# Solubility equilibrium A **solubility equilibrium** is the [[Chemical_equilibrium|dynamic equilibrium]] between a solid and the species it releases into a [[Solution_(chemistry)|solution]], reached when the solid dissolves at the same rate as the dissolved species return to it. For an ionic [[Salt_(chemistry)|salt]] MₘXₙ that dissociates as it dissolves, the equilibrium is described by the solubility product `Ksp = [M+]^m·[X−]^n`, an [[Equilibrium_constant|equilibrium constant]] written without the solid because a pure solid has unit activity; a solution whose ion product Q is below Ksp can dissolve more solid, one at Ksp is saturated, and one above Ksp drops a [[Precipitation_(chemistry)|precipitate]].[^af-ksp] In the microsim below the reader picks one of four salts, silver chloride, calcium carbonate, lead iodide or barium sulfate, and adds a common ion to the water; the equation `Ksp = [M+]^m·[X−]^n` answers how far the dissolved amount falls, and a precipitate appears the moment `Q > Ksp`.[^af-appj] On the Chemistry flagship's spine this page is the main article for Part VII — Ions and salts, section *Salts and solubility*, the sibling that follows Chemical equilibrium; the same sim, with the salt fixed, serves the calcium, silver and lead pages of the flagship's element section as their solubility variant. The [[Solubility|solubility]] of calcium carbonate governs the chemistry of [[Groundwater|groundwater]] in limestone country and the fate of carbon dioxide in the sea, and the insolubility of barium sulfate makes it safe to swallow as a contrast agent for X-rays.[^af-ksp] The rules are those of any equilibrium: [[Le_Chatelier's_principle|Le Chatelier's principle]] for the response to added ions, heat or pressure, and the [[Reaction_quotient|reaction quotient]] for the decision to dissolve or precipitate.[^af-lechatelier] ## Definitions Solubility is the amount of a substance that dissolves in a given amount of solvent at equilibrium, quoted in grams per litre or as a [[Molar_concentration|molar concentration]]; a solution holding that amount is saturated, one holding less is unsaturated, and one holding more, which can persist for a time if no crystal is present to seed it, is [[Supersaturation|supersaturated]].[^af-ksp] For a salt that dissolves by dissociating, the solubility product Ksp is the equilibrium constant of the dissolution reaction, the product of the ion concentrations each raised to its stoichiometric coefficient, with the solid omitted because its activity is constant. Ksp is a property of the salt and the temperature; solubility is a property of the salt, the temperature and everything else in the water, which is why the two must not be confused. The ion product Q has the same form as Ksp but is evaluated for the actual concentrations, and comparing Q with Ksp decides the direction of change.[^af-ksp] Two idealisations sit inside these definitions: concentrations stand in for activities, which is accurate only in dilute solution, and the dissolved ions are taken as free, whereas in many real solutions a fraction of them pair up or form complexes. The Portal Book introduces Ksp within these limits, and its Appendix J tabulates values for the common sparingly soluble salts, from which the microsim on this page takes its numbers.[^af-appj] The salts called insoluble in the solubility rules of introductory chemistry are not insoluble at all; they are salts whose Ksp is small enough that the saturated solution is dilute.[^ball-equilibrium] ## Effects of conditions Because a solubility equilibrium is an equilibrium, everything that moves an equilibrium moves it: a change of temperature, the addition of an ion the salt shares, an inert electrolyte, the size and form of the crystals, and, for gases, the pressure. Each is a separate lever, and the microsim's lever is the second. ### Temperature effect Most solids dissolve more readily in hot water than in cold, because dissolution is usually endothermic and Le Chatelier's principle then favours the dissolved side as heat is supplied; the Portal Book's solubility section shows the familiar rising curves of solubility against temperature for common salts and the exceptions, whose solubility falls on heating.[^af-solubility] The sign is set by the [[Enthalpy|enthalpy]] of solution, the balance between the [[Lattice_energy|lattice energy]] that must be paid to take the ions out of the crystal and the hydration energy recovered when water surrounds them.[^af-dissolution] Formally the temperature dependence of Ksp follows the [[Van_'t_Hoff_equation|van 't Hoff equation]], `d ln Ksp/dT = ΔH°/(R·T²)`, which follows from `ΔG° = −R·T·ln K`, so a salt with an endothermic dissolution enthalpy has a Ksp that rises with temperature and an exothermic one has a Ksp that falls.