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Worked example: Analyzing the purity of a mixture

Elemental analysis can be used to analyze the purity of a sample. For example, a pure sample of NaCl should contain 61% chlorine by mass. If elemental analysis tells us that the sample actually contains 73% chlorine by mass, this suggests that our sample has been contaminated by a compound containing a higher mass percent of chlorine. Created by Sal Khan.

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  • male robot hal style avatar for user Krish
    At , Sal says that you can figure out how much % of the sample is NaCl and LiCl based on the percentages of chlorine by mass(73%, 61%, and 84%) . How would you find how much % of the sample is NaCl and LiCl?
    (12 votes)
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    • aqualine ultimate style avatar for user Stefan van der Waal
      If the sample was pure NaCl, the % of chlorine by mass would be 61%. If it were pure LiCl, it would be 84%. We can use these two points to draw a line:
      percentage chlorine by mass = 61% + 23% * percentage LiCl by mass
      This becomes 73% = 61% + 23% * x
      Solving for x gives x = 52%. So 52% of the sample by mass is LiCl and 48% is NaCl
      (17 votes)
  • leaf green style avatar for user dyoffis
    so it contains 73% chlorine by mass, i know we used the concept of averages to get the idea about which one was increasing the percent mass of Cl but like how can we be sure it is only LiCl, there could be some KCl in there too and since the mass ratio is almost 1:1 for KCl, it wouldnt drag the Cl ratio down too heavily anyway, and if we add enough LiCl eventually the ratio will just jump back up for Cl, am i right? if so then this is such a frustrating question as it is not being specific in details and expecting us to be sure about our answer, i really cant get how can one even know where to start in questions like this, so thats just adding to my irritation, can someone please help?
    (3 votes)
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    • leaf red style avatar for user Richard
      Good point. Sal assumes that the only two options are a pure sample of sodium chloride (only sodium chloride) or a mixture (two or more compounds) of sodium chloride and only one other compound. However it possible that it could be a mixture of three or four compounds.

      If it contained NaCl, KCl, and LiCl, they would all effect the percentage of chloride in the sample.

      Additionally, sodium iodide could be in there too. We're checking for chloride, and just because sodium iodide doesn't have any chloride, that wouldn't rule it out as being part of the mixture. It just wouldn't be detected if we checked only chloride content.

      I guess we assume it could potentially only be a mixture of two compounds because of the wording of the question. "You suspect that it may have some NaI, KCl, or, LiCl as well.", with emphasis on the "or" part. It's saying that if indeed it is a mixture, it would only contain one of those three contaminants.

      Hope that helps.
      (5 votes)
  • old spice man green style avatar for user Alexander Kronen
    At , Sal says that you can figure out how much % of the sample is NaCl and LiCl based on the percentages of chlorine by mass(73%, 61%, and 84%) . How would you find how much % of the sample is NaCl and LiCl?
    (2 votes)
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    • piceratops ultimate style avatar for user ANB
      There are multiple ways to do this but the most intuitive way to write it out is .73=.61(1-x) + 84(x) with x being the percent of LiCl. You first expand to get .73=.61-.61x+.84x. This simplifies to .12=.23x. That simplifies to .52=x. This means that the 52% of the sample if LiCl while 48% of the sample is NaCl.
      (8 votes)
  • blobby green style avatar for user emilrichardwang
    I'm confused about whether or not there is only LiCl and NaCl. This is because LiCl is more than 50% of the mixture, but the question says that the substance is mostly NaCl. Does this mean that there are more elements present?
    (4 votes)
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  • blobby green style avatar for user nourhumaid6
    So, just adding those percentages together for NaCl and LiCl 61+84 then we divide it by 2 which would give us the percentage in the question 72.5 which is almost 73%
    Is that how to do it to make sure it’s correct?
    (2 votes)
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    • leaf red style avatar for user Richard
      Pretty much, yes. If we have a mixture of sodium chloride and lithium chloride with % chlorines of 61% and 84%, then their mixture’s % chlorine will be somewhere between those two numbers. Using an arithmetic average though assumes that the two salts are mixed in equal amounts which isn’t always true. So it’s not that their average, 72.5%, is close to the samples chlorine %, 73%, it’s that the sample’s chlorine % is in between the pure salt’s chlorine %s.

      Hope that helps.
      (4 votes)
  • boggle yellow style avatar for user iambush
    But how can we be sure that both NaCl and LiCl in the sample are exactly 1 mole? If we assume there is just more NaCl in the sample (for instance 2 moles), but the amount of LiCl is 1 mole, while the percentage of Cl in NaCl stays the same ~61%, in total we would get something like this:

    - Amount of Cl in NaCl = 71 g
    - Amount of not Cl in NaCl = 46 g
    - Amount of Cl in LiCl = 35.5 g
    - Amount of not Cl in LiCl = 7 g

    In total we would get this percentage of Cl in the sample:
    - (71 + 7)/(71+7+35.5+46) = ~49%
    Is there something wrong in this assumption?
    (0 votes)
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    • leaf red style avatar for user Richard
      Since we’re using mass percent the amount of moles is irrelevant. If we assume we had pure sodium chloride, we would have the same 61% mass percent for the chlorine in the sample if we had 1 mole or 100 moles. Likewise, if the sample is contaminated with lithium chloride, be it 1 mole or 100 moles, it would increase the sample’s chlorine percent mass above 61%.

