Consider a solution that is 1.0 x 10-5 M NaCl and 1.0 x 10-5 M AgNO3.

Question

The K_sp of AgCl at 25 ^oC is 1.6 x 10^-10. Consider a solution that is 1.0 x 10^-5 M NaCl and 1.0 x 10^-5 M AgNO₃.

Answer is Q < K_sp and a precipitate will not form.

I am confused why that is the answer

Answer 1

AgCl(s) ==> Ag+(aq) + Cl-(aq)

In this problem, we need to calculate Q, and then compare it to Ksp. Q is the reaction ratio (just like Ksp) but when the system isn't at equilibrium (unlike Ksp). If Q > Ksp, a precipitate will form. If Q < Ksp, no precipitate.

Also, in this problem, we have a common ion effect (actual, 2 common ions). The NaCl contributes Cl^- ions, and the AgNO₃ contributes Ag⁺ ions. From these two, we can find the [Ag⁺] and [Cl^-] and plug those values into the Q equation.

[Ag⁺] = 1.0x10^-5 M

[Cl^-] = 1.0x10^-5 M

Q = [Ag⁺][Cl^-] = (1.0x10^-5)(1.0x10^-5)

Q = 1x10^-10

Comparing this to the Ksp of 1.6x10^-10, we see that Q < Ksp, and thus no precipitate will form.