# Question 88388

Sep 19, 2017

${\text{SnO}}_{2}$

#### Explanation:

Your goal here is to figure out the smallest whole number ratio that exists between the number of atoms of tin and the number of atoms of oxygen in this compound, i.e. the empirical formula of the oxide.

In order to do that, you need to convert the mass of tin and the mass of oxygen to moles by using the molar masses of the two elements.

You will have

3.996 color(red)(cancel(color(black)("g"))) * "1 mole Sn"/(118.71color(red)(cancel(color(black)("g")))) = "0.03366 moles Sn"

1.077 color(red)(cancel(color(black)("g"))) * "1 mole O"/(15.9994color(red)(cancel(color(black)("g")))) = "0.06732 moles O"

Now, you need the ratio that exists between these two elements in the compound, so divide both values by the smallest one to get

"For Sn: " (0.03366 color(red)(cancel(color(black)("moles"))))/(0.03366color(red)(cancel(color(black)("moles")))) = 1

"For O: " (0.06732color(red)(cancel(color(black)("moles"))))/(0.03366color(red)(cancel(color(black)("moles")))) = 2#

Since $1 : 2$ is the smallest whole number ratio that can exist between these two elements in this compound--you can't have a whole number that is $< 1$ and $> 0$, so you must have $1$ as the smallest whole number for tin, you can say that the empirical formula is

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{Sn"_1"O"_2 => "SnO}}_{2}}}}$