Qsp

Meaning: Qsp is the reaction quotient for dissolving a sparingly soluble ionic solid. It has the same form as Ksp, but it uses the actual concentrations at a given moment. Comparing the two predicts which way the system shifts.

Qsp < Ksp: the solution is unsaturated, no precipitate forms, and any solid present keeps dissolving. Qsp = Ksp: the solution is saturated and at equilibrium. Qsp > Ksp: the solution is supersaturated, so the system shifts toward solid and precipitate forms until Qsp falls to Ksp. A supersaturated solution can sometimes persist for a while without a nucleation site.

Equation: Qsp = [A]ᵐ[B]ⁿ for AₘBₙ(s) ⇌ mA + nB, where [A] and [B] are the ion concentrations at that moment (mol/L) and m and n are the stoichiometric coefficients. The pure solid is left out. For CaF₂, Qsp = [Ca²⁺][F⁻]².

On the MCAT: A passage mixes two salt solutions, or adds a common ion, and asks whether a precipitate forms. Find the concentrations after dilution, calculate Qsp, and compare it with the given Ksp.

Common confusion: Students plug in the concentrations from before mixing. Mixing dilutes each ion, so use the concentrations after mixing. Ksp is a constant at a given temperature, while Qsp changes with the amounts of ions in solution.