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id="mf-section-0"> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about a chemical property. For the algebraic concept, see <a href="/wiki/Solvable_group" title="Solvable group">solvable group</a>. For other uses, see <a href="/wiki/Solution_(disambiguation)" class="mw-redirect mw-disambig" title="Solution (disambiguation)">solution (disambiguation)</a>.</div> In <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, solubility is the ability of a <a href="/wiki/Chemical_substance" title="Chemical substance">substance</a>, the <a href="/wiki/Solute" class="mw-redirect" title="Solute">solute</a>, to form a <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">solution</a> with another substance, the <a href="/wiki/Solvent" title="Solvent">solvent</a>. Insolubility is the opposite property, the inability of the solute to form such a solution. <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Chemical_precipitation_diagram_multilang.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Chemical_precipitation_diagram_multilang.svg/220px-Chemical_precipitation_diagram_multilang.svg.png" decoding="async" width="220" height="202" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Chemical_precipitation_diagram_multilang.svg/330px-Chemical_precipitation_diagram_multilang.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Chemical_precipitation_diagram_multilang.svg/440px-Chemical_precipitation_diagram_multilang.svg.png 2x" data-file-width="600" data-file-height="550"></a><figcaption>Example of a dissolved solid (left)</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Crystals_ammonium_sulfate.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Crystals_ammonium_sulfate.jpg/170px-Crystals_ammonium_sulfate.jpg" decoding="async" width="170" height="247" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Crystals_ammonium_sulfate.jpg/255px-Crystals_ammonium_sulfate.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Crystals_ammonium_sulfate.jpg/340px-Crystals_ammonium_sulfate.jpg 2x" data-file-width="2244" data-file-height="3264"></a><figcaption>Formation of crystals in a 4.2 <a href="/wiki/Molar_concentration" title="Molar concentration">M</a> <a href="/wiki/Ammonium_sulfate" title="Ammonium sulfate">ammonium sulfate</a> solution. The solution was initially prepared at 20 °C and then stored for 2 days at 4 °C.</figcaption></figure> The extent of the solubility of a substance in a specific solvent is generally measured as the <a href="/wiki/Concentration" title="Concentration">concentration</a> of the solute in a <a href="https://en.wiktionary.org/wiki/saturated#Chemistry" class="extiw" title="wikt:saturated">saturated</a> solution, one in which no more solute can be dissolved.<a href="#cite_note-iupac-1">[1]</a> At this point, the two substances are said to be at the <a href="/wiki/Solubility_equilibrium" title="Solubility equilibrium">solubility equilibrium</a>. For some solutes and solvents, there may be no such limit, in which case the two substances are said to be "<a href="/wiki/Miscibility" title="Miscibility">miscible</a> in all proportions" (or just "miscible").<a href="#cite_note-clug2000-2">[2]</a> The solute can be a <a href="/wiki/Solid" title="Solid">solid</a>, a <a href="/wiki/Liquid" title="Liquid">liquid</a>, or a <a href="/wiki/Gas" title="Gas">gas</a>, while the solvent is usually solid or liquid. Both may be pure substances, or may themselves be solutions. Gases are always miscible in all proportions, except in very extreme situations,<a href="#cite_note-swaan1966-3">[3]</a> and a solid or liquid can be "dissolved" in a gas only by passing into the gaseous state first. The solubility mainly depends on the composition of solute and solvent (including their <a href="/wiki/PH" title="PH">pH</a> and the presence of other dissolved substances) as well as on temperature and pressure. The dependency can often be explained in terms of interactions between the particles (<a href="/wiki/Atom" title="Atom">atoms</a>, <a href="/wiki/Molecule" title="Molecule">molecules</a>, or <a href="/wiki/Ion" title="Ion">ions</a>) of the two substances, and of <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamic</a> concepts such as <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> and <a href="/wiki/Entropy" title="Entropy">entropy</a>. Under certain conditions, the concentration of the solute can exceed its usual solubility limit. The result is a <a href="/wiki/Supersaturation" title="Supersaturation">supersaturated solution</a>, which is <a href="/wiki/Metastability" title="Metastability">metastable</a> and will rapidly exclude the excess solute if a suitable <a href="/wiki/Nucleation" title="Nucleation">nucleation</a> site appears.