# 24.2538 grams of an unknown compound was found to contain 50.15% sulfur and 49.85% oxygen. What is the empirical formula?

Mar 6, 2016

${\text{SO}}_{2}$

#### Explanation:

Here's a great example of an empirical formula problem that can be solved without doing any actual calculation. All you really need here is a periodic table.

Notice that atomic oxygen has a molar mass of a little under ${\text{16.0 g mol}}^{- 1}$ and the sulfur has a molar mass of a little over ${\text{32.0 g mol}}^{- 1}$.

This means that in order to have a percent composition of approximately 50% for both elements, a given compound (that only contains sulfur and oxygen, of course) needs to have twice as many moles of oxygen than moles of sulfur.

Why twice as many? Because a mole of sulfur atoms is twice as heavy than a mole of oxygen atoms.

This means that the empirical formula for any compound that has a percent composition of ~~50% for both oxygen and sulfur must be

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {\text{S"_1"O"_2 implies "SO}}_{2} \textcolor{w h i t e}{\frac{a}{a}}}} |}$

$\frac{\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a a a a a}}{\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a a a a a}}$

Now, let's do some calculations to prove that this is the case. Your sample of the unknown compound will contain

24.2538color(red)(cancel(color(black)("g compound"))) * overbrace("50.15 g S"/(100color(red)(cancel(color(black)("g compound")))))^(color(purple)("50.15% S")) = "12.2506 g S"

24.2538color(red)(cancel(color(black)("g compound"))) * overbrace("49.85 g O"/(100color(red)(cancel(color(black)("g compound")))))^(color(purple)("49.85% O")) = "12.0905 g O"

Use each element's molar mass to find how many moles you have present in the sample

$\text{For S: " 12.2506 color(red)(cancel(color(black)("g"))) * "1 mole S"/(32.065color(red)(cancel(color(black)("g")))) = "0.38205 moles S}$

$\text{For O: " 12.0905color(red)(cancel(color(black)("g"))) * "1 mole O"/(15.9994color(red)(cancel(color(black)("g")))) = "0.75568 moles O}$

To get the mole ratio that exists between the two elements in the sample, divide both values by the smallest one

"For S: " (0.38205color(red)(cancel(color(black)("moles"))))/(0.38205color(red)(cancel(color(black)("moles")))) = 1

"For O: " (0.75568color(red)(cancel(color(black)("moles"))))/(0.38205color(red)(cancel(color(black)("moles")))) = 1.9780 ~~ 2

Once again, the empirical formula of the unknown compound comes out to be

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {\text{S"_1"O"_2 implies "SO}}_{2} \textcolor{w h i t e}{\frac{a}{a}}}} |}$