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Adding an ion the salt already contains pushes the dissolution equilibrium backwards. For a 1:1 salt the ion product must still equal Ksp, so with the common ion fixed at C the solubility collapses to Ksp/C instead of the square root of Ksp. With Ksp = 1.8e-9 and 0.1 M of the common ion, solubility falls from about 4.2e-5 to 1.8e-8 mol/L - roughly a 2000-fold suppression.
Suppressed solubility
s = Ksp / [common ion]
Unsuppressed solubility
s0 = sqrt(Ksp) for a 1:1 salt
Because the salt is so much less soluble than the added ion is concentrated, the contribution is negligible - the standard simplifying assumption.
Yes. Saturating the solvent with a shared ion forces more of the product out of solution and improves recovery.