Final answer:
The mole fraction of 10.0 g of naphthalene in 50.0 mL of water is calculated by first determining the moles of naphthalene and the moles of water, and then dividing the moles of naphthalene by the total moles. The correct mole fraction is approximately 0.0273.
Step-by-step explanation:
The student is asking for the mole fraction of naphthalene in water. To find the mole fraction, we need to calculate the moles of naphthalene and water, and then divide the moles of naphthalene by the total moles of both substances.
Naphthalene has a molecular formula of C10H8. Using the atomic weights provided (C = 12.0, H = 1.00), the molar mass of naphthalene is calculated as follows:
(10 × 12.0 g/mol) + (8 × 1.0 g/mol) = 120.0 g/mol + 8.0 g/mol = 128.0 g/mol.
Using this molar mass:
moles of naphthalene = mass of naphthalene / molar mass of naphthalene = 10.0 g / 128.0 g/mol = 0.0781 mol.
Since density of water is approximately 1 g/mL, 50.0 mL of water is roughly 50.0 g. The molar mass of water (H2O) is 18.02 g/mol. Therefore, the moles of water are:
moles of water = mass of water / molar mass of water = 50.0 g / 18.02 g/mol = 2.775 mol.
Finally, the mole fraction of naphthalene can be calculated as follows:
moles of naphthalene / (moles of naphthalene + moles of water) = 0.0781 mol / (0.0781 mol + 2.775 mol) ≈ 0.028.
Therefore, the correct option is B. 0.0273.