[^af-freeenergy] Calcium carbonate is one of the salts whose solubility falls on heating, which contributes to the scale in a kettle, and gases follow the same rule in the other direction, since their dissolution is exothermic.[^ball-solutions] ### Common-ion effect The [[Common-ion_effect|common-ion effect]] is the fall in a salt's solubility when the solution already contains one of its ions. Silver chloride in pure water dissolves until `[Ag+][Cl−] = Ksp`; in a solution of [[Sodium_chloride|sodium chloride]] the chloride is supplied in advance, so far less silver ion can dissolve before the product reaches Ksp.[^af-commonion] With the value carried by the microsim, Ksp = 1.8 × 10⁻¹⁰ for AgCl, the molar solubility in pure water is the square root, 1.3 × 10⁻⁵ mol/L; in 0.10 mol/L sodium chloride the silver-ion concentration at saturation is `Ksp/[Cl−] = 1.8 × 10⁻⁹ mol/L`, more than 7,000 times lower (derived figures).[^af-appj] The microsim on this page is built around this lever. The reader picks the salt, and a second control adds a common ion, chloride for silver chloride, carbonate for calcium carbonate, iodide for lead iodide, sulfate for barium sulfate, from zero to a tenth of a mole per litre on a logarithmic slider. The dissolved amount, shown as a bar and as a number, falls as the common ion is added, following `Ksp = [M+]^m·[X−]^n` solved for the metal ion at each setting; a second mode starts from a solution that already holds the salt at its pure-water solubility, and the moment the added ion pushes the ion product over Ksp a precipitate settles in the beaker and the dissolved concentration drops back to the saturated line. The HUD reads `Ksp = [M+]^m·[X−]^n` and the current Q. Concentrations are used in place of activities throughout, which is an ILLUSTRATIVE simplification stated in the sim header; in real 0.10 mol/L salt solutions the activity coefficients are well below one, and the true fall in solubility is somewhat smaller than the ideal calculation gives. For lead iodide the stoichiometry matters: with `Ksp = [Pb2+][I−]²`, added iodide enters squared, and the solubility falls faster with the common ion than it does for a 1:1 salt. ### Particle size effect Very small crystals are more soluble than large ones, because the ions at a surface are less tightly bound than those in the interior and a fine powder is mostly surface. The effect is negligible for crystals of ordinary size and becomes appreciable only well below a micrometre, but it has a large consequence over time: in a suspension of mixed sizes the small crystals dissolve and the large ones grow, the process of [[Ostwald_ripening|Ostwald ripening]], which is why a freshly formed precipitate is left to age before it is filtered. The same surface energy sets the barrier to [[Nucleation|nucleation]] that allows a supersaturated solution to persist until a seed crystal or a scratch on the glass starts [[Crystal_growth|crystal growth]]. ### Salt effects An [[Electrolyte|electrolyte]] that shares no ion with the salt still changes its solubility, usually raising it. The added ions surround each dissolved ion with an atmosphere of opposite charge that lowers its activity, so more of the salt must dissolve before the product of activities reaches Ksp; the effect grows with the ionic strength of the solution and with the charges of the ions. This "salting in" is why the microsim's ideal calculation overstates the common-ion effect at high salt concentrations, and why Ksp is formally defined with activities rather than concentrations. At very high electrolyte concentrations the opposite effect, salting out, can appear as the added ions compete for the water itself. ### Phase effect A substance that can exist in more than one solid form has a different solubility for each, and the equilibrium is defined only for a named [[Phase_(matter)|phase]]. Calcium carbonate as calcite is less soluble than as aragonite, an anhydrous salt and its hydrate have different Ksp values, and an amorphous solid is always more soluble than the crystalline form with the same composition, because the ordered [[Crystal_structure|crystal]] has the lower free energy. A precipitate often forms first in its least stable, most soluble form and converts to the stable one on standing, so a solubility measured minutes after precipitation may not be the equilibrium value. ### Pressure effect Pressure has almost no effect on the solubility of a solid or a liquid, because their volumes hardly change on dissolving, but it controls the solubility of a gas. [[Henry's_law|Henry's law]] states that the concentration of a dissolved gas is proportional to its partial pressure above the solution, which the Portal Book's solubility section applies to carbonated drinks and to the nitrogen dissolved in a diver's blood;[^af-solubility] the constant of proportionality is the gas's own solubility equilibrium constant. Lowering the pressure over a saturated solution