The acidity of the compounds `RCOOH, H_(2)CO_(3),C_(6)H_(5)OH, ROH` decreases in the order:

Answer

To determine the acidity of the compounds \( RCOOH \) (carboxylic acid), \( H_2CO_3 \) (carbonic acid), \( C_6H_5OH \) (phenol), and \( ROH \) (alcohol), we need to analyze the stability of their conjugate bases after they donate a proton (H⁺). The more stable the conjugate base, the stronger the acid.

### Step-by-Step Solution:

1. **Identify the Compounds and Their Structures**:
- **Carboxylic Acid (\( RCOOH \))**: Contains a carboxyl group (-COOH) which can donate one proton.
- **Carbonic Acid (\( H_2CO_3 \))**: Contains two hydroxyl groups (-OH) and can donate two protons.
- **Phenol (\( C_6H_5OH \))**: Contains a hydroxyl group attached to a benzene ring.
- **Alcohol (\( ROH \))**: Contains a hydroxyl group but lacks resonance stabilization.

2. **Determine the Conjugate Bases**:
- When \( RCOOH \) donates a proton, it forms \( RCOO^- \).
- When \( H_2CO_3 \) donates two protons, it forms \( HCO_3^- \) and then \( CO_3^{2-} \).
- When \( C_6H_5OH \) donates a proton, it forms \( C_6H_5O^- \).
- When \( ROH \) donates a proton, it forms \( RO^- \).

3. **Analyze Stability of Conjugate Bases**:
- **\( RCOO^- \)**: The conjugate base has resonance stabilization, which increases its stability.
- **\( HCO_3^- \)**: This conjugate base also has resonance stabilization, but less than \( RCOO^- \).
- **\( C_6H_5O^- \)**: The negative charge is stabilized by resonance with the benzene ring, making it quite stable.
- **\( RO^- \)**: This conjugate base lacks resonance stabilization, making it the least stable.

4. **Rank the Acidity Based on Conjugate Base Stability**:
- **Most Acidic**: \( H_2CO_3 \) (can donate two protons, more stable conjugate base)
- **Next**: \( RCOOH \) (stable conjugate base due to resonance)
- **Then**: \( C_6H_5OH \) (stable due to resonance with benzene)
- **Least Acidic**: \( ROH \) (no resonance stabilization)

5. **Final Order of Acidity**:
- The order of acidity is:
\[ H_2CO_3 > RCOOH > C_6H_5OH > ROH \]