Final answer:
To find the freezing point of a solution given its osmotic pressure, calculate the molarity from the osmotic pressure, and then use the freezing point depression formula with the solvent's freezing point depression constant. Apply these steps to the data provided for water, assuming ideal solution behavior without electrolyte dissociation.
Step-by-step explanation:
To calculate the freezing point of a solution given its osmotic pressure, we first need to use the formula for osmotic pressure Π = MRT to find the molar concentration of the solution (M), where Π is the osmotic pressure, R is the universal gas constant, and T is the temperature in Kelvin. For the given osmotic pressure of 120 kPa, which converts to 1.184 atm (120 kPa / 101.325 = 1.184 atm), at a temperature of 300 K, the molar concentration (M) can be found by rearranging the equation to M = Π / (RT).
Once M is calculated, we can find the freezing point depression ΔTf using the formula ΔTf = iKfm, where i is the van 't Hoff factor (which is 1 for non-electrolytes), Kf is the freezing point depression constant for water, and m is the molality of the solution. If the solution is assumed to be an ideal solution and the solute does not dissociate into ions, then the final freezing point is the freezing point of pure water (0°C) minus ΔTf.
Finally, because the molarity (M) is based on the volume of the solution which can change with temperature, the molality (m), which is moles of solute per kg of solvent, is typically used for freezing point calculations since it does not change with temperature. The given value of Kf (1.86 K kg mol⁻¹) can be used directly in the equation to calculate ΔTf and thus the freezing point of the aqueous solution.