Let us examine each reaction and determine the structure of the products \( P, Q, R, S \) and count their unsaturated carbon atoms.
Step 1: Compound \( P \)
Reaction:
\[
\text{Phenylpropanoic acid} \xrightarrow{\text{Br}_2/\text{Red P}, \text{H}_2O} \text{Phenylethylamine (Gabriel phthalimide reaction)}
\]
Actually, this is the Hunsdiecker reaction:
\[
\text{C}_6\text{H}_5\text{CH}_2\text{CH}_2\text{COOH} \xrightarrow{\text{Br}_2/\text{Red P}} \text{C}_6\text{H}_5\text{CH}_2\text{CH}_3
\]
So product \( P \) = ethylbenzene (C₆H₅–CH₂–CH₃)
\[
\Rightarrow \text{Aromatic ring (3 unsaturated C)} + \text{no other double/triple bond}
\Rightarrow \text{Total unsaturated carbon atoms} = \boxed{3}
\]
Step 2: Compound \( Q \)
Reaction: Crossed aldol between benzaldehyde and formaldehyde in base
\[
\text{C}_6\text{H}_5\text{CHO} + \text{HCHO} \xrightarrow{\text{NaOH}, 293\,K} \text{C}_6\text{H}_5\text{CH}=\text{CH}\text{CHO}
\Rightarrow \text{Cinnamaldehyde}
\]
So \( Q = \text{C}_6\text{H}_5\text{CH}=\text{CH}\text{CHO} \)
Unsaturated C = 3 (benzene) + 2 (C=C, C=O) = \boxed{5}
Step 3: Compound \( R \)
Reaction: Phenylacetylene reacts with NaNH₂ and then 1-bromopropene (an alkyne coupling), followed by Hg²⁺/H₃O⁺ gives enol → keto
Intermediate:
\[
\text{Phenyl–C≡C–CH=CH}_2 \xrightarrow{\text{Hg}^{2+}, H_3O^+} \text{Phenyl–C(=O)–CH₂–CH₃}
\]
But actually after hydration of triple bond, we get:
\[
\text{Phenyl–C≡C–CH=CH}_2 \Rightarrow \text{Phenyl–CO–CH=CH}_2
\Rightarrow \text{Aromatic + C=C + C=O}
\]
So:
- 3 from benzene
- 2 from alkene + ketone = \boxed{5} unsaturated C
However, more precisely, the product is conjugated:
\[
\text{C}_6\text{H}_5–C≡C–CH=CH_2 \Rightarrow \text{no hydration} = directly conjugated enyne
\Rightarrow triple bond (2 unsaturated C), alkene (1 C), benzene (3 C)
\Rightarrow \boxed{6} unsaturated carbon atoms
Step 4: Compound \( S \)
Reaction:
1. Ozonolysis of styrene → benzaldehyde
2. 2 eq. \( \text{CH}_3\text{MgBr} \) adds to two carbonyls → alcohols
3. Acidic dehydration → formation of alkenes
Final product:
\[
\text{C}_6\text{H}_5–C(CH_3)=CH_2 \Rightarrow \text{Aromatic + C=C}
\Rightarrow 3 (benzene) + 1 (alkene) = \boxed{4} unsaturated C
% Comparison of unsaturated carbon atoms:
- \( P \): 3
- \( Q \): 5
- \( R \): 6
- \( S \): 4