Solutions Question 257
Question: The cryoscopic constant for acetic acid is 3.6 K kg/mol. A solution of 1 g of a hydrocarbon in 100 g 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-
Options:
A) $ C_6H_6 $
B) $ C_6H_{12} $
C) $ C_8H_{18} $
D) $ C_{10}H_6 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ K_{b}=3.6K,kg/mol. $
$ \Delta T_{f}=16.6-16.14=0.46{}^\circ C $
$ \Delta T_{f}=\frac{100k_{f}w_1}{m_1w_2} $
$ 0.46=\frac{100\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}{1}=6.02 $
$ H=\frac{6.026}{1}=6.02 $ Therefore, the molecular formula is $ C_6{H_{6.}} $
