When 0.500 g of an unknown compound was dissolved in 15.0 g benzene, the freezing point depression was determined to be 0320C . The molar mass of the unknown compound is ? g/mol.
(The freezing point depression constant for benzene is 512C kgmol .
To find the molar mass of the unknown compound, we need to use the formula for freezing point depression:
ΔT = Kf * m * i
Where:
ΔT = freezing point depression (in Celsius)
Kf = freezing point depression constant (in Celsius kg/mol)
m = molality of the solution (in mol/kg)
i = van't Hoff factor (the number of particles the compound dissociates into)
In this case, we are given the freezing point depression (ΔT = 0.320°C), the freezing point depression constant for benzene (Kf = 5.12°C kg/mol), and the mass of the benzene solvent (15.0 g).
First, we need to calculate the molality (m) of the solution:
molality (m) = moles of solute / mass of solvent (in kg)
To find the moles of solute, we need to convert the mass of the unknown compound (0.500 g) to moles using its molar mass.
Molar mass of the unknown compound = 0.500 g / moles of the unknown compound
Finally, we can substitute the values into the freezing point depression formula to find the molar mass of the unknown compound:
ΔT = Kf * (moles of solute / mass of solvent) * i
0.320°C = 5.12°C kg/mol * (moles of solute / 0.015 kg) * i
Now, solve the equation for the moles of the unknown compound:
moles of solute = (ΔT * 0.015 kg) / (5.12°C kg/mol * i)
Finally, substitute the moles of solute back into the molar mass formula:
Molar mass of the unknown compound = 0.500 g / (moles of the unknown compound)