In this video, we are going to look at how
we can use moles to count the number of atoms we have in something so for example here I've
got a container with a bunch of chunks of Carbon in it, I want to know how many Carbon
atoms do I have in here? You will learn how to figure that out here. So just a quick review of moles. A mole is kind of like a dozen except there
are 12 things in a dozen and there are 602 hexillion things in a mole and we often abbreviate
this number in scientific notation as 6.02 times 10 to the 23rd (6.02 x 10^23). Now let's take a look at a mole. Right here, I have a mole of Sulfur atoms
which is just about 602 hexillion Sulfur atoms. Now this is pretty crazy because it's such
a giant number of Sulfur atoms. Here's my question, how do I know that there
are 602 hexillion Sulfur atoms here, right? I couldn't count them out for two reasons. One, atoms are way too tiny, we can't even
see them with a very powerful microscope so there's no way that I could have seen the
atoms and counted them out. Second of all, even if I could count out the
Sulfur atoms, there are so many things in a mole that it would take 20 quadrillion years
to count from 0 up to a mole. So even if I could see these atoms, there
is no way I could count them out. Yet, I'm pretty confident that there are pretty
close to 602 hexillion Sulfur atoms in here. How do I know that? Well, we're going to learn more about this
but it turns out that I can figure out how much a mole, 602 hexillion Sulfur atoms, weighs
and then I can put this thing on a scale and weigh out the number of Sulfur atoms. Let's talk a little bit more about this so
that it makes a little bit more sense. Okay, so here's an analogy. Let's say that I work at a candy factory and
when someone places an order, it's my job to count out all the pieces of candy that
they ordered. One day, a giant rush job comes in for 10,000
jellybeans and the person who placed this order wants exactly 10,000 jellybeans. What a pain this is going to be right? I have to count out 10,000 jellybeans! This is going to take all day! What could make my life a whole lot easier? One thing that would be really awesome is
if I knew how much 10,000 jellybeans weigh. So what if I figured out that 10,000 jellybeans
weigh 27,130 grams? That would be really awesome because all I
would have to do is put a big bag on a scale and shovel the jellybeans in until I got 27,130
grams in them. So in other words instead of having to count,
if I know how much 10,000 jellybeans weigh, all I have to do is weigh out that amount. We can do the exact same thing here with moles. I told you there's about 602 hexillion Sulfur
atoms here, of course I didn't count that out, that's because I know that 602 hexillion
Sulfur atoms weigh just about 32.07 grams so all I have to do is put this container
on a scale, weigh out 32.07 grams and I'll know that I have just about 602 hexillion
of them. So how did I know that a mole of Sulfur atoms
weighed 32.07 grams? Well, all you have to do is look at the periodic
table. If I look Sulfur up on the periodic table,
I've got element name and the abbreviation and stuff and then I have this number down
here. This is what we call a molar mass and this
number down here tells us how much one mole of this element weighs in grams. So 32.07 is how much one mole or 602 hexillion
Sulfur atoms weighs. Now let's go back to the candy factory. Imagine that I get all kind of orders for
all sorts of different candies. I can figure out what 10,000 of many different
types of candies weigh. So for example, maybe I have to do M&M's one
day and I can find out 10,000 M&M's weigh 8,770 grams. They weigh less because one M&M is much lighter
than one jellybean so 10,000 of them are going to weigh less. On the other hand, a candy like one of these
chocolate malted balls are a bunch heavier than the jellybeans so 10,000 malted balls
are going to weigh a bunch more at 154,600 grams. So it's the same way with atoms, some are
lighter and some are heavier. So Carbon for example is a little bit lighter
than Sulfur and 602 hexillion Carbon atoms only weigh about 12.01 grams because Carbon
atoms are just lighter than Sulfur atoms. On the other hand, something like Zinc atoms
are heavier than Sulfur atoms so 602 hexillion zinc atoms or a mole of zinc atoms weigh 65.38
grams and just as I did with Sulfur, I know how much the Carbon and Zinc moles weigh because
I can look up the atoms on the periodic table. So here we got Carbon, 12.01 is its molar
mass, it's how much one mole weighs and Zinc, 65.38 and that tells me how much one mole
of Zinc, 602 hexillion atoms, weighs. So if I want 602 hexillion, one mole, of any
kind of atom all I have to do is look at the periodic table and find out how much a mole
of that atom weighs and I don't have to count any atoms, all I have to do is just weigh
out this amount on a scale. This is just like me being lazy in the candy
factory. I don't want to have to count out these jellybeans
or M&Ms, so I can just weigh them instead. I can do all my counting by weighing and that's
what I do with these atoms, I count by weighing out their molar masses. So now that we know how to figure out how
much a mole of atoms weigh, let's go back to that original question I asked at the beginning
of the video. I have here in this container a whole bunch
of Carbon. I want to know how many atoms of Carbon are
in here. Let's see how we'll answer this. Okay so how many atoms of Carbon do I have
in this container? Well, let's think about moles of Carbon. I look up Carbon on the periodic table and
I find out that one mole weighs 12.01 grams and I also know that in that one mole there
are 602 hexillion atoms. The first thing I want to know is how many
moles of Carbon do I have here? In order to figure that out, we can do some
weighing, alright? I know that one mole weighs 12.01 grams so
let's weigh this and figure out how many total moles we have. I put this on a scale and find out that there
are 31.87 grams of Carbon atoms in here. Now that's more than a mole. If we had 12.01 grams of Carbon we would have
one mole but we have more than that so let's figure out how many total moles we have. We'll do that by taking 31.87 grams, the total
mass of Carbon atoms here, and divide that by 12.01 grams which is how much one moles
weigh. When we do that we get 2.654 moles so that
is how many moles of Carbon I have in here. Okay, we'll take this number and hold on to
it because it's going to be important for what we do next. So how many atoms of Carbon do we have in
here? Well we know that in each mole there are 602
hexillion atoms but here I've got 2.654 moles. This isn't too hard though because all I have
to do is multiply 2.654 by the number of atoms that are in one mole. So I can do 2.654 moles times 602 hexillion
atoms. So now this is kind of a pain because I've
got all these zeros so I'm going to rewrite this using a shortened version of this in
scientific notation. I'm going to multiply this by 6.02 times 10
to the 23rd which is usually the version of 602 hexillion that we want to use when we're
doing math. When I do this, I can just plug it into a
calculator and I'm going to get 1.60x10^24 Carbon atoms. Sometimes when you see things in scientific
notation it can be a little bit scary so let's put this out
of scientific notation and this is the number of Carbon atoms that we have when we put all
those zeros in. One hep-trillion six hundred hexillion Carbon
atoms. So that is how we can use moles to figure
out the number of atoms we have in something. We can figure out how many moles we have by
weighing it and then once we know how many moles we have, all we have to do is multiply
that by the number of things that are in a mole and we get our final answer.