0.0833 mole of a carbohydrate of empirical formula CH2O contains 1.00 ...
- Empirical formula = CH2O.
- Empirical formula weight = 12 + 2×1 + 16 = 30 g/mol.
- Let the molecular formula be (CH2O)n = CnH2nOn.
- Moles of carbohydrate = 0.0833 mol.
- Mass of hydrogen in 0.0833 mol = 1.00 g.
- Molecular formula = CnH2nOn, so 2n hydrogen atoms per molecule.
- Atomic mass of hydrogen = 1 g/mol, so mass of hydrogen in 1 mole of carbohydrate = 2n g.
- For 0.0833 moles, mass of hydrogen = 0.0833 × 2n = 1.00 g.
- Solving: 2n × 0.0833 = 1.00
n = 1.00 / (2 × 0.0833) ≈ 6. - Molecular formula = C6H12O6.
Verification:
- Molecular weight of C6H12O6 = 6×12 + 12×1 + 6×16 = 180 g/mol.
- Hydrogen mass in 1 mole = 12 g.
- In 0.0833 moles, hydrogen mass = 12 × 0.0833 ≈ 1.00 g, which matches.
Thus, the correct answer is D. C6H12O6.
0.0833 mole of a carbohydrate of empirical formula CH2O contains 1.00 ...
Understanding the Problem
To determine the molecular formula of the carbohydrate, we start with the information given:
- Empirical formula: CH2O
- Moles of carbohydrate: 0.0833 moles
- Mass of hydrogen: 1.00 g
Calculating Moles of Hydrogen
- The empirical formula CH2O contains 2 moles of H per mole of the compound.
- Therefore, in 0.0833 moles of CH2O, the moles of hydrogen can be calculated as follows:
- Moles of H = 0.0833 moles CH2O * 2 moles H/1 mole CH2O = 0.1666 moles H
Converting Moles of Hydrogen to Grams
- To find the mass of hydrogen:
- Mass of H = moles of H * molar mass of H (1 g/mol)
- Mass of H = 0.1666 moles * 1 g/mol = 0.1666 g of H
This indicates a discrepancy as we need to consider that the given mass of hydrogen is 1.00 g.
Finding the Molecular Formula
- To find the molecular formula, we must determine the molar mass of the entire carbohydrate.
- The mass of hydrogen (1.00 g) suggests that the actual number of moles of H in the molecular formula is higher.
Molecular Formula Calculation
- Since there are 1.00 g of hydrogen, the moles of H in the molecular formula is 1.00 g / 1 g/mol = 1.00 mole of H.
- The ratio of moles (1.00 mole of H) to empirical formula (0.1666 moles) is approximately 6.
- Therefore, the molecular formula is (C1H2O1) * 6 = C6H12O6.
Conclusion
Thus, the molecular formula of the carbohydrate is C6H12O6, which corresponds to option 'D'.