Final answer:
The mole fraction of methanol in a 78g solution is 0.290, with a mass of 22.62g, while the mass of water is 55.38g.
Step-by-step explanation:
The mole fraction of a component in a solution is given by the number of moles of that component divided by the total number of moles in the solution. In this case, we are looking at a solution of methanol where the mole fraction of methanol is 0.290. This means that for every 1 mole of methanol, there are 0.290 moles of methanol in the solution.
The mass of each component can be calculated by multiplying the mole fraction by the total mass of the solution. Since the mole fraction of methanol is 0.290 and the total mass of the solution is 78g, we can calculate the mass of methanol as 0.290 x 78g = 22.62g. The mass of water can be calculated as the difference between the total mass of the solution and the mass of methanol: 78g - 22.62g = 55.38g.