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## AP®︎/College Chemistry

# Worked example: Calculating the mass of a substance in a mixture

AP.Chem:

SPQ‑2 (EU)

, SPQ‑2.B (LO)

, SPQ‑2.B.1 (EK)

Elemental analysis can be used to determine the amounts of substances in a mixture. For example, if elemental analysis tells us that a potassium supplement contains 22% K by mass, and we know that the K is present as KCl, we can calculate the grams of KCl in the supplement. Created by Sal Khan.

## Video transcript

- [Instructor] We're
told that a 0.450 gram potassium supplement contains
22% 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. So 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. And 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, could write it like that. And that is, I think, all we will need the periodic table of elements for. And so, how do we think
about how many grams of potassium chloride are
in the potassium supplement? Well what I could do is, I could say, "All right, what's the total
mass of my supplement," and multiply it by 22% to figure out what is the mass of potassium I have. So let me figure that out. So mass of potassium, that is going to be my 0.450 grams times 22%, which is going to be equal to, I'll get my calculator out, 0.450 times 22%, or .22, is equal to 0.099. 0.099. So that's how many grams
of potassium I have. And 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, and
then I could figure out, well, based on. 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. So we have 0.099 grams of potassium. And I wanna figure out how
many moles of potassium I have. So I'm gonna multiply that times, one mole of potassium has a mass of how many grams of potassium? And 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. And so, whatever this number is, I'm gonna 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. And you could 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 wanna know the mass
of potassium chloride. So then I will multiply
this by the molar mass, times 74, and I'm gonna
do this in another color, just makes it look nice, 74.55 grams of potassium chloride for every mole of potassium chloride. And so then, 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 one, times 74.55, times 74.55, is going to be equal to that. And then let me think about
my significant figures or my significant digits here. So let's see, out of all
of the information I used, 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, let me do this in a new color, 0.189 grams of potassium chloride, which is exactly what they are asking us. And we are done.