Question

The cryoscopic constant for acetic acid is $3.6Kkg/mol$. A solution of $1g$ of a hydrocarbon in $100g$ of acetic acid freezes at ${16.14}^{\circ }C$ instead of the usual ${16.60}^{\circ }C$. The hydrocarbon contains $92.3\%$ carbon. If the molecular formula is $C_6{H}_6$. Find the value of $x$ and $y$.

• A. $x=2,y=4$
• B. $x=3,y=5$
• C. $x=4,y=4$
• D. $x=6,y=6$

Answer 1

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

Let M g/mol be the molar mass of hydrocarbon. The number of moles of hydrocarbon $=\frac{1}{M}$
$100$ g of acetic acid $=0.1$ kg
The molality (m) of the hydrocarbon $=\frac{1}{M\times 0.1}=\frac{10}{M}$

The depression in the freezing point

$\Delta T_f=16.60-16.14={0.46}^{o}C$

$\Delta T_f=K_{f}m$

$0.46=3.6\times \frac{10}{M}$

$M=\frac{36}{0.46}=78$ g/mol

Percent of carbon $=92.3$ %

Mass of $C$ $=78\times \frac{92.3}{100}=72g$

Mass of hydrogen $=78-72=6g$

The atomic masses of $C$ and $H$ are $12$ g/mol and $1$ g/mol respectively.

Number of moles of $C$ $=\frac{72}{12}=6$

Number of moles of $H$ $=\frac{6}{6}=1$

Molecular formula is $C_x{H}_y=C_6{H}_6$

Hence, $x=6,y=6$