Worked example: Calculating the mass of a substance in a mixture | AP Chemistry | Khan Academy

We're told that a 0.450 gram potassium supplement contains 22 percent potassium by mass. The potassium is present in the supplement as potassium chloride, which has a molar mass of 74.55 grams per mole. How many grams of potassium chloride are in the potassium supplement?

So, pause this video and see if you can figure that on your own, and I will give you a hint: you might need a periodic table, so I'll give you one right over there.

All right, now let's work through this together. They already give us the molar mass of potassium chloride, but it'll be useful for us to know the molar mass of potassium itself. We can see it's 39.10. So, for potassium, it is 39.10; that's its average atomic mass. But you could also view it as 39.10 grams per mole of potassium. I could write it like that, and that is, I think, all we will need the periodic table of elements for.

So, how do we think about how many grams of potassium chloride are in the potassium supplement? Well, what I could do is say, "All right, what's the total mass of my supplement?" and multiply it by 22 percent to figure out what is the mass of potassium I have.

So let me figure that out. The mass of potassium, that is going to be my 0.450 grams times 22 percent, which is going to be equal to, I'll get my calculator out: 0.450 times 0.22, is equal to 0.099.

0.099, so that's how many grams of potassium I have. Now I can use that to figure out how many moles of potassium I have. And if I know how many moles of potassium I have, all the potassium is present as potassium chloride, because then I'll have the same number of moles of potassium chloride.

Then I could figure out, well, based on the... and if I know the number of moles of potassium chloride, well then I know the mass of potassium chloride because they give us the molar mass. So let's do that.

We have 0.099 grams of potassium, and I want to figure out how many moles of potassium I have. So I'm going to multiply that by one mole of potassium, which has a mass of how many grams of potassium. We can see it right over there: it's 39.10 grams per mole.

So, 39.10, one mole is equivalent to 39.10 grams if we're dealing with potassium. So this calculation will tell me moles of potassium. Now I have exactly one potassium atom for every potassium chloride molecule.

Whatever this number is, I'm going to have the same number of moles of potassium chloride. But just to make that clear, I will write this down: I have one mole of potassium chloride for every one mole of potassium.

You can already see how the units will cancel out. That will cancel with that, that will cancel with that, and so this calculation is going to tell me moles of potassium chloride. But I want to know the mass of potassium chloride.

So then I will multiply this by the molar mass times 74.55 grams of potassium chloride for every mole of potassium chloride. This will cancel with this, and this will tell me how many grams of potassium chloride I actually have.

So let's get the calculator out again. So I have 0.099 divided by 39.10, divided by 39.10, times 1, times 74.55.

I'm going to do this in another color; just makes it look nice. 74.55 is going to be equal to that. And then let me think about my significant figures or my significant digits here.

See, out of all of the information I used, I had this: I have three significant figures here, I have three here, I have four here, I have four here. So I'm multiplying a bunch of things and dividing, so I have to take the minimum number of significant figures, which is three.

So I will round to three significant figures, which is 0.189 grams. So this is... I'll do this in a new color: 0.189 grams of potassium chloride, which is exactly what they are asking us, and we are done.