Chemistry Question on Solutions

Question

At 50 °C, the vapour pressure of pure benzene is 268 torr. The number of moles of non-volatile solute per mole of benzene required to prepare a solution having a vapour pressure of 167 torr at the same temperature is

Answer 1

Solution

The correct option is: (C): 0.605.

The decrease in vapor pressure when a non-volatile solute is added to a solvent follows Raoult's law. According to Raoult's law, the vapor pressure of a solvent in a solution is proportional to its mole fraction in the solution.

The formula for Raoult's law is:

P_solvent = x_solvent * P°_solvent

Where:

P_solvent is the vapor pressure of the solvent in the solution
x_solvent is the mole fraction of the solvent in the solution
P°_solvent is the vapor pressure of the pure solvent

In this case, you want to find the mole fraction of benzene (the solvent) that results in a vapor pressure of 167 torr at 50 °C. You're given the vapor pressure of pure benzene as 268 torr at the same temperature.

Rearranging the Raoult's law equation to solve for x_solvent:

x_solvent = P_solvent / P°_solvent

Plug in the values:

x_solvent = 167 torr / 268 torr ≈ 0.6231

Now, the mole fraction of the solute (non-volatile solute) can be calculated as:

x_solute = 1 - x_solvent ≈ 1 - 0.6231 ≈ 0.3769

The number of moles of non-volatile solute per mole of benzene can be calculated using the mole fractions:

Moles of solute / Moles of benzene = x_solute / x_solvent

Moles of solute / 1 = 0.3769 / 0.6231

Moles of solute ≈ 0.605

So, the answer is approximately 0.605