Why Does the Common Ion Effect Increase Ksp for AgCl in the Presence of Cl-?

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The discussion centers on the solubility product constant (Ksp) of AgCl in solutions with varying concentrations of chloride ions. The Ksp for pure water is 1.77x10^-10, while the calculated concentration of Ag+ in a solution with 0.01M Cl- is 1.77x10^-8. This raises questions about the interpretation of Ksp, as the higher concentration of Ag+ suggests increased dissociation of AgCl in the presence of Cl-. However, it is clarified that Ksp remains constant under stable temperature conditions, and the observed increase in Ag+ concentration does not imply a higher Ksp but rather reflects the effect of the common ion (Cl-) on the solubility equilibrium. The presence of Cl- shifts the equilibrium, leading to a higher concentration of Ag+ ions without changing the Ksp value itself.
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I'm working Ksp problems comparing pure water solutions w/ those with an ion already present in solution. Example: AgCl and NaCl both in solution.

The pure water Ksp for AgCl is given as 1.77x10^-10. The question is what the Ksp would be with .01M of Cl- already present. After working the problem, I get an answer (verified as correct) as: 1.77x10^-8. This makes mathematic sense, but it doesn't intuitively make sense to me. The Ksp is larger (10^-8) with the extra ion than for pure water (10^-10)? Doesn't this indicate that AgCl dissociates MORE with .01M Cl- already present? How?
 
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1.77x10-8 is not Ksp, but concentration of Ag+ in the solution. Ksp is constant (as long as temperature doesn't change).
 
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