Will a precipitate form if 20 mL of #1 x 10^-7# M #AgNO_3# is mixed with 20 mL of #2 x 10^9# M #NaCl# at 25°C? For #AgCl#, #K_(sp) = 1.8 x 10^-10#

1 Answer
Mar 16, 2017

Answer:

#"Non..........."#

Explanation:

We assess the equilibrium reaction:

#Ag^(+) + Cl^(-) rightleftharpoons AgCl(s)darr#, #K_"sp"=1.8xx10^-10#

Now #K_"sp"=[Ag^+][NO_3^-]#, and initially, we have the following concentrations:

#[Ag^+]=(20xx10^-3Lxx1.0xx10^-7*mol*L^-1)/(40xx10^-3*L)=5xx10^-8*mol*L^-1#

#[Cl^-]=(20xx10^-3Lxx2.0xx10^-9*mol*L^-1)/(40xx10^-3*L)=1xx10^-9*mol*L^-1#

Note that I assume you meant that #[NaCl]=2xx10^-9*mol*L^-1#, the given concentration is unreasonably high.

Now the ion product, #Q_"rxn"=[Ag^+][Cl^-]=5xx10^-8xx1xx10^-9=5xx10^-17#.

And since #Q_"rxn"# #<# #K_"sp"# precipitation of #AgCl# should not occur.