Collinear Carbon Atoms in Product of Butadiyne Reaction

To determine the maximum number of collinear carbon atoms in the major product $\mathbf{X}$, let us analyze the reaction step-by-step:

Step 1: Deprotonation of Buta-1,3-diyne

Buta-1,3-diyne contains two acidic terminal alkyne protons: $\text{H}-\text{C}\equiv\text{C}-\text{C}\equiv\text{C}-\text{H}$

Treatment with 2 equivalents of a strong base like sodium amide ($\text{NaNH}_2$) deprotonates both terminal acetylenic hydrogens to yield the sodium salt of the diacetylide dicarbanion: $\text{H}-\text{C}\equiv\text{C}-\text{C}\equiv\text{C}-\text{H} + 2\text{NaNH}_2 \longrightarrow \text{Na}^+ \text{ }^-\text{C}\equiv\text{C}-\text{C}\equiv\text{C}^- \text{Na}^+ + 2\text{NH}_3$

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Step 2: Nucleophilic Substitution ($S_N2$) Reaction

The diacetylide dicarbanion reacts with an excess of trans-1-bromo-but-2-ene ($trans\text{-CH}_3\text{-CH}=\text{CH-CH}_2\text{-Br}$) via an $S_N2$ mechanism: $\text{Na}^+ \text{ }^-\text{C}\equiv\text{C}-\text{C}\equiv\text{C}^- \text{Na}^+ + 2 \, trans\text{-CH}_3\text{-CH}=\text{CH-CH}_2\text{-Br} \longrightarrow \mathbf{X} + 2\text{NaBr}$

The structure of the major product $\mathbf{X}$ is: $\overset{1}{\text{C}}\text{H}_3-\overset{2}{\text{C}}\text{H}=\overset{3}{\text{C}}\text{H}-\overset{4}{\text{C}}\text{H}_2-\overset{5}{\text{C}}\equiv\overset{6}{\text{C}}-\overset{7}{\text{C}}\equiv\overset{8}{\text{C}}-\overset{9}{\text{C}}\text{H}_2-\overset{10}{\text{C}}\text{H}=\overset{11}{\text{C}}\text{H}-\overset{12}{\text{C}}\text{H}_3$

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Step 3: Geometry and Collinearity Analysis

To find the maximum number of collinear carbon atoms, we analyze the hybridization and bond angles along the carbon chain:

1. $sp$-hybridized carbons ($\text{C}_5, \text{C}_6, \text{C}_7, \text{C}_8$):

   • Each $sp$-hybridized carbon atom forms two $\sigma$-bonds with a bond angle of $180^\circ$.
   • Angle $\angle \text{C}_4-\text{C}_5-\text{C}_6 = 180^\circ \implies \text{C}_4, \text{C}_5, \text{C}_6$ are collinear.
   • Angle $\angle \text{C}_5-\text{C}_6-\text{C}_7 = 180^\circ \implies \text{C}_5, \text{C}_6, \text{C}_7$ are collinear.
   • Angle $\angle \text{C}_6-\text{C}_7-\text{C}_8 = 180^\circ \implies \text{C}_6, \text{C}_7, \text{C}_8$ are collinear.
   • Angle $\angle \text{C}_7-\text{C}_8-\text{C}_9 = 180^\circ \implies \text{C}_7, \text{C}_8, \text{C}_9$ are collinear.

   Combining these linear segments, all six carbon atoms ($\text{C}_4, \text{C}_5, \text{C}_6, \text{C}_7, \text{C}_8, \text{C}_9$) lie strictly on a single straight line.

2. Adjacent $sp^3$-hybridized carbons ($\text{C}_4$ and $\text{C}_9$):

   • Carbons $\text{C}_4$ and $\text{C}_9$ are $sp^3$-hybridized with tetrahedral geometry.
   • The bond angles $\angle \text{C}_3-\text{C}_4-\text{C}_5 \approx 109.5^\circ$ and $\angle \text{C}_8-\text{C}_9-\text{C}_{10} \approx 109.5^\circ$ deviate significantly from $180^\circ$.
   • Thus, neither $\text{C}_3$ nor $\text{C}_{10}$ lies on the straight line defined by the central six carbons.

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Conclusion

The continuous chain of collinear carbon atoms consists of $\text{C}_4, \text{C}_5, \text{C}_6, \text{C}_7, \text{C}_8, \text{C}_9$.

The maximum number of carbon atoms that are collinear in $\mathbf{X}$ is 6.