The vapor pressure of pure acetone (propanone) is 266 torr. When a non-volatile solute is added, the vapor pressure of acetone above the solution falls to 232 torr. What is the mole fraction of acetone in the solution? Show work.

A) 0.69
B) 0.32
C) 0.13
D) 0.045
E) 0.87

C ) 0.13

what is 232/266 ? What is Dalton's law?

To find the mole fraction of acetone in the solution, we can use Raoult's law, which states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution.

According to Raoult's law:

P(solution) = X(solvent) * P(solvent)

Where:
P(solution) = vapor pressure of the solution
X(solvent) = mole fraction of the solvent in the solution
P(solvent) = vapor pressure of the pure solvent

Given:
P(solvent) = 266 torr
P(solution) = 232 torr

Using the formula, we can rearrange it to solve for X(solvent):

X(solvent) = P(solution) / P(solvent)

X(solvent) = 232 torr / 266 torr

X(solvent) ≈ 0.87

Therefore, the mole fraction of acetone in the solution is approximately 0.87.

The correct answer is E) 0.87.

To find the mole fraction of acetone in the solution, we can use Raoult's Law. According to Raoult's Law, the vapor pressure of a component in a solution is proportional to its mole fraction.

First, we need to determine the mole fraction of the solute (non-volatile solute). Since it is a non-volatile solute, its vapor pressure is negligible, so the total vapor pressure above the solution is solely due to the acetone.

We can use the following equations:

P_total = P_acetone(solvent) + P_solute

Since the vapor pressure of the solvent (acetone) is given as P_acetone(solvent) = 266 torr, and the vapor pressure of the solution is P_total = 232 torr, we can substitute these values into the equation:

232 torr = 266 torr + P_solute

Now, we can solve for P_solute:

P_solute = 232 torr - 266 torr
P_solute = -34 torr

Since the solute is non-volatile, its vapor pressure should be zero. However, we obtained a negative value. This implies that the solute has a negative pressure, which is impossible. Therefore, there must be an error in the given data or calculation.

Without the correct value for the vapor pressure of the solute, we cannot accurately determine the mole fraction of acetone in the solution. Therefore, the correct answer cannot be determined based on the given information.