Step 1: Understanding the acidity of the compounds
- \( \text{CH}_3\text{OH} \) (Methanol) is a weak alcohol and a weak acid.
- \( \text{CH}_3\text{COOH} \) (Acetic acid) is a weak acid, but stronger than methanol due to the presence of the carboxyl group (\( \text{COOH} \)).
- \( \text{HCl} \) (Hydrochloric acid) is a strong acid due to its complete dissociation in water.
- \( \text{H}_2\text{SO}_4 \) (Sulfuric acid) is a very strong acid, known for its strong dissociation and ability to donate two protons.
Step 2: Rank the acidity based on strength
- Methanol is the weakest acid.
- Acetic acid is stronger than methanol but weaker than strong acids like HCl and H\(_2\)SO\(_4\).
- Hydrochloric acid is stronger than acetic acid.
- Sulfuric acid is the strongest acid in this list.
Step 3: Correct order of increasing acidity
Thus, the order of increasing acidity is:
\[
\text{CH}_3\text{OH}<\text{CH}_3\text{COOH}<\text{HCl}<\text{H}_2\text{SO}_4
\]
Answer:
Therefore, the correct answer is option (1).