>> Welcome to a screencast on moles and chemical formulas.
Here's an example of determining a chemical formula.
This is actually a lab that we sometimes do in class.
If you take a piece of lead, in this case it weighs 4.380 grams, cover it with lots and lots
of sulfur, and then put it in the fume hood and heated very vigorously with a Bunsen burner.
And you'll have -- you'll do this in a crucible with the lid on,
what ends up happening is a reaction takes place between the lead and the sulfur.
The excess sulfur burns off, and in this case, 0.678 grams of sulfur actually reacted
with the 4.380 grams of lead and made a lead sulfur compound.
So a couple questions.
How many moles of lead does the compound contained?
How many moles of sulfur does the compound contain?
And then what's the formula of this compound?
OK. So the first thing we're going
to do is determine how many moles of lead the compound contains.
And we start with the number of grams of lead we know we have,
and we're going to want to convert this into moles.
So we look on the periodic table and see that the atomic mass of lead is 207.2 grams.
One mole of lead equals 207.2 grams of lead.
We set up our conversion factor to cancel out grams of lead, and we do the calculation,
and we find that this is 0.02114 moles of lead.
Second part of this question, how many moles of sulfur does the compound contain?
And we do this in pretty much the same way as we did the previous part of the problem
with simply we have different numbers because we have a different substance.
So we have 0.678 grams of sulfur, and the atomic mass of sulfur is 32.06 grams.
So one mole of sulfur weighs 32.06 grams, we want grams of sulfur to cancel,
and when we do the math, we get 0.211 moles of sulfur in this compound.
Now, you might notice something about the numbers we got for moles,
and we're going to now try to find the formula of the compound.
And the key idea is that if we have a compound, the ratio of the particles that make
up the compound is the same as the ratio of the moles of the particle --
of the substances that make up the compound, and that's going to give us the chemical formula.
In this case, we have lead and sulfur which are going to be ions, it's a metal with a nonmetal.
So the ratio of ions of lead to ions of sulfur is going to be the same as the ratio of moles
of lead to moles of sulfur, and that's the same as the ratio in the formula.
OK, let's see how this works.
Usually the easiest thing to do is to take your moles of each substance,
and then see what they give you for a ratio.
And in this one, you have 0.02114 and 0.0211.
Those are about the same number.
So the ratio is going to be one to one.
But if you don't have an obvious ratio, it's usually good to take the bigger number divided
by the smaller number and see what you get.
And in this case, of course, you get approximately one.
Remember, we're doing an experiment, so we round off to the right number of significant figures,
and we may have to kind of pay attention to the approximation, but essentially,
this is a one mole of lead to one mole of sulfur ratio.
Therefore, the empirical or simplest formula for this compound would be Pb1S1.
And of course, we typically just write that as PbS.
And the name of this would be lead II sulfide.
Remember, sulfur is going to make a negatively charged sulfide ion, and lead is not going
to be too predictable with it's ionic charges, but if it's a one to one ratio,
then that means that the lead has to be the plus two ion.
So this is an important kind of summary concept.
In any sample of a chemical compound, the mole ratio of the elements is going to be the same
as the atom or potentially ion ratio of the things that make it up.
And we just saw this with a one to one ratio for lead and sulfur.
But if we have the compound -- molecular compound C2H6O,
then that's going to contain carbon, hydrogen, and oxygen, and exactly a two to six
to one ratio, both in terms of atoms and in terms of moles.
Now, that we've determined the empirical formula of this compound,
let's also find its formula mass, its molar mass, and the mass percent
of lead and sulfur in this compound.
First of all, the formula mass.
The formula mass is the mass of either one molecule if we're dealing
with a molecular compound, or one formula unit if we're dealing with an ionic compound,
which is what we have in this case.
So the formula unit for PbS for lead II sulfide is one lead ion and one sulfide ion.
And the mass of one lead ion is essentially the same as the mass
of one lead atom, which is 207.2 amu.
The mass of a sulfur atom is about the same as the mass of a sulfide ion, 32.06 amu.
Add those together, 239.3 amu.
So the basic unit, the fundamental unit of this compound,
the formula unit has a mass of 239.3 amu.
How about the molar mass of PbS?
Well, the molar mass is actually going to be the same value, but different units.
Molar mass is the mass of one mole of the substance.
And since PbS is made up of lead and sulfur, and one mole of PbS contains one mole of lead,
that's 207.2 grams, and one mole of sulfur 32.6 grams, that adds up to 239.3 grams.
So one mole of lead sulfide -- lead II sulfide weighs 239.3 grams,
and we often write the molar mass with the units
that weigh 239.3 grams per mole is what we would say the molar mass is of this compound.
Now, how about mass percent?
Well, the mass percent of anything is going to be the mass of that substance,
in this case lead, compared to the mass of the entire substance or compound, in this case,
the lead sulfide, and then multiplied by 100 to make it a percent.
So specifically, since one mole of lead sulfide weighs 239.3 grams,
so we're choosing that as our amount of substance, one mole of it,
it's going to contain one mole of lead which weighs 207.2 grams.
And then when you divide those two and multiply by 100, you get 86.59%.
And that is the mass percent of lead in this compound.
Very similarly, the mass percent of sulfur is going to be the mass of sulfur compared
to the massive total compound multiplied by 100, gives you percent 13.40%.
And since this compound is made up of two elements only, then the mass percent of sulfur
and the mass percent of lead is going to add up to 100%.
If we had more substances, then we'd add all of them together,
and that would give us a total of 100%.
One other thing to note is depending upon your significant figures and your roundoff,
it is possible to get your mass percents to not exactly add up to 100.
Of course, they really do.
But within your significant figures, sometimes there's a slight discrepancy.
So notice in this case, if you add up the mass percent of lead
and the mass percent of sulfur, you only get 99.99%.
And that's just a little artifact of the uncertainty and the significant figures.
And that's it for moles and chemical formulas.