The correct order of decreasing `S_N2` respectively

Options

A. `RCH_2X gt R_2CHXgt R_3CX`
B. `RCH_2X gt R_3CXgt R_2CHX`
C. `R_2CHX gt R_3CH gt RCH_2X`
D. `R_3CHX gt R_2CHXgt RCH_2X `

Explanation

To determine the correct order of decreasing \( S_N2 \) reactivity for the given alkyl halides, we need to analyze the structure of each compound based on the steric hindrance around the carbon atom bonded to the halogen. The \( S_N2 \) mechanism involves a backside attack by the nucleophile, which is more favorable in less hindered environments. Here’s a step-by-step solution:

### Step 1: Identify the Type of Alkyl Halides
- **Primary Alkyl Halide**: This has one carbon atom attached to the carbon bonded to the halogen (e.g., \( RCH_2X \)).
- **Secondary Alkyl Halide**: This has two carbon atoms attached to the carbon bonded to the halogen (e.g., \( R_2CHX \)).
- **Tertiary Alkyl Halide**: This has three carbon atoms attached to the carbon bonded to the halogen (e.g., \( R_3CX \)).

### Step 2: Analyze Steric Hindrance
- **Primary Alkyl Halide**: Has the least steric hindrance, allowing the nucleophile to easily attack the carbon atom. Therefore, it reacts the fastest in \( S_N2 \) reactions.
- **Secondary Alkyl Halide**: Has moderate steric hindrance, making the nucleophilic attack slower than in primary alkyl halides.
- **Tertiary Alkyl Halide**: Has the most steric hindrance due to three alkyl groups around the carbon, which makes it very difficult for the nucleophile to attack. Thus, it reacts the slowest in \( S_N2 \) reactions.

### Step 3: Determine the Order of Reactivity
Based on the analysis of steric hindrance:
- **Fastest Reactivity**: Primary Alkyl Halide (\( RCH_2X \))
- **Moderate Reactivity**: Secondary Alkyl Halide (\( R_2CHX \))
- **Slowest Reactivity**: Tertiary Alkyl Halide (\( R_3CX \))

### Step 4: Write the Decreasing Order of Reactivity
The correct order of decreasing \( S_N2 \) reactivity is:
\[ RCH_2X > R_2CHX > R_3CX \]

### Step 5: Verify with Options
Finally, check the options provided in the question to confirm that the order matches with the identified reactivity pattern.

### Final Answer
The correct order of decreasing \( S_N2 \) reactivity is:
\[ RCH_2X > R_2CHX > R_3CX \]

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