Out of two bromoderivatives
`C_(6)H_(5)CH(CH_(3))Br and C_(6)H_(5)CH(C_(6)H_(5))Br`, which one is more reactive in `S_(N^(1))` reaction and why?

Explanation

In `S_(N)1` reaction, reactivity depends upon the stability of the intermediate carbocation. Thus,

The carbocation (II) derived from `C_(6)H_(5)CH(C_(6)H_(5))Br` is stabilized by +R-effect of the two `C_(6)H_(5)` groups the carbocation (I) derived from `C_(6)H_(5)CH(CH_(3))Br` is stabilized by +R-effect of one `C_(6)H_(5)` group and +I-effect of the `CH_(3)` group. since +R-effect is much stronger than +I-effect, therefore, carbocation (II) is more stable than carbocation (I). thus, `C_(6)H_(5)CH(C_(6)H_(5))Br` is more reactive than `C_(6)H_(5)CH(C_(6)H_(5))Br` is more reactive than `C_(6)H_(5)CH(CH_(3))Br` in `S_(N)1` substitution reaction.