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A colourless gas $'x'$ forms a brown coloured gas $'y'$ when mixed with air. $x$ and $y$ could be:
A. $NO, N{O_2}$
B. $NO, {O_2}$
C. $N{O_2}, {N_2}{O_4}$
D. $NO, {N_2}{O_4}$

Answer
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Hint: We know that air is made up of many gases, but oxygen gas and nitrogen gas are the major constituents of the air. So we will try to react $'x'$ which is colourless with nitrogen gas or oxygen gas to form $'y'$ which is brown coloured gas .

Complete step by step answer:
We already know that the major constituents of the air are oxygen gas and nitrogen gas. It is given to us that $x$ is a colourless gas and when $x$ is mixed with air it forms a brown coloured gas $y$. When $NO$ is mixed in air , it will react with oxygen gas . The chemical equation we will get will be $NO + {O_2} \to N{O_2}$. If we try to balance, we will get $2NO + {O_2} \to 2N{O_2}$. $NO$ is a colourless gas and $N{O_2}$ is a brown coloured gas. When $N{O_2}$ is mixed in air, it reacts with oxygen gas to form ${N_2}{O_5}$. The chemical equation can be written as $4N{O_2} + {O_2} \to 2{N_2}{O_5}$. ${N_2}{O_5}$ is also colourless.
From the above explanation and discussion it is clear to us that $x$ is $NO$ which is colourless and $y$ is $N{O_2}$ which is brown coloured gas .

So, the correct answer of the given question is option: A. $NO, N{O_2}$

Additional information:
$N{O_2}$ is highly soluble in water. ${N_2}{O_5}$ is also known as nitrogen pentoxide or nitric anhydride. ${N_2}{O_5}$ has one bridged oxygen atom.

Note:
Always remember that whenever $NO$ will react with oxygen gas the chemical reaction we will get is $2NO + {O_2} \to 2N{O_2}$ and when $N{O_2}$ will reacts with oxygen gas the chemical reaction we will get is $4N{O_2} + {O_2} \to 2{N_2}{O_5}$. $NO$ and ${N_2}{O_5}$ are colourless gases. $N{O_2}$ is a brown coloured gas.