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A copper coin was kept dipped in silver nitrate solution for a few hours/days. What will happen to the copper coin? What will happen to the colour of the solution?

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Copper is more reactive than silver. Hence, it displaces silver from the silver nitrate solution according to the given reaction. 
Cu(s) +   2AgNO3(aq) --------> Cu(NO3)2(aq)   +    2Ag(s) 
Copper       Silver nitrate       Copper(lI) nitrate           Silver 
The silver thus forrmed is deposited on the surface of copper, thereby giving it a u,hite shining appearance. 
The solution becomes blue due to the formation of copper-nitrate

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