Question

Elemental analysis of an organic compound containing C, H, and O gives percentage composition: C: 39.9% and H: 6.7%. If the molecular weight of the compound is 180, the number of carbon atoms present in the molecule is ............

Hint:

To calculate the number of atoms in a molecule, use the formula: \[ \text{Number of atoms} = \frac{\text{Mass of element}}{\text{Molar mass}} \times 6.022 \times 10^{23} \]

Answer 1

Correct Answer: 6

To determine the number of carbon atoms in the molecule, we first calculate the moles of carbon and hydrogen based on the given percentage composition and the molecular weight of the compound.

The molecular formula is unknown, but we know:
C = 39.9%, H = 6.7%. Therefore, O = 100% - (39.9% + 6.7%) = 53.4%.

1. **Calculate the moles of each element based on 100 g of the compound:**
C: \(\frac{39.9\, \text{g}}{12.01\, \text{g/mol}} = 3.32\, \text{mol}\)
H: \(\frac{6.7\, \text{g}}{1.008\, \text{g/mol}} = 6.65\, \text{mol}\)
O: \(\frac{53.4\, \text{g}}{16.00\, \text{g/mol}} = 3.34\, \text{mol}\)

2. **Determine the simplest ratio of C:H:O by dividing by the smallest number of moles:**
\(C \approx \frac{3.32}{3.32} = 1, H \approx \frac{6.65}{3.32} = 2, O \approx \frac{3.34}{3.32} = 1\)
The empirical formula is CH₂O.

3. **Calculate the empirical formula weight:**
CH₂O = 12.01 + (2 × 1.008) + 16.00 = 30.03 g/mol.

4. **Find the ratio of the molecular formula weight to the empirical formula weight:**
\(n = \frac{180}{30.03} \approx 6\).

5. **Determine the molecular formula:**
The molecular formula is (CH₂O)₆ = C₆H₁₂O₆.

Thus, the molecule contains **6 carbon atoms**.