Concept:To find an empirical formula, assume a 100g sample. Convert the mass percentages to moles by dividing by atomic masses, and simplify to the smallest whole-number ratio.
Formula:$$ \text{Moles} = \frac{\text{Mass}}{\text{Atomic Mass}} $$
Solution:- In a 100g sample, Mass of Oxygen = 43.6g. Therefore, Mass of Phosphorus = \( 100 - 43.6 = 56.4\text{g} \).
- Moles of P = \( 56.4 / 31 \approx 1.81 \text{ moles} \).
- Moles of O = \( 43.6 / 16 \approx 2.72 \text{ moles} \).
- Divide by the smallest value (1.81) to find the atomic ratio:
- Ratio for P = \( 1.81 / 1.81 = 1 \).
- Ratio for O = \( 2.72 / 1.81 = 1.5 \).
- Since we cannot have half an atom, multiply both numbers by 2 to achieve whole integers: P = \( 1 \times 2 = 2 \), O = \( 1.5 \times 2 = 3 \).
- The empirical formula is \( \text{P}_2\text{O}_3 \).
Why other options are incorrect:- \( \text{P}_2\text{O}_5 \): Would require ~56% oxygen by mass.
- \( \text{P}_3\text{O}_2 \) & \( \text{PO}_2 \): Math errors in the mole division step lead to these incorrect ratios.
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