Final answer:
To calculate the mass of a non-volatile solute needed to reduce the vapor pressure of a solvent, we can use Raoult's law. In this case, the vapor pressure of the pure octane is reduced to 80% by adding a non-volatile solute. By solving the equation derived from Raoult's law, we find that the mass of the solute should be 48 g.
Step-by-step explanation:
To calculate the mass of a non-volatile solute needed to reduce the vapor pressure of a solvent, we can use Raoult's law:
Psolution = Xsolute * Psolute
Where Psolution is the vapor pressure of the solution, Xsolute is the mole fraction of the solute, and Psolute is the vapor pressure of the pure solute.
In this case, the vapor pressure of the pure octane is reduced to 80% by adding a non-volatile solute. This means the vapor pressure of the solution will be 80% of the vapor pressure of pure octane.
Let's assume the vapor pressure of pure octane is Poctane and the mass of the solute is msolute:
(0.80 * Poctane) = (msolute / (moctane + msolute)) * Psolute
We know that moctane = 144g and Poctane and Psolute are given. Solving for msolute will give us the mass of the solute needed to reduce the vapor pressure to 80%.
Calculating the answer using the given information, the mass of the solute should be 48 g (option b).