`Mg(s)+C(s) underset("high" T)overset(Delta)rarr X overset(H_(2)O)rarr Mg(OH)_(2)+Y`
X and Y are respectively:

Options

A. `Mg_(2)C` and `CH_(4)`
B. `Mg_(4)C_(3)` and `CH_(4)`
C. `Mg_(2)C_(3)` and `C_(3)H_(4)`
D. `MgC_(2)` and `C_(2)H_(2)`

Explanation

To solve the question, we need to identify the compounds X and Y in the given reaction sequence.

1. **Identify the Reaction**: The reaction starts with magnesium (Mg) and carbon (C) at high temperature.

**Hint**: Look for the product formed when metals react with carbon at elevated temperatures.

2. **Determine Product X**: When magnesium reacts with carbon at high temperatures, it forms magnesium carbide. The chemical formula for magnesium carbide is \( Mg_2C_3 \).

**Hint**: Recall the common compounds formed from the reaction of metals with carbon.

3. **Identify the Next Step**: The magnesium carbide (X) then reacts with water (\( H_2O \)).

**Hint**: Consider what happens when metal carbides react with water.

4. **Determine Product Y**: The reaction of magnesium carbide with water produces magnesium hydroxide (\( Mg(OH)_2 \)) and a hydrocarbon. The hydrocarbon produced from this reaction is propyne, which has the formula \( C_3H_4 \).

**Hint**: Think about the types of hydrocarbons that can be produced from the reaction of metal carbides with water.

5. **Final Products**: Therefore, we conclude that:
- X is magnesium carbide (\( Mg_2C_3 \))
- Y is propyne (\( C_3H_4 \))

**Final Answer**:
- X = Magnesium Carbide (\( Mg_2C_3 \))
- Y = Propyne (\( C_3H_4 \))

### Summary of Steps:
1. Identify the reaction between magnesium and carbon.
2. Determine that magnesium carbide is formed (X).
3. Recognize the reaction of magnesium carbide with water.
4. Identify the products: magnesium hydroxide and propyne (Y).
5. Conclude the identities of X and Y.