Write the chemical reactions for the preparation of ethane from the following compounds:
$(i)$ Bromo-methane
$(ii)$ Propanoic acid

(N/A) $(i)$ Preparation of ethane from Bromo-methane (Wurtz reaction):
$2CH_3Br + 2Na \xrightarrow{\text{dry ether}} CH_3-CH_3 + 2NaBr$
$(ii)$ Preparation of ethane from Propanoic acid (Decarboxylation):
$CH_3CH_2COOH + NaOH \rightarrow CH_3CH_2COONa + H_2O$
$CH_3CH_2COONa + NaOH \xrightarrow{CaO, \Delta} CH_3-CH_3 + Na_2CO_3$