Provide a chemical test to distinguish between butane and but-$1$-ene and write the corresponding reactions.

(N/A) To distinguish between butane (an alkane) and but-$1$-ene (an alkene),the Baeyer's test or Bromine water test can be used.
$1$. Baeyer's Test: But-$1$-ene reacts with cold dilute alkaline $KMnO_{4}$ solution (Baeyer's reagent) to form a vicinal diol,causing the purple color of $KMnO_{4}$ to disappear. Butane does not react.
$CH_{3}CH_{2}CH=CH_{2} + H_{2}O + [O] \xrightarrow{\text{Cold, dil. } KMnO_{4}} CH_{3}CH_{2}CH(OH)CH_{2}OH$ (Butane-$1,2$-diol)
$2$. Bromine Water Test: But-$1$-ene reacts with $Br_{2}$ in $CCl_{4}$ to form a colorless addition product,discharging the reddish-brown color of bromine. Butane does not react.
$CH_{3}CH_{2}CH=CH_{2} + Br_{2} \xrightarrow{CCl_{4}} CH_{3}CH_{2}CH(Br)CH_{2}Br$ ($1,2$-Dibromobutane)