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# Worked example: Analyzing the purity of a mixture

AP.Chem:

SPQ‑2 (EU)

, SPQ‑2.B (LO)

, SPQ‑2.B.2 (EK)

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.

## Want to join the conversation?

- At6:26, 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?(6 votes)
- 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(11 votes)

- 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?(1 vote)
- 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)

- At6:26, 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?(1 vote)
- 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.(4 votes)

- 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?(2 votes)
- 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.(1 vote)- Sal explains that NaI would decrease the chlorine % starting at3:32.(2 votes)

- At6:26, 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?(1 vote)
- 6:26, 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?(1 vote)
- For the question: 1.02g of Mg supplement contains 25% Mg by mass also Mg is present in the supplement as MgO with a molar mass of 40.30g/mol. how many grams of MgO is in the magnesium supplement?

my approach to this question was somewhat intuitive and I was wondering what was off with my method since the question kept grading me wrong

25% of the sample is Mg which means that from 1.02g equivalent to 100%, Mg in grams in the sample is 0.255g

the relationship between Mg and MgO is 1 mol to 1 mol

- Mg which has an atomic mass of 24.31g/mol; meaning that 0.255g of Mg represents 0.01 mol of Mg and since the relationship with MgO is 1 to 1 then, Oxygen with an atomic mass of 16g/mol 0.01 mol will give us a corresponding weight in grams of 0.16g which in addition to the 0.255g of the Mg the total weight in grams of MgO in the supplement with a concentration of Mg 25% would be 0.415g

what is wrong with my approach that keeps grading me wrong?(0 votes)- That's an interesting way of getting to the answer, using the oxygen's molar mass. The math works and your method is valid. What looks like the issue is that you're rounding off you're intermediate answers too early. Really you should only round off at the final answer, accounting for sig figs. Otherwise you introduce rounding errors.

If you round off only at the end, and use correct sig figs, your answer should be 0.423 grams of MgO.

Hope that helps.(1 vote)

## 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.