 # Converting between Moles, Atoms, and Molecules (Part 2) This is the second

to

## converting

between

,

, and

### molecules

. We're going to do some more practice problems but if you haven't seen the first video, check that out first and then come and watch this. How many

in 0.63

of

### molecules

here, before we were talking about

#### atoms

but it doesn't matter what we're talking about because there is always 602 hexillion things in a mole. So if we have a mole of

### molecules

, a mole of jellybeans, a mole of coins, a mole of

#### atoms

, they all have 602 hexillion things in them and the process we go through is exactly the same. Okay, so just to think through this as we did before, we're talking about 0.63

of

### molecules

. What would we do if we had 0.63 dozen

### molecules

? There are 12 things in a dozen so we do 0.63 times 12 which is the number of things in one dozen okay? That kind of makes intuitive sense. We're not talking about dozens here though we're

### moles

so we want to multiply this by the number of things in one mole. Let's rewrite this in scientific notation, 602 hexillion as 6.02 x 10^23. We're going to put it in the calculator like this: 0.63*(6.02E23) and get 3.7926E23 as an answer. The first thing let's do is write this in regular scientific notation, 3.7926 x 10^23, and now let's use significant figures to round this since calculators don't round. We have two significant figures here, the zero
doesn't count, we have three significant figures here so we're going to round this to two significant figures, the smaller of the two. We keep the 3 and we look at the 7 and then next door to see if we round up or keep it the same, it's a 9 and higher than 5 so we're going to round up. So we're going to do 3.8 x 10^23

### molecules

. And this is our answer here and as I always say, please keep in mind that this is just a shorthand abbreviation for this super long number. This isn't some weird Martian number, it's just an abbreviation for this number with all the zeros and you can totally write this out with all the zeros if it makes you feel better. We'll put this up here to remind ourselves what the answer is and now let's use conversion factors to solve this problem in case you have to do that. We are going to start with 0.63

### moles

and we're going to want to multiply that by a conversion factor that's going to get rid of the

### moles

okay? So
we're going to use this relationship here, we're going to put

### moles

on the bottom. So I'm going to put 1 mole here, we're talking about 602 hexillion things so I'm going to do 6.02 x 10^23

up here.

on the top and

### moles

on the bottom, cancel them out. The math here is going to be 0.63 times 6.02 x 10^23 divided by 1. Dividing it by 1 doesn't really change anything so the only math that we're really doing is 0.63 times 6.02 x 10^23, it's exactly
what we did up here but again if you want to type this in with a whole fraction, 0.63*(6.02E23/1), the answer is exactly the same and if we round it using significant figures we get this number of

in 0.63

of

### molecules

. Let's do one more. How many

### moles

is 3.9 x 10^20 Magnesium

#### atoms

? Okay, this number here is not a scary Martian number, it's actually a real number, let's think about what we do if we were talking about dozens instead of

### moles

. We would take this and we would divide it by 12 because there are 12 things in a dozen. We want to know how many this 12 goes into this number, okay? It's intuitive to divide this number by 12 but instead we're talking about

### moles

so we're going to want to divide this by 602 hexillion. Now let's put these numbers into scientific notation, (3.9 x 10^20)/(6.02 x 10^23). Put that into the calculator like this, (3.9E20)/(6.02E23), and we're going to get this as our final answer. Let's put it into
scientific notation, 6.478405316 x 10^-4, which means 10 to the negative 4th, and now let's use significant figures to round this. There are two significant figures here and three significant figures here so we'll round this to two numbers, 6.4, you look next door to the 7 to see if we round up or keep it the same, it's a 7 so we round up, we're going to do 6.5 x 10 ^-4

### moles

. That is our answer there and here very quickly is how we would do this problem using conversion factors.

#### atoms

and we would multiply that by a conversion factor that gets rid of

#### atoms

. So 1 mole on top, 6.02 x 10^23

down here, the

#### atoms

cancel out on the top and on the bottom, and the math that we do is 3.9 x 10^20 times 1 divided by 6.02 x 10^23, this one doesn't make much of a difference, all we're really doing is this divided by this which is the math that I did up here. Or you can type this into your calculator like this and get the same answer,
(3.9E20)*(1/6.02E23)=6.478405316E-4. And just once again, keep in mind that this 10^-4 isn't some creepy Martian number but we're doing 6.5 and moving the decimal back four. And if we wanted to take this out of scientific notation, it would be 0.00065

### moles

. You can make this look like a real number as well. So that is how we can convert back and forth between

### moles

and the number of

or

we have.