Final answer:
The mole fraction of methanol is calculated by dividing the moles of methanol by the total moles of the solution, which includes both methanol and water. After converting the mass of water to moles, the calculation shows that the mole fraction of methanol is 0.44.
Step-by-step explanation:
To find the mole fraction of methanol when 2.0 mol of methanol is dissolved in 45 g of water, we first need to convert the mass of water into moles.
The molar mass of water (H2O) is approximately 18.015 g/mol.
45 g H2O × (1 mol H2O / 18.015 g) = 2.5 mol H2O
Total moles in the solution = moles of methanol + moles of water
= 2.0 mol CH3OH + 2.5 mol H2O
= 4.5 mol
To find the mole fraction of methanol (XCH3OH), we divide the moles of methanol by the total moles of the solution:
XCH3OH = moles of CH3OH / total moles
= 2.0 mol / 4.5 mol
= 0.44
Therefore, the correct answer for the mole fraction of methanol is a. 0.44.