Final answer:
To find the mass of phosphorus in a 15.5 g sample of diphosphorus pentoxide, we calculate the proportion of phosphorus' molar mass in the compound's molar mass and multiply by the sample's mass. Our calculation yields 6.752 g, which rounds to the nearest option as 6.54 g.
Step-by-step explanation:
To determine how many grams of phosphorus are in a 15.5 grams sample of diphosphorus pentoxide (P2O5), we first need to know the molar mass of P2O5 and phosphorus (P). The molar mass of P2O5 is approximately 283.9 grams per mole, and the molar mass of phosphorus is approximately 30.97 grams per mole. Since there are two atoms of phosphorus in one molecule of diphosphorus pentoxide, we multiply the molar mass of phosphorus by two for the molar mass contribution of phosphorus in the compound, which is 61.94 grams per mole.
Next, we use the formula:
mass of element in sample = (mass of sample) x (molar mass of element in compound / molar mass of compound)
Plugging in the values we get:
mass of phosphorus in sample = (15.5 g) x (61.94 g/mol P / 283.9 g/mol P2O5)
This calculation gives us approximately 3.376 g of phosphorus per mole of P2O5. Since there are two moles of phosphorus in this compound, we multiply by two to find the answer.
6.752 g of phosphorus would be in a 15.5 g sample of diphosphorus pentoxide, which we would round up to the nearest option, therefore the answer is (A) 6.54 g.