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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.

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  • blobby green style avatar for user deross23
    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?
    (4 votes)
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    • piceratops ultimate style avatar for user Hecretary Bird
      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.
      (19 votes)
  • blobby green style avatar for user Sam Towney
    I'm so confused... why doesn't all the KCl equal 0.45g?
    And what constitutes the other mass?
    (7 votes)
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    • leaf red style avatar for user Richard
      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.
      (9 votes)
  • blobby green style avatar for user 808natedelamarter
    Is the reason the final answer isn’t equal to the total mass of the supplement because the supplement isn’t just KCl?
    (4 votes)
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  • starky sapling style avatar for user rip_braincells
    I am thoroughly confused. I really don't get the stuff about moles or how to use them. Can anyone please clarify that for me?
    (3 votes)
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    • leaf red style avatar for user Richard
      A mole of something is an Avogadro’s number of that thing, where Avogadro’s number is 6.022x10^(23). In the same way a dozen of something is 12 of that thing. So if I had a dozen atoms, I would have 12 atoms. If I had a mole of atoms, I would have 6.022x10^(23) atoms.

      Molar mass of a chemical is the mass, in grams, one mole that that chemical has. And it usually is in units of grams per mole, or g/mol. So here the molar mass of potassium chloride is 74.55 g/mol, which means that one mole of potassium chloride, 6.022x10^(23) potassium chlorides, has a mass of 74.55 grams.

      Hope that helps.
      (4 votes)
  • blobby green style avatar for user algifarihaikal123
    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)?
    (3 votes)
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    • blobby green style avatar for user johnminegammer
      Let's remember that mole e quantity measurement not a mass measurement, it means that, if I have a compound made of potassium and chlorine and the mass of the 22% of K is present in the supplement as KCl i have the same mole of both, cause for each molecule of KCl e have one potassium, lets callback the fact that mole is a quantity measurement
      (2 votes)
  • blobby green style avatar for user Ev
    Multiplying the mass of potassium by the percent present give us the grams of what?
    (1 vote)
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    • leaf red style avatar for user Richard
      The 0.450 gram isn’t the mass of potassium, it’s the mass of the entire potassium supplement. There are other ingredients in the supplement other than potassium.

      So, multiplying the mass of the supplement by the mass percent of potassium yields the mass of potassium in the supplement.

      Hope that helps.
      (5 votes)
  • sneak peak purple style avatar for user Lyric
    I want to understand this clearly. At first, the question states that there are 0.450 grams of a "potassium supplement". Then they gave us the percentage of potassium in it and the molar mass of KCl. But the question they ask is that "how many grams of KCl are in the supplement?" So, starting with the first line, what exactly is the potassium supplement? I thought it was KCl.
    (2 votes)
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    • leaf red style avatar for user Richard
      The potassium supplement is not entirely potassium chloride (KCl). As a potassium supplement, KCl would be the active ingredient since that contains the potassium. However, medication contains additional inactive ingredients which also contributes to the mass. These inactive ingredients can include sugar to make essentially a salt tablet more appetizing, the casing of the supplement to keep the pill intact, or a food dye.

      If the total mass of the supplement is 0.450 g, and the mass of KCl is 0.189 g, then only 42 % of the supplement contains the active ingredient while the remaining 58 % are the inactive ingredients.

      Hope that helps.
      (2 votes)
  • blobby green style avatar for user clowntown
    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)
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    • leaf red style avatar for user Richard
      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.
      (3 votes)
  • blobby green style avatar for user kalpal527
    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)
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    • leaf red style avatar for user Richard
      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.
      (3 votes)
  • blobby green style avatar for user Anshu
    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)
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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.