# Solubility equilibrium

Solubility equilibrium is any type chemical equilibrium between solid and dissolved states of a compound at saturation.

Solubility equilibria involve application of chemical principles and constants to predict solubility of substances under specific conditions (because solubility is sensitive to the conditions, while the constants are less so).

The substance that is dissolved can be an organic solid such as sugar or an ionic solid such as table salt. The main difference is that ionic solids dissociate into constituent ions when they dissolve in water. Most commonly water is the solvent of interest, although the same basic principles apply with any solvent.

In the case of environmental science studies of water quality, the total concentration of dissolved solids (not necessarily at saturation) is referred to as total dissolved solids.

## Non-ionic compounds

Dissolution of an organic solid can be described as an equilibrium between the substance in its solid and dissolved forms:

${\displaystyle \mathrm {{C}_{12}{H}_{22}{O}_{11}(s)} \rightleftharpoons \mathrm {{C}_{12}{H}_{22}{O}_{11}(aq)} }$

An equilibrium expression for this reaction can be written, as for any chemical reaction (products over reactants):

${\displaystyle K={\frac {\left\{\mathrm {{C}_{12}{H}_{22}{O}_{11}} (aq)\right\}}{\left\{\mathrm {{C}_{12}{H}_{22}{O}_{11}} (s)\right\}}}}$

where K is called the equilibrium constant (or solubility constant). The curly brackets indicate activity. The activity of a pure solid is, by definition, unity. If the activity of the substance in solution is constant (i.e. not affected by any other solutes that may be present) it may be replaced by the concentration.

${\displaystyle K_{s}=\left[\mathrm {{C}_{12}{H}_{22}{O}_{11}} (aq)\right]\,}$

The square brackets mean molar concentration in mol dm-3 (sometimes called molarity with symbol M).

This statement says that water at equilibrium with solid sugar contains a concentration equal to K. For table sugar (sucrose) at 25 °C, K = 1.971 mol/L. (This solution is very concentrated; sucrose is extremely soluble in water.) This is the maximum amount of sugar that can dissolve at 25 °C; the solution is saturated. If the concentration is below saturation, more sugar dissolves until the solution reaches saturation, or all the solid is consumed. If more sugar is present than is allowed by the solubility expression then the solution is supersaturated and solid will precipitate until the saturation concentration is reached. This process can be slow; the equilibrium expression describes concentrations when the system reaches equilibrium, not how fast it gets there.

## Ionic compounds

Ionic compounds normally dissociate into their constituent ions when they dissolve in water. For example, for calcium sulfate:

${\displaystyle \mathrm {CaSO} _{4}(s)\rightleftharpoons {\mbox{Ca}}^{2+}(aq)+{\mbox{SO}}_{4}^{2-}(aq)\,}$

As for the previous example, the equilibrium expression is:

${\displaystyle K={\frac {\left\{{\mbox{Ca}}^{2+}(aq)\right\}\left\{{\mbox{SO}}_{4}^{2-}(aq)\right\}}{\left\{{\mbox{CaSO}}_{4}(s)\right\}}}}$

where K is called the equilibrium (or solubility) constant and curly brackets indicate activity.

The activity of a pure solid is, by definition, equal to one. When the solubility of the salt is very low the activity coefficients of the ions in solution will also be equal to one and this expression reduces to the solubility product expression:

${\displaystyle K_{\mathrm {sp} }=\left[{\mbox{Ca}}^{2+}(aq)\right]\left[{\mbox{SO}}_{4}^{2-}(aq)\right].\,}$

This expression says that an aqueous solution in equilibrium with (saturated) solid calcium sulfate has concentrations of these two ions such that their product equals Ksp; for calcium sulfate Ksp = 4.93×10−5. If the solution contains only calcium sulfate, and the conditions are such that dissolved species are only Ca2+ and SO42-, then the concentration of each ion (and the overall solubility of calcium sulfate) is

${\displaystyle {\sqrt {K_{\mathrm {sp} }}}={\sqrt {4.93\times 10^{-5}}}=7.02\times 10^{-3}=\left[{\mbox{Ca}}^{2+}\right]=\left[{\mbox{SO}}_{4}^{2-}\right].\,}$

When a solution dissociates into unequal parts as in:

${\displaystyle \mathrm {Ca(OH)_{2}} (s)\rightleftharpoons {\mbox{Ca}}^{2+}(aq)+{\mbox{2OH}}^{-}(aq)\,}$,

then determining the solubility from Ksp is slightly more difficult. Generally, for the dissolution reaction:

