What is the largest mass of solid NaCl that can be dissolved in 1.000 L of 5.00 ?

Question

What is the largest mass of solid NaCl that can be dissolved in 1.000 L of 5.00  10-3 M AgNO3 without a precipitate of AgCl forming? Ksp for AgCl is 1.8 e-10.

The answer is this 2.1 micrograms. But how?

Answer 1

To start with, the Ag+ exists as an ion with
5x10-3M conc. The Ag+ stays in solution until the Ksp is exceeded by the product [Ag+][Cl-].
So..........set up 5x10-3 [Cl-] = 1.8x10-10 . The answer is 3.6x10-7 moles/L Cl-. Since the Cl- comes only from NaCl, the NaCl is restricted to this in moles (you have a 1 Liter solution). So multiply the mole/l above by the mol wt of NaCl. The answer looks reasonable.