This is the second part to converting between moles, atoms, 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 molecules in 0.63 moles of molecules?
Now we're talking about 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 moles
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 talking about 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 molecules up here.
Moles 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 molecules in 0.63 moles 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.
We would start with 3.9 x 10^20 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 atoms 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 atoms or molecules
we have.