th#### atoms

(4.6 x 10^24) and we want to multiply...this by a conversion factor that is going to get rid of

#### atoms

and move me to### moles

. So let's look at the two conversion factors that we can write using this relationship here. The first one is going to put one mole on top and we're talking about#### atoms

here so there are 6.02 x 10^23#### atoms

in one mole. Or we can write this other conversion factor where we put 6.02 x 10^23#### atoms

on top and 1 mole on the bottom. Which of these do we want to use? We want to use the one that gets rid of#### atoms

.#### Atoms

is on top right here, it's on the bottom right here so they're going to cancel out. Get rid of this, get rid of this, and then what's the math we're going to do? The math is going to be 4.6 x 10^24 times 1 divided by 6.02 x 10^23. Now multiplying this number by 1 isn't really going to change anything so all we're really doing is we're taking this number and dividing it by this number, the exact same math that we did right here. But just as we did previously if you'd prefer to put this as a big fraction into the calculator that's totally cool too. It's going to look like this: (4.6E24)*(1/6.02E23). All you're doing is dividing this by this because this 1 doesn't really matter and we're going to get the same number here which rounds to 7.6### moles

. So that's how we go from a number of things like#### atoms

,### molecules

, jellybeans, or coins to figure out how many### moles

are in it. We divide it by number of things in one mole. Okay, so...if you want some more practice with these kinds of problems, check out the next video,