Question

tert-Butyl alcohol is a solvent with a Kf of 9.10 ∘C/m and a freezing point of 25.5 ∘C. When 0.807 g of an unknown colorless nonelectrolyte liquid was dissolved in 11.6 g of tert-butyl alcohol, the solution froze at 15.3 ∘C.Which of the following is most likely the identity of this unknown liquid?

A. ethylene glycol (molar mass = 62.07 g/mol)
B. 1-octanol (molar mass = 130.22 g/mol)
C. glycerol (molar mass = 92.09 g/mol)
D. 2-pentanone (molar mass = 86.13 g/mol)
E. 1-butanol (molar mass = 74.12 g/mol)

Answer 1

Answer: A. ethylene glycol (molar mass = 62.07 g/mol)

Explanation:

Depression in freezing point is given by:

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

$\Delta T_f=T_f-T_f^0=(25.5-15.3)^0C=10.2^0C$ = Depression in freezing point

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

$K_f$ = freezing point constant = $9.10^0C/m$

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 (t-butyl alcohol)= 11.6 g = 0.0116 kg

Molar mass of unknown non electrolyte = M g/mol

Mass of unknown non electrolyte added = 0.807 g

$10.2=1\times 9.10\times \frac{0.807g}{M g/mol\times 0.0116kg}[/tex ]

[texM=62.07g/mol$

Thus the most likely the identity of this unknown liquid is ethylene glycol with molar mass of  62.07 g/mol.