# 8g of "E"_2"O"_3 contain 5.6g of "E". How many moles of "E" does a 16.8-g smaple of element "E" contain?

Nov 15, 2016

$\text{0.3 moles}$

#### Explanation:

The first thing to notice here is that $1$ mole of your unknown compound contains

• two moles of element $\text{E}$, $2 \times \text{E}$
• three moles of oxygen, $3 \times \text{O}$

Now, use the total mass of the sample and the mass of element $\text{E}$ to calculate the mass of oxygen.

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{mass of sample" = "mass of E" + "mass of O}}}}$

Plug in your values to find

$\text{mass of O" = "8 g" - "5.6 g" = "2.4 g}$

Use the molar mass of oxygen to calculate how many moles you have in this sample of ${\text{E"_2"O}}_{3}$

2.4 color(red)(cancel(color(black)("g"))) * "1 mole O"/(16.0color(red)(cancel(color(black)("g")))) = "0.15 moles O"

This means that the $\text{8-g}$ sample of ${\text{E"_2"O}}_{3}$ contains

0.15 color(red)(cancel(color(black)("moles O"))) * "2 moles E"/(3color(red)(cancel(color(black)("moles O")))) = "0.10 moles E"

Now, notice that you have

$\left(16.8 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g E"))))/(5.6 color(red)(cancel(color(black)("g E}}}}\right) = 3$

This means that $\text{16.8 g}$ of element $\text{E}$ will contain three times as many moles as $\text{5.6 g}$ of element $\text{E}$.

Therefore, you can say that

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{moles E in 16.8 g" = 3 xx "0.10 moles" = "0.3 moles}}}}$

The answer must be rounded to one significant figure.