Peroxyacylnitrate (PAN) is one of the components of smog. It...

Peroxyacylnitrate (PAN) is one of the components of smog. It is a compound of $\mathrm{C}, \mathrm{H}, \mathrm{N},$ and $\mathrm{O} .$ Determine the percent composition of oxygen and the empirical formula from the following percent composition by mass: 19.8 percent $\mathrm{C}, 2.50$ percent $\mathrm{H}, 11.6$ percent $\mathrm{N}$. What is its molecular formula given that its molar mass is about $120 \mathrm{~g}$ ?

Key Concepts

Molecular Formula Determination

The molecular formula represents the actual number of atoms in a molecule and may be a whole-number multiple of the empirical formula. To find the molecular formula, the molar mass of the empirical formula is compared to the given molar mass of the compound. This comparison yields a multiplication factor that, when applied to the subscripts in the empirical formula, gives the molecular formula. This concept links empirical data with the molecular dimension of chemical compounds.

Percent Composition

This concept involves expressing the mass fraction of each element in a compound as a percentage of the total mass. In problems where some elemental percentages are given, and others must be found, the missing percentage is calculated by subtracting the sum of the given percentages from 100%. This is fundamental in analyzing the composition of compounds and is the first step in determining the empirical formula from mass data.

Empirical Formula Determination

Determining the empirical formula involves converting the percent compositions of the elements into moles by dividing by their atomic masses and then finding the simplest whole?number ratio among the elements. This process provides the simplest representation of the compound’s composition, which is an essential skill in stoichiometry and understanding chemical composition.

Transcript

00:01 So for this problem we have some compound abbreviated pan, and we know that it only contains carbon, hydrogen, nitrogen, and oxygen.

00:08 And the first thing we want to do is we want to find the percent composition of oxygen.

00:12 Well, we know we can do that by subtracting out the percent compositions of the other three elements to isolate oxygen.

00:20 So if you have 100 percent, we subtract out the percent mass of carbon, which is 19 .8 percent.

00:32 Subtract out the percent mass of hydrogen, 5 percent, and we do the same thing for nitrogen.

00:44 And when you do that, we will see that the percent composition of hydrogen is 66 .1 percent.

00:53 And the second thing we're supposed to do is worth to find the empirical formula.

00:57 So if we assume that the compound has a mass of 100 grams, which we will always do for percent composition problems, then that means we can isolate the mass of each of these and then subsequently find moles.

01:13 So let's see that for carbon.

01:15 Well, if the compound is 19 .8 % carbon and it hypothetically weighs 100 grams, then we know it weighs 19 .8 grams.

01:28 To get moles of carbon divided by its atomic mass, which is 12 .01, and we get 1 .65 moles of carbon.

01:38 For hydrogen, we have 2 .50 grams of hydrogen.

01:45 We divide by its atomic mass to get moles of hydrogen.

01:49 And we get 2 .48 moles of hydrogen.

01:54 We do the same thing for nitrogen.

01:57 11 .6 grams, because it's 11 .6 % nitrogen.

02:07 Divide by the atomic mass, which is 14 .01.

02:11 And you get 0 .83 moles of nitrogen...