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Converting Between Moles, Atoms, and Molecules

Feb 23, 2020
In this video, we will 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, we sometimes refer to

atoms

and

molecules

as particles. A particle is just a word for any individual thing, so a particle could be a jelly bean, a coin, a paper clip, an atom, or a molecule. So we will solve problems like this where we have to go from

moles

to atoms or where we have to go from atoms and convert them back to moles. Well, here's our first question.
converting between moles atoms and molecules
For each of these problems I am going to do it in two ways. First, I'm going to show you how to think about it in a simple and direct way so you can really understand what you're doing. Then, I'll show you how to use conversion factors. I think conversion factors don't always make a lot of sense and I know 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 as well. Well, how many atoms are there in 5.5 moles of atoms?
converting between moles atoms and molecules

More Interesting Facts About,

converting between moles atoms and molecules...

We're talking about moles and atoms, so let's refresh our memory about moles, okay? The 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 power of 23 (6.02x10^23). Moles can be a little tricky at first, so I want to keep talking about the similarity with dozens as we solve this first problem, okay? We want to know how many atoms there are in 5.5 moles of atoms, but to understand how to think about this, let's first think about how we would solve this type of problem if we were talking about dozens instead of moles.
converting between moles atoms and molecules
So instead of 5.5 moles we were talking about 5.5 dozen? Well, this math is probably pretty simple. There are 12 things in a dozen, so if you calculate that there are many atoms in 5.5 dozen, we take 5.5 and then multiply it by 12, which is the number of things in a dozen, and that would tell us how many atoms or how many things. They are at 5.5 dozen. Well? 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'll take 5.5 and multiply it by 602 hexillion, which is the number of things in a mole.
converting between moles atoms and molecules
Now this big number here is a real pain with all these zeros and if you're really going to do these calculations, you probably don't want to use this long version here, you'll 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 form of 6.02 x 10^23. This is the same number as 602 hexillion but it is just a shortened version. Okay, so you've written this. You'll most likely use a scientific calculator or graphing calculator to solve this problem, so here's how to write it: 5.5*(6.02E23). This E23 is usually how we do exponents on a scientific calculator.
The E is "ten to the exponent" and the 23 here is the exponent. Plug this into the calculator and we will get this as the final answer. There are two things I need to do with this answer. The first thing I need to do is take this out of the calculator's scientific notation and into "regular person" scientific notation. So I'm going to write 3.311 and E24 is 10 to the power of 24 (10^24). Now it's in normal scientific notation, but the next thing we need to do is take significant figures into account. We'll look at the numbers included in this to figure out how to round it properly, okay?
There are two significant figures in 5.5 and there are three significant figures in 6.02, so we'll round this number to the smallest number of significant figures, we'll round it to two. We're going to take 3, and this 3, and then we'll look at the 1 to decide if we should round it or keep it the same. It's a 1, it's less than 5, so we keep it the same. We'll do 3.3 times 10 to the power of 24 (3.3 x 10^24) and what we're solving for here are the atoms. This is our final answer. Now, many people see a number like this 3.3 x 10^24 and don't consider it a real number, so keep in mind that this number is just an abbreviation for this super long number with all these zeroes.
This is three heptillion three hundred hexillion atoms. So 3.3x10^24 is not a Martian number, note that it is just a shortened 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 it by hand, I have another video on how to do mole calculations by hand instead of a calculator so you can check it out. Anyway, this is how we solve this problem using a simple and direct method. We multiply 5.5 by the number of things in a mole, plug it into the calculator and this is what you get.
