# Problem: If we have three different solutions, A, B, and C, each containing 100 g of water, plus respectively 6.84 g of sucrose (C 12H 22O 11), 0.72 g of ethanol, and 0.40 g of sodium hydroxide, which statement is true?

###### FREE Expert Solution

We’re being asked to identify which is true about the solutions regarding the colligative properties.

Recall that the freezing point of a solution is lower than that of the pure solvent and the change in freezing point (ΔT­f) is given by:

The change in freezing point is also related to the molality of the solution:

$\overline{){{\mathbf{\Delta T}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{imK}}}_{{\mathbf{f}}}}$

where:

i = van’t Hoff factor

m = molality of the solution (in m or mol/kg)

Kf = freezing point depression constant (in ˚C/m) of the solvent

Recall that the boiling point of a solution is higher than that of the pure solvent and the change in boiling point (ΔT­b) is given by:

The change in boiling point is also related to the molality of the solution:

$\overline{){{\mathbf{\Delta T}}}_{{\mathbf{b}}}{\mathbf{=}}{{\mathbf{imK}}}_{{\mathbf{b}}}}$

where:

i = van’t Hoff factor

m = molality of the solution (in m or mol/kg)

Kb = boiling point elevation constant (in ˚C/m) of the solvent

The problem states that we have aqueous solutions which means the solvent is water. This means the value of Kf is the same for all the given solutions.

Therefore, ΔTf and ΔTb  will just depend on the osmolality of each solution, given by:

$\overline{){\mathbf{Osmolality}}{\mathbf{=}}{\mathbf{i}}{\mathbf{×}}{\mathbf{m}}}$

higher osmolality or concentration will result in a lower freezing point.

higher osmolality or concentration will result in a higher boiling point. ###### Problem Details

If we have three different solutions, A, B, and C, each containing 100 g of water, plus respectively 6.84 g of sucrose (C 12H 22O 11), 0.72 g of ethanol, and 0.40 g of sodium hydroxide, which statement is true?