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

Md Ariful Islam

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Md Ariful Islam

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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

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

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