${\displaystyle \mathrm {A} (s)\rightleftharpoons {\mbox{xB}}^{p+}(aq)+{\mbox{yC}}^{q-}(aq)\,}$

the solubility and solubility product are tied with the equation:

${\displaystyle {\sqrt[{n}]{K_{\mathrm {sp} } \over {x^{x}\cdot y^{y}}}}={C \over M_{M}}}$

where:
n is the total number of moles on the right hand side, i.e., x+y, dimensionless
x is the number of moles of the cation, dimensionless
y is the number of moles of the anion, dimensionless
Ksp is the solubility product, (mol/kg)n
C is the solubility of A expressed as a mass fraction of the solute A in the solvent (kg of A per kg of solvent)
MM is the molecular mass of the compound A, kg/mol.

Again, the above equation assumes that the dissolution takes place in pure solvent (no common ion effect), that there is no complexation or hydrolysis (i.e., only ions Bp+ and Cq- are present in the solution), and that the concentrations are sufficiently low for the activity coefficients to be taken as unity.

### Common ion effect

The common-ion effect refers to the fact that solubility equilibria shift in accordance with Le Chatelier's Principle. In the above example, addition of sulfate ions to a saturated solution of calcium sulfate causes CaSO4 to precipitate until the concentration of the ions in solution are such that they again satisfy the solubility product. (Addition of sulfate ions can, for example, be accomplished by adding a very soluble salt, such as Na2SO4.)

### Salt effect

The salt effect[1] refers to the fact that the presence of another salt, even though there is no common ion, has an effect on the ionic strength of the solution and hence on the activity coefficients of the ions, so that solubility changes even though Ksp remains constant (assuming that the activity of the solid remains unity).

### Speciation effect

On dissolution, ionic salts typically dissociate into their constituent ions, but the ions may speciate in the solution. On speciation, the solubility will always increase although the solubility product does not change. For example, solubility equilibrium for calcium carbonate may be expressed by:

${\displaystyle \mathrm {CaCO} _{3}(s)\rightleftharpoons {\mbox{Ca}}^{2+}(aq)+{\mbox{CO}}_{3}^{2-}(aq)\,}$
${\displaystyle K_{\mathrm {sp} }=\left[{\mbox{Ca}}^{2+}(aq)\right]\left[{\mbox{CO}}_{3}^{2-}(aq)\right].\,}$

Now, if the conditions (e.g., pH) are such that other carbonate (or calcium) species appear in the solution (for example, bicarbonate ion HCO3-), then the solubility of the solid will increase so that the solubility product remains constant.

Similarly, if a complexing agent, for example EDTA, was present in the solution, solubility will increase because of the complexation of calcium (a complex has a different chemical identity than uncomplexed Ca2+ and therefore does not enter the solubility equilibrium).

To correctly predict solubility from a given solubility product, the speciation need to be known (or evaluated, at least approximately). A failure to do so is a common problem and can lead to large errors.

### Phase effect

Equilibria are defined for specific crystal phases. Therefore, the solubility product is expected to be different depending on the phase of the solid. For example, aragonite and calcite will have different solubility products even though they have both the same chemical identity (calcium carbonate). Nevertheless, under given conditions, most likely only one phase is thermodynamically stable and therefore this phase enters a true equilibrium.

### Particle size effect

The thermodynamic solubility constant is defined for large monocrystals. Solubility will increase with decreasing size of solute particle (or droplet) because of the additional surface energy. This effect is generally small unless particles become very small, typically smaller than 1 μm. The effect of the particle size on solubility constant can be quantified as follows:

${\displaystyle \log(^{*}K_{A})=\log(^{*}K_{A\to 0})+{\frac {2\gamma A_{m}}{3\ln(10)RT}}}$

where ${\displaystyle ^{*}K_{A}}$ is the solublity constant for the solute particles with the molar surface area A, ${\displaystyle ^{*}K_{A\to 0}}$ is the solubility constant for substance with molar surface area tending to zero (i.e., when the particles are large), γ is the surface tension of the solute particle in the solvent, Am is the molar surface area of the solute (in m2/mol), R is the universal gas constant, and T is the absolute temperature[2].

