Final answer:
To determine the molecular formula of the compound, calculate the mole ratios of C, H, and O using their percent composition and atomic masses, find the empirical formula by simplifying these ratios to the smallest whole numbers, and then compare the empirical formula mass to the molecular formula mass to determine the molecular formula.
Step-by-step explanation:
To find the subscripts in the actual molecular formula of a compound with a molecular formula mass of 210 amu and a percent composition of 40.0% C, 6.70% H, and 53.3% O, we need to determine the empirical formula and then the ratio of the molecular mass to the empirical formula mass.
First, we assume 100 grams of the substance to easily convert percentage to grams. This gives us 40.0 g of C, 6.7 g of H, and 53.3 g of O. We then divide these masses by their respective atomic masses to find the mole ratios:
- C: 40.0 g / 12.01 g/mol = 3.33 mol
- H: 6.7 g / 1.008 g/mol = 6.65 mol
- O: 53.3 g / 16.00 g/mol = 3.33 mol
Next, we determine the simplest whole number ratios by dividing each of the mole ratios by the smallest mole ratio obtained:
- C: 3.33 / 3.33 = 1
- H: 6.65 / 3.33 ≈ 2
- O: 3.33 / 3.33 = 1
So, the empirical formula is CH₂O. Then we calculate the empirical formula mass: C(12.01) + 2 * H(1.008) + O(16.00) = 30.03 amu. Comparing the empirical formula mass with the given molecular mass (210 amu), we find the ratio:
210 amu / 30.03 amu ≈ 7
Therefore, we multiply the subscripts of the empirical formula by this ratio to get the molecular formula:
C(1x7)H(2x7)O(1x7) = C7H14O7