Element X is extracted by the electrolysis of a molten compound of elements X and Y . The electrode reactions are as shown:
At the cathode : `X^(2+)("I") + 2e^(-) to X`
(I) At the anode : `2Y^(2-)("I") to Y_(2)("g")+4e^(-)`

Options

A. Aluminium oxide
B. Calcium chloride
C. Magnesiuim oxide
D. Potassium chloride

Explanation

To solve the problem of extracting element X through the electrolysis of a molten compound of elements X and Y, we need to analyze the provided electrode reactions and identify the appropriate compound from which X can be extracted. Here’s a step-by-step solution:

### Step 1: Understand the Electrode Reactions
The reactions at the electrodes are given as:
- At the cathode: \( X^{2+} + 2e^- \rightarrow X \)
- At the anode: \( 2Y^{2-} \rightarrow Y_2(g) + 4e^- \)

This indicates that X is being reduced at the cathode, while Y is being oxidized at the anode.

### Step 2: Identify the Charges
From the reactions, we can deduce:
- X has a charge of \( +2 \) (as indicated by \( X^{2+} \)).
- Y has a charge of \( -2 \) (as indicated by \( Y^{2-} \)).

### Step 3: Determine the Compound
The compound formed by X and Y must balance the charges. Therefore, if X has a \( +2 \) charge and Y has a \( -2 \) charge, the simplest formula for the compound would be \( XY_2 \). This means for every one atom of X, there are two atoms of Y.

### Step 4: Analyze Possible Compounds
We need to find a suitable molten compound that fits the charge requirements. The options given in the video transcript include:
1. Aluminum oxide (Al2O3)
2. Calcium chloride (CaCl2)
3. Magnesium oxide (MgO)
4. Potassium chloride (KCl)

### Step 5: Check Each Compound
- **Aluminum oxide (Al2O3)**: Breaks into \( Al^{3+} \) and \( O^{2-} \). Not suitable.
- **Calcium chloride (CaCl2)**: Breaks into \( Ca^{2+} \) and \( Cl^{-} \). Not suitable.
- **Magnesium oxide (MgO)**: Breaks into \( Mg^{2+} \) and \( O^{2-} \). This fits our requirement.
- **Potassium chloride (KCl)**: Breaks into \( K^{+} \) and \( Cl^{-} \). Not suitable.

### Step 6: Conclusion
The only compound that fits the criteria for the electrolysis reactions provided is magnesium oxide (MgO). Thus, element X is magnesium (Mg), and element Y is oxygen (O).

### Final Answer
Element X is extracted from magnesium oxide (MgO).

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