To determine the exceptions to the octet rule, analyze each molecule:
CO$_2$: Follows the octet rule. (C has 8 electrons in its valence shell.
NO$_2$: Exception. It has an odd number of valence electrons (11), making it a free radical.
H$_2$SO$_4$: Follows the octet rule.
BF$_3$: Exception. Boron has only 6 electrons in its valence shell (electron-deficient compound).
CH$_4$: Follows the octet rule.
SiF$_4$: Follows the octet rule.
ClO$_2$: Exception. It is a free radical with an odd number of valence electrons.
PCl$_5$: Exception. Phosphorus has 10 valence electrons (expanded octet).
BeF$_2$:Exception. Beryllium has only 4 valence electrons (electron-deficient compound).
C$_2$H$_6$: Follows the octet rule.
CHCl$_3$: Follows the octet rule.
CBr$_4$: Follows the octet rule.
Molecules that are exceptions to the octet rule:
\[\text{NO}_2, \text{BF}_3, \text{ClO}_2, \text{PCl}_5, \text{BeF}_2\]
Total number of exceptions = 6.
Final Answer:\[6\]