If a sample of N2O4 contains 5.55 x 10^22 nitrogen atoms, what is the mass of the sample (in g)?

Since we are dealing with atoms and converting to a mass, we will need Avogadro's number at some point.  As a reminder, Avogadro's number is 6.022x10²³, and it is equal to 1 mole.

We will also need the molar mass of our compound as a conversion factor.  This can be calculated using the Periodic Table.  According to the Periodic Table, nitrogen has a molar mass of 14.01 g/mol and oxygen has a molar mass of 16.00 g/mol (both are approximate, of course).  Therefore, the molar mass of N₂O₄ is (14.01*2) + (16.00*4), which is 92.02 g/mol.

To solve for mass, start with the given data:

As shown, there are 2 moles of nitrogen in every 1 mole of dinitrogen tetroxide; I used this ratio to cancel the moles of nitrogen, and then multiplied by the molar mass of the compound for a mass in grams.

4.15 g N₂O₄

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