Pure water freezes at 273 K and 1 bar. The addition of 34.5 g of ethanol to 500 g of water changes the freezing point of the solution. Use the freezing point depression constant of water as 2 K kg mol–1. The figures shown below represent plots of vapour pressure (V.P.) versus temperature (T).
[molecular weight of ethanol is 46 g mol–1]
Among the following, the option representing change in the freezing point is
Tf = Kf × m
= 2 × 1.5
= 3
Freezing point of ethanol + water mixture = 273- 3 = 270
Freezing point depression is a colligative property, meaning it depends on the number of solute particles in a solution, not their identity. When a non-volatile solute is added to a solvent, the freezing point of the solution is lower than that of the pure solvent.
The change in freezing point (ΔTf) is given by:
Where:
First, find the number of moles of ethanol (solute).
Mass of ethanol = 34.5 g
Molar mass of ethanol = 46 g mol–1
Moles of ethanol = mass / molar mass = 34.5 g / 46 g mol–1
Now, find the mass of the solvent (water) in kg.
Mass of water = 500 g = 0.5 kg
Molality (m) is defined as moles of solute per kg of solvent.
Now, plug the values into the freezing point depression formula.
The freezing point is depressed by 3 K.
The pure solvent (water) freezes at 273 K. The new freezing point (Tf, solution) is the pure solvent's freezing point minus the depression.
The question provides vapor pressure (V.P.) vs. temperature (T) plots. For a solution, the vapor pressure is lower than that of the pure solvent at any given temperature. This is why the boiling point increases and the freezing point decreases.
The curve for the solution will lie below the curve for the pure solvent. The freezing point is the temperature at which the solid and liquid phases have the same vapor pressure and can coexist.
On the graph, this is the temperature where the vapor pressure curve of the liquid (solvent or solution) intersects the vapor pressure curve of the solid (which is typically very low and often approximated).
For the pure solvent, this intersection is at 273 K. For the solution, the entire liquid vapor pressure curve is shifted down. This means the intersection point with the solid's vapor pressure curve will occur at a lower temperature (270 K).
Therefore, the correct plot will show the solution's curve below the solvent's curve, and the freezing point (the temperature at a given, very low vapor pressure) will be clearly lower for the solution.
Given that ΔTf = 3 K, the new freezing point is 270 K. You must identify the plot where the solution's freezing point is 3 degrees less than the pure solvent's freezing point of 273 K.
The change in freezing point, ΔTf, is 3 K. The new freezing point of the solution is 270 K. The correct option is the plot that shows the solution's vapor pressure curve below the pure solvent's curve, with its freezing point depressed to 270 K.
1. Freezing Point Depression:
Where i is the van't Hoff factor (approximately 1 for non-electrolytes like ethanol).
2. Molality:
3. New Freezing Point: