the empirical formula is C3H8O2
You need to determine the relative number of moles of hydrogen and carbon. So you first calculate the molar mass of CO2 and H20
Atomic weight of carbon = 12.0107
Atomic weight of hydrogen = 1.00794
Atomic weight of oxygen = 15.999
Molar mass CO2 = 12.0107 + 2 * 15.999 = 44.0087
Molar mass H2O = 2 * 1.00794 + 15.999 = 18.01488
Now calculate the number of moles of CO2 and H2O you have
Moles CO2 = 2.086 g / 44.0087 g/mole = 0.0474 mole
Moles H2O = 1.134 g / 18.01488 g/mole = 0.062948 mole
Calculate the number of moles of carbon and hydrogen you have. Since there's 1 carbon atom per CO2 molecule, the number of moles of carbon is the same as the number of moles of CO2. But since there's 2 hydrogen atoms per molecule of H2O, The number of moles of hydrogen is double the number of moles of H2O
Moles Carbon = 0.0474
Moles Hydrogen = 0.062948 * 2 = 0.125896
Now we need to determine how much oxygen is in the compound. Just take the mass of the compound and subtract the mass of carbon and hydrogen. What's left will be the mass of oxygen. Then divide that mass by the atomic weight of oxygen to get the number of moles of oxygen we have.
1.200 - 0.0474 * 12.0107 - 0.125896 * 1.00794 = 0.503797
Moles oxygen = 0.503797 / 15.999 = 0.031489
So now we have a ratio of carbon:hydrogen:oxygen of
0.0474 : 0.125896 : 0.031489
We need to find a ratio of small integers that's close to that ratio. Start by dividing everything by 0.031489 (selected because it's the smallest value) getting
1.505288 : 3.998095 : 1
The 1 for oxygen and the 3.998095 for hydrogen look close enough. But the 1.505288 for carbon doesn't work. But it looks like if we double all the numbers, we'll get something close to an integer for everything. So do so.
3.010575 : 7.996189 : 2
Now this looks good. Rounding everything to an integer gives us
3 : 8 : 2
So the empirical formula is C3H8O2