<a href="#cite_note-4">[4]</a> The concept of solubility does not apply when there is an irreversible <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reaction</a> between the two substances, such as the reaction of <a href="/wiki/Calcium_hydroxide" title="Calcium hydroxide">calcium hydroxide</a> with <a href="/wiki/Hydrochloric_acid" title="Hydrochloric acid">hydrochloric acid</a>; even though one might say, informally, that one "dissolved" the other. The solubility is also not the same as the <a href="/wiki/Rate_of_solution" class="mw-redirect" title="Rate of solution">rate of solution</a>, which is how fast a solid solute dissolves in a liquid solvent. This property depends on many other variables, such as the physical form of the two substances and the manner and intensity of mixing. The concept and measure of solubility are extremely important in many sciences besides chemistry, such as <a href="/wiki/Geology" title="Geology">geology</a>, <a href="/wiki/Biology" title="Biology">biology</a>, <a href="/wiki/Physics" title="Physics">physics</a>, and <a href="/wiki/Oceanography" title="Oceanography">oceanography</a>, as well as in <a href="/wiki/Engineering" title="Engineering">engineering</a>, <a href="/wiki/Medicine" title="Medicine">medicine</a>, <a href="/wiki/Agriculture" title="Agriculture">agriculture</a>, and even in non-technical activities like <a href="/wiki/Painting" title="Painting">painting</a>, <a href="/wiki/Cleaning" title="Cleaning">cleaning</a>, <a href="/wiki/Cooking" title="Cooking">cooking</a>, and <a href="/wiki/Brewing" title="Brewing">brewing</a>. Most chemical reactions of scientific, industrial, or practical interest only happen after the <a href="/wiki/Reagent" title="Reagent">reagents</a> have been dissolved in a suitable solvent. <a href="/wiki/Water" title="Water">Water</a> is by far the most common such solvent. The term "soluble" is sometimes used for materials that can form <a href="/wiki/Colloid" title="Colloid">colloidal suspensions</a> of very fine solid particles in a liquid.<a href="#cite_note-korm1988-5">[5]</a> The quantitative solubility of such substances is generally not well-defined, however. <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><label class="toctogglelabel" for="toctogglecheckbox"></label></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Quantification_of_solubility">1 Quantification of solubility</a> <ul> <li class="toclevel-2 tocsection-2"><a href="#Per_quantity_of_solvent">1.1 Per quantity of solvent</a></li> <li class="toclevel-2 tocsection-3"><a href="#Per_quantity_of_solution">1.2 Per quantity of solution</a></li> <li class="toclevel-2 tocsection-4"><a href="#Liquid_and_gaseous_solutes">1.3 Liquid and gaseous solutes</a></li> <li class="toclevel-2 tocsection-5"><a href="#Conversion_of_solubility_values">1.4 Conversion of solubility values</a></li> </ul> </li> <li class="toclevel-1 tocsection-6"><a href="#Qualifiers_used_to_describe_extent_of_solubility">2 Qualifiers used to describe extent of solubility</a></li> <li class="toclevel-1 tocsection-7"><a href="#Molecular_view">3 Molecular view</a></li> <li class="toclevel-1 tocsection-8"><a href="#Factors_affecting_solubility">4 Factors affecting solubility</a> <ul> <li class="toclevel-2 tocsection-9"><a href="#Temperature">4.1 Temperature</a></li> <li class="toclevel-2 tocsection-10"><a href="#Pressure">4.2 Pressure</a></li> </ul> </li> <li class="toclevel-1 tocsection-11"><a href="#Solubility_of_gases">5 Solubility of gases</a></li> <li class="toclevel-1 tocsection-12"><a href="#Polarity">6 Polarity</a></li> <li class="toclevel-1 tocsection-13"><a href="#Rate_of_dissolution">7 Rate of dissolution</a></li> <li class="toclevel-1 tocsection-14"><a href="#Theories_of_solubility">8 Theories of solubility</a> <ul> <li class="toclevel-2 tocsection-15"><a href="#Solubility_product">8.1 Solubility product</a></li> <li class="toclevel-2 tocsection-16"><a href="#Other_theories">8.2 Other theories</a></li> </ul> </li> <li class="toclevel-1 tocsection-17"><a href="#Applications">9 Applications</a> <ul> <li class="toclevel-2 tocsection-18"><a href="#Differential_solubility">9.1 Differential solubility</a></li> </ul> </li> <li class="toclevel-1 tocsection-19"><a href="#Solubility_of_ionic_compounds_in_water">10 Solubility of ionic compounds in water</a></li> <li class="toclevel-1 tocsection-20"><a href="#Solubility_of_organic_compounds">11 Solubility of organic compounds</a></li> <li class="toclevel-1 tocsection-21"><a href="#Solid_solution">12 Solid solution</a></li> <li class="toclevel-1 tocsection-22"><a href="#Incongruent_dissolution">13 Incongruent dissolution</a></li> <li class="toclevel-1 tocsection-23"><a href="#Solubility_prediction">14 Solubility prediction</a></li> <li class="toclevel-1 tocsection-24"><a href="#See_also">15 See also</a></li> <li class="toclevel-1 tocsection-25"><a href="#Notes">16 Notes</a></li> <li class="toclevel-1 tocsection-26"><a href="#References">17 References</a></li> <li class="toclevel-1 tocsection-27"><a href="#External_links">18 External links</a></li> </ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"><h2 id="Quantification_of_solubility">Quantification of solubility</h2></div><section class="mf-section-1 collapsible-block" id="mf-section-1"> The solubility of a specific solute in a specific solvent is generally expressed as the concentration of a saturated solution of the two.