Final answer:
The empirical formula of the compound is determined by converting the given masses of carbon, hydrogen, and oxygen to moles, and then finding the simplest whole number ratio of these moles, which is CH2O2.
Step-by-step explanation:
To determine the empirical formula of a compound, we first convert the mass of each element to moles by using their atomic masses. For carbon (C), hydrogen (H), and oxygen (O), the atomic masses are approximately 12 g/mol for carbon, 1 g/mol for hydrogen, and 16 g/mol for oxygen.
- Carbon: 24 g C × (1 mol C / 12 g C) = 2 moles C
- Hydrogen: 4 g H × (1 mol H / 1 g H) = 4 moles H
- Oxygen: 64 g O × (1 mol O / 16 g O) = 4 moles O
Next, we find the simplest ratio of the moles of each element by dividing all by the smallest mole value, which in this case is 2 moles (for carbon).
- C: 2 moles / 2 = 1 mole C
- H: 4 moles / 2 = 2 moles H
- O: 4 moles / 2 = 2 moles O
Since the resulting ratio is one carbon to two hydrogen atoms to two oxygen atoms, the empirical formula is CH₂O₂.