– [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 periodic table handy to do it. All right, so let’s get our
periodic table of elements. And so I don’t have to keep going back to the periodic table of elements, let’s get all of the information
that we need from it. So I wanna think about
the average atomic masses of sodium, chlorine, iodine, potassium, and lithium. And 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
periodic table of elements. 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 different color just to make things interesting. So sodium chloride. Well, the average atomic
mass of chlorine is 35.45. 35.45. And if we divide that by
the average atomic mass of the entire compound,
the entire molecule here, well, then we’re going to have
the percent chlorine by mass. So that’s going to be 35.45 divided by. Sodium has an average
atomic mass of 22.99. And then the chlorine, of course, has an average atomic mass of 35.45. 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 is approximately 61%, 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 ’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
percent chlorine by mass. It wouldn’t increase it. So we already can rule out this character. Now let’s look at the next
one, potassium chloride. I’ll write that right over here. Potassium chloride. And so its percent
chlorine by mass is going to be the average atomic mass
of chlorine, which is 35.45, divided by the average atomic
mass of the whole thing. Average atomic mass of potassium is 39.10. And then the average atomic mass of chlorine of course is 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 chloride. What is its percent chlorine by mass? Well, it’s going to be
the average atomic mass of the chlorine divided
by the average atomic mass of the whole thing. I’ll just put the chlorine in here just ’cause I’m already in that mode. And then lithium, see, lithium, which has a fairly small
average atomic mass of 6.94. 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%. So out of all of the candidates, I’m liking lithium chloride. We can actually figure out this value. Actually, let me get the calculator out. 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 sodium
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?