Step 1: Understanding the reaction between egg-shells and a solution:
Egg-shells are primarily composed of calcium carbonate (CaCO₃). When calcium carbonate reacts with an acidic solution, it produces a colorless gas. This gas, when bubbled through lime water, causes lime water to turn milky, indicating the presence of carbon dioxide (CO₂).
Step 2: Analyzing the solution (S):
The solution that reacts with egg-shells to produce a colorless gas must be acidic, as the acid reacts with calcium carbonate to release CO₂. The most common acid used in such reactions is hydrochloric acid (HCl). When calcium carbonate reacts with hydrochloric acid, the reaction is as follows:
\[
\text{CaCO}_3 + 2\text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2
\]
Here, the acid (HCl) reacts with calcium carbonate (CaCO₃) to release carbon dioxide (CO₂), water (H₂O), and calcium chloride (CaCl₂).
Step 3: Analyzing the gas (G):
The gas produced is carbon dioxide (CO₂), which is colorless and reacts with lime water (a solution of calcium hydroxide, Ca(OH)₂) to form calcium carbonate, turning the lime water milky:
\[
\text{Ca(OH)}_2 + \text{CO}_2 \rightarrow \text{CaCO}_3 + \text{H}_2\text{O}
\]
This reaction indicates that the gas is indeed CO₂.
Step 4: Conclusion:
The solution (S) is HCl (hydrochloric acid), and the colorless gas (G) produced is CO₂ (carbon dioxide). When CO₂ is passed through lime water, it turns milky due to the formation of calcium carbonate.