To determine the empirical formula and the molecular formula for the compound, you need to follow a step-by-step process. Let's break it down together:
1. Start by assuming you have 100 grams of the compound. This assumption simplifies the calculations, as percentages can be directly converted into grams.
2. Convert the percentages of carbon, hydrogen, and oxygen into grams. Given that the compound is 39.10% carbon, 8.77% hydrogen, and 52.13% oxygen, you would have:
- Carbon: 100g * 0.3910 = 39.10g
- Hydrogen: 100g * 0.0877 = 8.77g
- Oxygen: 100g * 0.5213 = 52.13g
Now, we have the gram amounts for each element.
3. Convert the grams of each element into moles by dividing by their respective molar masses:
- Carbon: 39.10g / 12.01g/mol = 3.257 moles
- Hydrogen: 8.77g / 1.008g/mol = 8.7 moles
- Oxygen: 52.13g / 16.00g/mol = 3.257 moles
4. Divide each number of moles by the smallest value obtained. In this case, the smallest value is 3.257 moles. Divide each number of moles by 3.257:
- Carbon: 3.257 moles / 3.257 moles = 1 mole
- Hydrogen: 8.7 moles / 3.257 moles = 2.67 moles (rounded to 2)
- Oxygen: 3.257 moles / 3.257 moles = 1 mole
5. Based on the whole number ratio obtained from dividing by the smallest value, determine the empirical formula. The empirical formula represents the simplest, most reduced ratio of atoms in the compound. In this case, it would be CH2O.
Now, for the molecular formula:
6. Calculate the empirical formula's molar mass by adding up the molar masses of its components:
- Carbon: 1 * 12.01g/mol = 12.01g/mol
- Hydrogen: 2 * 1.008g/mol = 2.016g/mol
- Oxygen: 1 * 16.00g/mol = 16.00g/mol
Therefore, the empirical formula's molar mass is 30.03g/mol.
7. Divide the given molecular weight (276g) by the empirical formula's molar mass (30.03g/mol) to determine the whole number ratio between the molecular formula and the empirical formula:
- 276g / 30.03g/mol = 9.19
8. Round the whole number ratio obtained to the nearest whole number. In this case, round 9.19 to 9.
9. Multiply the empirical formula by the rounded whole number to obtain the molecular formula:
- Empirical formula: CH2O
- Multiply by 9: 9 * CH2O = C9H18O9
Therefore, the empirical formula for the compound is CH2O, and the molecular formula is C9H18O9.
Note: In this particular case, rounding to the nearest whole number resulted in a molecular formula that is a multiple of the empirical formula. However, it's important to note that this may not always be the case. Sometimes the empirical and molecular formulas can be the same, while other times they may differ.