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$[X] + {H_2}S{O_4}\xrightarrow{{}}[Y]$ a colourless gas with an irritating smell.
$[Y] + {K_2}C{r_2}{O_7} + {H_2}S{O_4}\xrightarrow{{}}$ green solution. X and Y are:

Answer
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Hint: As per given data in above question we get there in first equation we have to form a colourless gas which had an irritating smell too and that’s for second equation we have to form a green solution whereas, firstly we have to find the X particle from which we can easily found the substituent present on Y. For which we have to know the properties of similar molecules which have these same kinds of properties.

Complete Step by Step Solution:
As we know that the definition of \[{H_2}S\]: When drilling for and producing crude oil and natural gas, as well as in wastewater treatment and utility facilities and sewers, hydrogen sulphide \[({H_2}S)\] is a gas that is frequently encountered. The breakdown of organic molecules by microorganisms in the absence of oxygen results in the production of the gas.

Now, look at the symbol \[Hg_2^{2 + }\], As we know that Mercury \[(I)\] compounds often undergo disproportionation, producing black metallic mercury and mercury \[(II)\] compounds.

The middle oxidation state of an element will probably be less stable than the higher and lower oxidation levels, depending on whether the element's three oxidation states are listed in increasing or decreasing order. The entire process must be capable of thermodynamic stability.

\[Hg_2^{2 + } + \;{H_2}S\; \to \;HgS\; + \;Hg\; + \;2{H^ + }\]
Therefore, when \[{H_2}S\] is passed through \[Hg_2^{2 + }\]​then we obtain: \[HgS + Hg\]
Thus, the correct option is: (C) \[HgS + Hg\].

Note: When we are doing this type of question it is necessary to you to know all the properties of that element and molecule used in the full equation because if we did not know the nature of such element then we did not justify the result on the base of only theory we have to know the after reaction changes and nature of element to correct the reaction.