To calculate the mass of diphosphorus pentoxide (P₂O₅) that contains a trillion (1.0 × 10¹²) oxygen atoms, we need to follow these steps:
1. **Determine the number of moles of oxygen atoms:**
Given that 1 mole of any substance contains Avogadro's number (\( N_A \approx 6.022 \times 10^{23} \)) of entities (in this case, atoms), we can calculate the moles of oxygen atoms as follows:
\[
\text{Moles of oxygen atoms} = \frac{\text{Number of oxygen atoms}}{N_A} = \frac{1.0 \times 10^{12}}{6.022 \times 10^{23}} \approx 1.66 \times 10^{-12} \text{ moles}
\]
2. **Determine the moles of P₂O₅ molecules:**
Each molecule of P₂O₅ contains 5 oxygen atoms. Therefore, the moles of P₂O₅ can be calculated by dividing the moles of oxygen atoms by 5.
\[
\text{Moles of P₂O₅} = \frac{\text{Moles of oxygen atoms}}{5} = \frac{1.66 \times 10^{-12}}{5} \approx 3.32 \times 10^{-13} \text{ moles}
\]
3. **Calculate the molar mass of P₂O₅:**
The molar mass of P₂O₅ can be calculated by summing the atomic masses of its constituent atoms (phosphorus and oxygen). The atomic masses are approximately 30.97 g/mol for phosphorus (P) and 16.00 g/mol for oxygen (O).
\[
\text{Molar mass of P₂O₅} = 2 \times 30.97 \text{ g/mol} + 5 \times 16.00 \text{ g/mol} = 61.94 \text{ g/mol} + 80.00 \text{ g/mol} = 141.94 \text{ g/mol}
\]
4. **Calculate the mass of P₂O₅:**
Finally, multiply the moles of P₂O₅ by its molar mass to get the mass.
\[
\text{Mass of P₂O₅} = \text{Moles of P₂O₅} \times \text{Molar mass of P₂O₅} = 3.32 \times 10^{-13} \text{ moles} \times 141.94 \text{ g/mol} \approx 4.71 \times 10^{-11} \text{ g}
\]
Rounding to two significant digits:
\[
\approx 4.7 \times 10^{-11} \text{ g}
\]
Therefore, the mass of diphosphorus pentoxide (P₂O₅) that contains a trillion (1.0 × 10¹²) oxygen atoms is approximately \(4.7 \times 10^{-11} \text{ g}\).
Calculate the mass of diphosphorus pentoxide (P_2O_5) that contains a trillion (1.0 × 10^12) oxygen atoms.
Be sure your answer has a unit symbol if necessary, and round it to 2 significant digits.
1 answer