Starting with sodium chloride,how would you proceed to prepare:
$(i)$ sodium metal
$(ii)$ sodium hydroxide
$(iii)$ sodium peroxide
$(iv)$ sodium carbonate?

(N/A) $(i)$ Sodium metal can be extracted from sodium chloride by the Downs process. This process involves the electrolysis of fused $NaCl$ $(40 \%)$ and $CaCl_{2}$ $(60 \%)$ at a temperature of $1123 \ K$ in a Downs cell.
Steel is the cathode and a block of graphite acts as the anode. Metallic $Na$ is formed at the cathode. Molten sodium is taken out of the cell and collected over kerosene.
$NaCl \xrightarrow{\text{Electrolysis}} Na^{+} + Cl^{-}$
At Cathode: $Na^{+} + e^{-} \longrightarrow Na$
At Anode: $2Cl^{-} \longrightarrow Cl_{2} + 2e^{-}$
$(ii)$ Sodium hydroxide can be prepared by the electrolysis of an aqueous solution of sodium chloride (brine). This is called the Castner-Kellner process. In this process,the brine solution is electrolysed using a carbon anode and a mercury cathode.
The sodium metal,which is discharged at the cathode,combines with mercury to form an amalgam.
Cathode: $Na^{+} + e^{-} \xrightarrow{Hg} Na-\text{amalgam}$
Anode: $Cl^{-} \longrightarrow \frac{1}{2} Cl_{2} + e^{-}$
$(iii)$ Sodium peroxide: First,$NaCl$ is electrolysed to result in the formation of $Na$ metal (Downs process). This sodium metal is then heated on aluminium trays in air (free of $CO_{2}$) to form its peroxide.
$2Na + O_{2(air)} \longrightarrow Na_{2}O_{2}$
$(iv)$ Sodium carbonate is prepared by the Solvay process. Sodium hydrogen carbonate is precipitated in a reaction of sodium chloride and ammonium hydrogen carbonate.
$NH_{3} + H_{2}O + CO_{2} \longrightarrow NH_{4}HCO_{3}$
$NH_{4}HCO_{3} + NaCl \longrightarrow NH_{4}Cl + NaHCO_{3}$
These sodium hydrogen carbonate crystals are heated to give sodium carbonate.
$2NaHCO_{3} \longrightarrow Na_{2}CO_{3} + CO_{2} + H_{2}O$