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(A) The stability of carbocations is determined by the inductive effect and hyperconjugation,following the order: $methyl < 1^{\circ} < 2^{\circ} < 3^

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$5 < 4 < 3 < 1 < 2$

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(A) The stability of carbocations is determined by the inductive effect and hyperconjugation,following the order: $methyl Analyzing the given carbocations:$5. \, \overset{+}{C} H_3$ (Methyl carbocation)$4. \, CH_3 - \overset{+}{C} H_2$ ($1^{\circ}$ carbocation)$3. \, (CH_3)_2 - \overset{+}{C} H$ ($2^{\circ}$ carbocation)$1. \, (CH_3)_2 - \overset{+}{C} - CH_2 - CH_3$ ($3^{\circ}$ carbocation)$2. \, (CH_3)_3 - \overset{+}{C}$ ($3^{\circ}$ carbocation)Note that $1$ and $2$ are both $3^{\circ}$ carbocations. However,$(CH_3)_3 - \overset{+}{C}$ (tert-butyl) is slightly more stable than $(CH_3)_2 - \overset{+}{C} - CH_2 - CH_3$ due to more hyperconjugative structures.Thus,the increasing order of stability is: $5 < 4 < 3 < 1 < 2$.

Arrange the following carbocations in increasing order of stability:
$1. \, (CH_3)_2 - \overset{+}{C} - CH_2 - CH_3$
$2. \, (CH_3)_3 - \overset{+}{C}$
$3. \, (CH_3)_2 - \overset{+}{C} H$
$4. \, CH_3 - \overset{+}{C} H_2$
$5. \, \overset{+}{C} H_3$

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Arrange the following carbocations in increasing order of stability:$1. \, (CH_3)_2 - \overset{+}{C} - CH_2 - CH_3$$2. \, (CH_3)_3 - \overset{+}{C}$$3. \, (CH_3)_2 - \overset{+}{C} H$$4. \, CH_3 - \overset{+}{C} H_2$$5. \, \overset{+}{C} H_3$