To determine how many P atoms are present in a sample of [tex]\( \text{P}_2\text{O}_5 \)[/tex] given that the sample has [tex]\( 5.2 \times 10^{23} \)[/tex] oxygen atoms, you need to follow these steps:
1. Convert the number of oxygen atoms to moles of oxygen atoms:
- Use Avogadro's number, which is [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mole, to convert atoms to moles.
- Moles of oxygen (O) in the sample = [tex]\(\frac{\text{Number of O atoms}}{\text{Avogadro's number}}\)[/tex]
- [tex]\( moles\_O = \frac{5.2 \times 10^{23}}{6.022 \times 10^{23}} \approx 0.8635 \)[/tex] moles
2. Use the molar ratio of P to O in [tex]\( \text{P}_2\text{O}_5 \)[/tex] to find moles of phosphorus atoms:
- [tex]\( \text{P}_2\text{O}_5 \)[/tex] implies 2 moles of P atoms for every 5 moles of O atoms.
- Moles of P atoms = [tex]\(\frac{\text{Moles of O} \times 2}{5}\)[/tex]
- [tex]\( moles\_P = \frac{0.8635 \times 2}{5} \approx 0.3454 \)[/tex] moles
3. Convert the moles of phosphorus atoms back to the number of phosphorus atoms:
- Use Avogadro's number again to convert moles to atoms.
- Number of P atoms = [tex]\( \text{Moles of P} \times \text{Avogadro's number} \)[/tex]
- [tex]\( atoms\_P = 0.3454 \times 6.022 \times 10^{23} \approx 2.08 \times 10^{23} \)[/tex] atoms
Therefore, the pathway you should follow is:
particles O [tex]\(\rightarrow\)[/tex] moles O [tex]\(\rightarrow\)[/tex] moles P [tex]\(\rightarrow\)[/tex] particles P
Given these steps, the correct number of phosphorus atoms, [tex]\( \text{atoms}_P \)[/tex], is [tex]\( 2.08 \times 10^{23} \)[/tex].
