Which solution will have the lowest freezing point?
0.25 molal aqueous solution of sucrose
0.5 molal aqueous solution of glucose
solution of 180 g of glucose (MW = 180.2 g/mol) in one kg of water.
pure water
delta T = Kf*m will tell you. Since Kf is a constant, the largest m will give the largest delta T.
To determine which solution will have the lowest freezing point, we need to understand the concept of freezing point depression.
Freezing point depression occurs when a solute, such as sugar or glucose, is added to a solvent, such as water. The presence of the solute disrupts the formation of the solvent's crystalline lattice, preventing it from solidifying at its normal freezing point. As a result, the freezing point of the solution is lower than that of the pure solvent.
The extent of the freezing point depression depends on the molality (moles of solute per kilogram of solvent) of the solution. The higher the molality, the greater the freezing point depression.
Let's analyze each of the given solutions to determine the one with the lowest freezing point:
1. 0.25 molal aqueous solution of sucrose: This solution has a molality of 0.25 molal, which means there are 0.25 moles of sucrose per kilogram of water.
2. 0.5 molal aqueous solution of glucose: This solution has a molality of 0.5 molal, which means there are 0.5 moles of glucose per kilogram of water.
3. Solution of 180 g of glucose (MW = 180.2 g/mol) in one kg of water: Here, we need to convert the given mass of glucose to moles to determine the molality. The molar mass of glucose is 180.2 g/mol.
Number of moles of glucose = mass / molar mass
= 180 g / 180.2 g/mol
≈ 0.999 moles
The molality of this solution is approximately 0.999 molal, as there are 0.999 moles of glucose per kilogram of water.
4. Pure water: This is a solution with no solute added, so its molality is zero.
Based on the molality values, we can conclude that the 0.5 molal aqueous solution of glucose will have the lowest freezing point among the given options, as a higher molality leads to a greater freezing point depression.
Remember, the freezing point depression of a solution can be calculated using the formula: ∆T = Kf * m, where ∆T is the freezing point depression, Kf is the cryoscopic constant specific to the solvent, and m is the molality of the solution.