A solution of 0.2113 g of water dissolved in 25.0 g of a solvent freezes at 11.5 °C below the freezing point of the solvent. What is Kf for this solvent?
see above.
To determine the freezing point depression (△Tf) and calculate the cryoscopic constant (Kf) for the solvent, you can use the following formula:
△Tf = Kf * m
Where:
△Tf = freezing point depression (in °C)
Kf = cryoscopic constant (in °C/m)
m = molality of the solution (in mol/kg)
First, we need to calculate the molality of the solution.
Step 1: Calculate the molality (m) of the water solution.
Molality (m) = moles of solute / mass of solvent (in kg)
Given that the mass of water (solute) is 0.2113 g and the mass of the solvent is 25.0 g, we need to convert the masses to kg:
Mass of water (solute) = 0.2113 g = 0.2113 / 1000 = 0.0002113 kg
Mass of solvent = 25.0 g = 25.0 / 1000 = 0.025 kg
m = 0.0002113 kg water / 0.025 kg solvent = 0.008452 mol/kg
Step 2: Calculate the freezing point depression (△Tf).
△Tf = -11.5 °C (given)
Step 3: Rearrange the formula to solve for Kf.
Kf = △Tf / m
Kf = -11.5 °C / 0.008452 mol/kg
Kf ≈ -1361 °C kg/mol
Therefore, the cryoscopic constant (Kf) for this solvent is approximately -1361 °C kg/mol.