<a href="#cite_note-iupac-1">[1]</a> Any of the several ways of expressing concentration of solutions can be used, such as the <a href="/wiki/Mass" title="Mass">mass</a>, <a href="/wiki/Volume" title="Volume">volume</a>, or <a href="/wiki/Mole_(unit)" title="Mole (unit)">amount in moles</a> of the solute for a specific mass, volume, or mole amount of the solvent or of the solution. <div class="mw-heading mw-heading3"><h3 id="Per_quantity_of_solvent">Per quantity of solvent</h3></div> In particular, chemical <a href="/wiki/Handbook" title="Handbook">handbooks</a> often express the solubility as <a href="/wiki/Gram" title="Gram">grams</a> of solute per 100 <a href="/wiki/Millilitres" class="mw-redirect" title="Millilitres">millilitres</a> of solvent (g/(100 mL), often written as g/100 ml), or as grams of solute per <a href="/wiki/Decilitre" class="mw-redirect" title="Decilitre">decilitre</a> of solvent (g/dL); or, less commonly, as grams of solute per <a href="/wiki/Litre" title="Litre">litre</a> of solvent (g/L). The quantity of solvent can instead be expressed in mass, as grams of solute per 100 grams of solvent (g/(100 g), often written as g/100 g), or as grams of solute per <a href="/wiki/Kilogram" title="Kilogram">kilogram</a> of solvent (g/kg). The number may be expressed as a percentage in this case, and the abbreviation "w/w" may be used to indicate "weight per weight".<a href="#cite_note-abler2021-6">[6]</a> (The values in g/L and g/kg are similar for water, but that may not be the case for other solvents.) Alternatively, the solubility of a solute can be expressed in moles instead of mass. For example, if the quantity of solvent is given in <a href="/wiki/Kilograms" class="mw-redirect" title="Kilograms">kilograms</a>, the value is the <a href="/wiki/Molality" title="Molality">molality</a> of the solution (mol/kg). <div class="mw-heading mw-heading3"><h3 id="Per_quantity_of_solution">Per quantity of solution</h3></div> The solubility of a substance in a liquid may also be expressed as the quantity of solute per quantity of solution, rather than of solvent. For example, following the common practice in <a href="/wiki/Titration" title="Titration">titration</a>, it may be expressed as moles of solute per litre of solution (mol/L), the <a href="/wiki/Molarity" class="mw-redirect" title="Molarity">molarity</a> of the latter. In more specialized contexts the solubility may be given by the <a href="/wiki/Mole_fraction" title="Mole fraction">mole fraction</a> (moles of solute per total moles of solute plus solvent) or by the <a href="/wiki/Mass_fraction_(chemistry)" title="Mass fraction (chemistry)">mass fraction</a> at equilibrium (mass of solute per mass of solute plus solvent). Both are <a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">dimensionless</a> numbers between 0 and 1 which may be expressed as <a href="/wiki/Percentages" class="mw-redirect" title="Percentages">percentages</a> (%). <div class="mw-heading mw-heading3"><h3 id="Liquid_and_gaseous_solutes">Liquid and gaseous solutes</h3></div> For solutions of liquids or gases in liquids, the quantities of both substances may be given volume rather than mass or mole amount; such as litre of solute per litre of solvent, or litre of solute per litre of solution. The value may be given as a percentage, and the abbreviation "v/v" for "volume per volume" may be used to indicate this choice. <div class="mw-heading mw-heading3"><h3 id="Conversion_of_solubility_values">Conversion of solubility values</h3></div> Conversion between these various ways of measuring solubility may not be trivial, since it may require knowing the density of the solution — which is often not measured, and cannot be predicted. While the total mass is conserved by dissolution, the final volume may be different from both the volume of the solvent and the sum of the two volumes.<a href="#cite_note-lee2012-7">[7]</a> Moreover, many solids (such as <a href="/wiki/Acid" title="Acid">acids</a> and <a href="/wiki/Salt_(chemistry)" title="Salt (chemistry)">salts</a>) will <a href="/wiki/Dissociation_(chemistry)" title="Dissociation (chemistry)">dissociate</a> in non-trivial ways when dissolved; conversely, the solvent may form <a href="/wiki/Coordination_complex" title="Coordination complex">coordination complexes</a> with the molecules or ions of the solute. In those cases, the sum of the moles of molecules of solute and solvent is not really the total moles of independent particles solution. To sidestep that problem, the solubility per mole of solution is usually computed and quoted as if the solute does not dissociate or form complexes—that is, by pretending that the mole amount of solution is the sum of the mole amounts of the two substances. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"><h2 id="Qualifiers_used_to_describe_extent_of_solubility">Qualifiers used to describe extent of solubility</h2></div><section class="mf-section-2 collapsible-block" id="mf-section-2"> The extent of solubility ranges widely, from infinitely soluble (without limit, i.e. <a href="/wiki/Miscible" class="mw-redirect" title="Miscible">miscible</a><a href="#cite_note-clug2000-2">[2]</a>) such as <a href="/wiki/Ethanol" title="Ethanol">ethanol</a> in water, to essentially insoluble, such as <a href="/wiki/Titanium_dioxide" title="Titanium dioxide">titanium dioxide</a> in water. A number of other descriptive terms are also used to qualify the extent of solubility for a given application. For example, <a