Calculate the empirical formula for each of the following natural flavors based on their elemental mass percent composition.
vanillin (responsible for the taste and smell of vanilla): C 63.15% H 5.30% O 31.55%.
To calculate the empirical formula for vanillin, we need to determine the simplest whole-number ratio of carbon (C), hydrogen (H), and oxygen (O) atoms in the compound, based on their mass percent composition.
1. Start by assuming we have 100g of the compound (this makes the mass percent equal to the mass in grams).
2. Determine the mass of each element in the compound using the given mass percent composition:
- Carbon (C): 63.15% of 100g = 63.15g
- Hydrogen (H): 5.30% of 100g = 5.30g
- Oxygen (O): 31.55% of 100g = 31.55g
3. Convert the given masses into moles using the atomic masses of the elements:
- Carbon (C): molar mass = 12.01 g/mol, moles = mass/molar mass = 63.15g/12.01g/mol ≈ 5.2585 mol
- Hydrogen (H): molar mass = 1.008 g/mol, moles = mass/molar mass = 5.30g/1.008g/mol ≈ 5.2539 mol
- Oxygen (O): molar mass = 16.00 g/mol, moles = mass/molar mass = 31.55g/16.00g/mol ≈ 1.9719 mol
4. Divide the number of moles by the smallest number of moles to determine the mole ratio:
- C: 5.2585 mol / 1.9719 mol ≈ 2.67 (rounded to the nearest whole number)
- H: 5.2539 mol / 1.9719 mol ≈ 2.66 (rounded to the nearest whole number)
- O: 1.9719 mol / 1.9719 mol = 1.00
5. Adjust the mole ratios to the simplest possible whole-number ratio by dividing all the values by the smallest value (which is 1 in this case):
- C: 2.67 / 1 ≈ 2.67 ≈ 3 (rounded to the nearest whole number)
- H: 2.66 / 1 ≈ 2.66 ≈ 3 (rounded to the nearest whole number)
- O: 1.00 / 1 ≈ 1
Therefore, the empirical formula for vanillin is C3H3O.