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I've taken this problem from
Chapter 4 of the Chemistry & Chemical Reactivity book by
Kotz, Treichel and Townsend, and I've done it with
their permission. So let's do this example. A 1.034 gram sample of impure
oxalic acid is dissolved in water and an acid-base
indicator added. The sample requires 34.47
milliliters of 0.485 molar sodium hydroxide to reach
the equivalence point. What is the mass of oxalic acid,
and what is its mass percent in the sample? So before we even break into the
math of this, let's just think about what's happening. We have some oxalic acid,
which looks like this. It's really two carbolic acid
groups joined together, if that means anything to you. Watch the organic chemistry play
list if you want to learn more about that. So we have a double bond to one
oxygen, and then another bond to a hydroxide. We have that on the other
carbon as well. This right here is what
oxalic acid is. And it's an interesting acid,
because it can actually donate two protons. This proton can be nabbed off,
and this proton can also be contributed. And it's actually resident
stabalized. If that doesn't mean anything
to you, don't worry. You'll learn more about that
in organic chemistry. But the important thing to
realize here is that there's two protons to nab off of it. Now each molecule of sodium
hydroxide-- remember when you put it in the water it really
just dissolves, and you can really just think of it as
hydroxide-- each molecule of hydroxide can nab one of
the hydrogen protons. So for every one molecule of
oxalic acid, you're going to need two hydroxides-- one to nab
this hydrogen proton, and then another one to nab
that hydrogen proton. So let's write down the balanced
equation that we're dealing with here. So we're going to start off
with some oxalic acid. So that has two hydrogens-- so
it's H2-- two carbons, and then four oxygens-- O4. It's dissolved in water, so
it's an aqueous solution. And to that, we're going to
add sodium hydroxide. Now I just told you that you're
going to need two of the hydroxides to fully
neutralize the oxalic acid. So you're going to
need two of them. And this is also in our
aqueous solution. And once the reaction happens,
this guy will have lost both of the hydrogen protons,
so let me draw that. So it will look like this. No more hydrogen,
so it's C2O4. It'll have a negative
2 charge. And actually, you could imagine
that it might be attracted to these positively
charged sodiums. And 2 sodiums in particular. So this has a negative
2 charge. We could even write it there
if you want-- 2 minus. And then you could have
the sodiums over here. You have these two sodiums
that have two plus. And this entire molecules
becomes neutral. They are attracted
to each other. They are still in an
aqueous solution. And then, the hydroxide nabs the
protons, and then you are left with just water. So plus 2 moles-- or 2 molecules
depending on how we're viewing this--
plus two waters. I'll just use that same
orange color. Plus two H2Os. One of the hydrogens in each
of the water molecules are coming from the oxalic acid, and
so two of these hydrogens in these two moles of the water
are coming from one entire molecule of
oxalic acid. Now let's actually
do the math. We have 34.47 milliliters of
the solution that has the sodium hydroxide. And I'm just going to convert
that to liters just so it's easier to deal with the molarity
right over there. So we have 34.47 milliliters--
we could write it of the solution, but we understand
that, that's the case. So let's just So this is times,
we have one liter for every 1,000 milliliters. And then this will give us-- the
milliliters cancel out-- 34.47 divided by 1,000 is
0.03447 liters of this 0.485 molar sodium hydroxide
solution. So let's figure out how many
actual molecules of sodium hydroxide we have. This
is the solution. And we know its concentration,
0.485 molar-- so let me do that in a different color--
0.485 molar, this information allows us to figure
out the actual molecules of sodium hydroxide. So we want to multiply this by--
we have 0.485 moles of sodium hydroxide for every
1 liter of this solution. That's what the molarity
tells us. We have 0.485 moles per liter. So the liters cancel out, and
then now we're going to actually have to get
a calculator out. And this'll tell us how many
moles of sodium hydroxide we have in this solution. So let me get my calculator. There we go. All right, let me just multiply
these two numbers. So we have 0.03447 times 0.485
is equal to-- let me put this down here-- 0.167. And we only have three
significant digits here, so we're going to round to three
significant digits. So we'll just go with 0.0167. So let me move that over
off the screen. So this is going to be equal
to 0.0167, and all we have left here are moles of
sodium hydroxide. Now we know that this many moles
of sodium hydroxide are going to completely react with
however many moles of oxalic acid we have. Now we know that
we need two moles of this for every mole of oxalic acid. Or for every mole of oxalic acid
that completely reacts, we need two moles of this. So let's write that down. And then you color. So we need two moles of sodium
hydroxide, we got that from our balanced equation right
there, and it's obvious it needs one mole, or one molecule
will take this proton, and then you need
another molecule to take that proton. So we need two moles of sodium
hydroxide for every one mole of oxalic acid. For every one mole of H2C2O4. So essentially, we are
just going to divide this number by 2. Let me get the calculator
back. So we're just going to divide
0.0167 divided by 2. Once again, three significant
digits 0.00835. So this is going to 0.00835
moles of oxalic acid, H2C2O4. So we have the number
of moles, but we to figure out the mass. And we know the molar
mass of oxalic acid. Let me write these down. We know that hydrogen has a
molar mass-- let me write it this way-- molar mass if you
have a mole of hydrogen, it has a molar mass of one gram. If you have-- and this comes
from its atomic weight-- if you have carbon its molar mass
is 12 grams. And if you have oxygen, its molar mass
is 16 grams. So what's the molar mass
of oxalic acid? Well we have two hydrogens,
so that's going to be two grams, right? 2 times 1 gram. That's the hydrogens there. We have two carbons, so it's
going to be plus 24 grams. 12 grams for each of
these carbons. And then we're going to have
four oxygens that weigh in, if we have a mole of them,
at 16 grams. So that's going to be plus 64. So what does this come out to? 24 plus 64 is 88, right? 2 plus 6 is 88, right. So it's 88 plus 2 more is 90
grams. So if you had a mole of oxalic acid, it would be 90
grams. So we could say 90 grams per mole of H2C2O4. So let's go back to
the math here. I'll rewrite it over here. We know we're dealing with
0.00835 moles of oxalic acid, H2C2O4. And now we know its
molar mass. We know that there are 90
grams-- let me do this in a different color, this color's
getting motonous-- we know that there are 90 grams
of H2C2O4 for every one mole of H2C2O4. This is its molar mass. And now we just multiply this
number, and we'll figure out the grams of oxalic acid. That and that cancels out. and. Then we just take the number
that we had and multiply it by 90, so times 90. This just says the previous
answer, which is the number of moles of oxalic acid times its
molar mass will tell us the grams of oxalic acid. So we get 0.75. I'll just round it to
2 since we only have three significant digits. The 90 isn't exact, so it's a
little bit-- but I'll just round it to three significant
digits. So 7--.752. This is equal to 0.752 grams
of oxalic acid: H2C2O4. And I think we've answered
part of the question. So the first question is, what
is the mass of oxalic acid? We've just answered it. That answer right there
is 0.752 grams. Now the next part is,
what is its mass percent in the sample? Well the sample of impure oxalic
acid right over here, was 1.034 grams. So we just have
to say, what percentage is 0.752 of 1.034? So let's get the calculator
back. So we have the 0.752 divided
by 1.034 and we get 72.7%. So the answer to the
second part right over there is, 72.7%. We were able to figure out that
this impure oxalic acid sample is 72.7% actual
oxalic acid.