Can 10.ml of glacial acetic acid mixed with 0.50 g of benzoic acid crystals (dissolved) freeze? And if so, what is the freezing point?

Think about what you are asking. Can't anything freeze if the temperature is lowered enough?

moles = grams benzoic acid/molar mass
solve for moles benzoic acid.

molality = moles/kg solvent\
m = moles/0.01 kg

delta T = Kf*m
solve for delta T and convert to freezing point.

To determine if the given mixture of glacial acetic acid and benzoic acid will freeze, we need to compare the freezing points of the individual components and consider their interactions.

Glacial acetic acid has a freezing point of approximately 16.6°C, while benzoic acid has a slightly higher freezing point of around 122.4°C.

In this case, the benzoic acid is dissolved in glacial acetic acid, which means its concentration is lower. Dissolving a solute (benzoic acid) in a solvent (glacial acetic acid) typically lowers the freezing point of the mixture due to the formation of a solution.

To precisely determine the freezing point of this mixture, we need additional information. Specifically, we require the molal concentration of the benzoic acid in the solution (mol of solute per kg of solvent). Once we have that, we can use the equation:

ΔT = Kf × m

where ΔT is the change in freezing temperature, Kf is the cryoscopic constant (which is specific to the solvent), and m is the molal concentration of the solute.

Given that the information about the molal concentration of benzoic acid is not provided, it is not possible to calculate the freezing point of the mixture accurately.