The total number of sp² hybridised carbon atoms in the major product P (a non-heterocyclic compound) of the following reaction is:

The correct answer is 28.

Step 1: Understand the given reaction sequence
The reaction starting material is ethane-1,1,2,2-tetracarbonitrile, which contains four nitrile groups (−CN).

The reaction steps are as follows:

1. Reduction with excess LiAlH₄, followed by H₂O:
Lithium aluminium hydride (LiAlH₄) reduces all four nitrile (−CN) groups to primary amine groups (−CH₂NH₂).
Thus, reduction converts the compound into a tetraamine: butane-1,2,3,4-tetraamine derivative, having four −CH₂NH₂ groups attached to the central C−C backbone.

2. Reaction with excess Acetophenone:
Acetophenone is Ph−CO−CH₃ (C₆H₅COCH₃). Primary amines react with carbonyl compounds (ketones/aldehydes) to form imines (Schiff bases):

$\text{R}-{\text{NH}}_2+\text{O}=\text{C}\left({\text{CH}}_3\right)\text{Ph}\to \text{R}-\text{N}=\text{C}\left({\text{CH}}_3\right)\text{Ph}+{\text{H}}_2\text{O}$

Since there are 4 primary amine groups and excess acetophenone is used, all four amine groups condense with four molecules of acetophenone to form a tetra-imine product P (a non-heterocyclic compound).

Step 2: Structure of Product P
Product P contains four imine units attached to the aliphatic core:

$\text{Structure of P:}{[\text{Ph}-\text{C}({\text{CH}}_3)=\text{N}-{\text{CH}}_2]}_2\text{CH}-\text{CH}{[{\text{CH}}_2-\text{N}=\text{C}({\text{CH}}_3\left)\text{Ph}\right]}_2$

Step 3: Count the total number of sp² hybridised carbon atoms in P
Let us analyze each part of product P:

1. Phenyl rings (Ph = C₆H₅):
Each phenyl ring contains 6 sp² hybridised carbon atoms.
Since 4 acetophenone molecules reacted, there are 4 phenyl rings in P.
Total sp² carbons from phenyl rings = 4 × 6 = 24.

2. Imine carbons (−N=C(CH₃)Ph):
The carbon involved in the imine double bond (−N=C−) is sp² hybridised.
There are 4 imine groups in P, so there are 4 imine sp² carbon atoms.
Total sp² carbons from imine groups = 4 × 1 = 4.

3. Other carbons in the molecule:
- Methyl carbons attached to imine (−CH₃) are sp³ hybridised.
- Methylene carbons (−CH₂−) and central CH carbons of the core are sp³ hybridised.

Step 4: Final Summation
Total number of sp² hybridised carbon atoms = (4 phenyl rings × 6 sp² carbons) + (4 imine sp² carbons) = 24 + 4 = 28.