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\[{{\rm{H}}_{\rm{2}}}{{\rm{O}}_{\rm{2}}}\] restores the colour of old lead paintings, blackened by the action of \[{{\rm{H}}_{\rm{2}}}{\rm{S}}\] gas by:
Option 1: Converting \[{\rm{Pb}}{{\rm{O}}_{\rm{2}}}\] to Pb
Option 2: By oxidising PbS to \[{\rm{PbS}}{{\rm{O}}_{\rm{4}}}\]
Option 3: Converting \[{\rm{PbC}}{{\rm{O}}_{\rm{3}}}\] to Pb
Option 4: Oxidising \[{\rm{PbS}}{{\rm{O}}_{\rm{3}}}\] to \[{\rm{PbS}}{{\rm{O}}_{\rm{4}}}\]

Answer
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Hint: Hydrogen sulphide is gas of no colour. It is corrosive and poisonous in nature. The hydrogen sulphide gas is chemically written as \[{{\rm{H}}_{\rm{2}}}{\rm{S}}\]. The production of hydrogen sulphide gas is due to the action of bacteria on animal and plant material.

Complete Step by Step Solution:
Let's discuss the action of hydrogen sulphide gas on lead paint. We know, that lead paint has lead ions in it. When hydrogen sulphide undergoes a reaction with lead ion, the production of lead sulphide (PbS) occurs. The colour of lead sulphide is black. The chemical reaction is,
 \[{\rm{P}}{{\rm{b}}^{{\rm{2 + }}}} + {{\rm{H}}_{\rm{2}}}{\rm{S}} \to {\rm{PbS}}\]

Let discuss about hydrogen peroxide gas in detail. The hydrogen peroxide is represented chemically by the formula of \[{{\rm{H}}_{\rm{2}}}{{\rm{O}}_{\rm{2}}}\] . It is useful in the restoration of the colour of an old painting. As we understand above, the formation of lead sulphide causes decolourisation of the lead paintings. When a lead painting is coated with hydrogen peroxide, the following reaction happens.
\[{\rm{PbS}} + 4{{\rm{H}}_{\rm{2}}}{{\rm{O}}_{\rm{2}}} \to {\rm{PbS}}{{\rm{O}}_{\rm{4}}} + 4{{\rm{H}}_{\rm{2}}}{\rm{O}}\]

The lead sulphate formed is of white colour. Therefore, the lead paint blackened due to the action of hydrogen sulphide got removed and the original colour was restored.
Therefore, option 2 is right.

Note: It is to be noted that hydrogen peroxide functions as both oxidizing and reducing agents. In an acidic medium, it functions as an oxidizing agent and in a basic medium, it functions as a reducing agent. The reaction's pH determines the reactivity of hydrogen peroxide.