href="/wiki/U.S._Pharmacopoeia" class="mw-redirect" title="U.S. Pharmacopoeia">U.S. Pharmacopoeia</a> gives the following terms, according to the mass msv of solvent required to dissolve one unit of mass msu of solute:<a href="#cite_note-8">[8]</a> (The solubilities of the examples are approximate, for water at 20–25 °C.) <table class="wikitable"> <tbody><tr> <th>Term </th> <th>Range (msv/msu) </th> <th>Example </th> <th>g/dL </th> <th>msv/msu </th></tr> <tr> <td>Very soluble </td> <td><1 </td> <td><a href="/wiki/Calcium_nitrate" title="Calcium nitrate">calcium nitrate</a> </td> <td>158.7 </td> <td>0.63 </td></tr> <tr> <td>Freely soluble </td> <td>1 to 10 </td> <td><a href="/wiki/Calcium_chloride" title="Calcium chloride">calcium chloride</a> </td> <td>65 </td> <td>1.54 </td></tr> <tr> <td>Soluble </td> <td>10 to 30 </td> <td><a href="/wiki/Sodium_oxalate" title="Sodium oxalate">sodium oxalate</a> </td> <td>3.9 </td> <td>26 </td></tr> <tr> <td>Sparingly soluble </td> <td>30 to 100 </td> <td> </td> <td> </td> <td> </td></tr> <tr> <td>Slightly soluble </td> <td>100 to 1000 </td> <td><a href="/wiki/Calcium_sulfate" title="Calcium sulfate">calcium sulfate</a> </td> <td>0.21 </td> <td>490 </td></tr> <tr> <td>Very slightly soluble </td> <td>1000 to 10,000 </td> <td><a href="/wiki/Dicalcium_phosphate" title="Dicalcium phosphate">dicalcium phosphate</a> </td> <td>0.02 </td> <td>5000 </td></tr> <tr> <td>Practically insoluble or insoluble </td> <td>≥ 10,000 </td> <td><a href="/wiki/Barium_sulfate" title="Barium sulfate">barium sulfate</a> </td> <td>0.000245 </td> <td>409000 </td></tr></tbody></table> The thresholds to describe something as insoluble, or similar terms, may depend on the application. For example, one source states that substances are described as "insoluble" when their solubility is less than 0.1 g per 100 mL of solvent.<a href="#cite_note-9">[9]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"><h2 id="Molecular_view">Molecular view</h2></div><section class="mf-section-3 collapsible-block" id="mf-section-3"> Solubility occurs under dynamic equilibrium, which means that solubility results from the simultaneous and opposing processes of <a href="/wiki/Solvation" title="Solvation">dissolution</a> and phase joining (e.g. <a href="/wiki/Precipitation_(chemistry)" title="Precipitation (chemistry)">precipitation</a> of <a href="/wiki/Solids" class="mw-redirect" title="Solids">solids</a>). A stable state of the solubility equilibrium occurs when the rates of dissolution and re-joining are equal, meaning the relative amounts of dissolved and non-dissolved materials are equal. If the solvent is removed, all of the substance that had dissolved is recovered. The term solubility is also used in some fields where the solute is altered by <a href="/wiki/Solvolysis" title="Solvolysis">solvolysis</a>. For example, many metals and their <a href="/wiki/Oxide" title="Oxide">oxides</a> are said to be "soluble in hydrochloric acid", although in fact the aqueous acid irreversibly degrades the solid to give soluble products. Most ionic solids dissociate when dissolved in polar solvents. In those cases where the solute is not recovered upon evaporation of the solvent, the process is referred to as solvolysis. The thermodynamic concept of solubility does not apply straightforwardly to solvolysis. When a solute dissolves, it may form several species in the solution. For example, an <a href="/wiki/Aqueous" class="mw-redirect" title="Aqueous">aqueous</a> solution of cobalt(II) chloride can afford <style data-mw-deduplicate="TemplateStyles:r1123817410">.mw-parser-output .template-chem2-su{display:inline-block;font-size:80%;line-height:1;vertical-align:-0.35em}.mw-parser-output .template-chem2-su>span{display:block;text-align:left}.mw-parser-output sub.template-chem2-sub{font-size:80%;vertical-align:-0.35em}.mw-parser-output sup.template-chem2-sup{font-size:80%;vertical-align:0.65em}</style>[Co(H2O)6]2+, [CoCl(H2O)5]+, CoCl2(H2O)2, each of which interconverts. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"><h2 id="Factors_affecting_solubility">Factors affecting solubility</h2></div><section class="mf-section-4 collapsible-block" id="mf-section-4"> Solubility is defined for specific <a href="/wiki/Phase_(matter)" title="Phase (matter)">phases</a>. For example, the solubility of <a href="/wiki/Aragonite" title="Aragonite">aragonite</a> and <a href="/wiki/Calcite" title="Calcite">calcite</a> in water are expected to differ, even though they are both <a href="/wiki/Polymorphism_(materials_science)" class="mw-redirect" title="Polymorphism (materials science)">polymorphs</a> of <a href="/wiki/Calcium_carbonate" title="Calcium carbonate">calcium carbonate</a> and have the same <a href="/wiki/Chemical_formula" title="Chemical formula">chemical formula</a>.