Question

The cryoscopic constant for acid is 3.6 K kg/mol. A solution of 1 g of a hydrocarbon in 100 g of acetic acid freezes at ${16.60}^{\circ }C.$ The hydrocarbon contains 92.3% carbon.If the molecular formula is $C_x{H}_y$. Find the value of x and y:

• A. $x=2,y=4$
• B. $x=3,y=8$
• C. $x=4,y=10$
• D. $x=6,y=6$

Answer 1

The correct option is D $x=6,y=6$

Freezing point depression is a colligative property observed in solutions that result from the introduction of solute molecules to a solvent. The freezing points of solutions are all lower than that of the pure solvent and is directly proportional to the molality of the solute.

$\Delta T_f={T_f}^0-T_f=i.K_b.m$.

$\Delta T_f$ is freezing point depression.

$T_f$ is freezing point of solution.

$K_b$ is depression constant.

Molecular weight of hydrocarbon is $12x+y$.

Molality $m=\frac{\frac{1}{12x+y}}{\frac{100}{1000}}$

$\Delta T_f=16.6-16={0.60}^{o}C$

$K_f=3.6$

Carbon content in hydrocarbon will be $\frac{92.3}{100}$.

$⟹\frac{92.3}{100}=\frac{12x}{12x+y}⟹92.3x-92.3y=0⟹x=y$

From above temperature difference , we get

$0.60=3.6\times \frac{10}{12x+y}$

As $x=y$, we get

$x=6$ and $y=6$