Solubility Product (Ksp) & the Common-Ion Effect

Pick a sparingly soluble salt, and if you like add an ion it shares. The page solves its solubility product for how much actually dissolves, shows the ion concentrations that result, and ranks every salt in the list by Ksp and by solubility side by side.

Worked example — Solubility Product (Ksp) & the Common-Ion Effect

Solubility in pure water	1.330×10⁻⁵ mol/L
Solubility here	1.330×10⁻⁵ mol/L
The same, in milligrams per litre	1.907 mg/L
Ag+ in solution	1.330×10⁻⁵ mol/L
Cl− in solution	1.330×10⁻⁵ mol/L
How many times less than in pure water	1.000×

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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Lesson

The theory — Solubility Product (Ksp) & the Common-Ion Effect

A sparingly soluble salt MₓAᵧ in contact with its solution sets up MₓAᵧ(s) ⇌ x Mⁿ⁺ + y Aᵐ⁻, and its solubility product is the equilibrium constant, Ksp = [Mⁿ⁺]ˣ [Aᵐ⁻]ʸ; the solid does not appear, because its activity is 1. The molar solubility s is how many moles of the salt dissolve per litre. In pure water [M] = xs and [A] = ys, so Ksp = xˣ yʸ s^(x+y). An ion already present in the water, a common ion, stays in the product, and less of the salt has to dissolve to reach Ksp.

What each symbol means

Ksp: the solubility product, at 25 °C. Its units depend on the formula, which is one sign that it is not itself a solubility
s: molar solubility, in mol of salt per litre of solution
x, y: how many cations and anions one formula unit releases: 1 and 1 for AgCl, 2 and 1 for Ag₂CrO₄, 1 and 3 for Fe(OH)₃

Assumes: Concentrations stand in for activities, which is fair while the solution is dilute and the ions are few; in 0.01 mol/L of added salt the activity coefficients are already around 0.9 for singly charged ions and lower for doubly charged ones. Nothing happens to the ions after they dissolve. That is false for carbonate and hydroxide, which react with water, so the figures for calcium carbonate and the two hydroxides are what Ksp alone would give. Iron(III) hydroxide's pure-water figure ignores the 10⁻⁷ mol/L of hydroxide that water supplies by itself, a common ion far larger than the iron salt's own.
Breaks when: When the ions combine with each other or with the added ion. Silver chloride is the standard example: past a small excess, chloride binds silver as AgCl and AgCl₂⁻ in solution, and in strong brine silver chloride dissolves again. The first panel's line, which keeps falling however much chloride is added, is the ideal law, not silver. That is why this page shows the common-ion effect on calcium fluoride, where such complexes are small at these concentrations.

A smaller Ksp does not mean less dissolves 🖖

Press Silver chloride, then Silver chromate. Silver chromate's Ksp is 158 times smaller, and it dissolves 4.92 times more. Ksp multiplies the ion concentrations, each raised to its count in the formula, so AgCl gives Ksp = s² while Ag₂CrO₄ gives (2s)²·s = 4s³, and undoing a cube shrinks a small number far less than undoing a square. The second panel shows it for all eleven salts: salts of one shape lie on one line, the lines have different slopes, and ranking by Ksp ranks by solubility only along one of them. In the table, six of the eleven change places when you sort by what actually dissolves.

0.01 mol/L of fluoride does 85 times what calcium does 🖖

Press CaF₂ with fluoride: 0.01 mol/L of fluoride already in the water cuts calcium fluoride's solubility 594.5-fold. Press CaF₂ with calcium: the same 0.01 mol/L of calcium cuts it only 6.993-fold. Ksp = [Ca²⁺][F⁻]², so extra fluoride enters squared, and on the first panel the solid line falls a hundredfold for every tenfold of fluoride past the bend, while the dashed calcium line falls only by √10. A common ion is not one effect with one size. Its size is the exponent that ion carries in the formula.

