Question

A forensic chemist is given a white powder for analysis. She dissolved 0.5g in 8.0g of benzene. The solution freezes at 3.9 degrees Celsius. Is the powder cocaine?
Cocaine is C₁₇H₂₁NO₄. Benzene freezes at 5.5 degrees Celsius and its K_f is 5.13 kg K/mole.

Answer 1

First lets calculate the molality given the Freezing point depression:

∆ Tf = Kf m

m = ∆ Tf / Kf

m= (5.5 - 3.9)/ 5.13

m = 0.31

Next, Calculate number of moles from molality (moles solute / Kg solvent)

Moles = molality x Kg solvent

Moles = 0.31 (moles/Kg) x (0.0080 Kg)

Moles = 2.5 x 10-3 White Powder

Is The Powder COCAINE (C₁₇H₂₁NO₄) ?

Calculate Molecular Weight of White Powder

Moles = 2.5 x 10^-3   Grams = 0.50

MW = m / mol = 0.50 /2.5 x 10^-3 = 200

MW _cocaine = 303,353 g/mol

Then it is not cocaine.