of a gas moves the equilibrium toward the gas phase, which is the fizz of an opened bottle. ## Quantitative aspects The arithmetic of a solubility equilibrium depends on what the solid becomes when it dissolves. Three cases cover most of it: a molecule that dissolves intact, a salt that dissociates into ions, and a solid whose dissolved species go on to react with something else in the water. ### Simple dissolution A molecular solid or a gas that dissolves without dissociating, sugar in water or oxygen in water, has the equilibrium A(s or g) ⇌ A(aq), whose constant is simply the saturated concentration, `K = [A(aq)]`, with the pure solid or the gas at fixed pressure omitted. Solubility and equilibrium constant are then the same number, and the temperature dependence of one is the temperature dependence of the other. For a gas the constant is the Henry's law constant; for a solid it is the molar solubility. ### Dissolution with dissociation For a salt MₘXₙ(s) ⇌ m M⁺(aq) + n X⁻(aq), the constant is `Ksp = [M+]^m·[X−]^n`, and the molar solubility s follows by counting ions: for a 1:1 salt such as silver chloride or barium sulfate `Ksp = s²`, so `s = sqrt(Ksp)`; for a 1:2 salt such as lead iodide `Ksp = s·(2s)² = 4s³`, so `s = (Ksp/4)^(1/3)`.[^af-ksp] The exponents are the reason two salts with the same Ksp can have very different solubilities, and why lead iodide, with the largest Ksp of the sim's four salts, is by a wide margin the most soluble of them in molar terms, while barium sulfate and silver chloride, each with a Ksp near 10⁻¹⁰, dissolve to about 10⁻⁵ mol/L.[^af-appj] Converting molar solubility to grams per litre multiplies by the molar mass, so the 1.3 × 10⁻⁵ mol/L of silver chloride is about 1.9 mg per litre of water (derived from the sim's Ksp value). The microsim's arithmetic is exactly this. For the chosen salt the page solves `Ksp = [M+]^m·[X−]^n` for the metal-ion concentration with the anion set to the sum of the dissolved and the added common ion, which for a 1:1 salt is a quadratic and for a 1:2 salt a cubic, solved numerically at each slider position. In the reverse direction the sim evaluates Q from the actual ion concentrations and compares it with Ksp to decide whether the beaker clouds. The same comparison is the textbook test for whether mixing two solutions gives a precipitate: mixing equal volumes of 1.0 × 10⁻⁴ mol/L silver nitrate and 1.0 × 10⁻⁴ mol/L sodium chloride gives 5.0 × 10⁻⁵ mol/L of each ion and Q = 2.5 × 10⁻⁹, above the Ksp of 1.8 × 10⁻¹⁰, so silver chloride precipitates until the product falls to Ksp (derived).[^af-ksp] ### Dissolution with reaction When a dissolved ion reacts further, the solubility rises above the value Ksp alone predicts, because the reaction removes the ion from the product [M⁺]^m[X⁻]^n and the solid dissolves to replace it. Three reactions dominate. An anion that is a weak base, carbonate, phosphate or hydroxide, takes up protons in acid, so calcium carbonate dissolves in acidic water and the solubility of a metal hydroxide falls steeply as the [[PH|pH]] rises; the [[Acid_dissociation_constant|acid dissociation constant]] of the anion's conjugate acid sets how strongly. A cation that forms a [[Coordination_complex|complex ion]] with a ligand is pulled into solution, so silver chloride dissolves in ammonia as [Ag(NH₃)₂]⁺, and the formation constant of the complex multiplies the effective solubility. And a redox reaction can consume either ion. The Portal Book treats these as coupled equilibria, in which Ksp, an acid constant and a formation constant are combined into one overall constant for the net reaction.[^af-coupled] In natural water the first of these is the chemistry of caves and of ocean acidification, in which carbon dioxide lowers the pH and dissolves carbonate. ## Experimental determination Ksp is measured by measuring a solubility and converting it, or by measuring an ion concentration directly in a saturated solution. The methods divide by whether the system is allowed to reach equilibrium and then sampled, or is followed as it changes; both must control the [[Temperature|temperature]], since Ksp is a function of it. ### Static methods In a static method an excess of the solid is shaken with the solvent at a fixed temperature until equilibrium, the solution is filtered or centrifuged, and the dissolved amount is analysed: by evaporating a known volume and weighing the residue, by [[Titration|titration]], by [[Spectrophotometry|spectrophotometry]] if an ion absorbs or can be made to absorb, or by an ion-selective electrode. The Portal Book's examples run in both directions, from a measured solubility to Ksp and from a tabulated Ksp to a predicted solubility.