      Hope that helps.
      (3 votes)
  • old spice man green style avatar for user Alexander Kronen
    At , Sal says that you can figure out how much % of the sample is NaCl and LiCl based on the percentages of chlorine by mass(73%, 61%, and 84%) . How would you find how much % of the sample is NaCl and LiCl?
    (0 votes)
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  • marcimus purple style avatar for user l
    i tried calculating the cl percentage by mass for the whole sample in the same way we did for each compound.
    (35.45+35.45)/(22.99+35.45)+(6.94+35.45) = 0.7031 = 70% cl by mass in NaCl and LiCl. shouldnt it be 73%? why did i get 70%?
    (0 votes)
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  • blobby green style avatar for user Matrew File
    Shouldn't the Na% also be counted when analyzing NaI?

    If it's pure NaCl, then the mass percentage is equal to the relative atomic mass ratio, but when NaI is present, for the same amount of matter it's like replacing some Cl with I, so Cl% should decrease rather than stays the same.
    (0 votes)
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  • blobby green style avatar for user yousifemad31
    if the percentage of nacl was 72% would that have made it a pure sample?
    (0 votes)
    Default Khan Academy avatar avatar for user

Video transcript

- [Instructor] We're told, you have a solid that you know is mostly sodium chloride, you suspect that it might have or it may have some sodium iodide, potassium chloride or lithium chloride as well. When you analyze a sample you see that it contains 73% chlorine by mass. Is the sample pure sodium chloride? If not, what else does it likely have in it? So pause this video and see if you can figure that out and it will likely be useful to have a period table handy to do it. All right, so the way we're going to approach it is we're gonna think about each of these compounds and try to figure out the percent chlorine by mass. And to do that, we have to think about the molar masses of the various constituent atoms or the various constituent elements that make up those compounds. And to figure out the molar mass for each element I just have to look at its average atomic mass and say, okay I'm going to have that many grams per mole, if I have a mole of that atom. Sodium, chlorine, iodine, potassium, and lithium. And the sodium's average atomic mass is 22.99, chlorine is 35.45, iodine is 126.90, potassium is 39.10, and lithium is 6.94. And so now I can remove my period table of elements. And so let's first think about sodium chloride. So, percent chlorine... Actually let me make a little table here, I think that will be the most useful thing to do. So here I will put the various compounds. Compound. And here I will put the percent Cl by mass. By mass. So first we can think about sodium chloride and I'll do all of these in a different color just to make things interesting. So sodium chloride. So chlorine's molar mass is 35.45 grams per mole. And then we need to divide that by the molar mass of the entire compound. So that's going to be the molar mass of sodium at 22.99 grams per mole. Plus the molar mass of chlorine again at 35.45 grams per mole. So we have 35.45 divided by, open parentheses, 22.99 plus 35.45, close the parentheses. Then I get it equal. So it looks like it's a little bit over 60%. And that's actually enough for us to go on, because if this si approximately 61% we see that's that a very different than 73%. So already it's very clear that to the first question, is the sample pure sodium chloride? No it's not, cause it has a different percentage of chlorine by mass than pure sodium chloride would. This would be what pure sodium chloride would look like. So it must have been mixed in with something that has a higher percentage of chlorine by mass. So let's look at the other candidates. So we can look at sodium iodide. So sodium iodide. What's its percent chlorine by mass going to be? Well this has no chlorine by mass, so this is zero. So if you had sodium iodide mixed in with sodium chloride, that would reduce the average. That would reduce the percent chlorine by mass. It wouldn't increase it. So we already can rule out this character. Let's look at the next candidate. Potassium chloride. I'll write that right over here. Potassium chloride. And so its percent chlorine would be the molar mass of chlorine, 35.45 divided by the molar mass of the entire compound. And so that would be the molar mass of potassium, 39.10. Plus the molar mass of chlorine, 35.45. And we could try to calculate this, but even when you look at the numbers you can see that the denominator here, this denominator right over here is bigger than what we had for sodium chloride. And we have the same numerator. So if the denominator is bigger, that means we're going to get a lower value than 61%. This is less than 61%. And since this has a lower percent chlorine by mass, if it was mixed in, it would average down from 61%. It wouldn't go up to 73%, so we can rule that one out as well. And now let's look at this last candidate and I'm feeling good about it because something got mixed in. So let's look at lithium, lithium chloride. What is its percent chlorine by mass? Well it's going to be the molar mass of chlorine, 35.45. Divided by the molar mass of the entire compound, and I'll just write chlorine's molar mass. And then I'm gonna add that to the molar mass of lithium which is actually quite low, 6.94 grams per mole. So once again, when we compare to sodium chloride, we have the same numerator. We have the same numerator but we clearly have a smaller denominator. This value is smaller than this value and the other number is the same. So this has a smaller denominator, which means that the whole value is going to be larger. This is going to be greater than 61%. We take 35.45, divided by, open parentheses, 6.94 plus 35.45, close parentheses, is equal to it's roughly 84% chlorine by mass. So this thing is approximately 84% chlorine by mass. So that does the trick. If you had some lithium chloride mixed in with your sodium chloride, it could increase or it would increase the percent chlorine by mass above 61%. And actually based on these values, based on the 61%, the 84% and the 73%, you could actually figure out what percent is your sample of sodium chloride and lithium chloride if you assume those are the only two things in it.