Arrange the folliwing compounds in increasing order of `SN^(-1)` reactivity.
a. I.m `ClCH_(2)CH = CHCH_(2)CH_(3)`
II. `CH_(3)C(Cl) = CHCH_(2) CH_(3)`
III. `CH_(3)CH = CHCH_(2)CH_(2)Cl`
IV. `CH_(3)CH = CHCH_(2)(Cl) CH_(3)`
b. I. `CH_(3)CH_(2)Br`
II. `CH_(2) = CHCH(Br) CH_(3)`
III. `CH_(2) = CHBr`
IV. `CH_(3)CH (Br) CH_(3)`
C. I. `(CH_(3))_(3)CCl`, II. `C_(6)H_(5)C(CH_(3))_(2)Cl`
III. `(CH_(3))_(2)CHCl`, IV. `CH_(3)CH_(2)CH_(2)Cl`

Explanation

To arrange the given compounds in increasing order of SN1 reactivity, we need to analyze the structure of each compound and determine their reactivity based on the stability of the carbocation that would form during the SN1 reaction. The more stable the carbocation, the more reactive the compound will be in an SN1 reaction.

### Group A:
1. **Compound I: `ClCH2CH=CHCH2CH3`** - This is a primary allylic compound. The carbocation formed would be a primary allylic carbocation.
2. **Compound II: `CH3C(Cl)=CHCH2CH3`** - This is a vinylic compound. The carbocation formed would be a secondary allylic carbocation.
3. **Compound III: `CH3CH=CHCH2CH2Cl`** - This is a primary carbocation. The carbocation formed would be a primary carbocation.
4. **Compound IV: `CH3CH=CHCH2(Cl)CH3`** - This is a secondary allylic compound. The carbocation formed would be a secondary carbocation.

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