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.