In this video we're gonna look at how to convert back and forth between moles and
the number of atoms or molecules that 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 jelly bean 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,
say atoms, 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 and do it two ways.
First, I’m gonna show you how to think through it,
in kinda simple straightforward way, so you can understand what you’re doing.
Then, I’m gonna show you how to use conversion factors.
I think conversion factors don’t always make a lot of sense and
I know 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 lets just refresh our memory about moles, okay?
A mole is like a dozen, but
there are 12 things in a dozen,and there are 602 hexillion things in a mol.
We often abbreviate this super long number with all these 0s,
602 hexillion, as 6.02 x 10 to the 23rd.
Mols can be a little bit tricky at first, and so
I wanna keep talking about the similarity to dozen.
As we work through this first problem, okay?
We wanna 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 if instead of 5.5 moles we're talking about 5.5 dozen?
Well, this math is probably pretty straightforward.
There are 12 things in a dozen, so
if you figure out how many atoms are in 5.5 dozen.
We take 5.5 and then we multiply it by 12, 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 dozen here, we're talking about moles instead.
So, instead of multiplying this by 12, the number of things in a dozen.
We're gonna take 5.5 and we're gonna multiply it
by 602,000,000,000,000,000,000,000, the number of things in one mole.
Now, this big number here is a real pain with all the zeroes.
And if you were actually gonna do this math,
chances are you wouldn't wanna use this long version here.
You'd wanna use the shorter version in scientific notation.
So, let's take this big number, 602 hexillion,
and write it in a more manageable form of 6.02 x10 to the 23rd.
This is the same number,
6.02, as 602 hexillion, it's just an abbreviated version here.
So, you've written this out.
Chances are you're going to use a calculator, scientific calculator or
graphic calculator to solve this problem.
So, here's how you're gonna type it 5.5*(6.02E23).
Yes, E23 is usually how we do exponents in a scientific calculator.
The E is 10 to the exponent.
And then 23 here is the exponent.
Plug this into the calculator, and we're gonna get this as our final answer.
There are two things that I need to do to this answer.
The first thing I need to do is sorta take it out of calculator scientific notation,
and put it into normal person scientific notation.
So, I'm gonna write 3.311E24
is 10 to the 24th, okay?
So now, it's in regular person scientific notation but
the next thing that we gotta do is take into account significant figures, okay?
We'll look at the numbers that went into this,
to figure out how to round it correctly, okay?
There are two significant figures in 5.5 and there three significant figures
in 6.02, so we're gonna round this number to lower number of significant figures.
We are gonna round it to two.
Okay, so we are gonna take 3 and we gonna take this 3 and
then we are gonna love the one to figure whether to round up or keep the same.
It's a 1 its lower than 5 so we keep it the same.
We'll do 3.3 x 10 to the 24th 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 to the 24th, 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 3 heptillion, 3 hundred hexillion atoms.
Okay, so 3.3 x 10 is 24.
It's not some weird martian number.
Keep in mind, that it is just a shorthand version of this very long number here.
And if for some reason, your teacher doesn't let you use a calculator and
you have to do this out by hand.
I have another video on doing more calculations
by hand instead of a calculator.
So, you can check that out.
So anyway,
this is how we do this problem using this sort of simple straight forward method.
We multiply 5.5 by the number of things in one mole, plug in the calculator and
this is what we get.
Now, let's look at how we could solve the same problem
using conversion factors instead.
In this case, we're gonna be starting with this number here, 5.5 moles 5.5 moles.
Now, we are going to want to multiply this by a conversion factor that's going to get
rid of moles and is 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 wanna rewrite this just as an equation with an equals sign, okay?
So, here we have 1 mole equals this much.
I really haven't changed anything.
But, I put the equals sign in here, because we use relationships like
this with one thing on either side of the equals 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, say, the top of the conversion factor.
And then, the thing that's on the other side of the equal sign,
we put that on the bottom.
So, I'll do 6.02 x 10 to the 23rd.
Things here, but we're talking about atoms.
And this conversion factor is just telling me that in one mole there are 6.02
times 10 to the 23rd atoms.
But, for every equation
like this with an equal sign there are two conversion factors that we can write.
We can write it like this or we can flip it, that's cool too.
So, I could also write 6.02 x 10 to the 23rd atoms
on top, with 1 mole on the bottom.
