Dilution | Intermolecular forces and properties | AP Chemistry | Khan Academy

In this video, we're going to talk about a concept in chemistry that's quite important, known as dilutions. So let's do an example.

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. What we want to do is create 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. First, let's just go over the intuition. You have a higher concentration here; you have a lower concentration here. Our intuition would tell us 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, we would then have a 0.125 molar solution.

So the question really 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, our one molar solution, do we need to take out to have that many moles.

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 of solute per liters of solution. Another way to think about it is if we multiply both sides by liters of solution, we would get: liters of solution times molarity equals the 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. This little decimal point right over here makes it clear that we're dealing with three significant figures.

When we have this goal right over here, we would round to the nearest two, the ones place, I guess. So our goal is to have half a liter of solution at a molarity of 0.125 molar, and that is going to give us the number of moles we need.

If we multiply this out, this is going to be zero point... let's see, half of 12 is six, and then half of 50 is 25. So we get 0.0625 moles of solute, and in this case, our solute is sodium sulfate.

Let's see if I got the significant figures right. I have three right over here, one, two, three. So if 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.

Now we just figure out how much of our original solution we need in order to have that many moles of sodium sulfate. 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.

When I take this product, I'm going to get 0.0625 moles of sodium sulfate. The math here is pretty straightforward. We can divide both sides by one molar, and what are we going to get? The units work out because we're in moles, and we have molar here.

So this is going to give us our answer in liters. You divide both sides by one molar, and 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. I 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 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 sodium sulfate aqueous solution.