At higher temperature sodium metal reacts with alumina to give a sodium compound `'X'.'X'` is dissolved in water and then carbon dioxide gas is passed through it, a compound `'Y'` is formed. The compound `'X'` and `'Y'` are respectively

Options

A. `Na_(2)O_(2)` and `Na_(2)CO_(3)`
B. `Na_(2)O` and `Na_(2)CO_(3)`
C. `Na_(2)O_(2)` and `NaAlO_(2)`
D. `NaAlO_(2)` and `Na_(2)CO_(3)`

Explanation

To solve the problem step by step, we need to analyze the reactions involving sodium metal, alumina, and the subsequent reactions with water and carbon dioxide.

### Step 1: Reaction of Sodium with Alumina
At higher temperatures, sodium metal reacts with alumina (Al₂O₃) to form a sodium compound. The balanced chemical equation for this reaction is:

\[ 6 \text{Na} + \text{Al}_2\text{O}_3 \rightarrow 3 \text{Na}_2\text{O} + 2 \text{Al} \]

From this reaction, we can identify the sodium compound \(X\) as sodium oxide (\(Na_2O\)).

### Step 2: Dissolving \(X\) in Water
Next, we dissolve the sodium oxide \(Na_2O\) in water. The reaction can be represented as:

\[ \text{Na}_2\text{O} + \text{H}_2\text{O} \rightarrow 2 \text{NaOH} \]

This shows that when \(Na_2O\) is dissolved in water, it forms sodium hydroxide (\(NaOH\)).

### Step 3: Passing Carbon Dioxide through the Solution
Now, we pass carbon dioxide (\(CO_2\)) through the solution of sodium hydroxide. The reaction is:

\[ 2 \text{NaOH} + \text{CO}_2 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} \]

This reaction produces sodium carbonate (\(Na_2CO_3\)), which we can identify as compound \(Y\).

### Summary of Compounds
- The compound \(X\) is sodium oxide (\(Na_2O\)).
- The compound \(Y\) is sodium carbonate (\(Na_2CO_3\)).

### Final Answer
Thus, the compounds \(X\) and \(Y\) are:
- \(X = \text{Na}_2\text{O}\)
- \(Y = \text{Na}_2\text{CO}_3\)