[<a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarification needed</a>] The solubility of one substance in another is determined by the balance of <a href="/wiki/Intermolecular_force" title="Intermolecular force">intermolecular forces</a> between the solvent and solute, and the <a href="/wiki/Entropy" title="Entropy">entropy</a> change that accompanies the solvation. Factors such as temperature and pressure will alter this balance, thus changing the solubility. Solubility may also strongly depend on the presence of other species dissolved in the solvent, for example, <a href="/wiki/Complex_(chemistry)" class="mw-redirect" title="Complex (chemistry)">complex-forming</a> anions (<a href="/wiki/Ligand" title="Ligand">ligands</a>) in liquids. Solubility will also depend on the excess or deficiency of a common ion in the solution[<a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarification needed</a>], a phenomenon known as the <a href="/wiki/Common-ion_effect" title="Common-ion effect">common-ion effect</a>. To a lesser extent, solubility will depend on the <a href="/wiki/Ionic_strength" title="Ionic strength">ionic strength</a> of solutions. The last two effects can be quantified using the equation for <a href="/wiki/Solubility_equilibrium" title="Solubility equilibrium">solubility equilibrium</a>. For a solid that dissolves in a redox reaction, solubility is expected to depend on the potential (within the range of potentials under which the solid remains the thermodynamically stable phase). For example, solubility of gold in high-temperature water is observed to be almost an order of magnitude higher (i.e. about ten times higher) when the redox potential is controlled using a highly oxidizing Fe3O4-Fe2O3 <a href="/wiki/Redox_buffer" class="mw-redirect" title="Redox buffer">redox buffer</a> than with a moderately oxidizing <a href="/wiki/Nickel" title="Nickel">Ni</a>-<a href="/wiki/Nickel(II)_oxide" title="Nickel(II) oxide">NiO</a> buffer.<a href="#cite_note-10">[10]</a> <figure class="mw-halign-right mw-image-border" typeof="mw:File"><a href="/wiki/File:SolubilityVsTemperature.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/SolubilityVsTemperature.png/400px-SolubilityVsTemperature.png" decoding="async" width="400" height="330" class="mw-file-element" data-file-width="583" data-file-height="481"></noscript><span class="lazy-image-placeholder" style="width: 400px;height: 330px;" data-mw-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/SolubilityVsTemperature.png/400px-SolubilityVsTemperature.png" data-width="400" data-height="330" data-srcset="//upload.wikimedia.org/wikipedia/commons/f/f9/SolubilityVsTemperature.png 1.5x" data-class="mw-file-element"> </a><figcaption></figcaption></figure> Solubility (metastable, at concentrations approaching saturation) also depends on the physical size of the crystal or droplet of solute (or, strictly speaking, on the <a href="/wiki/Specific_surface_area" title="Specific surface area">specific surface area</a> or molar surface area of the solute).<a href="#cite_note-hefter-11">[11]</a> For quantification, see the equation in the article on <a href="/wiki/Solubility_equilibrium#Particle_size_effect" title="Solubility equilibrium">solubility equilibrium</a>. For highly defective crystals, solubility may increase with the increasing degree of disorder. Both of these effects occur because of the dependence of solubility constant on the Gibbs energy of the crystal. The last two effects, although often difficult to measure, are of practical importance.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] For example, they provide the driving force for <a href="/wiki/Ostwald_ripening" title="Ostwald ripening">precipitate aging</a> (the crystal size spontaneously increasing with time). <div class="mw-heading mw-heading3"><h3 id="Temperature">Temperature</h3></div> The solubility of a given solute in a given solvent is function of temperature. Depending on the change in <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> (ΔH) of the dissolution reaction, i.e., on the <a href="/wiki/Endothermic_process" title="Endothermic process">endothermic</a> (ΔH > 0) or <a href="/wiki/Exothermic_process" title="Exothermic process">exothermic</a> (ΔH < 0) character of the dissolution reaction, the solubility of a given compound may increase or decrease with temperature. The <a href="/wiki/Van_%27t_Hoff_equation" title="Van 't Hoff equation">van 't Hoff equation</a> relates the change of solubility <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a> (Ksp) to temperature change and to reaction <a href="/wiki/Enthalpy" title="Enthalpy">enthalpy</a> change. For most solids and liquids, their solubility increases with temperature because their dissolution reaction is endothermic (ΔH > 0).<a href="#cite_note-hill-12">[12]</a> In liquid water at high temperatures, (e.g. that approaching the <a href="/wiki/Critical_temperature" class="mw-redirect" title="Critical temperature">critical temperature</a>), the solubility of ionic solutes tends to decrease due to the change of properties and structure of liquid water; the lower <a href="/wiki/Dielectric_constant" class="mw-redirect" title="Dielectric constant">dielectric constant</a> results in a less <a href="/wiki/Polar_solvent" class="mw-redirect" title="Polar solvent">polar solvent</a> and in a change of hydration energy affecting the ΔG of the dissolution reaction. <a href="/wiki/Gas" title="Gas">Gaseous</a> solutes exhibit more complex behavior with temperature. As the temperature is raised, gases usually become less soluble in water (exothermic dissolution reaction related to their hydration) (to a minimum, which is below 120 °C for most permanent gases<a href="#cite_note-13">[13]</a>), but more soluble in organic solvents (endothermic dissolution reaction related to their solvation).