Most Stable Conformation of Meso Butane Two Three Diol

To determine the most stable conformation of meso-butane-2,3-diol, we analyze its stereochemistry, steric interactions, and intramolecular non-covalent interactions.

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1. Stereochemistry of meso-Butane-2,3-diol

meso-Butane-2,3-diol contains two stereocenters at $\text{C}_2$ and $\text{C}_3$ with opposite absolute configurations, i.e., $(2R, 3S)$. Owing to this internal symmetry, the molecule is optically inactive.

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2. Factors Governing Conformational Stability

In butane-2,3-diol, the relative stability of staggered Newman projections is governed by two main factors:

1. Steric Repulsion between Methyl Groups ($-\text{CH}_3$):
   The methyl groups are the bulkiest substituents. To minimize steric hindrance and torsional strain, the dihedral angle between the two $-\text{CH}_3$ groups should ideally be $180^\circ$ (anti conformation).

2. Intramolecular Hydrogen Bonding between Hydroxyl Groups ($-\text{OH}$):
   When the two $-\text{OH}$ groups are positioned gauche to each other (dihedral angle $\approx 60^\circ$), a strong intramolecular hydrogen bond ($\text{O}-\text{H}\cdots\text{O}$) is formed. This stabilizing interaction significantly lowers the potential energy of the molecule, making the gauche-OH conformation more stable than the anti-OH conformation.

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3. Analysis of the Conformations of meso-Butane-2,3-diol

For the meso isomer, $(2R, 3S)$-butane-2,3-diol:

• When the two methyl groups ($-\text{CH}_3$) are arranged anti ($180^\circ$ apart) to minimize steric strain, the geometric requirement of the $(2R, 3S)$ configuration automatically places the two hydroxyl groups ($-\text{OH}$) in a gauche orientation ($60^\circ$ apart).
• This specific arrangement allows the molecule to simultaneously achieve:
  1. Minimum steric repulsion between the bulky methyl groups ($-\text{CH}_3 \text{ anti } -\text{CH}_3$).
  2. Maximum thermodynamic stabilization via intramolecular hydrogen bonding ($-\text{OH} \text{ gauche } -\text{OH}$).

Looking at the given choices:

• Option C shows the staggered projection of meso-butane-2,3-diol where the two $-\text{CH}_3$ groups are anti ($180^\circ$) and the two $-\text{OH}$ groups are gauche ($60^\circ$), forming an intramolecular hydrogen bond.

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Conclusion

The projection representing the most stable conformation of meso-butane-2,3-diol is given in Option C.