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For the purpose of systematic qualitative analysis, cations are classified into various groups on the basis of their behavior against some reagents. The group reagents used for the classification of most common cations are hydrochloric acid, hydrogen sulphide, ammonium hydroxide, and ammonium carbonate. Classification is based on whether a cation reacts with these reagents by the formation of precipitates or not.
An aqueous solution contains $H{g^{2 + }}$, $Hg_2^{2 + }$, $P{b^{2 + }}$and $C{d^{2 + }}$. The addition of $2$ M \[HCl\] will precipitate-
A.$H{g_2}C{l_2}$ only
B.$PbC{l_2}$ only
C.$PbC{l_2}$ and $H{g_2}C{l_2}$
D.$PbC{l_2}$ and $CdC{l_2}$

Answer
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Hint: We use qualitative analysis for identifying salts and identifying multiple cations present in the solution. Qualitative analysis tells us what is present in the solution as we mix the compound with different reagents. According to their behavior against the reagents, we have placed them in different groups. $Hg_2^{2 + }$and $P{b^{2 + }}$are placed in the first group and $H{g^{2 + }}$ and $C{d^{2 + }}$ are placed in the second group.

Complete step by step answer:
It is given that cations are classified into various groups on the basis of their behavior against reagents like hydrochloric acid, hydrogen sulphide, ammonium hydroxide, and ammonium carbonate.We have to find if the given cations $H{g^{2 + }}$,$Hg_2^{2 + }$, $P{b^{2 + }}$ and $C{d^{2 + }}$ give precipitate when reacted with $2$ M \[HCl\] or not.
The first group among the ions $Hg_2^{2 + }$and $P{b^{2 + }}$ are placed in the first group as they have low solubility products. When hydrochloric acid is dissolved in the solution of the ions $Hg_2^{2 + }$ and $P{b^{2 + }}$, then the both of them give white precipitate and two hydrogen ions are released. The reactions are given as-
\[ \Rightarrow P{b^{2 + }} + 2HCl \to \mathop {PbC{l_2}}\limits_{whiteppt} \downarrow + 2{H^ + }\]
$ \Rightarrow Hg_2^{2 + } + 2HCl \to \mathop {H{g_2}C{l_2}}\limits_{Whiteppt} \downarrow + 2{H^ + }$
$H{g^{2 + }}$ and $C{d^{2 + }}$ are placed in the second group because when they react with hydrochloric acid they do not give precipitate and the filtrate is used to perform experiment of second group. The solubility product of these two ions is more than the solubility product of the ions of the first group.

The correct answer is option C.

Note:
The ions $H{g^{2 + }}$ and $C{d^{2 + }}$ are reacted with dilute hydrochloric acid and then hydrogen sulphide gas is passed through their solution and they produce precipitate as they react with sulphur of hydrogen sulphide and give-
$HgS$ which is in the form of black precipitate
$CdS$ which is in the form of yellow precipitate.