Calculating moles based on molarity and volume

- [Instructor] We're asked
which of the following solutions

contains the greatest number
of moles of chloride ions?

So pause this video and see
if you can figure that out.

All right, now let's see
how we can think about it.

So the relationship between
molarity liters, and moles

is that molarity of some solute,

is defined as the number
of moles of that solute

divided by the liters of solution.

Or another way to think about
it is if you wanna solve

for the number of moles of solute,

you multiply both sides by liters.

So you could think about
it as liters of solution.

I'll try it this way for short,

times the moles per liter, or
you could say the molarity.

of the solute, that is going to give you

the number of moles of the solute.

And if you look at each of these choices,

they're giving us a volume.

They're giving us the
volume in milliliters,

but we could convert that
two liters in a pretty

straightforward way.

And then they're giving us the molarity.

So we essentially just have to
make sure that we're dealing

with the liters and then multiply these,

and we will get the number
of moles of this solute

or this solute, of this
solute, and then this salute.

But then we have to be
careful because they tell us

the greatest number of
moles of chloride ions,

and for choices A and B
each mole of the molecule

we are dealing with would
have a mole of chloride ions,

but in choices, C and D each mole of say,

magnesium chloride actually
has two moles of chloride.

Same thing with calcium chloride.

Each mole actually has
two moles of chloride.

So if we're thinking about the number

of moles of chloride ions,
whatever we get for choices,

C and D in terms of the number
of moles of these molecules,

we then multiply by two to figure out

the moles of chloride ions.

So if what I just said inspires
you, and you didn't get

the answer the first time,

pause the video again and
see if you can work it out.

All right, now let's work
through this together.

So in this first choice, A,

the number of moles of chloride ions,

it's going to be equal to,

I'm gonna convert 20
milliliters to liters.

So that's 0.020 liters of solution,

times we have 0.20, instead
of just writing molar,

I'm going to write moles of
lithium chloride per liter.

And this is the liter of solution.

I could write liters of solution here,

liters of solution here,

but what this is going to
result in the liters cancel out

and I am going to get 0.004
moles of lithium chloride.

So that's the first choice.

That's A, now let's do B and
I'll do it a different color,

15 milliliters, that's the
same thing as 0.015 liters.

That's 15/1,000 of a
liter, 15/1,000 of a liter,

times 0.10 moles of sodium
chloride per liter of solution.

That's going to get us to
0.0015, and these cancel out.

Moles of sodium chloride
in this situation,

I could write that out, sodium chloride.

This was the top one was
moles of lithium chloride.

All right, now let's
look at the next choice.

So here, 10 milliliters,

that's the same thing
as 10/1,000 of a liter.

So 10/1,000 of a liter, times 0.25 molar,

which is the same thing
as moles of in this case,

magnesium chloride per liter of solution,

which is going to get us to 0.0025 moles

of magnesium chloride.

And then in choice D,
we have 15 milliliters,

which we already know is
the same thing as 15/1,000

of a liter, times 0.20 molar.

That's the same thing as
moles of calcium chloride,

per liter of solution.

And that is going to be equal to 0.003,

moles of calcium chloride.

So far we have figured out our moles

of the molecules listed here.

So this first one over here,

this was moles of lithium chloride.

Then we have moles of sodium chloride,

moles of magnesium chloride.

Actually there's two chloride
ions per molecule there.

And then we have moles
of calcium chloride.

Now how many moles of
chloride are in each of these?

Well, in the first two it's one-to-one.

So if you have 0.004
moles of lithium chloride,

you're gonna have the same number of moles

of just chloride, same thing for choice B,

but for choices C and
D, as we said earlier,

we would multiply by two.

So for choice C, this would
translate into two times as many

moles of chloride or
0.005 moles of chloride.

I know I'm getting a little bit messy,

here is getting all squinched.

And this last choice,
I'd also multiply by two,

because for every mole
of calcium chloride,

I have two moles of chloride.

So this is going to result in 0.006 moles

of chloride anion in this situation.

And so when you just compare
the moles of chloride,

we see that choice D has the most,

I like this choice right over here.