Give the chemical conversions for the following:
$(i)$ $2-$Hydroxy$-2-$methylpropanoic acid from acetone
$(ii)$ Ethane from ethanol

(N/A) $(i)$ Conversion of acetone to $2-$hydroxy$-2-$methylpropanoic acid:
Acetone $(CH_3COCH_3)$ reacts with $HCN$ in the presence of $OH^-$ to form acetone cyanohydrin. This cyanohydrin is then hydrolyzed with $H_2O/H^+$ to yield $2-$hydroxy$-2-$methylpropanoic acid.
$CH_3COCH_3 + HCN$ $\xrightarrow{OH^-} CH_3C(OH)(CN)CH_3$ $\xrightarrow{H_3O^+} CH_3C(OH)(COOH)CH_3$
$(ii)$ Conversion of ethanol to ethane:
Ethanol $(CH_3CH_2OH)$ is first oxidized to ethanal $(CH_3CHO)$ using $PCC$ or $Cu/573K$. Then,ethanal undergoes Wolff-Kishner reduction using hydrazine $(NH_2NH_2)$ and $KOH$ in ethylene glycol to produce ethane $(CH_3CH_3)$.
$CH_3CH_2OH$ $\xrightarrow{[O]} CH_3CHO$ $\xrightarrow{NH_2NH_2, KOH, \Delta} CH_3CH_3$