Final answer:
The empirical formula of the organic sample containing carbon, hydrogen, and oxygen is determined by dividing the mass of each element by its atomic mass to calculate moles, finding the simplest whole number ratio, and then converting any non-integer ratios to integers, resulting in the empirical formula C3H6O2.
Step-by-step explanation:
The question involves finding the empirical formula of an organic compound given the masses of carbon, hydrogen, and oxygen in the sample. To determine the empirical formula, we first need to find the molar amounts of each element using their respective atomic masses (12.01 g/mol for carbon, 1.008 g/mol for hydrogen, and 16.00 g/mol for oxygen).
First, we divide the mass of carbon by its atomic mass to find moles of carbon: 97.30 g C / 12.01 g/mol = 8.10 mol C.
Then, we do the same for hydrogen: 16.22 g H / 1.008 g/mol = 16.09 mol H.
Lastly, to find the moles of oxygen, we subtract the mass of carbon and hydrogen from the total mass to get the mass of oxygen, and then divide by its atomic mass: (200 g - 97.30 g - 16.22 g) O / 16.00 g/mol = 5.36 mol O.
We then calculate the simplest whole number ratio of moles of each element to each other by dividing by the smallest number of moles, which in this case is the moles of oxygen:
8.10 mol C / 5.36 mol = 1.51 ≈ 1.5
16.09 mol H / 5.36 mol = 3.00 ≈ 3
5.36 mol O / 5.36 mol = 1
To convert non-integer ratios to integer ratios, we multiply by 2 to eliminate the decimal:
1.5 * 2 = 3 mol C
3 * 2 = 6 mol H
1 * 2 = 2 mol O
Therefore, the empirical formula is C3H6O2.