<a href="#cite_note-hill-12">[12]</a> The chart shows solubility curves for some typical solid inorganic <a href="/wiki/Salt_(chemistry)" title="Salt (chemistry)">salts</a> in liquid water (temperature is in degrees <a href="/wiki/Celsius" title="Celsius">Celsius</a>, i.e. <a href="/wiki/Kelvin" title="Kelvin">kelvins</a> minus 273.15).<a href="#cite_note-14">[14]</a> Many salts behave like <a href="/wiki/Barium_nitrate" title="Barium nitrate">barium nitrate</a> and <a href="/wiki/Disodium_hydrogen_arsenate" title="Disodium hydrogen arsenate">disodium hydrogen arsenate</a>, and show a large increase in solubility with temperature (ΔH > 0). Some solutes (e.g. <a href="/wiki/Sodium_chloride" title="Sodium chloride">sodium chloride</a> in water) exhibit solubility that is fairly independent of temperature (ΔH ≈ 0). A few, such as <a href="/wiki/Calcium_sulfate" title="Calcium sulfate">calcium sulfate</a> (<a href="/wiki/Gypsum" title="Gypsum">gypsum</a>) and <a href="/wiki/Cerium(III)_sulfate" title="Cerium(III) sulfate">cerium(III) sulfate</a>, become less soluble in water as temperature increases (ΔH < 0).<a href="#cite_note-Scientific_American-15">[15]</a> This is also the case for <a href="/wiki/Calcium_hydroxide" title="Calcium hydroxide">calcium hydroxide</a> (<a href="/wiki/Portlandite" title="Portlandite">portlandite</a>), whose solubility at 70 °C is about half of its value at 25 °C. The dissolution of calcium hydroxide in water is also an exothermic process (ΔH < 0). As dictated by the <a href="/wiki/Van_%27t_Hoff_equation" title="Van 't Hoff equation">van 't Hoff equation</a> and <a href="/wiki/Le_Chatelier%27s_principle" title="Le Chatelier's principle">Le Chatelier's principle</a>, low temperatures favor dissolution of Ca(OH)2. Portlandite solubility increases at low temperature. This temperature dependence is sometimes referred to as "retrograde" or "inverse" solubility.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] Occasionally, a more complex pattern is observed, as with <a href="/wiki/Sodium_sulfate" title="Sodium sulfate">sodium sulfate</a>, where the less soluble deca<a href="/wiki/Hydrate" title="Hydrate">hydrate</a> crystal (<a href="/wiki/Mirabilite" title="Mirabilite">mirabilite</a>) loses <a href="/wiki/Water_of_crystallization" title="Water of crystallization">water of crystallization</a> at 32 °C to form a more soluble <a href="/wiki/Anhydrous" title="Anhydrous">anhydrous</a> phase (<a href="/wiki/Thenardite" class="mw-redirect" title="Thenardite">thenardite</a>) with a smaller change in <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> (ΔG) in the dissolution reaction.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/File:Temperature_dependence_solublity_of_solid_in_liquid_water_high_temperature.svg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/en/thumb/a/a4/Temperature_dependence_solublity_of_solid_in_liquid_water_high_temperature.svg/400px-Temperature_dependence_solublity_of_solid_in_liquid_water_high_temperature.svg.png" decoding="async" width="400" height="311" class="mw-file-element" data-file-width="465" data-file-height="362"></noscript><span class="lazy-image-placeholder" style="width: 400px;height: 311px;" data-mw-src="//upload.wikimedia.org/wikipedia/en/thumb/a/a4/Temperature_dependence_solublity_of_solid_in_liquid_water_high_temperature.svg/400px-Temperature_dependence_solublity_of_solid_in_liquid_water_high_temperature.svg.png" data-width="400" data-height="311" data-srcset="//upload.wikimedia.org/wikipedia/en/thumb/a/a4/Temperature_dependence_solublity_of_solid_in_liquid_water_high_temperature.svg/600px-Temperature_dependence_solublity_of_solid_in_liquid_water_high_temperature.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/a/a4/Temperature_dependence_solublity_of_solid_in_liquid_water_high_temperature.svg/800px-Temperature_dependence_solublity_of_solid_in_liquid_water_high_temperature.svg.png 2x" data-class="mw-file-element"> </a><figcaption></figcaption></figure> The solubility of <a href="/wiki/Organic_compounds" class="mw-redirect" title="Organic compounds">organic compounds</a> nearly always increases with temperature. The technique of <a href="/wiki/Recrystallization_(chemistry)" title="Recrystallization (chemistry)">recrystallization</a>, used for purification of solids, depends on a solute's different solubilities in hot and cold solvent. A few exceptions exist, such as certain <a href="/wiki/Cyclodextrin" title="Cyclodextrin">cyclodextrins</a>.