Question

The formula for aluminum sulfate is `Al_2(SO_4)_3`. What is the molar mass of aluminum sulfate to the nearest gram?

Answer 1

`"342 g mol"^(-1)`

Explanation:

The idea here is that the molar mass of aluminium sulfate, `"Al"_ 2("SO"_4)_color(blue)(3)`, will be equal to the sum of the molar masses of all the atoms that make up a mole of this compound.

As you can see, `1` mole of aluminium sulfate contains

• two moles of aluminium, `2 xx "Al"`
• three moles of sulfur, `color(blue)(3)xx "S"`
• twelve moles of oxygen, `color(blue)(3) xx 4 xx "O"`

Now, grab a Periodic Table and look for the molar masses of aluminium, sulfur, and oxygen

• `M_ ("M Al") = "26.981538 g mol"^(-1)`
• `M_ ("M S") = "32.065 g mol"^(-1)`
• `M_ ("M O") = "15.9994 g mol"^(-1)`

In order to find the molar mass of aluminium sulfate, you will need to do

`2 xx M_ ("M Al") + color(blue)(3) xx M_ ("M S") + 12 xx M_ ("M O")`

You will thus have

`2 xx "26.981538 g mol"^(-1) + color(blue)(3) xx "32.065 g mol"^(-1) + 12 xx "15.9994 g mol"^(-1)`

which will get you

`M_ ("M Al"_ 2("SO"_ 4)_ 3) = "342.150876 g mol"^(-1)`

Rounded to the nearest gram, the answer will be

`M_ ("M Al"_ 2("SO"_ 4)_ 3) = color(darkgreen)(ul(color(black)("342 g mol"^(-1))))`