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## AP®︎/College Chemistry

### Course: AP®︎/College Chemistry>Unit 1

Lesson 4: Composition of mixtures

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

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.

## Want to join the conversation?

• At , why does 1 mole of K equal 1 mole of KCl? Shouldn't 1 mole of K and 1 mole of Cl equal 2 moles of KCl? • A mole tells you the amount of something, in units of Avogadro's number. It doesn't matter how big or small the molecule is, just how many of them there are. Here, it takes 1 mole of K and 1 mole of Cl to make 1 mole of KCl because KCl is a bigger molecule than K or Cl and one molecule needs exactly 1 K and 1 Cl atom. If you have 2 moles of KCl in a substance, you'd have 2 moles of K, not 1, because each KCl molecule contains 1 potassium atom.
• I'm so confused... why doesn't all the KCl equal 0.45g?
And what constitutes the other mass? • Well KCl is basically just salt so ingesting all that salt at once isn't the most pleasant. So pill manufacturers put in other ingredients to make these sort of things more palatable. This includes things like sugars and food dyes often. If the supplement comes in some kind of starch casing that will also contribute to the mass.

Hope that helps.
• Is the reason the final answer isn’t equal to the total mass of the supplement because the supplement isn’t just KCl? • why 1 mole KCl is equal to 1 mole K (since sal writes 1 mole KCl/1 mole K)?

am I right that this idea comes bcs KCl always contains atoms (no matter atoms K or Cl)?, so when I take 1 mole of KCl, it always counted as 6,22x10^23 atom (1 mole)? • Right, one mole of KCl is 6.022•10^23 molecuoes of KCl. When you split it apart, you get 6.022•10^23 atoms of potassium, and the same amount of chlorine atoms.

For something like H²0, one mole of water molecules has two moles of hydrogen atoms and one mole of oxygen atoms.

And don't get confused with this: mol is the abbreviation for mole, so they mean the same.
• Would 0.189g of K not be rounded to two sig figs (0.19g) because 0.099 is two sig figs, not three?
(1 vote) • Sal forgot to include all the digits for the 22.0% calculation around . And of course 22.0% has three sig figs which should have resulted in a product with three sigs as well (since the 0.450 g had three sig figs too). And so the answer should have been 0.0990 g. Which means his final answer of 0.189 g is correct and has the correct number of sig figs even if he didn't show it correctly in his work.

Hope that helps.
• Can someone please explain significent figs? That concept is new to me( I've only heard in on KA but I'm learning chem only from KA and none of it really makes sense)
(1 vote) • At , Sal says that all the potassium is present as potassium chloride. What if the supplement is a mixture of two molecules. Say for example potassium chloride and potassium oxide (KCl & K2O), or even potassium chloride and silver oxide (KCl & Ag2O) where potassium isn't present in the second molecule. Then how do we calculate the percentage of potassium here? What are the main differences in the calculation?
(1 vote) • In the first case you'd have to find one way of separating the two chemicals containing potassium. Then after measuring their individual masses the calculation becomes similar to what Sal did.

The second case you'd have to separate potassium containing chemical from the rest of the supplement. And again get the mass of the potassium chemical and do Sal's calculation. Most supplements don't solely contain the supplement but other things like flavorings or pill casings which need to be separated.

Hope that helps.
(1 vote)
• Just a simple question if anyone can assist me. How does he multiply the what decimal of a total potassium mole is present by 74.55 (molar mass of KCl). I mean, aren't they different. How can you multiply one unit by another, and get how many moles of KCl is present?
(1 vote) • So Sal is using something called dimensional analysis to solve this problem. This involves multiplying an initial number by a series of fractions to get your answer. Now the type of fraction (whether you want one fraction or its reciprocal) is what matters here to get the correct answer. Every time Sal multiplies two numbers together he also cross cancels the same unit along the diagonal so that each time his answer has a new unit.

So for example he fist multiples the mass of potassium in grams (0.099g of K) by the molar mass of potassium. But he doesn't multiply simply by 39.10 g/mol as the periodic table gave him, he takes the reciprocal of the molar mass so that the unit grams of K cross cancel and his answer will have units of moles of K.

Essentially he is doing a conversion at each step until he arrives at an answer with the correct units. So Sal converts grams of K to moles of K, then moles of K to moles of KCl, then moles of KCl to grams of KCl. Dimensional analysis is used quite widely in chemistry and physics as a quick conversion tool.

Hope that helps.
(1 vote)
• why are 3 sig figs used in the final answer and not 2? since we are multiplying 0.099, which only has 2 sig figs, do we not take that value into account for the final answer, since it was calculated from the given information?
(1 vote) • I've explained this before on this video before, but Sal made a mistake at by not including an extra zero at the end of 0.099 g. If Sal begins with 0.450 g and he multiplies it by 22% (0.22), which is an exact number, then he should retain the same number of sig figs from the 0.450, which is three here. So technically Sal should be doing the last calculation using 0.0990 g.

Hope that helps.
(1 vote)
• I am trying to do the question through Cl but am getting a different answer. Since there is 22% K isn't there going to be 78% Cl and if there is then I did the same process as Sal but didn't get the same answer as him.
(1 vote) ## 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.