How do you find the percentage composition of a compound that contains 17.6 g of iron and 10.3 g of sulfur? The total mass of the compound is 27.9 g.

Aug 28, 2017

Here's how you can do that.

Explanation:

Your goal here is to figure out the mass of iron and the mass of sulfur present in exactly $\text{100 g}$ of this compound, which is what you need in order to know the compound's percent composition.

The problem provides you with the mass of iron and with the mass of sulfur present in $\text{27.9 g}$ of this compound, so you must use this information to scale up your sample from $\text{27.9 g}$ to $\text{100 g}$.

To do that, set up the known composition of the compound as a conversion factor.

To find the number of grams of iron present in $\text{100 g}$ of compound, set up the conversion factor like this

$\text{17.6 g iron"/"27.9 g compound}$

You will end up with

100 color(red)(cancel(color(black)("g compound"))) * "17.6 giron"/(27.9color(red)(cancel(color(black)("g compound")))) = "63.1 g iron"

To find the mass of sulfur present in $\text{100 g}$ of compound, you can either use a conversion factor set up in a similar manner

100 color(red)(cancel(color(black)("g compound"))) * "10.3 g sulfur"/(27.9color(red)(cancel(color(black)("g compound")))) = "36.9 g sulfur"

or use the fact that the compound contains only iron and sulfur to say that the mass of sulfur will be equal to

$\text{100 g compound " - " 63.1 g iron = 36.9 g sulfur}$

You now know the mass of iron and the mass of sulfur present for every $\text{100 g}$ of compound, so you can say that the compound has the following percent composition

• $\text{63.1% iron}$
• $\text{36.9% sulfur}$

Here % means per $\text{100 g}$ of compound.

The values are rounded to three sig figs.