Provide the chemical reactions for the following conversions:
$1$. $2$-bromopropane and $1$-bromopropane from propene.
$2$. $2$-bromopropane from $1$-bromopropane.

(N/A) $1$. Conversion of propene to $2$-bromopropane and $1$-bromopropane:
- For $2$-bromopropane: Propene reacts with $HBr$ in the presence of $CCl_4$ (Markovnikov addition) to form $2$-bromopropane.
$CH_3CH=CH_2 + HBr \xrightarrow{CCl_4} CH_3CH(Br)CH_3$
- For $1$-bromopropane: Propene reacts with $HBr$ in the presence of organic peroxide (Anti-Markovnikov addition) to form $1$-bromopropane.
$CH_3CH=CH_2 + HBr \xrightarrow{\text{Peroxide}} CH_3CH_2CH_2Br$
$2$. Conversion of $1$-bromopropane to $2$-bromopropane:
- First,$1$-bromopropane undergoes dehydrohalogenation with alcoholic $KOH$ to form propene.
$CH_3CH_2CH_2Br + KOH (\text{alc.}) \rightarrow CH_3CH=CH_2 + KBr + H_2O$
- Then,propene reacts with $HBr$ (Markovnikov addition) to form $2$-bromopropane.
$CH_3CH=CH_2 + HBr \rightarrow CH_3CH(Br)CH_3$