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What is the chemical formula for corrosion in copper and silver?

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Hint :Metals when exposed to air or some chemicals for a long time, a coloured layer of their stable oxides, hydroxides or sulphides is formed on their surface. The metal is said to be corroded and this process mentioned above is known as corrosion of metal. Corrosion is an effect of oxidation reaction.

Complete Step By Step Answer:
Corrosion is an effect of oxidation reaction. Hence, we can say that it is a process in which metals are attacked by substances such as air, moisture or acids around it. Most commonly metals are oxidised by the oxygen present in air. The metal is said to be corroded and the process is corrosion.
So, when Silver metal exposed to air and undergoes corrosion, first silver oxide is formed by the following reaction:
 $ 4Ag + {O_2} \to 2A{g_2}O $
The silver oxide $ (A{g_2}O) $ formed then reacts with Hydrogen Sulphide $ ({H_2}S) $ present in the atmosphere to produce Silver Sulphide $ (A{g_2}S) $ as product:
 $ A{g_2}O + {H_2}S \to A{g_2}S + {H_2}O $
The silver sulphide formed is black in color and thus, we can understand that a thin black coating of silver sulphide is formed on the surface when silver gets corroded.
So, when Copper metal exposed to air, it reacts with many gases and forms a coloured coating on its surface and the reaction is as follows:
 $ 2Cu + {H_2}O + {O_2} + C{O_2} \to Cu{(OH)_2} + CuC{O_3} $
Therefore, from the above reaction, we can see that a mixture of copper carbonate and copper hydroxide $ (Cu{(OH)_2} + CuC{O_3}) $ is formed which is green in color.
Therefore, on corrosion thin coating formed on silver metal is black in colour and that on copper metal is green in colour.

Note :
Corrosion and rusting are two different terms. Metals when exposed to air or some chemicals for a long time, a coloured layer of their stable oxides, hydroxides or sulphides is formed on their surface and this process is known as corrosion. Rusting is a specific term for the corrosion of iron metal in presence of air and moisture.