A compound has an elemental analysis of 48.2% C, 8.2% H, and 43.2% O by mass. What is the empirical formula?

Question

BlackTom AI · Accepted Answer

We begin by restating the problem in our own words to ensure understanding: we have a compound with mass percentages 48.2% C, 8.2% H, and 43.2% O, and we need to determine its empirical formula from these percentages.
First, convert each element's mass percentage to moles using approximate atomic masses: carbon (C) ≈ 12.01 g/mol, hydrogen (H) ≈ 1.008 g/mol, and oxygen (O) ≈ 16.00 g/mol.
- For C: 48.2 g / 12.01 g/mol ≈ 4.01 mol
- For H: 8.2 g / 1.008 g/mol ≈ 8.14 mol
- For O: 43.2 g / 16.00 g/mol ≈ 2.70 mol
Next, we compare these mole values by dividing by the smallest quantity to get the simplest whole-number ratio. The smallest is ~2.70 mol (O).
- C: 4.01 / 2.70 ≈ 1.48
- H: 8.14 / 2.70 ≈ 3.02
- O: 2.70 / 2.70 = 1
These ratios approximate to C1.5H3O1. To obtain whole numbers, multiply all by 2, giving C3H6O2 as the empirical formula.
Now evaluate each option:
Option A: C6HO5. This would imply a much higher oxygen count relative to carbon and hydrogen than the given percentages suggest; the ratios C:H:O would be far from the computed 1.5:3:1, so this is not consistent with the data.
Option B: C2H6O2. The C:H:O ratio here is 2:6:2, which simplifies to 1:3:1. The corresponding empirical ratio would be CH3O, which does not match the derived C1.5:H3:O1 unless we consider a non-integer c, which we do not—empirical formulas require smallest whole-number ratios; this option does not align with our calculations.
Option C: CH3O. This would imply C:H:O ratios of 1:3:1, which again, when scaled, would give a different relationship than the smallest-integer ratio derived from the data. It does not reflect the C:R≈1.5, H:R≈3, O:R=1 pattern.
Option D: C3H6O2. This matches the calculated empirical formula after simplifying to the smallest whole-number ratio and then scaling to integers; the C:H:O ratios are 3:6:2, which reduces to 1:2:2/3 if not properly simplified, so careful checking shows the simplest whole-number form is indeed C3H6O2.
Option E: C3H6O. This would give a different oxygen count (1 instead of 2) and does not fit the 43.2% oxygen shown in the data when checked against the carbon and hydrogen percentages.
In sum, comparing the calculated empirical ratio with each option shows that the only option consistent with the measured mass percentages is C3H6O2, while the others fail to reproduce the same C:H:O relationship implied by the data.

A compound has an elemental analysis of 48.2% C, 8.2% H, and 43.2% O by mass. What is the empirical formula?

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