In this video, I want to talk about two very common types of questions about moles.
These two types of questions don't really fit into the other categories we've talked
about but they show up all the time on homework, in textbooks, on quizzes and particularly
on tests and exams.
Okay, here's the first one.
What is the mass in grams of a single atom of oxygen?
Okay, this is the type of question that asks us to calculate the mass of a single atom
of some element.
Here, we're going to use Oxygen as the example.
Now in order to solve problems like this, you have to pull in a few different pieces
of information about moles, okay?
The first one is going to be about mass, right?
We're talking about the mass of a single atom of Oxygen.
What do we know about the mass of Oxygen?
Well we can look up Oxygen on the periodic table and we can zoom in to this number, 16.00,
which tells us the molar mass of Oxygen.
It tells us how much a mole of Oxygen weighs in grams.
So we can say that from this information on the periodic table, 1 mole of Oxygen atoms
weighs 16.00 grams.
But we're not talking about a mole of Oxygen atoms, we're talking about a single atom of
Oxygen, one Oxygen atom.
So what do we know about the number of Oxygen atoms in a mole?
Well, you may know that 1 mole of Oxygen atoms contains 602 hexillion Oxygen atoms which
we often abbreviate as (6.02 x 10^23).
Now we want to combine these two pieces of information to make a third piece of information,
okay?
Check this out.
We know two things here.
On the one hand, we know that one mole of Oxygen atoms weighs 16.00 grams and we also
know that one mole of Oxygen atoms contains 602 hexillion Oxygen atoms.so we can combine
these two pieces of information to say that 602 hexillion Oxygen atoms weigh 16.00 grams,
okay?
We can even take this and express it kind of like an equation, kind of like a relationship
here.
We can say 6.02 times 10 to the 23rd Oxygen atoms equals or its equivalent to 16 grams
(6.02 x 10^23 Oxygen atoms = 16.00 grams).
Now check out this last thing that I drew.
This thing here is an equation or a relationship that we can turn into a conversion factor
that will let us go from the number of Oxygen atoms we have to grams, okay?
So I'm going to use this equation as a conversion factor to go from one Oxygen atom to a certain
number of grams.
Here's how I'm going to do it.
Let's start here, I'm going to do 1 oxygen atom and now I'm going to multiply that by
a conversion factor made from this relationship.
I want to get rid of Oxygen atoms which is on top here so I'm going to write this relationship
as a conversion factor with Oxygen atoms on the bottom.
So I'm going to take this part here, 6.02 x 10^23 Oxygen atoms, put that on the bottom,
and make my fraction here a little bit longer.
Then I'm going to put the other side of the relationship, 16.00 grams, on top.
And now when I work through the math here, Oxygen atoms on the top, Oxygen atoms on the
bottom, they're going to cancel out and that's going to leave me with grants which is exactly
what I want.
I'm just going to rearrange this so we can go through the math.
So you write this out and you probably want to solve it by putting it into the calculator.
You can type it in like this although you don't really have to multiply it by 1 here
because multiplying something by 1 doesn't really change its value but it's totally up
to you.
You put this in, you're going to get this out as an answer, this E-23 in calculator
language just means this times 10 to the negative 23rd and then we're going to want to take
this number and round it to three significant figures.
We don't worry about significant figures in 1 here because this is a counting number.
We're saying 1 Oxygen atom, it's not a measurement, so this has an infinite number of significant
figures.
We're going to round this to three significant figures because there are three in 6.02 which
has the fewer numbers of significant figures.
So we round this to 2.6, we have the 5 here so we round up because of the 7, 2.66 times
10 to the negative 23rd (2.66 X 10^-23).
And what are our units?
They are grams.
That's what we're left over with after the conversion factors.
Here's our final answer in scientific notation and if we write this out in regular decimal
notation, we can see that it is a tiny, tiny, tiny number.
2.66 X 10^-23 grams, the mass of a single atom of Oxygen.
So the key to solving that problem was being able to take this information and write conversion
factors with it, okay?
We knew that 1 mole of Oxygen weighed this much and we know how many Oxygen atoms are
in 1 mole.
So we can take this information and write these two conversion factors.
It could let us go from number of Oxygen atoms to grams and back and forth.
What mass of Mercury has the same number of atoms as 64.2 grams of Calcium?
I don't know about you but I find the wording in this question really confusing so I want
to try to explain what they're actually trying to ask here so you can understand how to solve.
So we have Mercury and we have Calcium.
We can look them up on the periodic table and this number here, the molar mass, tells
us how much a mole of each of these types of atoms would weigh.
So Mercury here, we know that one mole of Mercury (602 hexillion Mercury atoms) would
weigh 200.6 grams and for Calcium here, one mole of Calcium atoms (602 hexillion Calcium
atoms) weighs 40.08 grams.
So here is the main point, the main point is that 200.6 grams of Mercury and 40.08 grams
of Calcium both have the same number of atoms in this, okay?
The masses are different.
This weighs a whole lot more, this is a lot lighter but the point is that even though
the masses are different, the number of atoms is the same because 602 hexillion Mercury
atoms weigh this much and 602 hexillion Calcium atoms weigh this much, okay?
So we can say that this amount of Mercury and this amount of Calcium have the same number
of atoms in them.
What the question is really asking is sort of like X grams of Mercury and 64.2 grams
of Calcium have the same number of atoms, right?
That's not really a question but it's a statement, okay?
It's like what amount of Mercury has the same number of atoms as 64.2 grams
of Calcium.
This amount of Mercury and this amount of Calcium have the same number of atoms.
This amount of Calcium and how much Mercury have the same number of atoms?
So here's how we're going to solve it.
We're going to do two steps.
Step 1: We're going to ask, how many atoms are in 64.2 grams of Calcium?
And then we're going to take that number of atoms that are in this amount of Calcium and
we're going to ask, if we had that number of Mercury atoms, how much would that weigh?
So let's start here with part one.
Okay, so I'm going to start here with 64.2 grams of Calcium.
And now I want to figure out how many atoms are in them.
So I'm going to multiply it by a conversion factor that I can make from this information
here.
I want to get rid of grams so I'm going to put grams on the bottom.
I'm going to do 42.08 grams of Calcium and then on the top I'm going to put 6.02 x 10^23
atoms.
So now we got grams Calcium here, grams Calcium here, they're going to cancel out, I'm going
to be left with atoms of Calcium.
I can put this into the calculator, I get this out as my answer and I'm going to round
it to three significant figures so I'm going to get 9.64 x 10^23, okay? 9.64 x 10^23 Calcium
atoms.
This is how many Calcium atoms are in this much Calcium.
Now the next thing I want to do here is ask, if we had this number of Mercury atoms how
much would that weigh?
So we have this many Calcium atoms.
If we had that much of Mercury, how much would that weigh?
So here's how we're going to do that.
Take this and we're going to multiply it by a conversion factor that we can write from
this information.
It tells us about how much a certain number of Mercury atoms weigh.
So we're going to multiply that by 6.02 x 10^23 Hg atoms on the bottom and then multiply
it by 200.6 grams of Mercury on top.
And now Mercury atoms on the top, Mercury atoms on the bottoms, cancels out, I'm left
with grams of Mercury.
The math I'm going to do is this.
I get this out of the calculator and my final answer rounded to three significant figures
is 321 grams of Mercury and that tells us how much Mercury, what mass of Mercury would
have the same number of atoms as 64.2 grams of Calcium.