What is the freezing point of a solution of AlCl3 that contains 55.0 g AlCl3 dissolved in 390 g of water?
To find the freezing point of a solution, you need to use the concept of freezing-point depression. This concept states that when a solute is dissolved in a solvent, it lowers the freezing point of the resulting solution compared to the pure solvent.
To calculate the freezing point depression, you will need to know the molality of the solution and the freezing point depression constant (Kf) for the solvent.
The molality (m) of a solution is defined as the moles of solute (AlCl3) per kilogram of solvent (water).
First, convert the given masses of AlCl3 and water into moles:
1. Calculate the number of moles of AlCl3:
- Convert the mass of AlCl3 (55.0 g) into moles using the molar mass of AlCl3 (133.34 g/mol).
- Divide the mass by the molar mass: 55.0 g / 133.34 g/mol = 0.413 mol
2. Calculate the number of moles of water:
- Convert the mass of water (390 g) into moles using the molar mass of water (18.015 g/mol).
- Divide the mass by the molar mass: 390 g / 18.015 g/mol = 21.64 mol
Next, calculate the molality of the solution:
3. Calculate the molality (m) using the formula:
molality (m) = moles of solute / mass of solvent (in kg)
- Divide the moles of AlCl3 by the mass of water in kilograms (convert grams to kilograms by dividing by 1000):
m = 0.413 mol / 0.390 kg = 1.059 mol/kg
Finally, use the freezing point depression constant (Kf) for water, which is 1.86 °C/m, to calculate the change in freezing point (∆Tf):
4. Calculate the change in freezing point (∆Tf) using the formula:
∆Tf = Kf * molality
- Multiply the molality (1.059 mol/kg) by the freezing point depression constant (1.86 °C/m):
∆Tf = 1.86 °C/m * 1.059 mol/kg = 1.97 °C
The freezing point depression (∆Tf) is the amount by which the freezing point of the solution is decreased compared to the pure solvent. In this case, it is 1.97 °C.
To find the freezing point of the solution, subtract the freezing point depression (∆Tf) from the freezing point of pure water, which is 0 °C:
Freezing point = 0 °C - ∆Tf = 0 °C - 1.97 °C = -1.97 °C
Therefore, the freezing point of the AlCl3 solution is approximately -1.97 °C.