To determine the empirical formula and molecular formula for ibuprofen, we start with the given mass percentages of its elements: 75.69% carbon (C), 8.80% hydrogen (H), and 15.51% oxygen (O).
1. **Convert the percentages to grams** (assuming a sample size of 100 g):
C: 75.69 g
H: 8.80 g
O: 15.51 g
2. **Convert grams to moles** using the atomic masses:
Moles of C = 75.69 g / 12.01 g/mol = 6.297 moles
Moles of H = 8.80 g / 1.008 g/mol = 8.731 moles
Moles of O = 15.51 g / 16.00 g/mol = 0.969 moles
3. **Divide each by the smallest number of moles** (0.969 moles for O):
C: 6.297 / 0.969 = 6.49 ≈ 6.5
H: 8.731 / 0.969 = 9.00 ≈ 9
O: 0.969 / 0.969 = 1.00 ≈ 1
4. **To convert the non-integer ratio (6.5) to integers**, we multiply all ratios by 2:
C: 6.5 x 2 = 13
H: 9 x 2 = 18
O: 1 x 2 = 2
Thus, the empirical formula for ibuprofen is C13H18O2.
5. **Next, we find the molecular formula:** The empirical formula mass is:
(13*12.01) + (18*1.008) + (2*16.00) = 206.28 g/mol
Since the given molecular mass is 206.3 g/mol, which is approximately the same as the empirical formula mass, the molecular formula is the same as the empirical formula. Therefore, the molecular formula for ibuprofen is also C13H18O2.