Worked example: Analyzing the purity of a mixture | AP Chemistry | Khan Academy

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. It will likely be useful to have a periodic table handy to do it.

All right, so the way we're going to approach it is we're going to think about each of these compounds and try to figure out the percent chlorine by mass. 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.

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. 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.

Now I can remove my periodic table of elements. Let's first think about sodium chloride. So, percent chlorine... Actually, let me make a little table here; I think that'll be the most useful thing to do.

So here I will put the various compounds, and here I will put the percent Cl by mass.

So first, we can think about sodium chloride. I'll do all of these in a different color just to make things interesting. So sodium chloride... Chlorine's molar mass is 35.45 grams per mole. Then we need to divide that by the molar mass of the entire compound. 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 (22.99 + 35.45). Then I get it equal... It looks like it's a little bit over 60 percent. That's actually enough for us to go on because if this is approximately 61 percent, we see that that's 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 because 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. 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.

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. Its percent chlorine would be the molar mass of chlorine, 35.45, divided by the molar mass of the entire compound.

So that would be the molar mass of potassium, 39.10, plus the molar mass of chlorine, 35.45. We could try to calculate this, but even when you look at the numbers, you can see that the denominator 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 percent.

This is less than 61 percent, 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 percent. So we can rule that one out as well.

Now let's look at this last candidate, and I'm feeling good about it because something got mixed in. 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. I'll just write chlorine's molar mass, and I'm going to add that to the molar mass of lithium, which is actually quite low, 6.94 grams per mole.

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 (6.94 + 35.45) is equal to... It's roughly 84 percent chlorine by mass.

So this thing is approximately 84 percent chlorine by mass. 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.

Actually, based on these values—based on the 61 percent, the 84, and the 73 percent—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.