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The formula of basic lead carbonate is ${\left( {PbC{O_3}} \right)_x} \cdot Pb{\left( {OH} \right)_x}$. The value of $x$ is:

Answer
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Hint: A complex salt is a salt which contains a complex molecule acting as the cationic as well as the anionic part of the salt. Basic Lead carbonate also commonly known as White Lead is a complex salt which contains both carbonate and Hydroxide ions in it alongside the same central metal which is lead $\left( {Pb} \right)$.

Complete step-by-step answer:Basic lead carbonate is a complex salt, containing both carbonate and hydroxide ions. It occurs naturally as a mineral hydrocerussite which means a hydrate of cerussite. It was formerly used as an ingredient for lead paint due to its opacity and the capability to form satiny smooth mixture with dryable oils. The basic lead carbonate compound known as lead soap is also used as an additive for lubricants for bearings and in machine soaps. The formula of basic lead carbonate is ${\left( {PbC{O_3}} \right)_2} \cdot Pb{\left( {OH} \right)_2}$. Therefore, the value of $'x'$ is $2$ in our given question.

Additional Information: Theophrastus of Eresos who lived around $300B.C.$ is the first in recorded history to have prepared this compound white lead or Basic Lead Carbonate. Other names for these compounds are Berlin white, Dutch white lead, London white etc.
Some properties of basic lead carbonates are:
It is white powder which is insoluble in water but soluble in linseed oil. It is poisonous in nature and reacts with ${H_2}S$ in the presence of air and becomes black due to formation of lead acetate.

Note:For solving questions of the given type we must have a prior knowledge about the compound and its structure as without such a knowledge we cannot write the correct answers in exam, To gain proper knowledge about such compounds we need to practise more and more often so as to widen our range of knowledge at least for the most commonly asked compounds.