[^af-ksp] Care is needed to establish that equilibrium was reached, usually by approaching it from both sides, from undersaturation and from supersaturation, and to record the phase of the solid at the end. ### Dynamic methods In a dynamic method the solubility is found from the point at which something starts to happen. A solution of one ion is titrated with a solution of the other until the first permanent turbidity, and the concentrations at that point give Ksp; a precipitation titration followed by [[Electrical_resistivity_and_conductivity|conductivity]] or by an electrode potential shows the end point as a break in the curve, since the free ions that carry the current are consumed until the precipitation is complete. Flow methods pass solvent over a bed of the solid and analyse the outflow, which is the laboratory version of what happens when [[Water|water]] moves through rock. All of these are the microsim's second mode run in glass: raise the ion product past Ksp and watch for the solid. ## See also - [[Salt_(chemistry)]] - [[Common-ion_effect]] - [[Precipitation_(chemistry)]] - [[Solubility]] - [[Chemical_equilibrium]] - [[Le_Chatelier's_principle]] - [[Henry's_law]] - [[Ostwald_ripening]] ## References [^af-ksp]: Flowers, Paul; Neth, Edward; Robinson, William et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 15 Equilibria of Other Reaction Classes, §15.1 Precipitation and Dissolution, pp. 719–752 (the solubility product; Q against Ksp; molar solubility from Ksp and Ksp from solubility; page to pin). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^af-appj]: Flowers, Paul; Neth, Edward; Robinson, William et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Appendix J Solubility Products, pp. 1117–1122 (Ksp values for silver chloride, calcium carbonate, lead iodide and barium sulfate; the sim's AgCl value of 1.8 × 10⁻¹⁰ is the one carried in the section contract, and the four values are to be pinned against the table). [^af-commonion]: Flowers, Paul; Neth, Edward; Robinson, William et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 15, §15.1 Precipitation and Dissolution, pp. 719–752 (the common ion effect; page to pin). [^af-coupled]: Flowers, Paul; Neth, Edward; Robinson, William et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 15, §15.3 Coupled Equilibria, pp. 719–752 (dissolution coupled with acid–base and complex-ion equilibria; page to pin). [^af-solubility]: Flowers, Paul; Neth, Edward; Robinson, William et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 11 Solutions and Colloids, §11.3 Solubility, pp. 545–596 (solubility against temperature; Henry's law and the pressure dependence of gas solubility; page to pin). [^ball-equilibrium]: Ball, David (2011). *Introductory Chemistry*. Chapter 13 Chemical Equilibrium, pp. 623–672 (solubility product equilibria as a special type of equilibrium; page to pin). https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry [^af-lechatelier]: Flowers, Paul; Neth, Edward; Robinson, William et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 13 Fundamental Equilibrium Concepts, §13.3 Shifting Equilibria: Le Châtelier's Principle, pp. 623–664 (response of an equilibrium to concentration, pressure and temperature; page to pin). [^af-freeenergy]: Flowers, Paul; Neth, Edward; Robinson, William et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 12 Thermodynamics, §12.4 Free Energy, pp. 597–622 (ΔG° = −RT ln K, from which the van 't Hoff temperature dependence of an equilibrium constant follows; page to pin). [^af-dissolution]: Flowers, Paul; Neth, Edward; Robinson, William et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 11 Solutions and Colloids, §11.1 The Dissolution Process, pp. 545–596 (enthalpy of solution as the balance of lattice and solvation energies; page to pin). [^ball-solutions]: Ball, David (2011). *Introductory Chemistry*. Chapter 11 Solutions, pp. 518–570 (solubility of solids and gases against temperature; page to pin). https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry ## External links - *Chemistry: Atoms First 2e* (OpenStax, 2019), Portal Book 051: https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first - *Introductory Chemistry* (Ball, 2011), Portal Book 056: https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry - The Wikipedia pair's External links section lists the pair's own links. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Solubility_equilibrium.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Solubility equilibrium* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Solubility_equilibrium.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Solubility_equilibrium.html" data-title="Solubility equilibrium"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Solubility_equilibrium) : [Wikitube](https://en.wikitube.io/wiki/Solubility_equilibrium) · pinned revision [1322412307](https://en.wikipedia.org/w/index.php?oldid=1322412307) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K38 · sim pending (matter/Solubility_equilibrium).*