Which of the following salts have the greatest solubility in water?

Question

AgCl: Ksp= 1.8 x 10^-10

LaF₃: Ksp- 2 x 10^-19

CuBr: Ksp= 5.3 x 10^-9

CaF₂: Ksp= 3.5 x 10^-11

^{CuBr is not the correct answer, must be trick question}

Answer 1

You can't always just look at the Ksp to determine the SOLUBILITY, because Ksp is the solubility PRODUCT, not the solubility, per se. If you are comparing two or more compounds that all have the same number of ions produced, then you can directly compare the Ksp values for an idea of relative solubility. But since Ksp is a PRODUCT, if you square or cube a concentration, that changes everything. See below for examples.

Comparing solubility based on Ksp values:

AgCl: 1.8x10^-10 = x² and x = 1.3x10^-5 M = solubility

LaF₃: 2x10^-19 = (x)(3x)³ = 27x⁴ and x = 9x10^-6 M = solubility

CuBr: 5.3x10^-9 = x² and x = 7.3x10^-5 M = solubility

CaF₂: 3.5x10^-11 = (x)(2x)² = 4x³ and x = 2.1x10^-4 M = solubility

So CaF₂ would have the greatest solubility in water even though the Ksp is less than that for CuBr, e.g.