Menthol (molar mass = 156.30g/mol), contains carbon, hydrogen, and oxygen. When 0.1595g of menthol is combusted, 0.449g of CO2 and 0.184g of H2O are formed. Determine the molecular formula of menthol.
The Correct Answer and Explanation is :
To determine the molecular formula of menthol (C₁₀H₂₀O) from combustion data, we analyze the masses of carbon dioxide (CO₂) and water (H₂O) produced during combustion.
Step 1: Calculate the moles of CO₂ and H₂O produced.
Given masses:
- Mass of CO₂ = 0.449 g
- Mass of H₂O = 0.184 g
Molar masses:
- Molar mass of CO₂ = 44.01 g/mol
- Molar mass of H₂O = 18.015 g/mol
Moles of CO₂ = 0.449 g / 44.01 g/mol ≈ 0.0102 mol
Moles of H₂O = 0.184 g / 18.015 g/mol ≈ 0.0102 mol
Step 2: Determine the moles of carbon and hydrogen in the sample.
Each mole of CO₂ contains 1 mole of carbon atoms, and each mole of H₂O contains 2 moles of hydrogen atoms.
Moles of carbon = 0.0102 mol
Moles of hydrogen = 0.0102 mol × 2 = 0.0204 mol
Step 3: Calculate the masses of carbon and hydrogen.
Mass of carbon = 0.0102 mol × 12.011 g/mol ≈ 0.122 g
Mass of hydrogen = 0.0204 mol × 1.008 g/mol ≈ 0.0206 g
Step 4: Determine the mass of oxygen in the sample.
Mass of oxygen = Total mass of sample – (Mass of carbon + Mass of hydrogen)
Mass of oxygen = 0.1595 g – (0.122 g + 0.0206 g) = 0.0169 g
Step 5: Calculate the moles of oxygen.
Moles of oxygen = 0.0169 g / 16.00 g/mol ≈ 0.00106 mol
Step 6: Determine the empirical formula.
The mole ratio of C:H:O is approximately 10:20:1.
Empirical formula: C₁₀H₂₀O
Step 7: Determine the molecular formula.
Given molar mass of menthol = 156.30 g/mol
Empirical formula mass = (10 × 12.011) + (20 × 1.008) + (1 × 16.00) = 156.30 g/mol
Since the empirical formula mass equals the molar mass, the empirical formula is also the molecular formula.
Molecular formula: C₁₀H₂₀O
Therefore, the molecular formula of menthol is C₁₀H₂₀O.
This analysis demonstrates how combustion data can be used to determine the molecular formula of a compound by calculating the moles of carbon, hydrogen, and oxygen, and comparing the empirical formula mass to the known molar mass.