Which one of the following statements regarding the population of different conformers butane -2, 3 - diol is true?

Options

A. The most populated conformer with have the hydroxyl groups of the gauche position.
B. The most populated conformer will have the hydroxyl groups at the anti position.
C. All staggered conformations will be equally populated.
D. Relative populations of different conformers is not predictable

Answer

To determine which statement regarding the population of different conformers of butane-2,3-diol is true, we need to analyze the conformations of the molecule and their stability.

### Step-by-Step Solution:

1. **Understanding the Structure**:
Butane-2,3-diol has the following structure:
- It contains two hydroxyl (OH) groups on the second and third carbon atoms of a butane chain.
- The molecular formula is C4H10O2.

2. **Drawing the Newman Projections**:
- To analyze the conformers, we can draw Newman projections for the molecule. We will focus on the conformations around the C2-C3 bond.
- The two hydroxyl groups can be positioned in various ways: staggered or eclipsed.

3. **Identifying Staggered Conformations**:
- In staggered conformations, the groups attached to the carbons are positioned to minimize steric hindrance.
- We can have different staggered conformations where the OH groups are positioned differently:
- One staggered conformation might have both OH groups in a gauche position relative to each other.
- Another staggered conformation could have the OH groups in an anti position.

4. **Evaluating Stability**:
- The stability of the conformers can be evaluated based on the interactions between the hydroxyl groups.
- In the staggered conformation where the OH groups are close enough to form hydrogen bonds, this conformation will be more stable due to the favorable interaction.

5. **Conclusion**:
- The most populated conformer is the one where the hydroxyl groups are in a position that allows for hydrogen bonding (the gauch position).
- Therefore, the statement that is true regarding the population of different conformers of butane-2,3-diol is: "The most populated conformer will have the hydroxyl groups in the gauch position."

### Final Answer:
The correct statement is: "The most populated conformer will have the hydroxyl groups in the gauch position."