J.R. S. answered 04/03/17
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In a double displacement reaction, all four species (metals and non-metals) dissociate and are free in solution. If, and only if a precipitate is formed, or a gas, or a liquid, or a weak electrolyte is formed, will there be a double displacement. If none of these occur, then there is no reaction. It isn't that the metal leaves and find the other non-metal, or vice versa. All become dissociated and in in solution, and then they combine to form a ppt, gas, liquid, or weak electrolyte, not not.
Examples: AgNO3(aq) + NaCl (aq)---> AgCl (s)+ NaNO3(aq) Notice that a ppt (AgCl) is formed
What happens is AgNO3 dissociates to Ag^+ and NO3^- and NaCl goes to Na^+ and Cl^- and then since AgCl precipitates out of solution, the Ag^+ finds the Cl^- and forms a solid.
If you had KNO3(aq) + NaCl(aq) there would be NO REACTION, and no double displacement. The KNO3 and NaCl would all dissociate giving you K^+, NO3^-, Na^+ and Cl^- all in solution, and since no combination makes a precipitate or a gas or a liquid, then there is no double displacement.