## Temperature effects

Solubility is sensitive to changes in temperature. For example, sugar is more soluble in hot water than cool water. It occurs because solubility constants, like other types of equilibrium constant, are functions of temperature. In accordance with Le Chatelier's Principle, when the dissolution process is endothermic (heat is absorbed,) solubility increases with rising temperature, but when the process is exothermic (heat is released) solubility decreases with rising temperature.[3]

## Solubility constants

Solubility constants have been experimentally determined for a large number of compounds and tables are readily available. For ionic compounds the constants are called solubility products. Concentration units are assumed to be molar unless otherwise stated. Solubility is sometimes listed in units of grams dissolved per liter of water.

Some values [4] at 25°C:

## Table

Table of Solubility Products
Compound Formula Temperature Ksp Data Source
(legend below)
Aluminium Hydroxide anhydrous Al(OH)3 20°C 1.9×10–33 L
Aluminium Hydroxide anhydrous Al(OH)3 25°C 3×10–34 w1
Aluminium Hydroxide trihydrate Al(OH)3 20°C 4×10–13 C
Aluminium Hydroxide trihydrate Al(OH)3 25°C 3.7×10–13 C
Aluminium Phosphate AlPO4 25°C 9.84×10–21 w1
Barium Bromate Ba(BrO3)2 25°C 2.43×10–4 w1
Barium Carbonate BaCO3 16°C 7×10–9 C, L
Barium Carbonate BaCO3 25°C 8.1×10–9 C, L
Barium Chromate BaCrO4 28°C 2.4×10–10 C, L
Barium Fluoride BaF2 25.8°C 1.73×10–6 C, L
Barium Iodate dihydrate Ba(IO3)2 25°C 6.5×10–10 C, L
Barium Oxalate dihydrate BaC2O4 18°C 1.2×10–7 C, L
Barium Sulfate BaSO4 18°C 0.87×10–10 C, L
Barium Sulfate BaSO4 25°C 1.08×10–10 C, L
Barium Sulfate BaSO4 50°C 1.98×10–10 C, L
Beryllium Hydroxide Be(OH)2 25°C 6.92×10–22 w1
Cadmium Carbonate CdCO3 25°C 1.0×10–12 w1
Cadmium Hydroxide Cd(OH)2 25°C 7.2×10–15 w1
Cadmium Oxalate trihydrate CdC2O4 18°C 1.53×10–8 C, L
Cadmium Phosphate Cd3(PO4)2 25°C 2.53×10–33 w1
Cadmium Sulfide CdS 18°C 3.6×10–29 C, L
Calcium Carbonate calcite CaCO3 15°C 0.99×10–8 C, L
Calcium Carbonate calcite CaCO3 25°C 0.87×10–8 C, L
Calcium Carbonate calcite CaCO3 18-25°C 4.8×10–9 P
Calcium Chromate CaCrO4 18°C 2.3×10–2 L
Calcium Fluoride CaF2 18°C 3.4×10–11 C, L
Calcium Fluoride CaF2 25°C 3.95×10–11 C, L
Calcium Hydroxide Ca(OH)2 18°C-25°C 8×10–6 P
Calcium Hydroxide Ca(OH)2 25°C 5.02×10–6 w1
Calcium Iodate hexahydrate Ca(IO3)2 18°C 6.44×10–7 L
Calcium Oxalate monohydrate CaC2O4 18°C 1.78×10–9 C, L
Calcium Oxalate monohydrate CaC2O4 25°C 2.57×10–9 C, L
Calcium Phosphate tribasic Ca3(PO4)2 25°C 2.07×10–33 w1
Calcium Sulfate CaSO4 10°C 6.1×10–5 C, L
Calcium Sulfate CaSO4 25°C 4.93×10–5 w1
Calcium Tartrate dihydrate CaC4H4O6 18°C 7.7×10–7 C, L