The Mohr titration works because of the first insight 🖖

In 1856 Karl Friedrich Mohr found a way to see the moment silver has used up the chloride in a sample: add a little chromate, and titrate with silver nitrate. White silver chloride forms first, and brick-red silver chromate appears only once the chloride is gone. By Ksp alone the chromate should have gone first, since its Ksp is 158 times smaller. It goes second because it is the more soluble of the two. At the equivalence point [Ag⁺] is √(1.77×10⁻¹⁰) = 1.330×10⁻⁵ mol/L, and red appears there if the chromate is 1.12×10⁻¹² / (1.330×10⁻⁵)² = 6.33×10⁻³ mol/L. In practice less is added, because that much chromate is strongly yellow and masks the first trace of red, and the small overshoot this costs is measured with a blank titration.

Problem solved in full

Silver chloride's Ksp from thermochemistry alone 4 steps
Nobody has to weigh a dissolved salt to know its Ksp. CODATA gives, at 25 °C: Ag⁺(aq) ΔfH° = 105.79 kJ/mol and S° = 73.45 J/(mol·K); Cl⁻(aq) −167.080 and 56.60; AgCl(s) −127.01 and 96.25. Find ΔG° for AgCl(s) ⇌ Ag⁺ + Cl⁻, then Ksp and the solubility, and compare them with the page's table.

Open this problem in the tool
1. The enthalpy of dissolving: products minus reactants. Dissolving silver chloride absorbs heat.
  
  $Δ H^{\circ} = 105.79 + (- 167.080) - (- 127.01) = + 65.72 kJ/mol$
2. The entropy of dissolving, the same way. It is positive but small, because the ions order the water around them.
  
  $Δ S^{\circ} = 73.45 + 56.60 - 96.25 = + 33.80 J/ (mol K)$
3. ΔG° = ΔH° − TΔS°. The entropy term pays for only about 15% of the enthalpy.
  
  $Δ G^{\circ} = 65.72 - 298.15 \times 0.03380 = + 55.64 kJ/mol$
4. Ksp = exp(−ΔG°/RT), which is the Gibbs free energy page's ΔG° = −RT ln K run the other way. The solubility is its square root.
  
  $K_{s p} = exp (- \frac{55 , 642}{8 . 3145 \times 298 . 15}) = 1.79 \times 1 0^{- 10} s = K_{s p} = 1.336 \times 1 0^{- 5} mol/L$
Answer

ΔG° = +55.64 kJ/mol, Ksp = 1.79×10⁻¹⁰ and s = 1.336×10⁻⁵ mol/L, against the table's 1.77×10⁻¹⁰ and 1.330×10⁻⁵. Two routes that share no measurement, heats of reaction and third-law entropies on one side and a solubility on the other, agree to 0.9% in Ksp. CODATA's own uncertainties allow about 8%. The positive ΔH° also says which way temperature moves the answer: silver chloride is more soluble in hot water than in cold.

$\frac{1 . 786 \times 1 0 ^{- 10}}{1 . 77 \times 1 0 ^{- 10}} = 1.009$

Learning path

Mixtures and solutions

References (3)

Every Ksp on the page. The table reprints the CRC Handbook's values, and it is cited because it can be opened, which the handbook cannot: Chemistry LibreTexts, Reference Tables: "E3. Solubility Constants for Compounds at 25°C", after CRC Handbook of Chemistry and Physics, 84th edition, 2004. CC BY-NC-SA 4.0.
The worked problem's thermochemistry: CODATA key values for Ag⁺(aq), Cl⁻(aq) and AgCl(cr): J. D. Cox, D. D. Wagman and V. A. Medvedev, CODATA Key Values for Thermodynamics. Hemisphere, New York, 1989. Online table at codata.info.
The titration insight block 3 describes, in the paper that introduced it: F. Mohr, "Neue maassanalytische Bestimmung des Chlors in Verbindungen." Justus Liebigs Annalen der Chemie 97(3), 1856, pp. 335-338. DOI 10.1002/jlac.18560970314

By the 42Math team · Reviewed against published sources. Corrections welcome.