Now let's see how we can solve the same problem using conversion factors. In this case, we'll start with this number, 5.5 moles, and now we want to multiply it by a conversion factor that will eliminate the moles and give us atoms. To write this conversion factor, let's think in moles, look at this definition up here. I want to rewrite this simply as an equation with an equal sign, okay? So here we have a mole that is equivalent to this quantity. I haven't really changed anything, but I put the equal sign 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? This is how we will 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, a mole, and we can put it on the top of the conversion factor and whatever is on the other side of the equal sign I'll put it on the bottom. So I'm going to do 6.02 x 10^23 things here, but we're talking about atoms and this conversion factor just tells me that in one mole there are 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 turn it around, that's fine too. Then I can also write 6.02 x 10^23 atoms on the top with one mole on the bottom. Now, both 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 removes the moles and leaves me with atoms. So the moles are up here, I'm going to want to choose the version of this conversion factor that will give me the moles down so they cancel out.
So I'm going to use this one and then I have the moles at the top here canceled, the moles at the bottom canceled here, and that will leave me with atoms. So what are the calculations I'm going to do? I'm going to do 5.5 times 6.02 x 10^23 divided by 1. You might notice that dividing this number by one doesn't actually change anything, so all the calculations we're actually doing are 5.5 times 6.02 x 10^23, which is exactly what we did here. So you can type this into your calculator and get this as an answer. Or you can decide that you want to put in this full conversion factor and write it like this: 5.5*(6.02E23/1).
Whoever you type, you're going to get the same number here, which in normal scientific notation will look like this and we round it up using sig figs to get this number here. Now, once again, don't forget that 3.3 x 10^24 is just a shortened version of this large number of atoms, okay? This is how we go from moles to atoms. Now let's see how to solve problems from the other direction, from atoms or molecules to the number of moles. How many moles are 4.6 x 10^24 sulfur atoms? Well, look at this number. I just want to remind you that this is not some weird Martian number, it's just a shorthand abbreviation of this very long number with a bunch of zeroes.
As we did before, instead of jumping straight to moles, let's take this common sense approach where we think about what we would do if instead of moles we were talking about a dozen. If we want to know how many dozen this big number is, we would recognize that there are 12 things in a dozen and then we would divide this number by 12. There are 12 things in a dozen, we want to know how many times 12 corresponds to this number, okay? So let's divide by the number of things into a dozen. But as before, we're not talking about dozens, we're talking about moles.
So instead of dividing by the number of things in a dozen, we want to know how many moles that is, so let's divide by the number of things in a mole. So let's divide by 602 hexillion. As before, you probably don't want to use these giant versions of each number with all these zeroes. This is where scientific notation comes in handy. Let's rewrite this in scientific notation. Let's do 4.6 times 10 to the power of 24 divided by 6.02 times 10 to the power of 23 (4.6 x 10^24)/(6.02 x 10^23). Put this in the calculator and you'll want to write it like this. We'll replace 10^24 with E24 or 10^23 with E23, hit return, and get a number like this.
Now it's not in scientific notation, so we don't have to worry about that, but we want to round it off with significant figures. There are two significant figures here, three significant figures here, so let's round this to two significant figures. We're going to take the 7 and the 6 and we're going to look to the side 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 for the moles here so it's going to be 7.6 moles of The atoms of sulfur are found in this enormous amount of sulfur atoms.
I'm going to introduce this here and now let's see how we use conversion factors to solve the same problem, okay? Here we are going to solve for 4.6 times 10 to the power of 24 atoms (4.6 x 10^24) and we want to multiply this by a conversion factor that will remove the 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 will put a mole on top and we are talking about atoms here, so there are 6.02 x 10^23 atoms in a 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 removes the atoms. The atoms are up here and down here, so they'll cancel out. Get rid of this, get rid of this and then what are the calculations that we're going to do? The math will 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 taking this number and dividing it by this number, exactly the same calculations we did here. But just like we did above, if you prefer to put this as a large fraction in the calculator, that's great too.
It will 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'll get the same number here, which rounds up to 7.6 moles. This is how we start from a series of things such as atoms, molecules, jelly beans or coins to calculate how many moles there are in them. We divide it by the amount of things in a mole. Well, if you want to practice more with these types of problems, watch the following video, Conversion between moles, atoms and molecules, part 2.

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