Write the balanced chemical equation for the preparation of :

(a)

Sodium hydroxide by electrolysis of brine solution

(b)

Sodium carbonate

\[2 \mathrm{NaCl}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 2 \mathrm{NaOH}(\mathrm{aq})+\mathrm{Cl}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \]

\(\displaystyle 2 \mathrm{NaHCO}_{3} \xrightarrow{\text { Heat }} \mathrm{Na}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\)