Two Step Mole Conversions

Two Step Conversions: Grams --> Formula Units/particles/molecules/atoms
The process is much the same except now you have to go two steps.  If you want to go from grams to formula units/particles/molecules/atoms then you multiply the number by 1 mol/grams and by 6.022 x 10^23/1 mol.

Ex.  There are 250g worth of pennies.  How many molecules of atoms of copper are present?
Atomic mass= 58.9
molar mass= 58.9g/mol

250g x   1 mol    x 6.022 x 10^23 -- 2.6 x 10^24 molecules C
           58.9g/mol         1 mol

Ex.  An Olympic sized pool has 2.5 x 10^9 g of water in it.  How many atoms of oxygen are present in an Olympic sized pool?
water=H2O
molar mass= 2 O @ 16.0
                     1 H @   1.0
                                        =33g/mol

2.5 x 10^9g x 1mol x 6.022 x 10^23 x   2 atoms   -- 9.1 x 10^31 atoms O
                      33.0g         1 mol            1 molecule  

Two Step Conversions: Formula Units/particles/molecules/atoms --> Grams
If you want to go from formula units/particles/molecules/atoms to grams you go through a similar process.  This time you multiple the number of molecules by 1 mol/6.022 x 10^23 and then by grams/1 mol.  If it is atoms and you have to account for multiple atoms in each molecule, you have to account for that and divide as necessary.

Ex. There are 300 atoms in a sheet of aluminum.  What is its mass in grams?
atomic mass= 27.0
molar mass  = 27.0g/mol

300 atoms x         1 mol        x 27.0g -- 1.3 x 10 ^-20g
                     6.022 x 10^23    1 mol

Ex. There are 2500 molecules of table salt (NaCl) in a salt shaker.  How many grams of salt is there present?
molar mass= 1 Na @ 23.0
                     1 Cl  @ 35.5
                                        = 58.5g/mol

2500 molecules x        1 mol        x 58.5g -- 2.4 x 10^-19g
                            6.022 x 10^23   1 mol