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In the reaction:
\[{\text{M}}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}\xrightarrow{{{{\text{H}}_{\text{2}}}{\text{O}}}}{\text{A}}\left( {{\text{gas}}} \right)\xrightarrow[{\text{\Delta }}]{{{\text{CuO}}}}{\text{B}} + {\text{C}}\left( {\text{g}} \right) + {{\text{H}}_{\text{2}}}{\text{O}}\]
\[{\text{C}}\left( {\text{g}} \right)\] can be obtained by heating:
A) ${\left( {{\text{N}}{{\text{H}}_{\text{4}}}} \right)_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$
B) ${\left( {{\text{N}}{{\text{H}}_{\text{4}}}} \right)_{\text{2}}}{\text{C}}{{\text{r}}_2}{{\text{O}}_{\text{7}}}$
C) ${\text{N}}{{\text{H}}_{\text{4}}}{\text{N}}{{\text{O}}_3}$
D) ${\text{N}}{{\text{H}}_{\text{4}}}{\text{Cl}}$

Answer
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Hint:To solve this we must know the gas produced when magnesium nitride reacts with water. Magnesium nitride on reaction with water produces a highly irritating gas with a sharp suffocating odour which on reaction with copper (II) oxide produces two gases.

 Complete step by step answer:
We are given a sequence of reactions as follows:
\[{\text{M}}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}\xrightarrow{{{{\text{H}}_{\text{2}}}{\text{O}}}}{\text{A}}\left( {{\text{gas}}} \right)\xrightarrow[{\text{\Delta }}]{{{\text{CuO}}}}{\text{B}} + {\text{C}}\left( {\text{g}} \right) + {{\text{H}}_{\text{2}}}{\text{O}}\]
Let us consider the first reaction,
\[{\text{M}}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}\xrightarrow{{{{\text{H}}_{\text{2}}}{\text{O}}}}{\text{A}}\left( {{\text{gas}}} \right)\]
Magnesium nitride reacts with water to produce magnesium hydroxide and ammonia gas. Ammonia is a highly irritating gas with a sharp suffocating odour. The reaction of magnesium nitride with water is as follows:
\[{\text{M}}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}\xrightarrow{{{{\text{H}}_{\text{2}}}{\text{O}}}}{\text{Mg}}{\left( {{\text{OH}}} \right)_{\text{2}}} + {\text{N}}{{\text{H}}_{\text{3}}}\left( {\text{g}} \right)\]
Thus, \[{\text{M}}{{\text{g}}_{\text{3}}}{{\text{N}}_{\text{2}}}\xrightarrow{{{{\text{H}}_{\text{2}}}{\text{O}}}}{\text{N}}{{\text{H}}_{\text{3}}}\left( {{\text{gas}}} \right)\]. Thus, A is ammonia gas.
Let us consider the second reaction,
\[{\text{A}}\left( {{\text{gas}}} \right)\xrightarrow[{\text{\Delta }}]{{{\text{CuO}}}}{\text{B}} + {\text{C}}\left( {\text{g}} \right) + {{\text{H}}_{\text{2}}}{\text{O}}\]
Where A is ammonia gas.
Ammonia on reaction with copper (II) oxide produces copper metal, nitrogen gas and water. The reaction occurs at a temperature of $500 - {500^ \circ }{\text{C}}$. The reaction of ammonia gas with copper (II) oxide is as follows:
\[{\text{N}}{{\text{H}}_{\text{3}}}\left( {{\text{gas}}} \right)\xrightarrow[{\text{\Delta }}]{{{\text{CuO}}}}{\text{Cu}} + {{\text{N}}_2}\left( {\text{g}} \right) + {{\text{H}}_{\text{2}}}{\text{O}}\]
Thus, \[{\text{N}}{{\text{H}}_{\text{3}}}\left( {{\text{gas}}} \right)\xrightarrow[{\text{\Delta }}]{{{\text{CuO}}}}{\text{Cu}} + {{\text{N}}_2}\left( {\text{g}} \right) + {{\text{H}}_{\text{2}}}{\text{O}}\]. Thus, B is copper metal and C is nitrogen gas.
Nitrogen gas can be obtained by decomposition of ammonium dichromate ${\left( {{\text{N}}{{\text{H}}_{\text{4}}}} \right)_{\text{2}}}{\text{C}}{{\text{r}}_2}{{\text{O}}_{\text{7}}}$. Ammonium dichromate decomposes on heating and produces chromium (III) oxide, nitrogen gas and water. The decomposition reaction of ammonium dichromate is as follows:
${\left( {{\text{N}}{{\text{H}}_{\text{4}}}} \right)_{\text{2}}}{\text{C}}{{\text{r}}_2}{{\text{O}}_{\text{7}}} \to {\text{C}}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{3}}} + {{\text{N}}_{\text{2}}} + {\text{4}}{{\text{H}}_{\text{2}}}{\text{O}}$
Thus, \[{\text{C}}\left( {\text{g}} \right)\] can be obtained by heating ${\left( {{\text{N}}{{\text{H}}_{\text{4}}}} \right)_{\text{2}}}{\text{C}}{{\text{r}}_2}{{\text{O}}_{\text{7}}}$.
Thus, the correct option is (B) ${\left( {{\text{N}}{{\text{H}}_{\text{4}}}} \right)_{\text{2}}}{\text{C}}{{\text{r}}_2}{{\text{O}}_{\text{7}}}$.

Thus, the correct option is (B).

 Note: Ammonium sulphate ${\left( {{\text{N}}{{\text{H}}_{\text{4}}}} \right)_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ on heating produces ammonia and hydrogen sulphate (sulphuric acid). Ammonium nitrate ${\text{N}}{{\text{H}}_{\text{4}}}{\text{N}}{{\text{O}}_3}$ on heating produces nitrous oxide and water. Ammonium chloride ${\text{N}}{{\text{H}}_{\text{4}}}{\text{Cl}}$ on heating produces ammonia and hydrogen chloride gas. Thus, ammonium sulphate ${\left( {{\text{N}}{{\text{H}}_{\text{4}}}} \right)_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$, ammonium nitrate ${\text{N}}{{\text{H}}_{\text{4}}}{\text{N}}{{\text{O}}_3}$ and ammonium chloride ${\text{N}}{{\text{H}}_{\text{4}}}{\text{Cl}}$ do not produce nitrogen gas.