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 for the given nucleophiles, we need to analyze the structure and resonance stabilization of each nucleophile. The nucleophiles provided are:

1. \( \text{CH}_3\text{CO}_2^- \) (Acetate ion)
2. \( \text{H}_2\text{O} \) (Water)
3. \( \text{CH}_3\text{SO}_3^- \) (Methanesulfonate ion)
4. \( \text{OH}^- \) (Hydroxide ion)

### Step-by-Step Solution:

**Step 1: Understand Nucleophilicity**
Nucleophilicity refers to the ability of a species to donate a pair of electrons to an electrophile. Stronger nucleophiles are better electron donors.

**Step 2: Analyze Each Nucleophile**
- **\( \text{CH}_3\text{CO}_2^- \)**: The acetate ion has resonance structures that delocalize the negative charge over the two oxygen atoms. This resonance stabilizes the ion, making it a weaker nucleophile compared to others without such stabilization.

- **\( \text{H}_2\text{O} \)**: Water is neutral and has two lone pairs of electrons. However, it is less nucleophilic than the negatively charged species because it does not have a negative charge to enhance its electron-donating ability.

- **\( \text{CH}_3\text{SO}_3^- \)**: The methanesulfonate ion also has resonance stabilization, similar to acetate, but it is a stronger nucleophile than acetate due to the presence of the sulfur atom, which can stabilize the negative charge more effectively.

- **\( \text{OH}^- \)**: The hydroxide ion carries a negative charge and has no resonance stabilization, making it a very strong nucleophile as it can readily donate its lone pair of electrons.

**Step 3: Compare Nucleophilicity**
Based on the analysis:
- \( \text{H}_2\text{O} \) is the weakest nucleophile.
- \( \text{CH}_3\text{CO}_2^- \) is weaker than \( \text{CH}_3\text{SO}_3^- \) due to resonance stabilization.
- \( \text{CH}_3\text{SO}_3^- \) is stronger than \( \text{CH}_3\text{CO}_2^- \) but weaker than \( \text{OH}^- \).
- \( \text{OH}^- \) is the strongest nucleophile.

### Final Order:
Thus, the increasing order of nucleophilicity is:
\[ \text{H}_2\text{O} < \text{CH}_3\text{CO}_2^- < \text{CH}_3\text{SO}_3^- < \text{OH}^- \]

### Answer:
The correct increasing order of nucleophilicity is:
**(b) \( \text{H}_2\text{O} < \text{CH}_3\text{CO}_2^- < \text{CH}_3\text{SO}_3^- < \text{OH}^- \)**