Step 1: Understanding the Question:
The question is about the chemical components of photochemical smog.
We need to determine the total number of $\text{sp}^2$ hybridized carbon atoms present in three specific organic molecules: acrolein, formaldehyde, and peroxyacetyl nitrate (PAN).
Step 2: Key Formula or Approach:
Hybridization of carbon is determined by the number of $\sigma$ bonds formed by the carbon atom.
A carbon atom forming three $\sigma$ bonds and one $\pi$ bond (e.g., in a double bond C=C or C=O) is $\text{sp}^2$ hybridized.
A carbon atom forming four $\sigma$ bonds is $\text{sp}^3$ hybridized.
Step 3: Detailed Explanation:
• Let us analyze each compound individually:
• 1. Acrolein ($\text{CH}_2=\text{CH}-\text{CHO}$):
The IUPAC name of acrolein is prop-2-enal.
Its structural formula is:
\[ \text{H}_2\text{C}=\text{CH}-\text{C}(=\text{O})\text{H} \]
There are three carbon atoms in acrolein:
The first carbon ($\text{C}_1$) is part of the aldehyde group ($\text{-C}(=\text{O})\text{H}$) and forms one double bond with oxygen, so it is $\text{sp}^2$ hybridized.
The second carbon ($\text{C}_2$) is part of the alkene double bond and is $\text{sp}^2$ hybridized.
The third carbon ($\text{C}_3$) is also part of the alkene double bond and is $\text{sp}^2$ hybridized.
Thus, acrolein contains 3 $\text{sp}^2$ carbon atoms.
• 2. Formaldehyde (HCHO):
Its structural formula is:
\[ \text{H}_2\text{C}=\text{O} \]
The single carbon atom forms a double bond with oxygen, meaning it is $\text{sp}^2$ hybridized.
Thus, formaldehyde contains 1 $\text{sp}^2$ carbon atom.
• 3. Peroxyacetyl nitrate (PAN, $\text{CH}_3-\text{CO}-\text{O}-\text{O}-\text{NO}_2$):
Its structural formula is:
\[ \text{H}_3\text{C}-\text{C}(=\text{O})-\text{O}-\text{O}-\text{NO}_2 \]
There are two carbon atoms in PAN:
The methyl carbon ($\text{-CH}_3$) forms four single $\sigma$ bonds, so it is $\text{sp}^3$ hybridized.
The carbonyl carbon ($\text{-C}(=\text{O})-$) forms a double bond with oxygen, so it is $\text{sp}^2$ hybridized.
Thus, PAN contains 1 $\text{sp}^2$ carbon atom.
• Total Calculation:
Adding the $\text{sp}^2$ carbons from all three compounds:
\[ \text{Total } \text{sp}^2 \text{ carbons} = 3\text{ (acrolein)} + 1\text{ (formaldehyde)} + 1\text{ (PAN)} = 5 \]
Step 4: Final Answer:
The total number of $\text{sp}^2$ hybridized carbon atoms in the three compounds is 5.