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.
