How do I calculate the freezing point of 11.3g FeCl3 in 155g water? I know how to calculate i and m but how do you find Kf?
It should be listed in the problem. If not in the problem then in your text. For water Kf = 1.86 degrees/m
To calculate the freezing point of a solution, you need to know the cryoscopic constant (Kf) of the solvent. Kf is a characteristic property of a solvent that represents the amount by which the freezing point of the pure solvent decreases per mole of solute particles added.
To find the Kf value for water, you can refer to a reliable source such as a chemistry handbook, textbook, or online database. Let's assume for this example that the Kf value for water is 1.86 °C/m.
Now, let's break down the steps to calculate the freezing point of the FeCl3 solution:
1. Determine the number of moles of FeCl3:
- Given mass of FeCl3 = 11.3 g
- Calculate the molar mass of FeCl3: 55.845 g/mol (atomic mass of Fe) + 3 * (35.453 g/mol) (atomic mass of Cl) = 162.204 g/mol
- Calculate the number of moles of FeCl3: 11.3 g / 162.204 g/mol = 0.0696 mol (rounded to four decimal places)
2. Determine the molality (m) of the solution:
- Given mass of water = 155 g
- Calculate the number of moles of water: 155 g / 18.015 g/mol (molar mass of water) = 8.605 mol (rounded to three decimal places)
- Calculate the molality: moles of solute / mass of solvent (in kg) = 0.0696 mol / 0.155 kg = 0.449 m (rounded to three decimal places)
3. Calculate the change in freezing point (∆Tf):
- ∆Tf = Kf * m, where Kf is the cryoscopic constant and m is the molality of the solution.
- ∆Tf = 1.86 °C/m * 0.449 m = 0.836 °C (rounded to three decimal places)
4. Determine the freezing point of the solution:
- The freezing point depression (∆Tf) indicates how much the freezing point of the solution decreases compared to the freezing point of the pure solvent. Since we have the change in freezing point (∆Tf), we need to subtract it from the freezing point of pure water, which is 0 °C.
- Freezing point = Freezing point of pure solvent - ∆Tf = 0 °C - 0.836 °C = -0.836 °C (rounded to three decimal places)
Therefore, the freezing point of the FeCl3 solution is approximately -0.836 °C.
To find the value of Kf, which represents the freezing point depression constant for a specific solvent, you typically need to refer to a reference table or use experimental data. However, let's assume we have the value of Kf for water readily available to us, which is 1.86 °C·kg/mol.
The freezing point depression equation is given by:
∆T = i * Kf * m
Where:
∆T is the freezing point depression (in Celsius)
i is the van't Hoff factor (the number of particles the solute breaks into when dissolved)
Kf is the freezing point depression constant
m is the molality of the solution (moles of solute per kilogram of solvent)
Now, let's calculate the freezing point depression for the given solution of 11.3g FeCl3 in 155g of water:
Step 1: Convert the mass of FeCl3 to moles.
Molar mass of FeCl3 = (55.85 g/mol + (3 * 35.45 g/mol)) = 162.2 g/mol
moles of FeCl3 = (11.3g) / (162.2 g/mol)
Step 2: Calculate the molality (m) of the solution.
molality (m) = (moles of solute) / (mass of solvent in kg)
mass of water in kg = (155g) / (1000g/kg)
Step 3: Calculate the van't Hoff factor (i).
In aqueous solutions, FeCl3 dissociates into four ions: Fe³⁺ and three Cl⁻ ions. Therefore, i = 4.
Step 4: Substitute the values into the freezing point depression equation to find ∆T.
∆T = (4) * (1.86 °C·kg/mol) * [(11.3g / 162.2 g/mol) / (155g / 1000g/kg)]
Simplifying further:
∆T ≈ 0.906 °C
Therefore, the freezing point of the solution is lowered by approximately 0.906 °C.