<a href="#cite_note-16">[16]</a> <div class="mw-heading mw-heading3"><h3 id="Pressure">Pressure</h3></div> For condensed phases (solids and liquids), the pressure dependence of solubility is typically weak and usually neglected in practice. Assuming an <a href="/wiki/Ideal_solution" title="Ideal solution">ideal solution</a>, the dependence can be quantified as: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial \ln N_{i}}{\partial P}}\right)_{T}=-{\frac {V_{i,aq}-V_{i,cr}}{RT}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ln</mi> <mo>⁡</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <mi>a</mi> <mi>q</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <mi>c</mi> <mi>r</mi> </mrow> </msub> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial \ln N_{i}}{\partial P}}\right)_{T}=-{\frac {V_{i,aq}-V_{i,cr}}{RT}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a83e47bdf99a5fdd64062862d928d1697ff5be33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:29.231ex; height:6.176ex;" alt="{\displaystyle \left({\frac {\partial \ln N_{i}}{\partial P}}\right)_{T}=-{\frac {V_{i,aq}-V_{i,cr}}{RT}}}"></noscript><span class="lazy-image-placeholder" style="width: 29.231ex;height: 6.176ex;vertical-align: -2.505ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a83e47bdf99a5fdd64062862d928d1697ff5be33" data-alt="{\displaystyle \left({\frac {\partial \ln N_{i}}{\partial P}}\right)_{T}=-{\frac {V_{i,aq}-V_{i,cr}}{RT}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> where the index <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  iterates the components, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{i}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fef58cebf23adff9199f17325aefb5515fdca99d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.666ex; height:2.509ex;" alt="{\displaystyle N_{i}}"></noscript><span class="lazy-image-placeholder" style="width: 2.666ex;height: 2.509ex;vertical-align: -0.671ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fef58cebf23adff9199f17325aefb5515fdca99d" data-alt="{\displaystyle N_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the mole fraction of the <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> -th component in the solution, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></noscript><span class="lazy-image-placeholder" style="width: 1.745ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" data-alt="{\displaystyle P}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the pressure, the index <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></noscript><span class="lazy-image-placeholder" style="width: 1.636ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" data-alt="{\displaystyle T}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  refers to constant temperature, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{i,aq}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <mi>a</mi> <mi>q</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{i,aq}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1cb7bf31f32fbc858e75924090cdc635b89401d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.238ex; height:2.843ex;" alt="{\displaystyle V_{i,aq}}"></noscript><span class="lazy-image-placeholder" style="width: 4.238ex;height: 2.843ex;vertical-align: -1.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1cb7bf31f32fbc858e75924090cdc635b89401d" data-alt="{\displaystyle V_{i,aq}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the <a href="/wiki/Partial_molar_volume" class="mw-redirect" title="Partial molar volume">partial molar volume</a> of the <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> -th component in the solution, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{i,cr}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <mi>c</mi> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{i,cr}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6854936c0ef7e91e91af9a38da440d3af146139d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.066ex; height:2.843ex;" alt="{\displaystyle V_{i,cr}}"></noscript><span class="lazy-image-placeholder" style="width: 4.066ex;height: 2.843ex;vertical-align: -1.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6854936c0ef7e91e91af9a38da440d3af146139d" data-alt="{\displaystyle V_{i,cr}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the partial molar volume of the <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></noscript><span class="lazy-image-placeholder" style="width: 0.802ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" data-alt="{\displaystyle i}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> -th component in the dissolving solid, and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></noscript><span class="lazy-image-placeholder" style="width: 1.764ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" data-alt="{\displaystyle R}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the <a href="/wiki/Universal_gas_constant" class="mw-redirect" title="Universal gas constant">universal gas constant</a>.<a href="#cite_note-17">[17]</a> The pressure dependence of solubility does occasionally have practical significance. For example, <a href="/wiki/Fouling#Precipitation_fouling" title="Fouling">precipitation fouling</a> of oil fields and wells by <a href="/wiki/Calcium_sulfate" title="Calcium sulfate">calcium sulfate</a> (which decreases its solubility with decreasing pressure) can result in decreased productivity with time. