Question

A solution is obtained by dissolving 171.2 g of sucrose (i = 1) with 360.4 g of H ₂ O at 55 ºC. Sucrose is a non-volatile solute.

The water vapor pressure at 55ºC is 118.1 torr. The molar mass of sucrose is 342.3 g / mol and H ₂ O is 18.02 g / mol.

To calculate the mole fraction, it is necessary to calculate the  total moles . The result of this computation is:

Calculate the vapor pressure on the solution:

The vapor pressure of the solution is due to which of the two compounds

How much is the change in vapor pressure, ΔP:

Answer 1

The mole fraction of sucrose(χ_sucrose) is given by:

where:

n_sucrose - number of moles of sucrose

n_water - number of moles of water

The number of moles is calculated using the formula:

Therefore the number of moles of sucrose(n_sucrose) is:

The number of moles of water(n_water) is:

The total moles of both sucrose and water is 20.50 moles.

Therefore the mole fraction of sucrose(χ_sucrose) is:

Hence the mole fraction of sucrose(χ_sucrose) is 0.02440

The relative lowering of vapor pressure is given by the formula:

where:

P⁰ - the vapor pressure of pure solvent (here, water)

P_solution - vapor pressure of the solution

Here solute is sucrose. Therefore we have:

This equation can be re-arranged as follows, to get vapor pressure of the solution:

Given:

P⁰ = 118.1 torr

χ_sucrose= 0.02440

Therefore  vapor pressure of the solution is:

The vapor pressure of the solution is due to the water since sucrose is non-volatile and little of it becomes vapor.

The change in vapor pressure, ΔP, given by:

We have:

Therefore we can write:

OR

Given:

P⁰ = 118.1 torr

χ_sucrose= 0.02440

Therefore the change in vapor pressure, ΔP is:

Therefore the answers are:

The total moles of both sucrose and water is 20.50 moles

The vapor pressure of the solution is 115.2 torr

The vapor pressure of the solution is due to the water(or the solvent) since sucrose is non-volatile and little of it becomes vapor.

The change in vapor pressure, ΔP is 2.882 torr