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

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

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To find molarity,
you take moles of solute and

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divide it by liters of solution.

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

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

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And we have 9.8 moles of that,
divided by liters

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of solution,
which is 3.62 liters right here.

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

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

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What should the units be for this?

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

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So this is 2.7 molar.

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But what 2.7 molar really means is that

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there are 2.7 moles of NaOH,
of the solute,

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for every one liter of the solution.

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

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each 1 liter of this solution up here.

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

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

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What is it's molarity?

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So, for molarity as you know,

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

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

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the water.

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

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

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

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

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So to convert this amount
in grams into moles,

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

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

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

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

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

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are two of these chlorines
in copper chloride.

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

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When I add these together,

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I get 134.45 grams

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per 1 mole, okay.

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That's like the molar mass of it.

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

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to go between grams and moles.

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So remember that when we have
conversion factors like this,

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we can always write them in two ways.

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

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

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

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moles for copper chloride.

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

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

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I wanna use the one,

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

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Since grams is on the top,

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

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

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

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And that is gonna give me 1.134 moles.

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

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

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

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Now I can go ahead and
calculate the molarity.

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So molarity is going
to be moles of solute,

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1.134 moles divided by liters
of solution equals 2.25 liters.

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

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

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

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means is that there
are 0.504 moles of CuCl2 for

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

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A solution has a volume
of 375 milliliters and

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contains 42.5 grams of NaCl,
sodium chloride.

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What is its molarity?

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

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calculate molarity, moles of solute and
liters of solution.

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

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

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sodium chloride is the solute.

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

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

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So before we can run this equation,

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

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

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then how we can do
the molarity at the end.

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

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turn it into moles of sodium chloride.

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

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

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And I'm gonna do 22.99 for sodium.

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

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So I'm just going to do 35.44 here.

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Add those together and

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

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

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That's one way to write it, or

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I can flip the conversion factor and

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I can write 1 mol divided by 58.44 g.

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

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

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

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So these cancel out.

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42.5 divided by 58.44.

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

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

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

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

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

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I can change it from
milliliters into liters.

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So there are 1,000
milliliters in one liter,

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which means that we can write
these two conversion factors.

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

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

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that puts milliliters on the bottom here.

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

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

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I'm left with 0.375 liters.

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Now I know my liters.

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

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And I can finish this by
saying molarity equals

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0.727 moles divided by 0.375 liters.

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

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two, three significant figures.

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For my molarity, 1.94 are the units.

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

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

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1.94 moles per 1 liter of solution.

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

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

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

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

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

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