The depression in freezing point (
ΔTf) is related to the cryoscopic constant (
Kf) by the formula:
ΔTf=Kf×m,
where
m is the molality of the solution, and
Kf is the cryoscopic constant of the solvent.
To calculate molality (
m), we use the formula:
m=mass of solvent in kgmoles of solute.
First, calculate the moles of the solute:
moles of solute=molar mass of solutemass of solute.
We are not provided with the molar mass of the solute, so we assume it is 10 g/mol for simplicity. Therefore, the moles of solute is:
moles of solute=1010=1mol.
Now, calculate the molality:
m=0.1kg1mol=10mol/kg.
Substitute this value into the depression in freezing point formula:
1.5=Kf×10⇒Kf=101.5=0.15kg/mol.
Thus, the cryoscopic constant
Kf of the solvent is
0.15kg/mol.