Question

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Explanation:

Step1: Find mass of sulfur

Mass of sulfur = Total mass - Mass of phosphorus.
Let total mass = 100 g (for % calculation).
Mass of S = $100\ \text{g} - 27.9\ \text{g} = 72.1\ \text{g}$

Step2: Convert mass to moles

Molar mass of P = $30.97\ \text{g/mol}$, Molar mass of S = $32.07\ \text{g/mol}$.
Moles of P: $\frac{27.9\ \text{g}}{30.97\ \text{g/mol}} \approx 0.901\ \text{mol}$
Moles of S: $\frac{72.1\ \text{g}}{32.07\ \text{g/mol}} \approx 2.248\ \text{mol}$

Step3: Divide by smallest mole value

Divide both by 0.901 to get mole ratio.
Ratio of P: $\frac{0.901}{0.901} = 1$
Ratio of S: $\frac{2.248}{0.901} \approx 2.5$

Step4: Multiply to get whole numbers

Multiply both ratios by 2 to eliminate decimals.
P: $1 \times 2 = 2$, S: $2.5 \times 2 = 5$

Answer:

The empirical formula is $\text{P}_2\text{S}_5$