As with all with these problems, we assume a mass of #100*g#, and we address the elemental makeup by dividing thru by the #"atomic mass"# of each component.
#"Moles of carbon"=(64.65*g)/(12.011*g*mol^-1)=5.38*mol#.
#"Moles of hydrogen"=(13.52*g)/(1.00794*g*mol^-1)=13.41*mol#.
#"Moles of oxygen"=(21.62*g)/(15.999*g*mol^-1)=1.351*mol#.
They are spoon-feeding you a bit here, in that combustion analysis gives #%C,H,N#. #%O# would normally NOT be measured, and determined by the difference #(100-%C-%H-%N)%#. And now we divide thru by the SMALLEST MOLAR QUANTITY, that of oxygen to give #C,H,O#
#C:(5.38*mol)/(1.351*mol)=3.98~=4#
#H:(13.41*mol)/(1.351*mol)=9.93~=10#
#O:(1.351*mol)/(1.351*mol)=1#
And thus an #"empirical formula"#, the simplest whole number defining constituent atoms in a species of #C_4H_10O#.
