Identify the structure of the final product (D) in the following sequence of the reactions :
Total number of $ sp^2 $ hybridised carbon atoms in product D is _____.
Step 1: Formation of A.
Acetophenone reacts with \( PCl_5 \) to give a geminal dichloride: \[ Ph-\overset{O}{\underset{||}{C}}-CH_3 \xrightarrow{PCl_5} Ph-CCl_2-CH_3 \quad (A) \]
Step 2: Formation of B.
Reaction with 3 equivalents of \( NaNH_2/NH_3 \) leads to elimination of HCl and formation of an alkyne: \[ Ph-CCl_2-CH_3 \xrightarrow{3eq. \, NaNH_2/NH_3} Ph-C \equiv C-CH_3 \quad (B) \]
Step 3: Formation of C.
Acidification does not change the structure of the alkyne.
Thus, C is also \( Ph-C \equiv C-CH_3 \).
Step 4: Formation of D (Hydroboration-oxidation).
Hydroboration-oxidation of a terminal alkyne with \( B_2H_6 \) followed by \( H_2O_2/OH^- \) proceeds with anti-Markovnikov regioselectivity, placing the hydroxyl group on the less substituted carbon after tautomerization. \[ Ph-C \equiv C-CH_3 \xrightarrow[1. \, B_2H_6]{2. \, H_2O_2/OH^-} Ph-\overset{OH}{C}=CH-CH_3 \xrightarrow{Tautomerization} Ph-CO-CH_2-CH_3 \quad (D) \] The final product D is 1-phenylpropan-2-one.
Step 5: Determine the number of \( sp^2 \) hybridized carbon atoms in D.
The structure of 1-phenylpropan-2-one is: \[ \underbrace{\overset{sp^2}{C}_6H_5}_{\text{6 } sp^2 \text{ carbons}} - \overset{sp^3}{CH_2} - \overset{sp^2}{C} = O - \overset{sp^3}{CH_3} \] The phenyl ring has 6 \( sp^2 \) hybridized carbon atoms. The carbonyl carbon is also \( sp^2 \) hybridized. The \( CH_2 \) and \( CH_3 \) carbons are \( sp^3 \) hybridized.
Total number of \( sp^2 \) hybridized carbon atoms in product D = 6 (from the phenyl ring) + 1 (carbonyl carbon) = 7.
For the thermal decomposition of \( N_2O_5(g) \) at constant volume, the following table can be formed, for the reaction mentioned below: \[ 2 N_2O_5(g) \rightarrow 2 N_2O_4(g) + O_2(g) \] Given: Rate constant for the reaction is \( 4.606 \times 10^{-2} \text{ s}^{-1} \).
A hydrocarbon which does not belong to the same homologous series of carbon compounds is
Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where \( b, c \in \mathbb{N} \), then \[ 3(b + c) \] is equal to:
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: