Video transcript
- [Instructor] In thisvideo, we're gonna talk about a concept in chemistrythat's quite important, known as dilutions. So let's do an example. So let's say we have a largevat, as much as we need. It's a one-molar solutionof sodium sulfate, and it's an aqueous solution. So sodium sulfate is dissolved in water. And let's say we also haveas much water as we need, and what we want to dois create a solution, another aqueous solutionof sodium sulfate, but one that has adifferent concentration, in this case, one thathas a lower concentration. So we want to createa 0.125-molar solution of sodium sulfate, andwe want 500 milliliters of this new solution. Pause this video and think about how you would approach that. All right, now let'sthink about this together. So, first let's justgo 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 takeless than 500 milliliters of our original solution,pour some of that in. That's going to have asufficient number of moles of sodium sulfate that, if we were to then fillthis up to 500 milliliters, that we would then havea 0.125-molar solution. So the question reallyis, is how much of this do we have to put in, whichwe 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 finalgoal solution, this one or this one, dependingon how we visualize it? And then, how much ofour 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 remindourselves what molarity is. We know already that molarityis 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 sidesby 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 justhave to say, all right, we want to eventually have500 milliliters of solution, or we could rewrite that as 0.500 liters, and this little decimalpoint 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 wehave 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 thisout, 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, oursolute is sodium sulfate. And let's see if I got thesignificant 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 originalsolution do we need in order to have that manymoles of sodium sulfate? So, one way to think about it is, there's some mystery volumeof our original solution we need, and we know whatit* 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 ispretty 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 moleswhere you have molar here. And so this is going to giveus our answer in liters. You divide both sides by one molar. You're going to get thatquestion mark is equal to 0.0625 liters of solution. Or another way to think aboutit is, this is equivalent to 62.5 milliliters of our original solution. I want to make sure I got allthe 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 mywater and then keep filling until I get to 500milliliters, and we're done. At that point, I'm goingto have a 0.125 molar of sodium sulfate aqueous solution.
