The increasing order of nucleophilicity of the following nucleophiles is:
(a) `CH_(3)CO_(2)^(-)` (b) `H_(2)O` (c) `CH_(3)SO_(3)^(-)` (d) `overset(O)H`

Options

A. `(b) lt (c) lt (d) lt (a)`
B. `(d) lt (a) lt (c) lt (b)`
C. `(b) lt (c) lt (a) lt (d)`
D. `(a) lt (d) lt (c) lt (b)`

Explanation

To determine the increasing order of nucleophilicity among the given nucleophiles: \( CH_3CO_2^- \), \( H_2O \), \( CH_3SO_3^- \), and \( OH^- \), we will analyze each nucleophile based on their charge and resonance stability.

### Step-by-Step Solution:

1. **Identify the Nucleophiles**:
- \( CH_3CO_2^- \) (acetate ion)
- \( H_2O \) (water)
- \( CH_3SO_3^- \) (methyl sulfonate ion)
- \( OH^- \) (hydroxide ion)

2. **Charge Consideration**:
- Nucleophiles with a negative charge are generally stronger than neutral nucleophiles. Therefore, \( H_2O \) will be the weakest nucleophile among the four.

3. **Stability of Negative Charge**:
- The stability of the negative charge affects nucleophilicity. A more stable negative charge corresponds to a weaker nucleophile.
- **Resonance Structures**:
- **For \( CH_3CO_2^- \)**: The negative charge can be delocalized over two oxygen atoms, giving it two resonance structures.
- **For \( CH_3SO_3^- \)**: The negative charge can be delocalized over three oxygen atoms, providing it with three resonance structures, which makes it more stable than \( CH_3CO_2^- \).
- **For \( OH^- \)**: The hydroxide ion has no resonance stabilization, making it a strong nucleophile.

4. **Comparing Nucleophilicity**:
- Since \( OH^- \) has no resonance stabilization, it is the strongest nucleophile.
- \( CH_3CO_2^- \) is next, as it has some resonance stabilization but is less stable than \( CH_3SO_3^- \).
- \( CH_3SO_3^- \) is the weakest nucleophile due to its highly stabilized negative charge from resonance.
- Finally, \( H_2O \) is the weakest nucleophile since it is neutral.

5. **Final Order**:
- The increasing order of nucleophilicity is:
\[ H_2O < CH_3SO_3^- < CH_3CO_2^- < OH^- \]

### Conclusion:
Thus, the increasing order of nucleophilicity is:
\[ H_2O < CH_3SO_3^- < CH_3CO_2^- < OH^- \]