How can we account for the color change of the solution?

Well, my best guess at what you're talking about is that maybe you're doing a Le Chatelier's Principle lab where you're reacting #"AgNO"_3# as one disturbance to the equilibrium shown below:

#overbrace("Co"("H"_2"O")_6^(2+))^(color(pink)"pink") + 4"Cl"^(-)(aq) rightleftharpoons overbrace("CoCl"_4^(2-)(aq))^(color(blue)"blue") + 6"H"_2"O"(l)#

In lab, you may have been given #"CoCl"_2(aq)#, a translucent purple liquid. It is an intermediate in the reaction, as it has two #"Cl"^(-)# on the #"Co"^(2+)#.

By adding #"AgNO"_3#, you introduce #"Ag"^(+)# into solution. This causes the reaction

#"Cl"^(-)(aq) + "Ag"^(+)(aq) rightleftharpoons "AgCl"(s)#

to occur. This consumes pretty much all of the #"Cl"^(-)# now, which leaves the equilibrium missing a lot of it. This is because this reaction is heavily skewed towards the solid.

As a result, Le Chatelier's principle suggests that the reaction shifts towards the reactants in the original reaction to restore #"Cl"^(-)#, thereby generating #"Co"("H"_2"O")_6^(2+)#.

That's a pink, probably clearer, solution.

Students in lab typically see a change from translucent purple to cloudy pink on the bottom with a fluffy white layer on top.