Chromium Hydroxide II Cr(OH)2 25°C 2×10–16 w2
Chromium Hydroxide III Cr(OH)3 25°C 6.3×10–31 w2
Cobalt Hydroxide II Co(OH)2 25°C 1.6×10–15 w2
Cobalt Sulfide (less soluble form) CoS 18°C 3×10–26 C, L
Cobalt Sulfide (more soluble form) CoS 18°C-25°C 10–21 P
Cupric Carbonate CuCO3 25°C 1×10–10 P
Cupric Hydroxide Cu(OH)2 18°C-25°C 6×10–20 P
Cupric Hydroxide Cu(OH)2 25°C 4.8×10–20 w1
Cupric Iodate Cu(IO3)2 25°C 1.4×10–7 C, L
Cupric Oxalate CuC2O4 25°C 2.87×10–8 C, L
Cupric Sulfide CuS 18°C 8.5×10–45 C, L
Cuprous Bromide CuBr 18°C-20°C 4.15×10–8 C
Cuprous Chloride CuCl 18°C-20°C 1.02×10–6 C
Cuprous Hydroxide
(in equilib. with Cu2O + H2O)
Cu(OH) 25°C 2×10–15 w1
Cuprous Iodide CuI 18°C-20°C 5.06×10–12 C
Cuprous Sulfide Cu2S 16°C-18°C 2×10–47 C, L
Cuprous Thiocyanate CuSCN 18°C 1.64×10–11 C, L
Ferric Hydroxide Fe(OH)3 18°C 1.1×10–36 C, L
Ferrous Carbonate FeCO3 18°C-25°C 2×10–11 P
Ferrous Hydroxide Fe(OH)2 18°C 1.64×10–14 C, L
Ferrous Hydroxide Fe(OH)2 25°C 1×10–15; 8.0×10–16 P; w2
Ferrous Oxalate FeC2O4 25°C 2.1×10–7 C, L
Ferrous Sulfide FeS 18°C 3.7×10–19 C, L
Lead Bromide PbBr2 25°C 6.3×10–6; 6.60×10–6 P; w1
Lead Carbonate PbCO3 18°C 3.3×10–14 C, L
Lead Chromate PbCrO4 18°C 1.77×10–14 C, L
Lead Chloride PbCl2 25.2°C 1.0×10–4 L
Lead Chloride PbCl2 18°C-25°C 1.7×10–5 P
Lead Fluoride PbF2 18°C 3.2×10–8 C, L
Lead Fluoride PbF2 26.6°C 3.7×10–8 C, L
Lead Hydroxide Pb(OH)2 25°C 1×10–16; 1.43×10–20 P; w1
Lead Iodate Pb(IO3)2 18°C 1.2×10–13 C, L
Lead Iodate Pb(IO3)2 25.8°C 2.6×10–13 C, L
Lead Iodide PbI2 15°C 7.47×10–9 C
Lead Iodide PbI2 25°C 1.39×10–8 C
Lead Oxalate PbC2O4 18°C 2.74×10–11 C, L
Lead Sulfate PbSO4 18°C 1.06×10–8 C, L
Lead Sulfide PbS 18°C 3.4×10–28 C, L
Lithium Carbonate Li2CO3 25°C 1.7×10–3 C, L
Lithium Fluoride LiF 25°C 1.84×10–3 w1
Lithium Phosphate tribasic Li3PO4 25° 2.37×10–4 w1
Magnesium Ammonium Phosphate MgNH4PO4 25°C 2.5×10–13 C, L
Magnesium Carbonate MgCO3 12°C 2.6×10–5 C, L
Magnesium Fluoride MgF2 18°C 7.1×10–9 C, L
Magnesium Fluoride MgF2 25°C 6.4×10–9 C, L
Magnesium Hydroxide Mg(OH)2 18°C 1.2×10–11 C, L
Magnesium Oxalate MgC2O4 18°C 8.57×10–5 C, L
Manganese Carbonate MnCO3 18°C-25°C 9×10–11 P
Manganese Hydroxide Mn(OH)2 18°C 4×10–14 C, L
Manganese Sulfide (pink) MnS 18°C 1.4×10–15 C, L
Manganese Sulfide (green) MnS 25°C 10–22 P
Mercuric Bromide HgBr2 25°C 8×10–20 L
Mercuric Chloride HgCl2 25°C 2.6×10–15 L
Mercuric Hydroxide
(equilib. with HgO + H2O)
Hg(OH)2 25°C 3.6×10–26 w1
Mercuric Iodide HgI2 25°C 3.2×10–29 L
Mercuric Sulfide HgS 18°C 4×10–53 to 2×10–49 C, L
Mercurous Bromide HgBr 25°C 1.3×10–21 C, L
Mercurous Chloride Hg2Cl2 25°C 2×10–18 C, L
Mercurous Iodide HgI 25°C 1.2×10–28 C, L
