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 ofatoms
ormolecules
we have. Now when we do conversions like this,atoms
andmolecules
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 frommoles
toatoms
or where we have to go fromatoms
and convertback
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 likeconversion factors so it's important to know how to solve questions like this using
conversion factors too. Okay, so how many
atoms
are in 5.5moles
ofatoms
? We're talking aboutmoles
andatoms
here so let's just refresh our memory aboutmoles
, 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 5.5moles
ofatoms
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 ofmoles
. So what instead of 5.5moles
, we were talking about 5.5 dozen? Well this math is probably pretty straight forward. There are 12 thingsin 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 manyatoms
or how many things are in 5.5 dozen. Okay? But we're not talking about dozens here, we're talking aboutmoles
. 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. Nowthis 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 numberis 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 wedo 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 ofmoles
and that's going to give usatoms
. To write thisconversion 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 aconversion 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 10^23atoms
. But for every equation like this with an equal sign, there aretwo 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 ofmoles
and leave me withatoms
. Somoles
is on top here, I'm going to want to choose the version of this conversion factor that'sgoing to give me
moles
on the bottom so they cancel out. So I'm going to use this one and then I havemoles
on the top here cancel out,moles
on the bottom cancels out here, and that's going to leave me withatoms
. 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 wedid 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 frommoles
toatoms
. Now let's look at how to do problems from the other direction fromatoms
ormolecules
to number ofmoles
. How manymoles
is 4.6 x 10^24 Sulfuratoms
? 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 tomoles
, let's dothis 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'retalking about
moles
. So instead of dividing by the number of things in a dozen, we want to find out how manymoles
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 24divided
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 7.6moles
of Sulfuratoms
are in this super huge number of Sulfuratoms
. 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 24thatoms
(4.6 x10^24) and we want to multiply this by a conversion factor that
is going to get rid of
atoms
and move me tomoles
. 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 aboutatoms
here so there are 6.02 x 10^23atoms
in one mole. Or we can write this other conversion factor where we put 6.02 x 10^23atoms
on top and 1 mole on the bottom. Which of these do we want to use? We want to usethe 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 likeatoms
,molecules
, jellybeans, or coins to figure out how manymoles
are in it. We divide it bynumber of things in one mole. Okay, so if you want some more practice with
these kinds of problems, check out the next video,