Step 1: Compound Acidity Assessment
- \( \text{CH}_3\text{OH} \) (Methanol): A weak alcohol and weak acid.
- \( \text{CH}_3\text{COOH} \) (Acetic acid): A weak acid, exhibiting greater acidity than methanol due to its carboxyl group (\( \text{COOH} \)).
- \( \text{HCl} \) (Hydrochloric acid): A strong acid, characterized by complete dissociation in aqueous solution.
- \( \text{H}_2\text{SO}_4 \) (Sulfuric acid): A very strong acid, noted for its extensive dissociation and capacity to donate two protons.
Step 2: Acidity Ranking
- Methanol: Weakest acid.
- Acetic acid: Stronger than methanol, but weaker than strong acids such as HCl and H\(_2\)SO\(_4\).
- Hydrochloric acid: Stronger than acetic acid.
- Sulfuric acid: Strongest acid among the listed compounds.
Step 3: Order of Increasing Acidity
The sequence of increasing acidity is as follows:
\[\text{CH}_3\text{OH}<\text{CH}_3\text{COOH}<\text{HCl}<\text{H}_2\text{SO}_4\]
Answer:
Accordingly, option (1) represents the correct answer.