How is silver extracted from argentite?

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Hint: Silver is mostly extracted from its ore by the process of smelting and chemical leaching. Argentite is the ore of silver with formula $A\mathop g\nolimits_2 S$. it is extracted by the process commonly known as Mac Arthur and Forrest‘s Cyanide process.

Complete answer:
There are many steps involved in this process:-
 The ore is firstly crushed.
Now the concentration of ore is done by the Froth floatation process.
Now the concentrated ore is treated with some percentage of NaCN, usually 0.4-0.6%. This mixture is continuously stirred by air current. Due to this, the silver present in the ore is now converted into the soluble argent complex.
$A\mathop g\nolimits_2 S + 4NaCN \to 2Na\left[ {Ag\mathop {\left[ {CN} \right]}\nolimits_2 } \right] + Na2S$
Now, this solution is precipitated and filtered to remove insoluble impurities and now when this is treated with Zn dust, silver gets precipitated from this.
$2Na\left[ {Ag\left\{ {CN} \right\}} \right] + Zn \to N\mathop a\nolimits_2 \left[ {Zn\mathop {\left\{ {CN} \right\}}\nolimits_4 } \right] + N\mathop a\nolimits_2 S$
Now the last step is electrolytic refining. In this pure, the impure silver is made the anode and a thin sheet of pure silver is made the cathode. Electricity is passed by the electrolytic solution of silver nitrate. Now the silver gets deposited at the cathode. the impure metal from the anode settles down now.

SMELTING: - The process in which ores are heated beyond their melting point to obtain metal usually in the presence of oxidizing agents.
FROTH-FLOATATION PROCESS: - This method is used in the separation of minerals. The hydrophobic substances are separated from hydrophilic substances.