Consider the following reaction,
`CH_(3)Br+Nu^(-)rarrCH_(3)-Nu+Br^(-)`
The decreasing order of the rate of the above reaction with `Nu^(-)` is
I. `PHO^(-)` II. `AcO^(-)`
III. `HO^(-)` IV. `CH_(3)O^(-)`

Options

A. `IVgtIIIgtIgtII`
B. `IVgtIIIgtIIgtI`
C. `IgtIIgtIIIgtIV`
D. `IIgtIVgtIIIgtI`

Explanation

To determine the decreasing order of the rate of the reaction between `CH₃Br` and various nucleophiles (`Nu⁻`), we need to analyze the nucleophiles based on their nucleophilicity, which is influenced by factors such as charge, electronegativity, and resonance stabilization.

### Step-by-Step Solution:

1. **Identify the Nucleophiles**: The nucleophiles given are:
- I. `PHO⁻` (Phenoxide ion)
- II. `AcO⁻` (Acetate ion)
- III. `HO⁻` (Hydroxide ion)
- IV. `CH₃O⁻` (Methoxide ion)

2. **Analyze Nucleophilicity**:
- **`CH₃O⁻` (Methoxide ion)**: This is a strong nucleophile due to the presence of a negative charge on oxygen, which is less electronegative than carbon. It can donate its electron pair readily.
- **`HO⁻` (Hydroxide ion)**: This is also a strong nucleophile, but slightly less nucleophilic than methoxide due to the lack of alkyl groups that can donate electron density through the inductive effect.
- **`PHO⁻` (Phenoxide ion)**: The negative charge on oxygen is stabilized by resonance with the aromatic ring, which makes it less nucleophilic compared to `CH₃O⁻` and `HO⁻`.
- **`AcO⁻` (Acetate ion)**: Similar to phenoxide, the negative charge is delocalized through resonance, making it the least nucleophilic among the four.

3. **Rank the Nucleophiles**: Based on the analysis:
- `CH₃O⁻` > `HO⁻` > `PHO⁻` > `AcO⁻`
- Therefore, the decreasing order of nucleophilicity (and thus the rate of reaction) is:
- `CH₃O⁻` (IV)
- `HO⁻` (III)
- `PHO⁻` (I)
- `AcO⁻` (II)

4. **Final Answer**: The correct decreasing order of the rate of reaction with `Nu⁻` is:
- IV > III > I > II