Question

The chemical formula of ilmenite is `FeTiO_3`. What mass of titanium can be obtained from 500.0 g of ilmenite?

Answer 1

`"157.7 g Ti"`

Explanation:

Your strategy here will be to determine how many grams of titanium, `"Ti"`, are present in one mole of ilmenite by using the molar masses of ilmenite and of titanium.

Ilmenite's molar mass is equal to `"151.71 g mol"^(-1)`. This tells you that every mole of ilmenite will have a mass of `"151.71 g"`.

As you can see by inspecting the compound's chemical formula, one mole of ilmenite will also contain

• one mole of iron, `1 xx "Fe"`
• one mole of titanium, `1 xx "Ti"`
• three moles of oxygen, `3 xx "O"`

Since titanium has a molar mass of `"47.857 g mol"^(-1)`, you can say that `"151.71 g"` of ilmenite will contain `"47.857 g"` of titanium.

So, if you get `"47.857 g"` of titanium for every `"151.71 g"` of ilmenite, it follows that `"500.0 g"` of ilmenite will contain

`500.0 color(red)(cancel(color(black)("g ilmenite"))) * "47.857 g Ti"/(151.71 color(red)(cancel(color(black)("g ilmenite")))) = color(green)(|bar(ul(color(white)(a/a)"157.7 g Ti"color(white)(a/a)|)))`

The answer is rounded to four sig figs.

Notice that it's more practical to determine the percent composition of the compound because it makes the ratio of titanium to ilmenite easier to work with.

`"% Ti" = (47.857 color(red)(cancel(color(black)("g"))))/(151.71color(red)(cancel(color(black)("g")))) xx 100 = 31.545%`

This means that you get `"31.545 g"` of titanium for every `"100 g"` of ilmenite.