How many atoms of aluminum are there in a sample with a mass of 100.0 grams?

In order to find the number of moles in a sample we are tasked with first finding the number of moles in that sample.  This is because the moles in a substance indicates the amount of the substance that contains the same number of particles as 12 g of the Carbon-12 isotope [or equivalent to 6.02 × 10²³ (which is used as a standard in the world of moles).

Now,
If moles = mass ÷ molar mass

then mol of aluminum = 100 g ÷ 27g/mol
                                   
                                     = 3.704 mol

Now that you have calculated the moles then you can do a simple ratio and multiplication at arrive at the number of atoms that would be present in the 100 g of aluminum.

                  if 1 mol of aluminum contains 6.02 × 10²³ atoms
                 then let 3.704 mol of aluminum contain x

                  ∴  x = 3.704 mol  × (6.02 × 10²³)
                         
                         = 2.23 × 10²⁴

∴ 100 g of Al would contain  ~ 2.23 × 10²⁴ atoms

Density and pressure

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