68.0g of solute were dissolved in 393 mL of benzene. The solution froze at -0.50°C. The normal freezing point of benzene is 5.5°C and the molar freezing point constant is 5.12°C kg/mol. The density of benzene is .879 g/mol. Calculate the molar mass of the solute.
delta T = Kf*m. You know delta T (normal freezing point - new freezing point) and Kf, solve for m = molality.
m = mols/Kg solvent. You know m and kg solvent (use density for kg solvent; i.e., mass = volume x density). solve for mols.
mols = grams/molar mass. You know mols and grams, calculate molar mass.
To calculate the molar mass of the solute, we first need to find the molality of the solution. We can use the freezing point depression equation to do this.
ΔT = Kf * m
Where:
ΔT = change in freezing point (-0.50°C - 5.5°C = -6.0°C)
Kf = freezing point depression constant (5.12 °C kg/mol)
m = molality of the solution
Rearranging the equation to solve for m:
m = ΔT / Kf
Plugging in the known values:
m = (-6.0°C) / (5.12 °C kg/mol)
Now, let's convert the mass of benzene to moles. The density of benzene is 0.879 g/mL, so for 393 mL of benzene:
mass = density * volume
mass = 0.879 g/mL * 393 mL
Now that we have the mass of benzene, we can convert it to moles using the molar mass of benzene:
moles = mass / molar mass
The molar mass of benzene is 78.11 g/mol.
Now we can calculate the molality of the solution:
m = moles / mass of solvent (in kg)
Next, we can rearrange the equation to solve for the moles of solute:
moles = m * mass of solvent (in kg)
Finally, we can calculate the molar mass of the solute:
molar mass = mass of solute / moles of solute
Substituting the known values:
molar mass = 68.0 g / (m * mass of solvent (in kg))
This will give you the molar mass of the solute in grams per mole.