Molarity Practice Problems

To see all my Chemistry videos, check out http://vespr.org/chemistry

Confused about molarity? Don't be! Here, we'll do practice problems with molarity, calculating the moles and liters to find the molar concentration. We'll also have to use conversion factors to convert between grams and moles, and between milliliters and liters.

Calculate the molarity of a solution
prepared by dissolving 9.8 moles of solid

NaOH, that's sodium hydroxide, in enough
water to make 3.62 liters of solution.

To find molarity,
you take moles of solute and

divide it by liters of solution.

So to set our equation up here,
we have Molarity = moles of solute,

sodium hydroxide is the solute here
cuz it's getting dissolved in water.

And we have 9.8 moles of that,
divided by liters

of solution,
which is 3.62 liters right here.

So find molarity, 9.8 divided by 3.62,
round the answer to

two significant figures cuz I
have 9.8 up here, and I get 2.7.

What should the units be for this?

When you find molarity the final answer
is in units of molar, capital M.

So this is 2.7 molar.

But what 2.7 molar really means is that

there are 2.7 moles of NaOH,
of the solute,

for every one liter of the solution.

So 2.7 M, but
don't forget that that means 2.7 moles for

each 1 liter of this solution up here.

You dissolve 152.5 g of CuCl2,
that's copper chloride,

in water to make a solution with
a final volume of 2.25 liters.

What is it's molarity?

So, for molarity as you know,

we wanna take moles of solute
divided by the liters of solution.

CuCl2, copper chloride is also a solute in
this case cuz it's getting dissolved in

the water.

But the problem doesn't tell us how
many moles of copper chloride we have.

It tells us how many grams
of copper chloride we have.

So 152.5, we can't use that number,
instead we have to convert

this to moles and then we can plug
it into the molarity equation.

So to convert this amount
in grams into moles,

the first thing that we've got to start
with is the molar mass of copper chloride.

And so to find the molar mass of copper
chloride, we got to find copper and

chlorine on the periodic table and
take a look at their atomic masses.

So copper, there is one copper
atom in copper chloride.

So I'll take the molar mass of copper,
63.55, and then there

are two of these chlorines
in copper chloride.

So I wanna take 2 times the molar
mass of chlorine which is 35.44.

When I add these together,

I get 134.45 grams

per 1 mole, okay.

That's like the molar mass of it.

Now we're gonna have to use
this as a conversion factor,

to go between grams and moles.

So remember that when we have
conversion factors like this,

we can always write them in two ways.

We can write it like this,
or we can flip it.

And so we can say 1 mole,
for every 134.45 grams.

Both of these are ways to express
the relationship between grams and

moles for copper chloride.

Now that I know how to go between grams
and moles, because of conversion factor,

I can take 152.5 grams and I can multiply
it by one of these two conversion factors.

I wanna use the one,

that gets rid of grams from
the top of the equation up here.

Since grams is on the top,

I'm gonna choose this conversion
factor with grams down here.

So now grams cancels out,
grams cancels out, I'm left with moles.

And I'm gonna do 152.5
times 1 divided by 134.45.

And that is gonna give me 1.134 moles.

I'm rounding to four significant figures
here because I have one, two, three,

four significant figures and I don't worry
about the 1 cuz it's part of a definition.

So now I know that I have
1.134 moles of CuCl2.

Now I can go ahead and
calculate the molarity.

So molarity is going
to be moles of solute,

1.134 moles divided by liters
of solution equals 2.25 liters.

And I wanna crank through that,
rounding it to three significant figures,

cuz I have three sig figs there,
it's gonna be 0.504 M.

And as I said before,
don't forget that what that

means is that there
are 0.504 moles of CuCl2 for

every 1 liter of this solution
that we're making here.

A solution has a volume
of 375 milliliters and

contains 42.5 grams of NaCl,
sodium chloride.

What is its molarity?

This is kind of a challenging question,
because there are two things we need to

calculate molarity, moles of solute and
liters of solution.

We aren't given either of these
two things in the problem.

Okay, instead of moles of solute,
we're given grams of solute,

sodium chloride is the solute.

So we can't use that right away,
we'll have to convert grams to moles.

And then instead of getting liters of
solution, we get milliliters of solution.

So before we can run this equation,

we're gonna have to convert milliliters
of solution into liters of solution.

So let's go step by step to show
how do we do these conversions and

then how we can do
the molarity at the end.

The first thing I'm gonna do is I'm gonna
take this 42.5 g of sodium chloride and

turn it into moles of sodium chloride.

So I'm gonna need to start with
a molar mass of sodium chloride.

We'll look at sodium and chlorine on
the periodic table to get their masses.

And I'm gonna do 22.99 for sodium.

I only have one sodium, and
I only have one chlorine here.

So I'm just going to do 35.44 here.

Add those together and

I'll get the molar mass which I'm
gonnabe using as a convergent factor.

Okay, so I'm going to write
this as 58.44 g over 1 mol.

That's one way to write it, or

I can flip the conversion factor and

I can write 1 mol divided by 58.44 g.

Now I have the two conversion
factors that I'll use for

taking 42.5 grams of sodium chloride,
multiplying it by one of these,

it's gonna be this one cuz I have
grams up here grams down there.

So these cancel out.

42.5 divided by 58.44.

And that is going,
I'll put the answer down here, and

that is going to give me 0.727
moles of sodium chloride.

Now I know how many moles of sodium
chloride I have, so I'm halfway there.

The next thing I have
to do is I have to take

the volume which is 375 milliliters and
multiply that by a conversion factor so

I can change it from
milliliters into liters.

So there are 1,000
milliliters in one liter,

which means that we can write
these two conversion factors.

I want to use a conversion factor that's
going to turn milliliters into liters.

So since it's on the top here, I will
use a version of this conversion factor

that puts milliliters on the bottom here.

So, I'll cancel this out, cancel this out,
I'll be left with liters.

And when I do that, 375 divided by 1,000.

I'm left with 0.375 liters.

Now I know my liters.

So now my moles of sodium chloride and
my liters of solution.

And I can finish this by
saying molarity equals

0.727 moles divided by 0.375 liters.

And I'm going to get 1.94,
that's rounded to one,

two, three significant figures.

For my molarity, 1.94 are the units.

And as before,
don't forget what this really means.

It means that for every liter of
this solution, there are 1.94 moles.

1.94 moles per 1 liter of solution.

So sometimes you won't always be given
moles, you won't always be given liters.

You'll probably have to convert from grams
to moles or from milliliters into liters.

So just make sure you've got your
conversion factors set up straight.

Now, in the next video instead of having
moles and liters and calculating molarity,

you'll be given molarity and then you'll
have to use that as a conversion factor

to move between moles in a solution and
liters of a solution.