a 20.3 sample of an organic compound was ground with 442 mg of camphor to form an intimate mixture melting at 170.3 degree C. What is the apparent formula weight of the organic compound ?
(Kf of camphor=37.7 degree C/m
M.P. of camphor= 178.4 degree C)
To find the apparent formula weight of the organic compound, we need to use the freezing-point depression caused by the compound when mixed with camphor.
First, we need to calculate the change in temperature (ΔT) using the formula:
ΔT = Kf * m
Where Kf is the freezing-point depression constant of camphor and m is the molality of the organic compound in the mixture.
To calculate the molality (m), we need to determine the moles of the organic compound. This can be done by finding the moles of camphor.
Moles of camphor = mass of camphor / molar mass of camphor
The molar mass of camphor (C10H16O) is:
(12.01 * 10) + (1.008 * 16) + (15.999 * 1) = 152.23 g/mol
Hence, the moles of camphor are:
442 mg / 152.23 g/mol = 2.9 mmol
Since camphor and the organic compound form an intimate mixture, the moles of the organic compound will be the same as the moles of camphor. Therefore, the moles of the organic compound are 2.9 mmol.
Next, we need to calculate the molality of the organic compound in the mixture. Molality (m) is defined as moles of solute per kilogram of solvent. In this case, camphor acts as the solvent.
Molality (m) = moles of organic compound / mass of camphor (in kg)
The mass of camphor is 442 mg, which is equal to 0.442 g or 0.000442 kg.
Molality (m) = 2.9 mmol / 0.000442 kg = 6.55 mol/kg
Now we can calculate the freezing-point depression:
ΔT = (Kf of camphor) * (molality)
Substituting the given values:
ΔT = 37.7 °C/m * 6.55 mol/kg = 247.635 °C
The change in temperature (ΔT) is 247.635 °C.
Finally, we can find the apparent formula weight of the organic compound using the formula:
ΔT = K * m * (formula weight of organic compound)
Where K is the cryoscopic constant and for simplicity, we can assume it to be 1.
1 = 247.635 °C * m * formula weight of organic compound
Rearranging the equation to solve for the formula weight of the organic compound:
Formula weight of organic compound = 1 / (247.635 °C * m)
Substituting the values:
Formula weight of organic compound = 1 / (247.635 °C * 6.55 mol/kg)
Calculating this, we find:
Formula weight of organic compound ≈ 0.000604 g/mol
Therefore, the apparent formula weight of the organic compound is approximately 0.000604 g/mol.