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. What is the molecular formula?

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

Answer 1

Answer: (A)

$K_b=3.6Kkg/mol$
$\Delta T_f=16.6-16.14=0.46^{\circ }C$
$\Delta T_f=\frac{1000k_f{w}_1}{m_1{w}_2}$
$0.46=\frac{1000\times 3.6\times 1}{m_1\times 100}$
$m_1=\frac{36}{0.46}=78.26g$
$C=\frac{92.3}{100}\times 78.26=72.23g$
$H=\frac{7.7\times 78.26}{100}=6.026g$
Whole ratio
$C=\frac{72.23}{12}=6.02$
$H=\frac{6.026}{1}=6.02$
Therefore, the molecular formula is $C_6{H}_6$