Given 400 mg of Olive oil, find the theoretical yield of hydrogenated olive oil. Molecular weight of olive oil is 885 g/mol and molecular weight of hydrogenated olive oil is 891 g/mol.
The correct answer and explanation is:
Correct Answer:
The theoretical yield of hydrogenated olive oil from 400 mg of olive oil is 402.71 mg.
Explanation (Approx. 300 words):
Hydrogenation is a chemical reaction that adds hydrogen (H₂) to unsaturated bonds (usually double bonds in fatty acids) in oils like olive oil, converting them to saturated fats. In this case, the molecular weight increases slightly due to the addition of hydrogen atoms.
Step-by-Step Calculation:
Given:
- Mass of olive oil (reactant) = 400 mg = 0.400 g
- Molecular weight (MW) of olive oil = 885 g/mol
- Molecular weight of hydrogenated olive oil = 891 g/mol
Step 1: Find moles of olive oil:
Moles of olive oil=MassMolecular Weight=0.400 g885 g/mol=4.519×10−4 mol\text{Moles of olive oil} = \frac{\text{Mass}}{\text{Molecular Weight}} = \frac{0.400 \text{ g}}{885 \text{ g/mol}} = 4.519 \times 10^{-4} \text{ mol}
Step 2: Use 1:1 mole ratio:
Assuming complete hydrogenation and a 1:1 molar ratio between olive oil and hydrogenated olive oil (i.e., 1 mole of olive oil gives 1 mole of hydrogenated olive oil): Moles of hydrogenated olive oil=4.519×10−4 mol\text{Moles of hydrogenated olive oil} = 4.519 \times 10^{-4} \text{ mol}
Step 3: Convert to mass using molecular weight of hydrogenated olive oil:
Mass=Moles×Molecular Weight=(4.519×10−4)×891=0.4027 g=402.7 mg\text{Mass} = \text{Moles} \times \text{Molecular Weight} = (4.519 \times 10^{-4}) \times 891 = 0.4027 \text{ g} = 402.7 \text{ mg}
Conclusion:
The theoretical yield of hydrogenated olive oil from 400 mg of olive oil is 402.7 mg. The small increase in mass is due to the addition of hydrogen atoms during the hydrogenation reaction. In practice, actual yield may be lower due to incomplete reaction or losses during processing, but this is the maximum theoretical amount possible.