In which of the following molecules gauche form is more stable than their anti form?

Options

A. 2-Aminoethanol
B. 2-Nitroethanol
C. 3-Hydroxypropanoic acid
D. 3-Hydroxypropanal

Explanation

To determine which of the following molecules has a gauche form that is more stable than its anti form, we will analyze the molecular structures and the interactions that occur in both conformations. The key factor in this analysis is the concept of hyperconjugation and intramolecular hydrogen bonding, which can stabilize the gauche conformation.

### Step-by-Step Solution:

1. **Identify the Molecules**:
We need to analyze the stability of the gauche and anti forms of the following molecules:
- 2-Aminoethanol
- Nitroethanol
- 3-Hydroxypropanoic acid
- (Assuming there is a fourth molecule, which we will analyze similarly)

2. **Draw the Structures**:
For each molecule, draw both the gauche and anti conformations. The anti conformation has substituents on opposite sides, while the gauche conformation has them on the same side.

3. **Analyze 2-Aminoethanol**:
- **Gauche Form**: The hydroxyl (OH) and amino (NH2) groups are on the same side.
- **Anti Form**: The OH and NH2 groups are on opposite sides.
- **Stability Factors**: In the gauche form, the anti orbital of the C-O bond can interact with the CH bond through hyperconjugation, leading to increased stability. Additionally, there may be intramolecular hydrogen bonding between the NH2 and OH groups.

4. **Analyze Nitroethanol**:
- **Gauche Form**: The hydroxyl (OH) and nitro (NO2) groups are on the same side.
- **Anti Form**: The OH and NO2 groups are on opposite sides.
- **Stability Factors**: Similar to 2-aminoethanol, the interaction between the anti orbital of the C-O bond and the hydrogen from the OH group can stabilize the gauche form. Intramolecular hydrogen bonding may also play a role.

5. **Analyze 3-Hydroxypropanoic Acid**:
- **Gauche Form**: The hydroxyl (OH) and carboxylic acid (COOH) groups are on the same side.
- **Anti Form**: The OH and COOH groups are on opposite sides.
- **Stability Factors**: The same hyperconjugation effects and potential for intramolecular hydrogen bonding apply here as well.

6. **Conclusion**:
Based on the analysis of the three molecules, we find that in each case, the gauche form is more stable than the anti form due to hyperconjugation and possible intramolecular hydrogen bonding. Therefore, all three molecules (2-aminoethanol, nitroethanol, and 3-hydroxypropanoic acid) exhibit this stability trend.

### Final Answer:
The gauche form is more stable than the anti form in all of the following molecules:
- 2-Aminoethanol
- Nitroethanol
- 3-Hydroxypropanoic Acid