The molal freezing point constant for water is 1.86 C/m. at what temperature will a micture of 2.00g of CalCl2 and 25.0g of water freeze?
moles = grams/molar mass.
Solve for moles CaCl2. (You have a typo in the formula for CaCl2.)
molality = moles/kg solvent.
Solve for molality
delta T = iKf*molality
Solve for delta T; i = 3
Convert delta T to freezing point remembering the normal freezing point for water is 0 celsius.
how do i convert delta T to freezing point?
To find the temperature at which the mixture of CalCl2 and water will freeze, we need to use the molal freezing point constant and the molality of the solution.
1. Calculate the molality (m) of the solution using the formula:
molality = moles of solute / mass of solvent (in kg)
The molar mass of CalCl2 is 110.98 g/mol.
number of moles of CalCl2 = mass of CalCl2 / molar mass of CalCl2
= 2.00 g / 110.98 g/mol
The molar mass of water is 18.02 g/mol.
number of moles of water = mass of water / molar mass of water
= 25.0 g / 18.02 g/mol
mass of water in kg = 25.0 g / 1000 g/kg
Now we can calculate the molality:
molality = (moles of CalCl2 + moles of water) / mass of water (in kg)
2. Calculate the change in freezing point (∆T) using the formula:
∆T = molality x molal freezing point constant
3. Finally, calculate the freezing point temperature by subtracting ∆T from the normal freezing point of water (0°C).
Let's calculate step by step.
1. Calculate the moles of CalCl2:
moles of CalCl2 = 2.00 g / 110.98 g/mol
moles of water = 25.0 g / 18.02 g/mol
mass of water in kg = 25.0 g / 1000 g/kg
molality = (moles of CalCl2 + moles of water) / mass of water (in kg)
2. Calculate the change in freezing point (∆T):
∆T = molality x molal freezing point constant
3. Calculate the freezing point temperature:
Freezing point temperature = 0°C - ∆T
Let's calculate the values:
1. Moles of CalCl2:
moles of CalCl2 = 2.00 g / 110.98 g/mol = 0.018 mol
Moles of water:
moles of water = 25.0 g / 18.02 g/mol = 1.388 mol
Mass of water in kg:
mass of water in kg = 25.0 g / 1000 g/kg = 0.025 kg
Molality:
molality = (moles of CalCl2 + moles of water) / mass of water (in kg)
= (0.018 mol + 1.388 mol) / 0.025 kg
= 55.04 mol/kg
2. Calculate the change in freezing point (∆T):
∆T = molality x molal freezing point constant
= 55.04 mol/kg x 1.86 °C/m
= 102.27 °C
3. Calculate the freezing point temperature:
Freezing point temperature = 0°C - ∆T
= 0°C - 102.27 °C
= -102.27 °C
Therefore, the mixture of 2.00 g of CalCl2 and 25.0 g of water will freeze at approximately -102.27 °C.
To determine the freezing temperature of the mixture, we need to apply the concept of molality and the freezing point depression equation.
The freezing point depression equation is expressed as:
ΔT = Kf * m,
Where:
- ΔT is the change in freezing point in degrees Celsius
- Kf is the molal freezing point constant (1.86 °C/m for water)
- m is the molality of the solution
To calculate the molality (m) of the solution, we need to determine the moles of both solute and solvent:
Step 1: Determine the moles of calcium chloride (CaCl2)
Molar mass of CaCl2 = 40.08 g/mol (Ca: 40.08 g/mol, Cl: 2 * 35.45 g/mol)
moles of CaCl2 = mass / molar mass = 2.00 g / 40.08 g/mol
Step 2: Determine the moles of water (H2O)
Molar mass of H2O = 18.02 g/mol
moles of H2O = mass / molar mass = 25.0 g / 18.02 g/mol
Step 3: Calculate the molality (m)
molality (m) = moles of solute / mass of solvent(kg)
mass of solvent = 25.0 g + 2.00 g (water + CaCl2)
Now, we have all the necessary information to calculate the change in freezing point (ΔT):
ΔT = Kf * m
Substitute the values into the equation:
ΔT = 1.86 °C/m * (moles of solute / mass of solvent (kg))
Finally, subtract the change in freezing point (ΔT) from the freezing point of pure water (0 °C) to find the freezing temperature of the mixture.