Write the reactions for the preparation of ethane from the following:
$(i)$ Acetic acid $(CH_3COOH)$
$(ii)$ Methane $(CH_4)$
$(iii)$ Acetate ion $(CH_3COO^{-})$

(N/A) $(i)$ From Acetic acid $(CH_3COOH)$:
$2CH_3COOH + 2NaOH \rightarrow 2CH_3COONa + 2H_2O$
$2CH_3COONa + 2H_2O \xrightarrow{\text{Electrolysis}} CH_3-CH_3 + 2CO_2 + H_2 + 2NaOH$ (Kolbe's Electrolysis)
$(ii)$ From Methane $(CH_4)$:
$2CH_4 + 2Cl_2 \xrightarrow{h\nu} 2CH_3Cl + 2HCl$
$2CH_3Cl + 2Na \xrightarrow{\text{dry ether}} CH_3-CH_3 + 2NaCl$ (Wurtz Reaction)
$(iii)$ From Acetate ion $(CH_3COO^{-})$:
$2CH_3COO^{-}$ $\xrightarrow{-2e^{-}} 2CH_3COO^{\bullet}$ $\rightarrow 2CH_3^{\bullet} + 2CO_2$
$2CH_3^{\bullet} \rightarrow CH_3-CH_3$ (Kolbe's Electrolysis mechanism)