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Lessons · Equilibrium & acid–base

Will it precipitate? Mixing calcium and fluoride solutions

Ion accounting machine-checked — mixing dilution + the quotient QKsp data-sourced (openstax-chemistry-2e)3 modeling assumptions (disclosed)

Two clear solutions sit on the bench — calcium nitrate, Ca(NO₃)₂, and sodium fluoride, NaF. Neither holds a speck of solid; both are perfectly transparent. Pour 40.0 mL of 0.010 M Ca(NO₃)₂ into 60.0 mL of 0.010 M NaF and does anything happen? Calcium fluoride is the sparingly soluble pair here — CaF2(s)⇌Ca2+(aq)+2 F−(aq)\mathrm{CaF_2(s)} \rightleftharpoons \mathrm{Ca^{2+}(aq)} + 2\,\mathrm{F^-(aq)} — but nothing says a solid must appear. The test is the reaction quotient: mix, dilute each ion into the combined 100.0 mL, evaluate Q=[Ca2+][F−]2Q = [\mathrm{Ca^{2+}}][\mathrm{F^-}]^2 at that instant, and compare it to KspK_{sp}. If Q>KspQ > K_{sp} the solution is supersaturated and CaF2\mathrm{CaF_2} crashes out; if Q<KspQ < K_{sp} it stays clear. No ICE table to solve — one comparison decides it.

CaF2 (s)⇌Ca2+ (aq)+2 F− (aq)\mathrm{CaF_{2}}\,\text{(s)} \rightleftharpoons \mathrm{Ca}^{2+}\,\text{(aq)} + 2\,\mathrm{F}^{-}\,\text{(aq)}
Ksp=[Ca2+][F−]2K_{sp} = [\mathrm{Ca}^{2+}][\mathrm{F}^{-}]^{2}=4×10⁻¹¹at 25 °C
Source solutionAddedProvidesAfter mixing (M)
Ca(NO₃)₂ calcium nitrate40.0 mL · 0.010 M[Ca²⁺] = 0.01[Ca²⁺] = 0.004
NaF sodium fluoride60.0 mL · 0.010 M[F⁻] = 0.01[F⁻] = 0.006

machine-checkedCombined volume 100 mL. Each ion is diluted byVsource / Vtotal — the same dimensional-analysis move as any dilution. Nothing has reacted yet; these are the concentrations at the instant of mixing.

The reaction quotientQ has the same form as Ksp — evaluated now, not at equilibrium.

Q=[Ca2+][F−]2Q = [\mathrm{Ca}^{2+}][\mathrm{F}^{-}]^{2}=(0.004)(0.006)²=1.44×10⁻⁷

Q = 1.44×10⁻⁷>Ksp = 4×10⁻¹¹
✓A precipitate forms.

Q exceeds Ksp by about 3600×, so the solution is supersaturated in CaF₂ and solid crashes out until Q falls back to Ksp.

VerificationProven at build time — not asserted.
  • ✓ Each mixed concentration = [ion]source × Vsource / Vtotal [mixing dilution]
  • ✓ Q = [Ca²⁺]1[F⁻]2 at the mixed concentrations [quotient computed]
  • ✓ The verdict follows the comparison: a precipitate forms exactly when Q > Ksp [verdict consistent]
✗ Common misconception: “Both solutions are clear and only 0.010 M — far too dilute for anything to precipitate when you pour them together.”

The clarity or dilution of each beaker on its own decides nothing — neither holds any CaF₂ to begin with. What matters is the ion product of the mixture versus Ksp. Here Q = 1.44×10⁻⁷ lands about 3600× above Ksp = 4×10⁻¹¹, because Ksp is so tiny that even millimolar [Ca²⁺] and [F⁻] blow past it. So CaF₂ precipitates — the Q-vs-Ksp test, not the look of the parts, is what predicts it.

Modeling assumptions — author-asserted, disclosed not discharged
  • model Both source salts are soluble strong electrolytes that dissociate completely, and volumes are additive — so mixing 40.0 mL and 60.0 mL simply dilutes each ion into the combined 100.0 mL. The spectators Na+\mathrm{Na^+} and NO3−\mathrm{NO_3^-} take no part.
  • model Activities are approximated by molar concentrations (the ideal-dilute-solution model), which is why QQ and KspK_{sp} are written with concentrations.
  • model The thermodynamic prediction is taken to hold: Q>KspQ > K_{sp} means the solid will actually form, with no metastable supersaturation delaying it.

Concepts in this lesson

Linked into the Chemical Atlas where an entry exists; the rest fill in as the Atlas grows.

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