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)`

Step-by-step explanation:

Depression in freezing point is given by:

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

Weight of solvent (ethanol)=
`density* volume=0.789g/cm^3* 1.50cm^3=1.18g=1.18* 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* 1.99* (0.082g)/(M g/mol* 1.18* 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 .