Answer:
148.5 g/mol
Step-by-step explanation:
We can use the freezing point depression equation to solve for the molar mass of the unknown compound:
ΔT = Kf × m × i
where ΔT is the freezing point depression, Kf is the freezing point depression constant for the solvent (benzene), m is the molality of the solution, and i is the van't Hoff factor, which is the number of particles that each molecule of the solute dissociates into in the solution.
First, we need to calculate the molality of the solution:
molality = moles of solute / mass of solvent in kg
We can calculate the moles of solute using the mass of the unknown compound:
moles of solute = mass of unknown compound / molar mass of unknown compound
We can rearrange the equation to solve for the molar mass:
molar mass of unknown compound = mass of unknown compound / moles of solute
Using the given values:
mass of unknown compound = 22.6 g
freezing point depression (ΔT) = 3.30°C
freezing point depression constant (Kf) = 5.12°C/m
mass of solvent (benzene) = 0.250 kg
We can calculate the molality of the solution:
molality = moles of solute / mass of solvent in kg
molality = (22.6 g / molar mass of unknown compound) / 0.250 kg
molality = (0.0226 kg / molar mass of unknown compound) / 0.250 kg
molality = 0.0904 / molar mass of unknown compound
We can plug this expression for molality into the freezing point depression equation:
ΔT = Kf × m × i
3.30°C = 5.12°C/m × (0.0904 / molar mass of unknown compound) × i
Solving for the molar mass of the unknown compound:
molar mass of unknown compound = (5.12°C/m × 0.0904 / 3.30°C) × i
molar mass of unknown compound = 0.1485 / i
The van't Hoff factor i depends on the degree of dissociation or association of the solute in the solution. For a molecular compound like the unknown compound, the value of i is 1. Therefore, we can calculate the molar mass:
molar mass of unknown compound = 0.1485 / 1
molar mass of unknown compound = 148.5 g/mol
So the molar mass of the unknown compound is 148.5 g/mol.
ALLEN