What is the approximate percentage by mass of oxygen in the compound aluminium sulphate, Al2(SO4)3?

Introduction / Context:
This numerical question tests your ability to calculate percentage composition by mass of an element in a compound, a fundamental skill in stoichiometry. Understanding how to work out mass percentages helps in preparing solutions, verifying empirical formulae and handling many types of chemical calculations in both school and competitive exams.

Given Data / Assumptions:

• Compound: aluminium sulphate, formula Al2(SO4)3.
• We need the percentage by mass of oxygen.
• Use approximate atomic masses: Al ≈ 27, S ≈ 32, O ≈ 16, unless otherwise specified.
• Assume one mole of Al2(SO4)3 for calculation.

Concept / Approach:
Percentage by mass of an element in a compound is given by the formula: (mass of that element in one mole of the compound / molar mass of the compound) * 100. So we first calculate total molar mass of Al2(SO4)3, then calculate total mass of oxygen atoms present in that formula unit. Finally we divide the mass of oxygen by the total molar mass and multiply by 100 to get the percentage.

Step-by-Step Solution:
Step 1: Write the formula Al2(SO4)3 clearly. This means there are 2 aluminium atoms, 3 sulphur atoms and 12 oxygen atoms in one formula unit. Step 2: Compute the total molar mass of the compound. Step 3: Use approximate atomic masses: Al = 27, S = 32, O = 16. Step 4: Mass contribution from aluminium: 2 * 27 = 54. Step 5: Mass contribution from sulphur: 3 * 32 = 96. Step 6: Mass contribution from oxygen: there are 12 oxygen atoms (3 sulphate groups, each having 4 oxygen atoms). So mass of oxygen = 12 * 16 = 192. Step 7: Total molar mass M of Al2(SO4)3 = 54 + 96 + 192 = 342. Step 8: Now calculate percentage of oxygen by mass: percentage of oxygen = (mass of oxygen / total molar mass) * 100. Step 9: Substitute values: percentage of oxygen = (192 / 342) * 100. Step 10: Evaluate the fraction 192 / 342 ≈ 0.561. Step 11: Multiply by 100 to obtain percentage: 0.561 * 100 ≈ 56.1%. Step 12: Therefore, the percentage by mass of oxygen in aluminium sulphate is approximately 56.1%.

Verification / Alternative check:
You can quickly check the reasonableness of this answer by noting that oxygen has a large share of the molar mass because there are 12 oxygen atoms. The mass from oxygen alone is 192, which is more than half of the total molar mass 342. Thus a value slightly above 50% makes sense. An answer around 56% is consistent with this logic, while values near 50% or 60% would need careful checking. Performing the division with a calculator or more precise atomic masses will still give a value close to 56.1%, confirming the option.

Why Other Options Are Wrong:
Option A, 57.7%, is a bit higher than the calculated value and would require either a different formula or different atomic masses. Option C, 53.1%, is too low relative to the large oxygen contribution. Option D, 52.6%, is also too low and not supported by the ratio 192 to 342. Option E, 60.0%, overestimates the oxygen fraction and would suggest oxygen mass dominates much more than it actually does. Only 56.1% matches the correct calculation using standard atomic masses and the correct formula.

Common Pitfalls:
Common mistakes include miscounting the number of oxygen atoms in the formula, sometimes taking only 4 instead of 12, or forgetting that the entire SO4 group is repeated three times. Another error is to use incorrect atomic masses or to round too aggressively early in the calculation. To avoid such issues, always expand the formula term by term, write the count of each element clearly, and only round the final percentage at the end.

Final Answer:
The percentage by mass of oxygen in Al2(SO4)3 is approximately 56.1%.