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Worked example: Analyzing the purity of a mixture

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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.

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.