To determine the empirical formula of the compound, we can follow these steps:
1. Find the number of moles of each element in the sample:
- For Phosphorus (P):
[tex]\[
\text{Mass of P} = 3.72 \text{ g}
\][/tex]
The molar mass of P is [tex]\(30.97 \text{ g/mol}\)[/tex].
[tex]\[
\text{Moles of P} = \frac{\text{Mass of P}}{\text{Molar mass of P}} = \frac{3.72}{30.97} \approx 0.120 \text{ moles}
\][/tex]
- For Chlorine (Cl):
[tex]\[
\text{Mass of Cl} = 21.28 \text{ g}
\][/tex]
The molar mass of Cl is [tex]\(35.45 \text{ g/mol}\)[/tex].
[tex]\[
\text{Moles of Cl} = \frac{\text{Mass of Cl}}{\text{Molar mass of Cl}} = \frac{21.28}{35.45} \approx 0.600 \text{ moles}
\][/tex]
2. Determine the simplest whole number ratio of moles of each element:
- Find the ratio of moles of P to moles of P:
[tex]\[
\text{Ratio of P} = \frac{\text{Moles of P}}{\text{Moles of P}} = \frac{0.120}{0.120} = 1.0
\][/tex]
- Find the ratio of moles of Cl to moles of P:
[tex]\[
\text{Ratio of Cl} = \frac{\text{Moles of Cl}}{\text{Moles of P}} = \frac{0.600}{0.120} \approx 5.0
\][/tex]
3. Determine the empirical formula:
The simplest whole number ratio of P to Cl is approximately 1:5. Therefore, the empirical formula of the compound is:
[tex]\[
\boxed{PCl_5}
\][/tex]
Thus, the empirical formula for the compound given the sample contents of [tex]\(3.72 \text{ g}\)[/tex] of [tex]\(P\)[/tex] and [tex]\(21.28 \text{ g}\)[/tex] of [tex]\(Cl\)[/tex] is [tex]\(PCl_5\)[/tex].
