Final answer:
AgCl is expected to have the highest solubility in the 0.020 M KCl solution due to the formation of complex ions, despite the common ion effect which normally would reduce solubility in solutions containing chloride ions.
Step-by-step explanation:
To determine which solution AgCl has the highest solubility in, we need to consider the common ion effect and the formation of complex ions. The solubility of AgCl in pure water is given as 1.33 × 10-5 M. However, in the presence of a common ion, like Cl-, we would expect the solubility to decrease due to the common ion effect.
For solutions containing chloride ions (BaCl₂, NaCl, KCl), the common ion effect would predict a lower solubility for AgCl compared to in pure water. However, Ag+ can form complex ions with Cl-, and as mentioned, AgCl dissolves in 1.0 M KCl to produce a 1.9 × 10-5 M solution of the AgCl₂⁻ complex ion. This complex ion makes AgCl more soluble in the KCl solution than it would be due to the common ion effect alone.
Comparing the given options, we would expect the highest solubility in the 0.020 M KCl solution due to the formation of complex ions provided the solution's KCl concentration is sufficiently high to allow for complex formation as described. The presence of AgNO₃ would not increase AgCl's solubility since it provides a common ion (Ag+) which would instead shift the equilibrium to favor the solid AgCl. The 0.020 M BaCl₂ and 0.015 M NaCl solutions would exhibit increased chloride concentration, contributing to a lower solubility of AgCl due to the common ion effect. Lastly, in pure water, the solubility is lower than in KCl solution with complex ion formation but higher than in other solutions where the common ion effect is not counteracted by complexation.