Step 1: Understand what "lime water" is.
Lime water is a common name for a dilute aqueous solution of calcium hydroxide, Ca(OH)\(_2\).
It is clear and colorless.
Step 2: Recall the reaction of common gases with lime water.
- Oxygen (O\(_2\)): Does not react with lime water to cause milkiness.
- Nitrogen (N\(_2\)): Generally unreactive, does not react with lime water.
- Benzene (C\(_6\)H\(_6\)): An organic compound, a liquid at room temperature (or gas if heated).
It does not typically react with lime water to cause milkiness.
- Carbon dioxide (CO\(_2\)): When carbon dioxide gas is passed through lime water, it reacts with calcium hydroxide to form calcium carbonate (CaCO\(_3\)), which is a white, insoluble precipitate.
This precipitate makes the lime water appear milky or turbid.
Reaction: \( \text{Ca(OH)}_2\text{(aq)} + \text{CO}_2\text{(g)} \rightarrow \text{CaCO}_3\text{(s)} \downarrow + \text{H}_2\text{O(l)} \)
If excess CO\(_2\) is passed, the milkiness disappears due to the formation of soluble calcium bicarbonate:
\( \text{CaCO}_3\text{(s)} + \text{H}_2\text{O(l)} + \text{CO}_2\text{(g, excess)} \rightarrow \text{Ca(HCO}_3\text{)}_2\text{(aq)} \)
Step 3: Identify the correct gas.
The gas that makes lime water milky is Carbon-di-oxide (CO\(_2\)).
This matches option (4).