Mercurous Sulfate Hg2SO4 25°C 6×10–7; 6.5×10–7 P; w1
Nickel Hydroxide Ni(OH)2 25°C 5.48×10–16 w1
Nickel Sulfide NiS 18°C 1.4×10–24 C, L
Nickel Sulfide (less soluble form) NiS 18°C-25°C 10–27 P
Nickel Sulfide (more soluble form) NiS 18°C-25°C 10–21 P
Potassium Acid Tartrate KHC4H4O6 18°C 3.8×10–4 C, L
Potassium Perchlorate KClO4 25°C 1.05×10–2 w1
Potassium Periodate KIO4 25° 3.71×10–4 w1
Silver Acetate AgC2H3O2 16°C 1.82×10–3 L
Silver Bromate AgBrO3 20°C 3.97×10–5 C, L
Silver Bromate AgBrO3 25°C 5.77×10–5 C, L
Silver Bromide AgBr 18°C 4.1×10–13 C, L
Silver Bromide AgBr 25°C 7.7×10–13 C, L
Silver Carbonate Ag2CO3 25°C 6.15×10–12 C, L
Silver Chloride AgCl 4.7°C 0.21×10–10 C, L
Silver Chloride AgCl 9.7°C 0.37×10–10 L
Silver Chloride AgCl 25°C 1.56×10–10 C, L
Silver Chloride AgCl 50°C 13.2×10–10 C, L
Silver Chloride AgCl 100°C 21.5×10–10 C, L
Silver Chromate Ag2CrO4 14.8°C 1.2×10–12 C, L
Silver Chromate Ag2CrO4 25°C 9×10–12 C, L
Silver Cyanide Ag2(CN)2 20°C 2.2×10–12 C, L
Silver Dichromate Ag2Cr2O7 25°C 2×10–7 L
Silver Hydroxide AgOH 20°C 1.52×10–8 C, L
Silver Iodate AgIO3 9.4°C 0.92×10–8 C, L
Silver Iodide AgI 13°C 0.32×10–16 C, L
Silver Iodide AgI 25°C 1.5×10–16 C, L
Silver Nitrite AgNO2 25°C 5.86×10–4 L
Silver Oxalate Ag2C2O4 25°C 1.3×10–11 L
Silver Sulfate Ag2SO4 18°C-25°C 1.2×10–5 P
Silver Sulfide Ag2S 18°C 1.6×10–49 C, L
Silver Thiocyanate AgSCN 18°C 0.49×10–12 C, L
Silver Thiocyanate AgSCN 25°C 1.16×10–12 C, L
Strontium Carbonate SrCO3 25°C 1.6×10–9 C, L
Strontium Chromate SrCrO4 18°C-25°C 3.6×10–5 P
Strontium Fluoride SrF2 18°C 2.8×10–9 C, L
Strontium Oxalate SrC2O4 18°C 5.61×10–8 C, L
Strontium Sulfate SrSO4 2.9°C 2.77×10–7 C, L
Strontium Sulfate SrSO4 17.4°C 2.81×10–7 C, L
Thallous Bromide TlBr 25°C 4×10–6 L
Thallous Chloride TlCl 25°C 2.65×10–4 L
Thallous Sulfate Tl2SO4 25°C 3.6×10–4 L
Thallous Thiocyanate TlSCN 25°C; 2.25×10–4 L
Tin Hydroxide Sn(OH)2 18°C-25°C 1×10–26 P
Tin Hydroxide Sn(OH)2 25°C 5.45×10–27; 1.4×10–28 w1; w2
Tin sulfide SnS 25°C 10–28 P
Zinc Hydroxide Zn(OH)2 18°C-20°C 1.8×10–14 C, L
Zinc Oxalate dihydrate ZnC2O4 18°C 1.35×10–9 C, L
Zinc Sulfide ZnS 18°C 1.2×10–23 C, L
data source legend: L=Lange's 10th ed.; C=CRC 44th ed.; P=General Chemistry by Pauling, 1970 ed.; w1=Web source 1; w2=Web source 2

## References

1. J. Mendham, R.C. Denney, J.D. Barnes and M. Thomas (ed.). Vogel's Quantitative Chemical Analysis, 6th edition. ISBN 0-582 22628 7.
2. Hefter, G.T., Tomkins, R.P.T. (editors), "The Experimental Determination of Solubilities", John Wiley and Sons, Ltd., 2003.
3. Pauling, Linus: General Chemistry, Dover Publishing, 1970, p 450
4. H.P.R. Frederikse, David R. Lide (ed.). CRC Handbook of Chemistry and Physics. ISBN 0-8493-0478-4.