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A deep colour brown gas is formed by mixing two colourless gases which are
A. $N{O_2}$ and ${O_2}$
B. $N{O_2}$ and $NO$
C. $NO$ and ${O_2}$
D. $N{H_3}$ and $HCl$

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Answer
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Hint: The chemical name of the deep coloured brown gas is nitrogen dioxide and its chemical formula is $N{O_2}$. It is yellowish brown gas below the temperature ${21.2^o}C$ but when the temperature rises above ${21.2^o}C$, it transforms into a reddish-brown coloured gas. We need to check the synthesis of nitrogen dioxide from the given pair of molecules.

Complete answer: On examining the reaction for each pair of gases given in the options, following observations are noted:
Pair of gases given in option (A) are $N{O_2}$ and ${O_2}$. As $N{O_2}$ is not a colourless gas and we cannot synthesize nitrogen dioxide from its own molecule. Moreover, the nitrogen dioxide gas reacts with oxygen gas to produce dinitrogen pentoxide which is a white solid. The reaction takes place as follows:
$4N{O_2} + {O_2} \to 2{N_2}{O_5}$
Pair of gases given in option (B) are $N{O_2}$ and $NO$. In this case also, $N{O_2}$ is not a colourless gas and we cannot synthesize nitrogen dioxide from its own molecule. Moreover, the nitrogen dioxide gas reacts with oxygen gas to produce dinitrogen trioxide which has a deep blue colour experience. The reaction takes place as follows:
$N{O_2} + NO \to {N_2}{O_3}$
Pair of gases given in option (C) are $NO$ and ${O_2}$. In this case, both $NO$ and ${O_2}$ gases are colourless and when nitrogen monoxide reacts with dioxygen in warm conditions, then the formation of deep coloured brown gas i.e., nitrogen dioxide takes place. The reaction is as follows:
$2NO + {O_2} \to 2N{O_2}$
Pair of gases given in option (D) are $N{H_3}$ and $HCl$. In this case, both $N{H_3}$ and $HCl$ gases are colourless and when ammonia reacts with hydrogen chloride, then the neutralization reaction takes place and ammonium chloride is formed as a product along with removal of white fumes. The reaction is as follows:
$N{H_3} + HCl \to N{H_4}Cl$
Hence, a deep coloured brown or reddish-brown gas is formed by mixing two colourless gases which are $NO$ and ${O_2}$.
Therefore, the correct answer is option C.

Note:
It is important to note that nitrogen dioxide can alternatively be prepared from the reduction of concentrated nitric acid i.e., $HN{O_3}$ in the presence of metal like copper. The reaction for the process is $4HN{O_3} + Cu \to Cu{(N{O_3})_2} + 2N{O_2} + 2{H_2}O$. In the solid form i.e., below ${15^o}F$, nitrogen dioxide structurally exists as ${N_2}{O_2}$.