Converting between Moles, Atoms, and Molecules (Part 2)

This is the second

part

of the conversion between

moles

,

atoms

and

molecules

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

molecules

are there in 0.63

moles

of molecules? Now we're talking about molecules, before we were talking about

atoms

, but it doesn't matter what we're talking about because there are always 602 hexillions of things in a mole. So if we have a mole of molecules, a mole of jelly beans, a mole of coins, a mole of atoms, they all have 602 hexillions of stuff and the process we go through is exactly the same.

Well, to think about this as we did before, we're talking about 0.63 moles of molecules. What would we do if we had 0.63 dozen molecules? There are 12 things in a dozen, so we make 0.63 times 12, which is the number of things in a dozen, okay? That makes intuitive sense. We're not talking about dozens, but we are talking about moles, so we want to multiply this by the amount of things in a mole. Let's rewrite this in scientific notation, 602 hexillion as 6.02 x 10^23. We will put it in the calculator like this: 0.63*(6.02E23) and we will get 3.7926E23 as an answer. The first thing we're going to 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, zero doesn't count, we have three significant figures here, so we'll round this to two significant figures, whichever is the smaller of the two. We keep the 3 and look at the 7 and then next to it to see if we round up or keep it the same, it's a 9 and greater than 5 so we're going to round up. So we're going to make 3.8 x 10^23 molecules. And this is our answer here and as I always say, keep in mind that this is just an abbreviation of this super long number. This isn't some weird Martian number, it's just an abbreviation of this number with all zeros and you can totally write it down with all zeros if it makes you feel better.

We'll put this here to remind us what the answer is and now let's use conversion factors to solve this problem in case you have to. We're going to start with 0.63 moles and we're going to want to multiply that by a conversion factor that will eliminate the moles, okay? So we're going to use this relationship here, we're going to put polka dots in the background. So I'm going to put 1 mole here, we're talking about 602 hexillions, so I'm going to make 6.02 x 10^23 molecules up here. Moles above and moles below, cancel them. The math here will 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 we're really doing is 0.63 times 6.02 x 10^23, it's exactly what we did here, but again, if you want to write this with an integer 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 molecules in 0.63 moles. of molecules. Let's do one more. How many moles are 3.9 x 10^20 magnesium atoms? Well, this number here is not some scary Martian number, it's actually a real number, let's think about what we would do if we were talking about dozens instead of moles.

We would take this and divide it by 12 because there are 12 things in a dozen. We want to know how many of this 12 fit into this number, okay? It's intuitive to divide this number by 12, but instead we're talking about moles, so we'll want to divide it by 602 hexillion. Now let's put these numbers into scientific notation, (3.9 x 10^20)/(6.02 x 10^23). Put it into the calculator like this, (3.9E20)/(6.02E23), and we'll get this as our final answer. Let's put it in scientific notation, 6.478405316 x 10^-4, which means 10 to the power of negative 4, and now let's use significant figures to round this off.

There are two significant figures here and three significant figures here, so we'll round this to two numbers, 6.4, you look next to the 7 to see if we round up or keep it the same, it's a 7, so we round up. Let's make 6.5 x 10 ^-4 moles. That's our answer there and here, very quickly, how we would solve this problem using conversion factors. We would start with 3.9 x 10^20 atoms and multiply it by a conversion factor that removes the atoms. So 1 mole up, 6.02 x 10^23 atoms down here, the atoms cancel at the top and bottom, and the calculations we do are 3.9 x 10^20 times 1 divided by 6.02 x 10^23, this one doesn't do much difference, all we're really doing is dividing this by this, which is the calculation I did 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 once again, keep in mind that this 10^-4 is not a spooky Martian number, but we are doing 6.5 and moving back the decimal four. And if we wanted to take this out of scientific notation, it would be 0.00065 moles. You can also make this look like a real number. This is how we can convert between moles and the number of atoms or molecules we have.