To solve this question, we need to understand the chemical reactions involved when aluminum oxide (\( \mathrm{Al_2O_3} \)) is processed with alkali and the subsequent reactions with gases to form different products.
- Aluminum oxide (\( \mathrm{Al_2O_3} \)) is leached with an alkali (like sodium hydroxide, \( \mathrm{NaOH} \)) to form a solution of sodium aluminate (\( \mathrm{Na[Al(OH)_4]} \)) by the reaction:
\mathrm{Al_2O_3 + 2NaOH + 3H_2O \rightarrow 2Na[Al(OH)_4]}
- The compound \( X \) is thus sodium aluminate, (\( \mathrm{Na[Al(OH)_4]} \)).
- When carbon dioxide (\( \mathrm{CO_2} \)) gas is passed through the solution of \( X \), aluminum hydroxide (\( \mathrm{Al(OH)_3} \)) is precipitated. This is because \( \mathrm{CO_2} \) reacts with water to form carbonic acid, which neutralizes the sodium aluminate to give precipitated aluminum hydroxide:
\mathrm{2Na[Al(OH)_4] + CO_2 \rightarrow 2Al(OH)_3 + Na_2CO_3 + H_2O}
- Upon aging or drying, the precipitated aluminum hydroxide can dehydrate partially to form hydrated aluminum oxide (\( \mathrm{Al_2O_3 \cdot xH_2O} \)), designated as compound \( Z \).
- Thus, the correct answer is that \( X \) is \( \mathrm{Na[Al(OH)_4]} \), \( Y \) is \( \mathrm{CO_2} \), and \( Z \) is \( \mathrm{Al_2O_3 \cdot xH_2O} \).
In conclusion, the correct option is: X = Na[Al(OH)_4], Y = CO_2, Z = Al_2O_3 . xH_2O.