Question

The cryoscopic constant for acetic acid is $3.6\text{Kkg/mol}$. A solution of $1\text{g}$ of a hydrocarbon in $100\text{g}$ of acetic acid freezes at $16.14{}^{\circ }\text{C}$ instead of the usual $16.60{}^{\circ }\text{C}$. The hydrocarbon contains 92.3% carbon. What is its molecular formula?

• A. $C_6{H}_6$
• B. $C_6{H}_{12}$
• C. $C_8{H}_{18}$
• D. $C_{10}{H}_6$

Answer 1

The correct option is A $C_6{H}_6$

The solute is a hydrocarbon which contains 92.3% carbon and 7.7% Hydrogen, Now
$\Delta T_f=16.60-16.14={0.46}^{0}C=i{K}_{f}m$
Difference of temperature in K will also be same =0.46K
i=1 for the hydrocarbon as it will not dissociate in acetic acid
$0.46=3.6\times \frac{1/M_H}{100}\times 1000$
$M_H=\frac{36}{0.46}=78.26g$ where $M_H$ is molar mass of the hydrocarbon
mass of carbon in given H.C. in 1 formula unit is $=78.26\times 0.923=72.23g$
$n_c=72.23/12=6.012$
mass of hydrogen in given H.C. in 1 formula unit is $=78.26\times 0.077=6.026g$
$n_{=}6.026/1=6.026$
So the molecular formula of the hydrocarbon is $C_6{H}_6$