Calculate Total Methyl Groups in Product S from Reaction Sequence

To determine the total number of methyl ($-\text{CH}_3$) groups in compound S, we analyze the reaction sequence step-by-step:

Step 1: Identification of Compound P

1. Molecular Formula & Degree of Unsaturation: The compound P has the molecular formula $\text{C}_6\text{H}_6\text{O}_3$. $\text{Degree of Unsaturation (DU)} = C + 1 - \frac{H}{2} = 6 + 1 - \frac{6}{2} = 4$

2. Chemical Tests & Structural Features:

   • Ferric chloride test: Gives a positive test, indicating the presence of phenolic hydroxyl group(s) or an enolic system.
   • No intramolecular hydrogen bonding: This rules out adjacent (ortho) hydroxyl groups (such as in pyrogallol) that readily form intramolecular hydrogen bonds.
   • Reaction with $\text{NH}_2\text{OH}$: Reacts with $3\text{ equivalents}$ of hydroxylamine to form a trioxime (Q). This indicates the presence of 3 carbonyl/enolic tautomeric sites.

   Therefore, compound P is benzene-1,3,5-triol (phloroglucinol), which exists in equilibrium with its keto tautomer, cyclohexane-1,3,5-trione.

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Step 2: Formation of Compound R

When phloroglucinol (P) is treated with excess methyl iodide ($\text{CH}_3\text{I}$) in the presence of a strong base ($\text{KOH}$), complete C-alkylation occurs at the active methylene carbons (positions 2, 4, and 6) of the trienolate intermediate.

Each of the three carbons between the carbonyl groups undergoes dimethylation to yield: $\text{Compound } \mathbf{R} = \text{2,2,4,4,6,6-hexamethylcyclohexane-1,3,5-trione}$

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Step 3: Formation of Compound S

Compound R contains 3 carbonyl groups ($>\text{C}=\text{O}$) at C-1, C-3, and C-5.

Reaction of R with excess iso-butylmagnesium bromide ($i\text{-BuMgBr}$), followed by acidic workup ($\text{H}_3\text{O}^+$), results in the nucleophilic addition of one iso-butyl group ($-\text{CH}_2-\text{CH}(\text{CH}_3)_2$) to each of the three carbonyl carbons, converting them into tertiary alcohol groups: $\text{Compound } \mathbf{S} = \text{1,3,5-tri-}\textit{iso}\text{-butyl-2,2,4,4,6,6-hexamethylcyclohexane-1,3,5-triol}$

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Step 4: Counting Methyl ($-\text{CH}_3$) Groups in Compound S

1. From the hexamethylated ring carbons (C-2, C-4, C-6): There are 2 methyl groups on each of the 3 ring carbons: $3 \times 2 = 6 \text{ methyl groups}$

2. From the iso-butyl groups added to C-1, C-3, C-5: Each iso-butyl group ($-\text{CH}_2-\text{CH}(\text{CH}_3)_2$) contains 2 methyl groups. Since 3 such groups are attached: $3 \times 2 = 6 \text{ methyl groups}$

3. Total number of methyl groups in compound S: $\text{Total } -\text{CH}_3 \text{ groups} = 6 + 6 = 12$