Question

In a 50.0-g50.0-g aqueous solution of methanol, CH_{4}O,CH_{4}O, the mole fraction of methanol is 0.270.

What is the mass of each component?

Answer 1

To find the mass of methanol and water in a 50.0-g solution with a methanol mole fraction of 0.270, we calculate using the molecular weight of methanol (32.04 g/mol) and the definition of mole fraction.

Step-by-step explanation:

In a 50.0-g aqueous solution of methanol (CH4O), if the mole fraction of methanol is 0.270, to find the mass of each component, we'll need to use the definition of mole fraction combined with the molecular weight of methanol.

Methanol has a molecular weight of approximately 32.04 g/mol. The mole fraction is the number of moles of methanol divided by the total number of moles in the solution. Since we know the total mass of the solution, we can find the mass of methanol (solute) and the mass of water (solvent).

To find the mass of methanol, we use the formula:

Mass of methanol = mole fraction of methanol * total mass of solution / (1 + [(molecular weight of methanol - 1) * mole fraction of methanol])

Plugging in the numbers:

Mass of methanol = 0.270 * 50.0 g / (1 + [(32.04 g/mol - 1) * 0.270])

With the mole fraction and molecular weights, we can calculate both components' masses accurately.

Answer 2

The mass of methanol in the solution is 13.5 g and the mass of water is 36.5 g.

Step-by-step explanation:

The mass of each component in a 50.0 g aqueous solution of methanol can be calculated using the mole fraction. The mole fraction of methanol is given as 0.270. We can find the mass of methanol by multiplying the mole fraction by the total mass of the solution:

Mass of methanol = Mole fraction of methanol x Total mass of solution

Mass of methanol = 0.270 x 50.0 g = 13.5 g

The mass of water can be calculated by subtracting the mass of methanol from the total mass of the solution:

Mass of water = Total mass of solution - Mass of methanol

Mass of water = 50.0 g - 13.5 g = 36.5 g