Finding the empirical formula of iron oxide?

Sam and Bob are conducting an investigation to determine the empirical formula of iron oxide. They start with an 85.65g piece of iron metal and burn it in air. The mass of the iron oxide produced is 118.37g. Sam thinks the empirical formula of iron oxide is Fe3O4 and Bob thinks it is FeO. Use what you know about how to determine the empirical formula of a compound.

Nov 21, 2015

${\text{Fe"_3"O}}_{4}$

Explanation:

So, if you assume that all the mass of iron took part in the reaction, you can say that the difference between the mass of the product and the mass of iron will represent the mass of oxygen.

${m}_{\text{product" = m_"iron" + m_"oxygen}}$

${m}_{\text{oxygen" = "118.37 g" - "85.65 g" = "32.72 g}}$

Now that you know how much iron and how much oxygen you have in the iron oxide, you can use the two elements' respective molar masses to figure out how many moles of each you have.

For iron, you will have

85.65color(red)(cancel(color(black)("g"))) * "1 mole Fe"/(55.845color(red)(cancel(color(black)("g")))) = "1.534 moles Fe"

For oxygen, you will have

32.72color(red)(cancel(color(black)("g"))) * "1 mole O"/(16.0color(red)(cancel(color(black)("g")))) = "2.045 moles O"

To determine the empirical formula of the iron oxide, you need to find the smallest whole number ratio that exists between the two elements in the compound.

To do that ,divide both values by the smallest one.

"For Fe: " (1.534color(red)(cancel(color(black)("moles"))))/(1.534color(red)(cancel(color(black)("moles")))) = 1

"For O: " (2.045color(red)(cancel(color(black)("moles"))))/(1.534color(red)(cancel(color(black)("moles")))) = 1.333

To get the smallest whole number ratio that exists between the two elements, multiply both values by $\textcolor{b l u e}{3}$. This will help you get rid of the decimal fraction for oxygen.

The empirical formula of the iron oxide will thus be

$\left({\text{Fe"_1"O"_1.333)_color(blue)(3) implies color(green)("Fe"_3"O}}_{4}\right)$