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A metal salt $MX$ when exposed to light splits up to form metal $M$ and a gas ${{X}_{2}}$ . Metal $M$ is used in making ornaments whereas gas ${{X}_{2}}$ is used in making bleaching powder. The salt $MX$ is itself used in black and white photography.
a) What do you think metal $M$ is?
b) What could be gas ${{X}_{2}}$ ?
c) Name the metal salt $MX$ .
d) Name any two salt solutions which on mixing together can produce a precipitate of salt $MX$ .
e) What type of chemical reaction takes place when salt $MX$ is exposed to light? Write the equation of the reaction.

Answer
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Hint: We can get by reading the question that this reaction is a decomposition reaction and basically it's a reaction in which a compound breaks down into more than two simpler materials. Here to we have a similar decomposition reaction; therefore general form of a decomposition reaction which is given by: \[AB\to A+B\]

Complete step-by-step answer:
We know that this question looks more like the reasoning based question and can only answer in an analytic method.
Firstly we can easily figure it out that the gas produced \[{{X}_{2}}\] from salt MX is also involved in formation of a bleaching powder, so we have to keep it in consideration that the formation of a bleaching powder involves of \[Ca\left( OCl \right)Cl\]
\[Ca{{\left( OH \right)}_{2}}\text{ }+\text{ }C{{l}_{2}}\text{ }\to \text{ }Ca\left( OCl \right)Cl\text{ }+\text{ }{{H}_{2}}O\]

Further, the given metal M which is used in fabrication of ornaments so typically it should from one of these three Gold \[\left( Au \right)\] ,Silver \[\left( Ag \right)\] , Platinum \[\left( Pt \right)\].But we already know that the given metal salt is MX Metal chloride right and as we know from periodic table Chlorine is monovalent that means with $-1$ oxidation state. Therefore, given metal should anyhow have $+1$ Oxidation state in order for formation $MX$ salt.

Henceforth our given metal should be with $+1$ oxidation state and that one is only one which is silver \[\left( Ag \right)\] which on usually formation of silver chloride with the $C{{l}_{2}}$ gas as \[AgCl\text{ }\left( MX\text{ }salt \right)\] and also in black and white photography process it is used.

Therefore the final answer is;
a) Metal $M$ is silver \[\left( Ag \right)\]
b) The gas ${{X}_{2}}$ is chlorine $C{{l}_{2}}$
c) The metal salt $MX$ is silver chloride or \[AgCl\]
d) Silver nitrate and Sodium chloride are the two salt solutions which on mixing together can produce a precipitate of salt $MX$ and reaction is given by:
\[AgN{{O}_{3}}\text{ }+\text{ }NaCl\text{ }\to \text{ }AgCl\text{ }+\text{ }NaN{{O}_{3}}\]
e) Chemical reaction of decomposition of AgCl is on exposure to light is known as photolysis and reaction is given by:
\[2AgCl\text{ }\xrightarrow[decomposition]{light}\text{ }2Ag\left( s \right)\text{ }+\text{ }C{{l}_{2}}\left( g \right)\]

Note: Note for such a question one can easily determine that it is an analytic method since analytical chemistry study as well as use instruments and methods required to separate, quantify matter and identify. Also in methods such as separation, identification and quantification does constitute an entire analysis similarly here by understanding the metallic salt and solution and given conditions that are gas ,etc help in determining the factors.