Final answer:
The freezing point of the solution, you first calculate the molarity using osmotic pressure, convert it to molality, and then apply the freezing point depression constant to determine how much lower the freezing point is compared to pure water.
Step-by-step explanation:
To calculate the freezing point of an aqueous solution using its osmotic pressure, we can use several formulas related to colligative properties. First, we have to calculate the molarity of the solution using the osmotic pressure formula (Π = MRT) and then use this to find the molality (m).
Given the osmotic pressure (Π) is 120.0 kPa (which is 1.184 atm when converted), temperature (T) is 300.0 K, and the universal gas constant (R) is 0.0821 L·atm/(mol·K), we find the molarity. The molarity (M) is calculated as M = Π / (RT), which gives us the molarity of the solute.
Next, since molality (m) is needed for the freezing point depression formula (ΔTf = Kf × m), we convert molarity to molality using the density of water. Given that the solution has a similar density to water (1.000 g/cm³), and assuming virtually no volume change when solute is added to the solvent (vsolution ≅ vwater), we approximate molality to be roughly the same as molarity.
Then, we use the freezing point depression formula ΔTf = Kf × m. We know from the data provided that water's molar freezing-point depression constant (Kf) is -1.86°C/m. Multiplying Kf by the molality (which approximates to the calculated molarity) gives us the amount the freezing point of the solution is depressed.
Finally, we subtract the freezing point depression from the normal freezing point of water, which is 0°C, to find the solution's freezing point.