Contains 63.65% nitrogen and 36.35% oxygen by mass what is the empirical formula for this compound

The empirical formula is NO₂.  

Assume that you have 100 g of the compound.

Then you have 63.65g N and 36.35 g O.

Now, we must convert these masses to moles and find their ratios.

From here on, I like to summarize the calculations in a table.

Element  Mass/g    Moles    Ratio     Integers  

     N         63.65     4.543      1                  1

     O        36.35      2.2719    2.000         2

The empirical formula is NO₂.

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