In this video, we're going to 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, atoms
and molecules 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 from moles to atoms or where
we have to go from atoms and convert back
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
like conversion factors so it's important
to know how to solve questions like this using
conversion factors too.
Okay, so how many atoms are in 5.5 moles of
atoms?
We're talking about moles and atoms here so
let's just refresh our memory about moles,
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 5.5
moles of atoms 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 of moles.
So what instead of 5.5 moles, we were talking
about 5.5 dozen?
Well this math is probably pretty straight
forward.
There are 12 things in 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 many atoms or how many things are in
5.5 dozen.
Okay?
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'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.
Now this 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 number is 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 we do 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 of moles and
that's going to give us atoms.
To write this conversion 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 a conversion 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 10^23 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 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 of moles and leave
me with atoms.
So moles is on top here, I'm going to want
to choose the version of this conversion factor
that's going to give me moles on the bottom
so they cancel out.
So I'm going to use this one and then I have
moles on the top here cancel out, moles on
the bottom cancels out here, and that's going
to leave me with atoms.
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 we did 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 from moles to atoms.
Now let's look at how to do problems from
the other direction from atoms or molecules
to number of moles.
How many moles is 4.6 x 10^24 Sulfur atoms?
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 to moles, let's do this 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're talking about moles.
So instead of dividing by the number of things
in a dozen, we want to find out how many moles
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 24 divided
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
7.6 moles of Sulfur atoms are in this super
huge number of Sulfur atoms.
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 24th atoms (4.6 x 10^24) and we want
to multiply this by a conversion factor that
is going to get rid of 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 is going to put one mole on
top and we're talking about atoms here so
there are 6.02 x 10^23 atoms in one 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 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
like atoms, molecules, jellybeans, or coins
to figure out how many moles are in it.
We divide it by number of things in one mole.
Okay, so if you want some more practice with
these kinds of problems, check out the next
video, Converting between Moles, Atoms, and
Molecules part 2.
