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

Jun 12, 2017

${\text{342 g mol}}^{- 1}$

#### 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, $2 \times \text{Al}$
• three moles of sulfur, $\textcolor{b l u e}{3} \times \text{S}$
• twelve moles of oxygen, $\textcolor{b l u e}{3} \times 4 \times \text{O}$

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

$2 \times {M}_{\text{M Al") + color(blue)(3) xx M_ ("M S") + 12 xx M_ ("M O}}$

You will thus have

$2 \times {\text{26.981538 g mol"^(-1) + color(blue)(3) xx "32.065 g mol"^(-1) + 12 xx "15.9994 g mol}}^{- 1}$

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))))