Question

how many molecules are in 75.0 g of diphosphorus pentoxide

Answer 1

To determine how many molecules are in 75.0 g of diphosphorus pentoxide (P₂O₅), we first need to calculate the number of moles of P₂O₅ in that mass, and then convert moles to molecules using Avogadro's number.

1. **Calculate the molar mass of P₂O₅**:
- Phosphorus (P): 30.97 g/mol
- Oxygen (O): 16.00 g/mol
- Molar mass of P₂O₅ = 2(30.97 g/mol) + 5(16.00 g/mol)
\[
= 61.94 \, \text{g/mol} + 80.00 \, \text{g/mol} = 141.94 \, \text{g/mol}
\]

2. **Calculate the number of moles of P₂O₅ in 75.0 g**:
\[
\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{75.0 \, \text{g}}{141.94 \, \text{g/mol}} \approx 0.527 \, \text{moles}
\]

3. **Convert moles to molecules**:
Using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules/mol:
\[
\text{Number of molecules} = \text{number of moles} \times \text{Avogadro's number}
\]
\[
= 0.527 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 3.17 \times 10^{23} \, \text{molecules}
\]

Thus, there are approximately \(3.17 \times 10^{23}\) molecules in 75.0 g of diphosphorus pentoxide (P₂O₅).