# The atomic weight of phosphorus is 30.974 u. What is the mass of a phosphorus sample which contains 0.585 moles of phosphorus atoms?

##### 1 Answer

#### Explanation:

You know that the atomic weight of phosphorus is equal to *unified atomic mass unit*.

The unified atomic mass unit is equivalent to

Now, the unified atomic mass unit is defined as

#"1 u" = 1.660539 * 10^(-24)"g"#

This means that the mass of **one phosphorus atom** will be

#30.974color(red)(cancel(color(black)("u"))) * (1.660539 * 10^(-24)"g")/(1color(red)(cancel(color(black)("u")))) = 5.14335 * 10^(-23)"g"#

You know that **one mole** of any element contains exactly **Avogadro's number**.

Well, if you know the mass of *one phosphorus atom*, you can use Avogadro's nubmer to determine what the mass of **one mole** of phosphorus atoms

#5.14335 * 10^(-23)"g"/color(red)(cancel(color(black)("atom"))) * (6.022 * 10^(23)color(red)(cancel(color(black)("atoms"))))/"1 mole" = "30.974 g/mol"#

Finally, if one mole of phosphorus atoms has a mass of

#0.585color(red)(cancel(color(black)("moles"))) * "30.974 g"/(1color(red)(cancel(color(black)("mole")))) = color(green)("18.1 g")#