(A) Sunita takes 0.5 g of Sodium Carbonate in a test-tube and adds 5 ml of Dilute Hydrochloric acid.

(B) She passes the gas produced in the above reaction through Lime water.

Which of the following represents the chemical reactions taking place in (A) and (B) ?

The correct option representing the chemical reactions in (A) and (B) is:
(A) - Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂
(B) - Ca(OH)₂ + CO₂ → CaCO₃ + H₂O

Step-by-step Explanation:

Step 1: Reaction in Test-tube (A)
In reaction (A), Sunita takes Sodium Carbonate (${\text{Na}}_2{\text{CO}}_3$) and reacts it with Dilute Hydrochloric acid ($\text{HCl}$).
When a metal carbonate reacts with an acid, it yields a salt, water, and carbon dioxide gas (${\text{CO}}_2$).
The balanced chemical equation for this reaction is:
${\text{Na}}_2{\text{CO}}_3+2\text{HCl}\to 2\text{NaCl}+{\text{H}}_2\text{O}+{\text{CO}}_2$

Step 2: Reaction in Lime Water (B)
In reaction (B), the carbon dioxide gas (${\text{CO}}_2$) evolved in reaction (A) is passed through lime water, which is a solution of Calcium Hydroxide [$\text{Ca}{\left(\text{OH}\right)}_2$].
Carbon dioxide reacts with calcium hydroxide to form an insoluble precipitate of Calcium Carbonate (${\text{CaCO}}_3$), turning the lime water milky, along with water (${\text{H}}_2\text{O}$).
The balanced chemical equation for this process is:
$\text{Ca}{\left(\text{OH}\right)}_2+{\text{CO}}_2\to {\text{CaCO}}_3+{\text{H}}_2\text{O}$

Therefore, option 3 correctly matches both balanced chemical equations.