To determine the empirical formula of the compound given the percentages of phosphorus and oxygen, follow these steps:
1. Convert percentages to masses: Assume 100 grams of the compound, so you have:
- 43.6 grams of phosphorus (P)
- 56.4 grams of oxygen (O)
2. Convert masses to moles:
- The atomic mass of phosphorus (P) is approximately 30.97 g/mol.
- The atomic mass of oxygen (O) is approximately 16.00 g/mol.
Calculate the moles of each element:
[tex]\[
\text{Moles of P} = \frac{43.6 \text{ grams}}{30.97 \text{ g/mol}} \approx 1.41 \text{ moles}
\][/tex]
[tex]\[
\text{Moles of O} = \frac{56.4 \text{ grams}}{16.00 \text{ g/mol}} = 3.525 \text{ moles}
\][/tex]
3. Find the simplest mole ratio:
- Divide each mole value by the smallest number of moles calculated:
[tex]\[
\text{Ratio of P} = \frac{1.41}{1.41} \approx 1
\][/tex]
[tex]\[
\text{Ratio of O} = \frac{3.525}{1.41} \approx 2.5
\][/tex]
4. Simplify the ratio to small whole numbers:
The ratio of phosphorus to oxygen is approximately 1:2.5. To convert this into a whole number ratio, multiply both values by 2:
[tex]\[
\text{Ratio of P} = 1 \times 2 = 2
\][/tex]
[tex]\[
\text{Ratio of O} = 2.5 \times 2 = 5
\][/tex]
Thus, the simplest whole number ratio is 2 phosphorus atoms to 5 oxygen atoms.
5. Determine the empirical formula:
Using the simplest whole number ratio, we find that the empirical formula of the compound is:
[tex]\[
\text{Empirical formula} = P_2O_5
\][/tex]
So, the empirical formula for the compound is [tex]\( P_2O_5 \)[/tex].