Now, both of these conversion factors are totally valid.
Which one do we wanna use for this problem?
Well, we wanna multiply this by a conversion factor that's gonna get rid of
moles, is gonna leave me with atoms.
So moles is on top here.
I'm gonna wanna choose the version of this conversion factor
that's going to give me moles on the bottom so they'll cancel out.
So I'm gonna use this one.
And then, I've got moles on the top here cancel out,
moles on the bottom cancel out here.
And that's gonna leave me with atoms, okay.
What's the math I'm gonna do?
I'm gonna do 5.5 x 6.02 x10 to the 23rd divided by 1.
Now, you might realize that dividing this number by one
doesn't really change anything.
So, all the math we're really doing is just 5.5 x 6.02 x 10^23.
Which is exactly what we did up here.
So, you could just type this into your calculator and get this as an answer, or
which would be totally fine.
You could decide that you wanna put this whole conversion factor in and
you could type it in like this 5.5 x and then parentheses 6.02E23 divided by 1.
Whichever one you type in, you are going to get the same number here,
which in regular person scientific notation is gonna look like this, and
then we round it using sig figs to get this number here.
Now, once again, don't forget that 3.3 x10 24,
is just an abbreviated version of this very long number of atoms here, okay.
So, that's how we go from moles to say atoms.
Now, let's look at how to do problems in the other direction from say atoms or
molecules to number of moles.
How many moles is 4.6 x 10 to the 24th Sulphur atoms?
Okay, check out this number.
I just wanna remind you that this isn't some weird martian number,
that this is just a shorthand abbreviation for
this very long number with a whole bunch of zeros.
As we did before,
instead of jumping right to moles, Let's redo this common sense approach, where we
think about what we would do if instead of moles we were talking about dozen.
If we wanna know how many dozen this big number were.
Well, we'd recognize that there are 12 things in dozen, and so
we would divide this number by 12.
12 things in a dozen,we wanna know how many times will 12 go into this one, okay?
So, we are gonna be dividing by the number of things in a dozen.
But, as before we are not talking about dozens, we are talking about moles.
So, instead of dividing by the number of things in a dozen,
we wanna find out how many moles is it, 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 gonna wanna use these giant
versions of each number with all these zeroes.
So, this is where the scientific notation comes in handy.
Let's rewrite this in scientific notation, okay.
We're 4.6 x 10 to the 24
divided 6.02 x 10 to
the 23, put this into the calculator.
And you'll wanna type it in like this where we replace the 10 to
the 24 with E24 or 10 x 23 with E23.
Hit return, and we're gonna 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 gonna round this to two significant figures.
We're gonna take the 7 and the 6,
look next door to figure out whether we round up or keep the same.
It's a 4, so we keep it the same.
And we're solving here for moles.
It's gonna be 7.6 moles of sulfur atoms
are in this super huge number of Sulfur atoms.
Okay, I am going to just stop.
Slip it in right here, and
now let's look at how we'd use conversion factors to solve this same problem.
Okay, here we're gonna be starting with 4.6 x 10 to the 24th atoms.
And we wanna multiple this by a conversion factor that's gonna get rid of atoms.
And is going to move me to moles, so let’s look at the two conversion
factors that we could write using this relationship here, okay.
The first one is gonna put one mole on top.
We are talking about atoms here, so there are 6.02 x 10 to
the 23rd atoms, in 1 mole.
Or we could write this other conversion factor where we put 6.02 x 10 to
the 23rd atoms on top and 1 mole on the bottom.
Which of these do we wanna use?
We want to use the 1 that is gonna get rid of atoms.
Atoms is on the top up here, it's on the bottom here.
So, they're gonna cancel out.
Okay, get rid of this.
And now what's the math we're going to do?
The math is going to be 4.6 x 10 to the 24th x 1 divided by 6.02 x 10 to the 23rd.
Now, multiplying this number by 1 isn't really gonna 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 up here.
But, just as we did previously, if you prefer to put this as a big fraction into
the calculator, that's totally cool too.
It's gonnalook like this 4.6E24 x this whole fraction,
1/6.02 x10 to the 23, but all you're doing is just dividing this by this,
because this 1 doesn't really matter.
We're gonna 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 the number of things in 1 mole.
Okay, so if you want some more practice with these kind of problems, check out
the next video, converting between moles, atoms, and molecules part two.