Final answer:
To determine the number of moles in a 39.25 gram sample of Cr₄(P₂O₇)₃, the molar mass of the compound is calculated and then used to convert the sample mass to moles. The calculation finds that the sample contains 0.0538 moles of Cr₄(P₂O₇)₃.
Step-by-step explanation:
The question asks how many moles of Cr₄(P₂O₇)₃ are present in a 39.25 gram sample of Cr₄(P₂O₇)₃. To solve this problem, we must first calculate the molar mass of Cr₄(P₂O₇)₃. Each molecule of Cr₄(P₂O₇)₃ contains 4 chromium (Cr) atoms, 6 phosphorus (P) atoms, and 21 oxygen (O) atoms. The atomic masses of Cr, P, and O are approximately 52.00 g/mol, 30.97 g/mol, and 16.00 g/mol, respectively.
Calculating the molar mass of Cr₄(P₂O₇)₃:
Molar mass = (4 × 52.00 g/mol) + (6 × 30.97 g/mol) + (21 × 16.00 g/mol)
Molar mass = 208.00 g/mol + 185.82 g/mol + 336.00 g/mol
Molar mass = 729.82 g/mol
Next, we use the molar mass to convert the sample mass to moles:
Moles of Cr₄(P₂O₇)₃ = mass of sample / molar mass = 39.25 g / 729.82 g/mol = 0.0538 moles
Thus, there are 0.0538 moles of Cr₄(P₂O₇)₃ in the 39.25 g sample.