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:

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

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

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

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, albeit under omission of the dimension(s) of the concentration measure(s) used. Activities are dimensionless quantities arrived at by dividing the concentration measure by a non-zero standard concentration.

$K\_s\; =\; left[mathrm\{\{C\}\_\{12\}\{H\}\_\{22\}\{O\}\_\{11\}\}(aq)right],$

The square brackets mean molar concentration, which is 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 when the standard concentration is taken to be 1 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:

$mathrm\{CaSO\}\_4(s)\; rightleftharpoons\; mbox\{Ca\}^\{2+\}(aq)\; +\; mbox\{SO\}\_4^\{2-\}(aq),$

As for the previous example, the equilibrium expression is:

$K\; =\; frac\{left\{mbox\{Ca\}\; ^\{2+\}(aq)right\}left\{mbox\{SO\}\_4^\{2-\}(aq)right\}\}\{\; left\{mbox\{CaSO\}\_4(s)right\}\}$

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:

$K\_\{mathrm\{sp\}\}\; =\; left[mbox\{Ca\}^\{2+\}(aq)right]left[mbox\{SO\}\_4^\{2-\}(aq)right].,$

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 K_sp; for calcium sulfate K_sp = 4.93×10⁻⁵. If the solution contains only calcium sulfate, and the conditions are such that dissolved species are only Ca²⁺ and SO₄^2-, then the concentration of each ion (and the overall solubility of calcium sulfate) is

$sqrt\{\; K\_\{mathrm\{sp\}\}\}=sqrt\{4.93times10^\{-5\}\}=7.02times10^\{-3\}=left[mbox\{Ca\}^\{2+\}right]=left[mbox\{SO\}\_4^\{2-\}right].,$

When a solution dissociates into unequal parts as in:

$mathrm\{Ca(OH)\_2\}(s)\; rightleftharpoons\; mbox\{Ca\}^\{2+\}(aq)\; +\; mbox\{2OH\}^\{-\}(aq),$,

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

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

the solubility and solubility product are tied with the equation:

$sqrt[n]\{K\_\{mathrm\{sp\}\}\; over\; \{x^x\; cdot\; y^y\}\}\; =\; \{C\; over\; M\_M\}$

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

K_sp 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)

M_M 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 B^p+ and C^q- 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 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 K_sp 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:

$mathrm\{CaCO\}\_3(s)\; rightleftharpoons\; mbox\{Ca\}^\{2+\}(aq)\; +\; mbox\{CO\}\_3^\{2-\}(aq),$

$K\_\{mathrm\{sp\}\}\; =\; left[mbox\{Ca\}^\{2+\}(aq)right]left[mbox\{CO\}\_3^\{2-\}(aq)right].,$

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:

$log(^*K\_\{A\})\; =\; log(^*K\_\{A\; to\; 0\})\; +\; frac\{2\; gamma\; A\_m\}\; \{3ln(10)RT\}$

where $^*K\_\{A\}$ is the solubility constant for the solute particles with the molar surface area A, $^*K\_\{A\; to\; 0\}$ 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, A_m is the molar surface area of the solute (in m²/mol), R is the universal gas constant, and T is the absolute temperature.

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.

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 at 25°C:

• Barium carbonate: 2.60
• Copper(I) chloride: 1.72
• Lead(II) sulfate: 1.81
• Magnesium carbonate: 1.15
• Silver chloride: 1.70
• Silver bromide: 7.7
• Calcium hydroxide: 8.0

See also

• IUPAC-NIST solubility database
• Solubility products of simple inorganic compounds

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