Discuss the various reactions that occur in the Solvay process.

The Solvay process is used for the industrial preparation of sodium carbonate $(Na_2CO_3)$.
Step $1$: Brine solution ($NaCl$ solution) is saturated with ammonia $(NH_3)$.
$2NH_3 + H_2O + CO_2 \longrightarrow (NH_4)_2CO_3$
Step $2$: Carbon dioxide is passed through the ammoniated brine to form insoluble sodium hydrogen carbonate $(NaHCO_3)$.
$NH_3 + H_2O + CO_2 \longrightarrow NH_4HCO_3$
$NaCl + NH_4HCO_3 \longrightarrow NaHCO_3 \downarrow + NH_4Cl$
Step $3$: The $NaHCO_3$ crystals are separated by filtration.
Step $4$: $NaHCO_3$ is heated strongly to obtain sodium carbonate $(Na_2CO_3)$.
$2NaHCO_3 \longrightarrow Na_2CO_3 + CO_2 + H_2O$
Step $5$: Ammonia is recovered by treating the filtrate (containing $NH_4Cl$) with calcium hydroxide $(Ca(OH)_2)$.
$Ca(OH)_2 + 2NH_4Cl \longrightarrow 2NH_3 + 2H_2O + CaCl_2$
The overall reaction is:
$2NaCl + CaCO_3 \longrightarrow Na_2CO_3 + CaCl_2$