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calculate the molarity of a solution
prepared by dissolving 9.8 moles of
solid NaOH the sodium hydroxide in
enough water to make three point six two
liters of solution define molarity you
take moles of solute and divide it by
liters of solution so to set our
equation up here we have molarity equals
moles of solute sodium hydroxide is the
solute here because it's getting
dissolved in water and we have nine
point eight moles of that divided by
liters of solution which is three point
six two liters right here so find
molarity nine point eight divided by
three point six two round the answer to
two significant figures because I have
nine point eight up here and I get two
point seven one should the units be four
this when you find molarity the final
answer is in units of molar capital M so
this two point seven molar
but what two point seven molar really
means is that there are two point seven
moles of NaOH of the solute for every
one litre of the solution so two point
seven molar
but don't forget that that means two
point seven moles for each one liter of
this solution up here you dissolve 152
point five grams of cucl two that's
copper chloride in water to make a
solution with a final volume of 2.25
liters what is its molarity so for
molarity as you know we want to take
moles of solute divided by liters of
solution cucl two copper chloride is our
solute in this case because 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 150
two point five we can't use that number
instead we have to convert this
two 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 got to start with is the
molar mass of copper chloride and so to
find the molar mass of copper chloride
we've 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
point five five and then there are two
of these chlorines and copper chloride
so I want to take two times the molar
mass of chlorine which is thirty five
point four four when I add these
together I get one thirty four point
four five grams per one 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
one mole for every one hundred and
thirty-four point four five 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 with this
conversion factor I can take one fifty
two point five grams and I can multiply
it by one of these two conversion
factors I want to use the one that gets
rid of grams from the top of the
equation up here since grams on the top
I'm going to 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 150 two
point five times one divided by one
thirty four point four five and that is
gonna give me one point one three four
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 one because it's part of a
definition so now I know that I have one
point one three four moles of C UCL two
now I can go ahead and calculate the
molarity so molarity is going to be
moles of solute one point one three four
moles divided by liters of solution
equals two point two five liters and
want to crank through that rounding it
to three significant figures because I
have three sig figs there it's going to
be zero point five zero four molar and
as I said before don't forget that what
that means is that there are one zero
point five zero four moles of C UCL two
for every one liter of this solution
that we're making here a solution has a
volume of 375 milliliters and contains
42 point five 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 a 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 we do these conversions
and then how we can do the molarity at
the end the first thing that I'm going
to do is I'm going to take this forty
two point five grams 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 look at
sodium and chlorine on the periodic
table to get their masses and I'm gonna
do 20 2.99 for sodium I only have one
sodium and I only only have one chlorine
here so I'm just gonna do 35 0.44 here
add those together
and I'll get the molar mass which I'm
going to be using as a conversion factor
okay so I'm gonna write this as 58.4 for
grams over one mole that's one way to
write it or I can flip the conversion
factor and I can write one mole divided
by eighty eight fifty eight point four
four grams now I have the two conversion
factors that I'll use for taking forty
two point five grams of sodium chloride
multiplying up by one of these it's
going to be this one because I have
grams up here grams down there so these
cancel out forty two point five divided
by fifty eight point four four and that
is going to I'll put the answer down
here and that is going to give me zero
point seven two seven moles sodium
chloride now I know how many moles of
sodium chloride I have so I'm halfway
there the next thing that 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 100 1000 milliliters in 1 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 a thousand I'm left with
0.375 liters now I know my leaders so
now my moles of sodium chloride and my
liters of solution and I can finish this
by saying molarity equals zero point
seven two seven moles divided by zero
point three seven five liters and I mean
yeah one point nine four that's
- one two three significant figures for
a my molarity 1.94 are the units and as
before
don't forget what this really means it
means that for every litre of this
solution there are one point nine four
moles one point nine four moles per one
liter of solution so sometimes you won't
always be given moles you won't always
be given liters and you'll probably have
to convert from grams to moles or from
milliliters into liters so just make
sure you got your conversion factors set
up straight now in the next video
instead of having moles and leaders in
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
