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A compound X on heating gives a colorless gas. The residue is dissolved in water to obtain Y. Excess carbon dioxide is bubbled through an aqueous solution of Y; Z is formed. Z on gently heating gives back X. The compound X is:
a.) \[CaC{{O}_{3}}\]
b.) \[N{{a}_{2}}C{{O}_{3}}\]
c.) \[Ca{{(HC{{O}_{3}})}_{2}}\]
d.) \[{{K}_{2}}C{{O}_{3}}\]

Answer
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Hint: According to the question, compound X on heating a colourless gas. That colourless gas is carbon dioxide.

Complete step by step answer:
We can write the reactions according to the given question as –
Compound X on heating gives a colorless gas (Carbon dioxide) along with the residue (Calcium Oxide)
\[CaC{{O}_{3}}\xrightarrow{\Delta }CaO+C{{O}_{2}}\uparrow \]
The residue (Calcium Oxide) is dissolved in water to obtain Y (Calcium Hydroxide)
\[CaO+{{H}_{2}}O\to Ca{{(OH)}_{2}}\]
Excess carbon dioxide is bubbled through an aqueous solution of Y (Calcium Hydroxide) to form Z (Calcium Bicarbonate).
\[Ca{{(OH)}_{2}}+2C{{O}_{2}}\xrightarrow{Excess}Ca{{(HC{{O}_{3}})}_{2}}\]
Z (Calcium Bicarbonate) on gently heating gives back X (Calcium Carbonate).
\[Ca{{(HC{{O}_{3}})}_{2}}\xrightarrow{\Delta }CaC{{O}_{3}}+C{{O}_{2}}\uparrow +{{H}_{2}}O\]
From the above reactions, we can see that the compound
X is \[CaC{{O}_{3}}\] - Calcium carbonate
Y is \[Ca{{(OH)}_{2}}\]- Calcium hydroxide
Z is \[Ca{{(HC{{O}_{3}})}_{2}}\]- Calcium bicarbonate
Therefore, the answer is – option (a) – The compound X is Calcium Carbonate - \[CaC{{O}_{3}}\]

Note: When excess carbon dioxide gas is passed through calcium hydroxide (compound Y), it turns milky first due to the formation of the calcium carbonate (compound X) as a precipitate which is insoluble in water and then become colorless due to the formation of calcium bicarbonate (compound Z). On passing excess carbon dioxide gas, the colorless calcium bicarbonate is formed.