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How is silver extracted from argentite ore?

Answer
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Hint: Remember that the chief ore of silver is argentite and silver is extracted by hydrometallurgy process. Silver is dissolved in a cyanide solution to form a soluble argento cyanide complex from which metal is obtained by reduction with more electropositive element.

Complete step by step solution:
Let us discuss the extraction of silver in details and in more comprehensive way:
There are various steps involved in extraction of silver are:
First step in the extraction of any material from its ore is: Ore – Concentration:
Argentite is a type of sulphide ore and is concentrated by the froth flotation process. The pulverized ore is made into a large tank which contains pine oil and water. The mixture is dispersed by passing compressed air where an ore forms in the form of froth with pine oil & comes to the surface while impurities are left in water.
Second step is the Treatment of ore with sodium cyanide:
The concentrated ore is treated with 0.4% to 0.7% Solution of cyanide and therefore the current of air undergoes it. The argentite ore dissolves in sodium cyanide forming sodium argento cyanide.
 $ A{g_2}S + GNaNC \to 2Na\left[ {Ag{{\left( {CN} \right)}_2}} \right] + N{O_2}S $
The reaction is reversible so is passed to oxidize $ N{a_2}S $ to $ N{a_2}S{O_4} $ such that the equilibrium shifts towards the product.
 $ N{a_2}S + {O_2} \to N{a_2}S{O_4} $
The solution is filtered and the filtrate containing sodium argento cyanide is used to recover silver metal.
Third step is Precipitation of Silver:
The solution obtained is treated with $ Zn $ scrap where $ Zn $ displaces silver from its complex.
 $ Zn + 2Na\left[ {Ag{{\left( {CN} \right)}_2}} \right] \to N{O_2}\left[ {Zn{{(CN)}_4}} \right]2Ag $
The precipitate is collected, washed and fused to get a compact mass of silver.
The end step is Refining:
The impure silver is purified by electrolytic method. A block of impure metal is anode while a thin strip of pure silver is cathode. A mixture of $ AgN{O_3} $ solution is electrolyte. On passing current into impure silver. It dissolves and an equivalent amount of pure silver is deposited at the cathode.

Note:
The main question which is very commonly asked in the process of extraction of silver is Role of $ NaCN $ in the extraction of silver is to do the leaching of silver ore in the presence of air from which the silver is obtained later by replacement.