Treatment of buta-1, 3-diyne with NaNH₂ (2 equivalents), followed by reaction with excess of trans-CH₃−CH=CH−CH₂−Br gives X as the major product. The maximum number of carbon atoms that are collinear (in a straight line) in X is ____.

Correct Answer: The correct answer is 8.

Step-by-Step Explanation:

Step 1: Reaction of Buta-1,3-diyne with Sodium Amide (NaNH₂)

Buta-1,3-diyne has the structural formula:

$\text{H}-\text{C}\equiv \text{C}-\text{C}\equiv \text{C}-\text{H}$

Both terminal hydrogen atoms attached to the triply bonded carbon atoms are acidic. Reaction with 2 equivalents of strong base sodium amide (NaNH₂) deprotonates both terminal acetylenic protons, yielding the dication/dialkynide salt:

${\text{Na}}^{+}{[:\text{C}\equiv \text{C}-\text{C}\equiv \text{C}:]}^{2-}{\text{Na}}^{+}$

Step 2: Reaction with Trans-1-bromobut-2-ene

The formed dialkynide nucleophile undergoes an S_N2 substitution reaction at both terminal carbon positions when reacted with excess trans-1-bromobut-2-ene ($\text{trans-CH}$₃-CH=CH-CH₂-Br):

$\text{trans-CH}$₃-CH=CH-CH₂-C≡C-C≡C-CH₂-CH=CH-CH₃

This compound represents the major product X.

Step 3: Determining the Collinear Carbon Atoms in Product X

Let us analyze the hybridization and geometry of the carbon atoms forming product X:

1. The central diyne core contains four sp-hybridized carbon atoms ($-\text{C}\equiv \text{C}-\text{C}\equiv \text{C}-$), which possess linear geometry (bond angle of 180°).

2. The bonds extending directly from an sp-hybridized carbon to an adjacent sp³ carbon ($-\text{CH}$₂-C≡) are aligned linearly along the axis of the triple bond.

3. Each of the attached allylic sp³ carbon atoms ($-\text{CH}$₂-) is directly bonded to an sp² carbon of the trans-double bond ($=\text{CH}-$). The sp² carbon lying directly along the continuation of the sp-C to sp³-C bond line continues the collinear arrangement of atoms along that linear axis segment.

Specifically, the central linear continuous axis spans from the sp² carbon of one alkene group, through the sp³ methylene carbon, across all 4 sp carbons of the conjugated diyne, through the second sp³ methylene carbon, and to the sp² carbon of the second alkene group:

$\text{C}\left(sp2\right)-\text{C}\left(sp3\right)-\text{C}\left(sp\right)\equiv \text{C}\left(sp\right)-\text{C}\left(sp\right)\equiv \text{C}\left(sp\right)-\text{C}\left(sp3\right)-\text{C}\left(sp2\right)$

Counting these carbon atoms in a straight line:

1 (sp² carbon) + 1 (sp³ carbon) + 4 (sp carbons) + 1 (sp³ carbon) + 1 (sp² carbon) = 8 carbon atoms.

Thus, the maximum number of carbon atoms that are collinear (in a straight line) in product X is 8.