Calculate the freezing point of the following solutions, assuming complete dissociation.3.7% KCL by mass (in water)
To calculate the freezing point of a solution, you can use the equation: ΔTf = Kf * m
ΔTf represents the change in freezing point, Kf is the cryoscopic constant, and m is the molality of the solution.
First, we need to calculate the molality by converting the mass percentage to molarity.
1. Determine the molar mass of KCl:
- K (potassium): 39.10 g/mol
- Cl (chlorine): 35.45 g/mol
Add the molar masses together:
39.10 g/mol + 35.45 g/mol = 74.55 g/mol
2. Calculate the mass of KCl in the solution:
Since the solution is 3.7% KCl by mass, we can assume we have 3.7 g of KCl in 100 g of solution.
3. Calculate the number of moles of KCl:
Divide the mass of KCl by its molar mass:
3.7 g / 74.55 g/mol = 0.0495 mol
4. Calculate the mass of water in the solution:
We initially had 100 g of solution, and we know that 3.7 g is KCl, so the remaining mass is water:
100 g - 3.7 g = 96.3 g of water
5. Calculate the molality of the solution:
Molality (m) is defined as the number of moles of solute (KCl) divided by the mass of the solvent (water) in kilograms.
Convert the mass of water to kilograms:
96.3 g ÷ 1000 = 0.0963 kg
Now, divide the number of moles of KCl by the mass of water in kilograms:
0.0495 mol ÷ 0.0963 kg = 0.514 mol/kg
Now that we have the molality (m), we can calculate the change in freezing point (ΔTf).
6. Find the cryoscopic constant (Kf) for water:
The cryoscopic constant for water is 1.86 °C/m.
7. Calculate ΔTf using the formula:
ΔTf = Kf * m
ΔTf = 1.86 °C/m * 0.514 mol/kg
ΔTf = 0.955 °C
Therefore, the freezing point of the 3.7% KCl solution (assuming complete dissociation) would be lowered by 0.955 °C compared to the freezing point of pure water.
3.7% KCl = 3.7 g KCl/100 g soln =
3.7 g KCl/(3.7 g KCl + 96.3 g H2O) =
Convert 3.7 g KCl to moles. moles = grams/molar mass
Then molality = moles/kg solvent.
delta T = i*kf*m
i = 2, kf you know and m from above.