- [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.