When NaOH is added to AgNO3 it produces a white precipitate. This is AgOH. But when NaOH is added to AgCl the precipitate is a grayish silver, NOT white. They can't both be AgOH, can they?
Yes they can't be both AgOH.
Because AgCl is insoluble salt and so it does not react with NaOH to form AgOH. That means AgCl doesn't split into ions and so no reaction with NaOH. But upon heating AgCl reacts with NaOH gets converted to Ag(s) which appears as greyish.
4NaOH + 4AgCl ----------> 4NaCl + 2H2O + 4Ag + O2
On the other hand, NaOH and AgNO3 are reacted with eachother to form AgOH. That means AgNO3 is a soluble salt so it splits into ions and reacts with NaOH to form AgOH precipitate which is white in colour.
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