Step 1: Understanding the Question:
The question asks to identify the substance that dissociates into positive and negative ions when dissolved in water, thus creating an electrolyte solution.
Detailed Explanation:
• Ionic vs. Covalent Compounds:
An ionic solution is formed by substances with ionic bonds that "break apart" or dissociate into charged particles (ions) in a polar solvent like water.
• Calcium Chloride ($CaCl_2$):
It is a classic ionic salt consisting of metal (Calcium) and non-metal (Chlorine).
In water: \( CaCl_2(s) \rightarrow Ca^{2+}(aq) + 2Cl^-(aq) \).
Since it produces ions, the solution will conduct electricity.
• Analyzing other options:
$O_2$ (Oxygen): A non-polar covalent molecule. It dissolves slightly in water but stays as $O_2$ molecules.
$CH_4$ (Methane): A non-polar covalent gas. It has extremely low solubility and does not ionize.
$C_{12H_{22}O_{11}$ (Sucrose/Sugar):} A polar covalent molecule. It dissolves well because it can form hydrogen bonds, but it stays as whole neutral sugar molecules. It is a non-electrolyte.
Step 2: Final Answer:
Calcium chloride ($CaCl_2$) is the only substance among the choices that produces an ionic solution.