Question

A mysterious white powder could be powdered sugar (C12H22O11), cocaine (C17H21NO4), codeine (C18H21NO3), norfenefrine (C8H11NO2), or fructose (C6H12O6). When 82 mg of the powder is dissolved in 1.50 mL of ethanol (d = 0.789 g/cm3, normal freezing point −114.6 ∘C, Kf = 1.99 ∘C/m), the freezing point is lowered to −115.5 ∘C. What is the identity of the white powder?

Answer 1

Answer: norfenefrine $(C_8H_{11}NO_2)$

Explanation:

Depression in freezing point is given by:

$\Delta T_f=i\times K_f\times m$

$\Delta T_f=T_f^0-T_f=(-114.6-(-115.5)^0C=0.9^0C$ = Depression in freezing point

i= vant hoff factor = 1 (for non electrolyte)

$K_f$ = freezing point constant = $1.99^0C/m$

m= molality

$\Delta T_f=i\times K_f\times \frac{\text{mass of solute}}{\text{molar mass of solute}}\times \text{weight of solvent in kg}}$

Weight of solvent (ethanol)= $density\times volume=0.789g/cm^3\times 1.50cm^3=1.18g=1.18\times 10^{-3}kg$

Molar mass of unknown non electrolyte = M g/mol

Mass of unknown non electrolyte added = 82 mg = 0.082 g (1g=1000mg)

$0.9=1\times 1.99\times \frac{0.082g}{M g/mol\times 1.18\times 10^{-3}}kg}$

$M=154g/mol$

The molecular mass of norfenefrine $(C_8H_{11}NO_2)$ is near to 154 and thus the identity of the white powder is norfenefrine .