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?

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

• two moles of element `"E"`, `2 xx "E"`
• three moles of oxygen, `3 xx "O"`

Now, use the total mass of the sample and the mass of element `"E"` to calculate the mass of oxygen.

`color(blue)(ul(color(black)("mass of sample" = "mass of E" + "mass of O")))`

Plug in your values to find

`"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 `"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 `"8-g"` sample of `"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

`(16.8 color(red)(cancel(color(black)("g E"))))/(5.6 color(red)(cancel(color(black)("g E")))) = 3`

This means that `"16.8 g"` of element `"E"` will contain three times as many moles as `"5.6 g"` of element `"E"`.

Therefore, you can say that

`color(darkgreen)(ul(color(black)("moles E in 16.8 g" = 3 xx "0.10 moles" = "0.3 moles")))`

The answer must be rounded to one significant figure.