Compound P reacts with 3 equivalents of NH2OH, indicating the presence of 3 carbonyl groups, forming oxime Q.
Excess CH3I with KOH reacts with Q to methylate all hydroxyl groups, resulting in compound R.
Compound R reacts with iso-butylmagnesium bromide (Grignard reagent) to add alkyl groups. Hydrolysis with \( \text{H}_3\text{O}^+ \) yields compound S.
\[ P \xrightarrow{\text{3 NH}_2\text{OH}} Q \xrightarrow{\text{CH}_3\text{I}, \text{KOH}} R \xrightarrow{\text{iso-BuMgBr}, \text{H}_3\text{O}^+} S \]
The structure of compound S contains a total of 12 methyl groups:
Total \( -\text{CH}_3 \) groups in compound S: 12
To solve this problem, we need to identify the structure of the organic compound P and follow its transformations to determine the number of methyl groups in compound S. Here's a breakdown of the analysis and reactions involved:
Conclusion: Each branch from original methoxy and appended iso-butyl raises the methyl group count beyond initial methoxy. Therefore, final computation on such rigorous assumptions stalwartly certifies the applicable number of methyl groups in S as 12.
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.