Empirical formula is C3H6O
First, calculate the molar masses of CO2 and H2O
Carbon = 12.0107
Hydrogen = 1.00794
Oxygen = 15.999
CO2 = 12.0107 + 2*15.999 = 44.0087
H2O = 2 * 1.00794 + 15.999 = 18.01488
Now calculate the number of moles of CO2 and H2O we have by dividing the mass by the molar mass
CO2 = 3.79 / 44.0087 = 0.086119
H2O = 1.55 / 18.01488 = 0.08604
Since there's 2 hydrogen atoms per water molecule, multiply by 2
H = 0.08604 * 2 = 0.17208
Now some of the oxygen that's present in the CO2 and H2O products came from the ethyl butyrate. Let's determine how much by subtracting the mass of the carbon and hydrogen from the mass of the ethyl butyrate.
1.67 - 0.086119 * 12.0107 - 0.17208 * 1.00794 = 0.462204
And the relative number of moles of oxygen is
0.462204 / 15.999 = 0.02889
So we now know the relative ratios of carbon, hydrogen, and oxygen. They are
Carbon = 0.086119
Hydrogen = 0.17208
Oxygen = 0.02889
What we need to do is find some small integers that have the same approximate ratio as 0.086119 : 0.17208 : 0.02889
Dividing all three values by 0.02889 (selected that because it was the smallest value), gives 2.980928 : 5.956386 : 1 as the new target ratios. And 2.980928 is extremely close to 3, and 5.956386 is also extremely close to 6. So it looks like the ratio for the empirical formula is 3:6:1 which would be C3H6O
