A solution of 100g of water contains 23 g of table salt. At what temperature will it begin to freeze?
molality m= moles salt/kg of water
freezing point depression = .52C * m
Thanks, I got -2.08 Celsius. Where did the "freezing point depression = .52C * m" come from?
delta T = K f*molality
K f is the molal freezing point constant for water.
Kf = 1.86 degrees C/m for water.
To determine the temperature at which a solution of water and table salt will begin to freeze, we need to understand the concept of freezing point depression.
Freezing point depression occurs when a solute is added to a solvent, which lowers the freezing point of the solution compared to the pure solvent. In this case, the solute is table salt (NaCl), and the solvent is water (H2O).
To calculate the freezing point depression, we need to use the formula:
ΔTf = Kf * m
where:
- ΔTf is the freezing point depression (in degrees Celsius),
- Kf is the cryoscopic constant (a constant value specific to the solvent),
- m is the molality of the solute (moles of solute per kilogram of solvent).
The cryoscopic constant for water is approximately 1.86 °C/m. However, to use this constant, we first need to calculate the molality of the solution.
Molality (m) is defined as the number of moles of solute divided by the mass of the solvent (in kilograms).
First, let's calculate the molality (m) using the given data:
mass of water = 100 g = 0.1 kg (since 1 kg = 1000 g)
mass of salt = 23 g
molar mass of table salt (NaCl) = 58.44 g/mol
moles of salt = mass of salt / molar mass of salt
moles of salt = 23 g / 58.44 g/mol
Next, we calculate the molality (m):
molality (m) = moles of salt / mass of water (in kg)
molality (m) = (23 g / 58.44 g/mol) / 0.1 kg
Once we have the molality, we can use the freezing point depression equation to determine ΔTf.
Now, to calculate the freezing point depression (ΔTf):
ΔTf = Kf * m
Substituting the values:
ΔTf = 1.86 °C/m * molality (m)
Finally, we can determine the temperature at which the solution will begin to freeze by subtracting the freezing point depression from the freezing point of pure water, which is 0 °C.
Freezing point of the solution = 0 °C - ΔTf
Now, we can substitute the calculated values and solve for the freezing point of the solution.