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Current time:0:00Total duration:5:53

AP Chem: SPQ‑3 (EU), SPQ‑3.A (LO), SPQ‑3.A.2 (EK)

- [Instructor] In this
video, we're gonna talk about a concept in chemistry
that's quite important, known as dilutions. So let's do an example. So let's say we have a large
vat, as much as we need. It's a one-molar solution
of sodium sulfate, and it's an aqueous solution. So sodium sulfate is dissolved in water. And let's say we also have
as much water as we need, and what we want to do
is create a solution, another aqueous solution
of sodium sulfate, but one that has a
different concentration, in this case, one that
has a lower concentration. So we want to create
a 0.125-molar solution of sodium sulfate, and
we want 500 milliliters of this new solution. Pause this video and think about how you would approach that. All right, now let's
think about this together. So, first let's just
go over the intuition. You have a higher concentration here. You have a lower concentration here. So our intuition would tell us is that we're going to take
less than 500 milliliters of our original solution,
pour some of that in. That's going to have a
sufficient number of moles of sodium sulfate that, if we were to then fill
this up to 500 milliliters, that we would then have
a 0.125-molar solution. So the question really
is, is how much of this do we have to put in, which
we can then dilute with water to get to our goal solution? Well, to answer that question,
we just have to figure out how many moles of sodium sulfate need to be in this final
goal solution, this one or this one, depending
on how we visualize it? And then, how much of
our original solution, of our one-molar solution,
do we need to take out to have that many moles? And to think about how many moles, we just have to remind
ourselves what molarity is. We know already that molarity
is equal to number of moles, number of moles, of solute per liters of solution, liters of solution. Or another way to think about it is, if we multiply both sides
by liters of solution, we would get liters of solution times molarity, times molarity, is equal to the number of moles of solute, number of moles of solute. So what we can do is say,
all right, how many moles of our solute do we need in our goal? Well, to do that, we just
have to say, all right, we want to eventually have
500 milliliters of solution, or we could rewrite that as 0.500 liters, and this little decimal
point right over here makes it clear that we're dealing with three significant figures, that we've rounded to the nearest one, when we got to this, when we
have this goal right over here, or we would round to the nearest, to the ones place, I guess. So, our goal is to have half a liter of solution at a molarity of 0.125 molar, and then that is gonna give us the number of moles we need. And, if we multiply this
out, this is going to be zero point, let's see, half of 12 is 6 and then half of 50 is 25, 0.0625 moles, moles of solute. And, in this case, our
solute is sodium sulfate. And let's see if I got the
significant figures right. I have three right over here, one, two, three, one, two, three. So I take the product. I'd still have one, two,
three significant figures. So this is our goal. We want to have this many moles of solute. So we just have to figure out how much of our original
solution do we need in order to have that many
moles of sodium sulfate? So, one way to think about it is, there's some mystery volume
of our original solution we need, and we know what
its concentration is. It's a one-molar concentration that, when I take this product, I am going to get 0.0625 moles of sodium sulfate. And the math here is
pretty straightforward. We can divide both sides by one molar, and what are we going to get? And the units work out because we're in moles
where you have molar here. And so this is going to give
us our answer in liters. You divide both sides by one molar. You're going to get that
question mark is equal to 0.0625 liters of solution. Or another way to think about
it is, this is equivalent to 62.5 milliliters of our original solution. I want to make sure I got all
the significant figures right. Had three over there. One,
two, three, one, two, three. And so, yes, right over here. I can still have one, two,
three significant figures or sometimes called significant digits. And so there we've answered our question. What I would do is I would take 62.5, 62.5 milliliters of my original solution, so that's this over here, and then I would take my
water and then keep filling until I get to 500
milliliters, and we're done. At that point, I'm going
to have a 0.125 molar of sodium sulfate aqueous solution.

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