Explain the preparation of sodium carbonate by the Solvay process with chemical reactions.

(N/A) Sodium carbonate $(Na_{2}CO_{3} \cdot 10H_{2}O)$ is generally prepared by the Solvay process. In this process,the low solubility of sodium hydrogen carbonate is utilized,causing it to precipitate during the reaction of sodium chloride with ammonium hydrogen carbonate.
The ammonium hydrogen carbonate is prepared by passing $CO_{2}$ through a concentrated solution of sodium chloride saturated with ammonia,where ammonium carbonate is formed first,followed by ammonium hydrogen carbonate. The equations for the complete process are as follows:
$2NH_{3} + H_{2}O + CO_{2} \rightarrow (NH_{4})_{2}CO_{3}$
$(NH_{4})_{2}CO_{3} + H_{2}O + CO_{2} \rightarrow 2NH_{4}HCO_{3}$
$NH_{4}HCO_{3} + NaCl \rightarrow NH_{4}Cl + NaHCO_{3}$
The sodium hydrogen carbonate crystals separate out. These are then heated to produce sodium carbonate:
$2NaHCO_{3} \rightarrow Na_{2}CO_{3} + CO_{2} + H_{2}O$
In this process,$NH_{3}$ is recovered when the solution containing $NH_{4}Cl$ is treated with $Ca(OH)_{2}$. Calcium chloride is obtained as a by-product:
$2NH_{4}Cl + Ca(OH)_{2} \rightarrow 2NH_{3} + CaCl_{2} + H_{2}O$