Answer :
To find out how many grams of phosphorus are in a 15.5 gram sample of diphosphorus pentoxide [tex](\text{P}_2\text{O}_5)[/tex], we need to determine the percentage of phosphorus in the compound by weight.
Step 1: Determine the molar mass of [tex]\text{P}_2\text{O}_5[/tex].
- The atomic mass of phosphorus [tex]\text{(P)}[/tex] is approximately 30.97 g/mol.
- The atomic mass of oxygen [tex]\text{(O)}[/tex] is approximately 16.00 g/mol.
The molar mass of [tex]\text{P}_2\text{O}_5[/tex] is calculated as follows:
[tex]\text{Molar mass of } \text{P}_2\text{O}_5 = (2 \times 30.97) + (5 \times 16.00) = 61.94 + 80.00 = 141.94 \text{ g/mol}[/tex]
Step 2: Calculate the mass percentage of phosphorus in [tex]\text{P}_2\text{O}_5[/tex].
- Total mass of phosphorus in [tex]\text{P}_2\text{O}_5[/tex] = [tex]2 \times 30.97 = 61.94 \text{ g}[/tex]
- Percentage of phosphorus:
[tex]\text{Percentage}\,\text{of}\,\text{Phosphorus} = \left(\frac{61.94}{141.94}\right) \times 100\%[/tex]
[tex]\approx 43.64\%[/tex]
Step 3: Calculate the grams of phosphorus in the 15.5 gram sample.
To find the grams of phosphorus in 15.5 g of [tex]\text{P}_2\text{O}_5[/tex], use the percentage calculated:
[tex]\text{Grams of } \text{Phosphorus} = 15.5 \times \left(\frac{43.64}{100}\right) \approx 6.76 \text{ g}[/tex]
Therefore, in a 15.5 gram sample of diphosphorus pentoxide, there are approximately [tex]6.76[/tex] grams of phosphorus.
The correct answer is C) 6.76 grams.
