What is the mass percent of nitrogen in the dyeing agent, picric acid (#C_6H_3N_3O_7#)?

A compound's percent composition tells you how many grams of each constituent element you per per #"100 g"# of compound.

In your case, the mass percent of nitrogen will tell you how many grams of nitrogen you get in #"100 g"# of picric acid.

Now, notice that the problem provides you with the molar masses of the three elements that make up picric acid. This means that you can use the chemical formula of the compound to determine the mass of one mole of picric acid.

As you can see, one mole of picric acid contains

• six moles of carbon, #6 xx "C"#
• three moles of hydrogen, #3 xx "H"#
• three moles of nitrogen, #3 xx "N"#
• seven moles of oxygen, #7 xx "O"#

This means that the mass of one mole of acid will be

#6 xx "12.01 g mol"^(-1) + 3 xx "1.0079 g mol"^(-1) + 3 xx "14.01 g mol"^(-1) + 7 xx "16.003 g mol"^(-1) = "229.13 g mol"^(-1)#

So, if one mole of acid has a mass of #"229.13 g"#, and it contains three moles of nitrogen, it follows that the mass percent of nitrogen in picric acid will be

#( 3 xx 14.01 color(red)(cancel(color(black)("g"))))/(229.13color(red)(cancel(color(black)("g")))) xx 100 = color(green)(|bar(ul(color(white)(a/a)"18.34% N"color(white)(a/a)|)))#