Solubility equilibrium

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

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.

1 Non-ionic compounds
2 Ionic compounds
3 Solubility constants
4 Table
5 References

[edit] Non-ionic compounds

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

$\mathrm{{C}_{12}{H}_{22}{O}_{11}}(s) \overrightarrow{\leftarrow} \mathrm{{C}_{12}{H}_{22}{O}_{11}}(aq)\,$

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

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

where K is called the equilibrium constant (or solubility constant) and the square brackets mean molar concentration in mol/L (sometimes called molarity with symbol M). Because a notion of concentration for a solid doesn't make sense, curly brackets are used, which mean activity, around the solid. Luckily, the activity of a solid is almost always equal to one. So, a very simple expression suffices:

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

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.

[edit] Ionic compounds

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

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

As for the previous example, the equilibrium expression is:

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

where K is called the equilibrium (or solubility) constant, the square brackets mean molar concentration (M, or mol/L), and curly brackets mean activity. Since the activity of a pure solid is equal to one, this expression reduces to the solubility product expression:

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

This expression says that an aqueous solution in equilibrium with (saturated with) 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 the concentration of each ion (and the overall solubility of calcium sulfate) is

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

[edit] 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 (moles per liter) unless otherwise stated. Solubility is sometimes listed in mass units such as grams dissolved per liter of water.

Solubility (and equilibrium) constants themselves are dimensionless (however, they may have units). The lack of units in the constant may look inconsistent, but it comes about because the use of molar concentration in the solubility expression is only an approximation to activity, a unitless quantity that is approximately equal to molarity at low concentrations.

The common-ion effect refers to the fact that solubility equilibria shift in response to 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 ions in solution again satisfy the solubility expression. (Addition of sulfate ions could be accomplished by adding a very soluble salt, such as Na₂SO₄.)

Solubility is sensitive to 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. A thermodynamic approach is required to predict how much and in what direction a particular constant changes.

Some values ^[1] at 25°C:

Barium carbonate: 2.60×10^-9
Copper(I) chloride: 1.72×10^-7
Lead(II) sulfate: 1.81×10^-8
Magnesium carbonate: 1.15×10^-5
Silver chloride: 1.70×10^-10
Silver bromide: 7.7×10^-13
Calcium hydroxide: 8.0×10^-6

[edit] Table

Table of Solubility Products
Compound	Formula	Temperature	K_sp	Data Source (legend below)
Aluminum Hydroxide anhydrous	Al(OH)₃	20°C	1.9×10^–33	L
Aluminum Hydroxide anhydrous	Al(OH)₃	25°C	3×10^–34	w₁
Aluminum Hydroxide trihydrate	Al(OH)₃	20°C	4×10^–13	C
Aluminum Hydroxide trihydrate	Al(OH)₃	25°C	3.7×10^–13	C
Aluminum 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	CdC₄O₄	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 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	HgCl	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