When an aqueous solution of `CaCl_(2)` is electrolyzed using inert electrods, which of the following is `(` are `)` true ?
(a)Calcium deposites on cathode.
(b) Calcium deposits an anode
(c) Chloride is liberated on anode
(d) Calcium hydroxide precipitates near cathode on prolonged hydrolysis

Options

A. Calcium deposites on cathode.
B. Calcium deposits an anode
C. Chloride is liberated on anode
D. Calcium hydroxide precipitates near cathode on prolonged hydrolysis

Explanation

To solve the question regarding the electrolysis of an aqueous solution of `CaCl₂` using inert electrodes, we need to analyze the reactions that occur at both the cathode and anode.

### Step-by-Step Solution:

1. **Identify the Components in the Solution**:
- The aqueous solution of `CaCl₂` contains `Ca²⁺` ions and `Cl⁻` ions, along with water (`H₂O`).

2. **Electrolysis Process**:
- Electrolysis involves the movement of ions towards the electrodes where reduction (gain of electrons) occurs at the cathode and oxidation (loss of electrons) occurs at the anode.

3. **Reactions at the Cathode**:
- At the cathode, two possible reduction reactions can occur:
- `Ca²⁺ + 2e⁻ → Ca` (calcium deposition)
- `2H₂O + 2e⁻ → H₂ + 2OH⁻` (hydrogen gas and hydroxide ions)
- Since water is more stable and has a lower reduction potential than calcium ions, the preferential reaction at the cathode will be the reduction of water, producing hydrogen gas and hydroxide ions. Therefore, calcium does **not** deposit at the cathode.

4. **Reactions at the Anode**:
- At the anode, two possible oxidation reactions can occur:
- `2Cl⁻ → Cl₂ + 2e⁻` (chlorine gas liberation)
- `4OH⁻ → O₂ + 2H₂O + 4e⁻` (oxygen gas liberation)
- The oxidation of chloride ions to chlorine gas is favored over the oxidation of hydroxide ions. Thus, chlorine gas is liberated at the anode.

5. **Prolonged Hydrolysis**:
- During prolonged electrolysis, the hydroxide ions produced at the cathode can react with calcium ions in the solution to form calcium hydroxide (`Ca(OH)₂`), which is insoluble and precipitates out of the solution.

### Conclusion:
Based on the analysis:
- (a) Calcium deposits on cathode: **False**
- (b) Calcium deposits at anode: **False**
- (c) Chloride is liberated on anode: **True**
- (d) Calcium hydroxide precipitates near cathode on prolonged hydrolysis: **True**

Thus, the correct statements are **(c)** and **(d)**.