Arrange the following halides in the decreasing order of `S_N1` reactivity:
`CH_3underset((I))CH_2CH_2Cl` `CH_2=CHunderset((II))CH(Cl)CH_3`,
`CH_3CH_2underset(III)CH(Cl)CH_3`

Options

A. I gt II gt III
B. II gt I gt III
C. II gt III gt I
D. III gt II gt I

Explanation

To arrange the given halides in the decreasing order of SN1 reactivity, we will analyze the stability of the carbocations formed during the reaction. The stability of carbocations is crucial in determining the reactivity in SN1 reactions, as the rate-determining step involves the formation of the carbocation.

### Step-by-Step Solution:

1. **Identify the Halides:**
- (I) CH₃CH₂CH₂Cl
- (II) CH₂=CHCH(Cl)CH₃
- (III) CH₃CH₂CH(Cl)CH₃

2. **Determine the Type of Carbocation Formed:**
- For (I) CH₃CH₂CH₂Cl: The leaving group (Cl) will create a primary carbocation (CH₃CH₂CH₂⁺), which is the least stable.
- For (II) CH₂=CHCH(Cl)CH₃: The leaving group will create a secondary allylic carbocation (CH₂=CHCH⁺CH₃). This carbocation can be stabilized by resonance due to the adjacent double bond.
- For (III) CH₃CH₂CH(Cl)CH₃: The leaving group will create a secondary carbocation (CH₃CH₂CH⁺CH₃), which is more stable than a primary carbocation but less stable than an allylic carbocation.

3. **Stability of Carbocations:**
- Primary carbocation (I) is the least stable.
- Secondary allylic carbocation (II) is the most stable due to resonance.
- Secondary carbocation (III) is stable but less stable than the allylic carbocation.

4. **Order of Reactivity:**
- Since the reactivity in SN1 reactions is directly related to the stability of the carbocation formed, we can arrange the halides based on the stability of the carbocations:
- (II) CH₂=CHCH(Cl)CH₃ (most stable, allylic)
- (III) CH₃CH₂CH(Cl)CH₃ (secondary)
- (I) CH₃CH₂CH₂Cl (least stable, primary)

5. **Final Arrangement:**
- The decreasing order of SN1 reactivity is:
- (II) > (III) > (I)

### Final Answer:
**The decreasing order of SN1 reactivity is: (II) > (III) > (I)**

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