Question

a 15.5 gram sample of diphosphorous pentoxide contains how many grams of phosphorous?
6.76
13.5
1.69
3.38
none of the above

Explanation:

Step 1: Find the molar mass of \( P_2O_5 \)

The atomic mass of \( P \) is approximately \( 30.97 \, \text{g/mol} \) and the atomic mass of \( O \) is approximately \( 16.00 \, \text{g/mol} \). For \( P_2O_5 \), the molar mass is calculated as:
\( 2 \times 30.97 + 5 \times 16.00 = 61.94 + 80.00 = 141.94 \, \text{g/mol} \).

Step 2: Determine the mass fraction of \( P \) in \( P_2O_5 \)

There are 2 moles of \( P \) in 1 mole of \( P_2O_5 \). The mass of \( P \) in 1 mole of \( P_2O_5 \) is \( 2 \times 30.97 = 61.94 \, \text{g} \).
The mass fraction of \( P \) is \( \frac{61.94}{141.94} \approx 0.4364 \).

Step 3: Calculate the mass of \( P \) in 15.5 g of \( P_2O_5 \)

Multiply the mass of \( P_2O_5 \) by the mass fraction of \( P \):
\( 15.5 \, \text{g} \times 0.4364 \approx 6.76 \, \text{g} \).

Answer:

6.76 (corresponding to the first option: 6.76)