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"><h2 id="Solubility_of_gases">Solubility of gases</h2></div><section class="mf-section-5 collapsible-block" id="mf-section-5"> <a href="/wiki/Henry%27s_law" title="Henry's law">Henry's law</a> is used to quantify the solubility of gases in solvents. The solubility of a gas in a solvent is directly proportional to the <a href="/wiki/Partial_pressure" title="Partial pressure">partial pressure</a> of that gas above the solvent. This relationship is similar to <a href="/wiki/Raoult%27s_law" title="Raoult's law">Raoult's law</a> and can be written as: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=k_{\rm {H}}\,c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=k_{\rm {H}}\,c}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/737f69fe6bc0df679796308faa937ba7b68ad7f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:8.427ex; height:2.509ex;" alt="{\displaystyle p=k_{\rm {H}}\,c}"></noscript><span class="lazy-image-placeholder" style="width: 8.427ex;height: 2.509ex;vertical-align: -0.671ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/737f69fe6bc0df679796308faa937ba7b68ad7f5" data-alt="{\displaystyle p=k_{\rm {H}}\,c}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{\rm {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\rm {H}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcdb87c38d186e137c30c99eeeac416618a814d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.676ex; height:2.509ex;" alt="{\displaystyle k_{\rm {H}}}"></noscript><span class="lazy-image-placeholder" style="width: 2.676ex;height: 2.509ex;vertical-align: -0.671ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fcdb87c38d186e137c30c99eeeac416618a814d0" data-alt="{\displaystyle k_{\rm {H}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is a temperature-dependent constant (for example, 769.2 <a href="/wiki/Litre" title="Litre">L</a>·<a href="/wiki/Atmosphere_(unit)" class="mw-redirect" title="Atmosphere (unit)">atm</a>/<a href="/wiki/Mole_(unit)" title="Mole (unit)">mol</a> for <a href="/wiki/Oxygen#Allotropes" title="Oxygen">dioxygen</a> (O2) in water at 298 K), <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></noscript><span class="lazy-image-placeholder" style="width: 1.259ex;height: 2.009ex;vertical-align: -0.671ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" data-alt="{\displaystyle p}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the partial pressure (in atm), and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></noscript><span class="lazy-image-placeholder" style="width: 1.007ex;height: 1.676ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" data-alt="{\displaystyle c}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is the <a href="/wiki/Concentration" title="Concentration">concentration</a> of the dissolved gas in the liquid (in mol/L). The solubility of gases is sometimes also quantified using <a href="/wiki/Bunsen_solubility_coefficient" class="mw-redirect" title="Bunsen solubility coefficient">Bunsen solubility coefficient</a>. In the presence of small <a href="/wiki/Liquid_bubble" class="mw-redirect" title="Liquid bubble">bubbles</a>, the solubility of the gas does not depend on the bubble radius in any other way than through the effect of the radius on pressure (i.e. the solubility of gas in the liquid in contact with small bubbles is increased due to pressure increase by Δp = 2γ/r; see <a href="/wiki/Young%E2%80%93Laplace_equation" title="Young–Laplace equation">Young–Laplace equation</a>).<a href="#cite_note-18">[18]</a> Henry's law is valid for gases that do not undergo change of chemical speciation on dissolution. <a href="/wiki/Sieverts%27_law" title="Sieverts' law">Sieverts' law</a> shows a case when this assumption does not hold. The <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a> solubility in <a href="/wiki/Seawater" title="Seawater">seawater</a> is also affected by temperature, pH of the solution, and by the <a href="/wiki/Carbonate" title="Carbonate">carbonate</a> buffer. The decrease of solubility of carbon dioxide in seawater when temperature increases is also an important retroaction factor (positive feedback) exacerbating past and future <a href="/wiki/Climate_change_(general_concept)" class="mw-redirect" title="Climate change (general concept)">climate changes</a> as observed in ice cores from the Vostok site in <a href="/wiki/Antarctica" title="Antarctica">Antarctica</a>. At the <a href="/wiki/Geological_time" class="mw-redirect" title="Geological time">geological time</a> scale, because of the <a href="/wiki/Milankovich_cycle" class="mw-redirect" title="Milankovich cycle">Milankovich cycles</a>, when the astronomical parameters of the Earth orbit and its rotation axis progressively change and modify the <a href="/wiki/Solar_irradiance" title="Solar irradiance">solar irradiance</a> at the Earth surface, temperature starts to increase. When a deglaciation period is initiated, the progressive warming of the oceans releases CO2 into the atmosphere because of its lower solubility in warmer sea water. In turn, higher levels of CO2 in the atmosphere increase the <a href="/wiki/Greenhouse_effect" title="Greenhouse effect">greenhouse effect</a> and carbon dioxide acts as an amplifier of the general warming. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"><h2 id="Polarity">Polarity</h2></div><section class="mf-section-6 collapsible-block" id="mf-section-6"> A popular <a href="/wiki/Aphorism" title="Aphorism">aphorism</a> used for predicting solubility is "like dissolves like" also expressed in the <a href="/wiki/Latin" title="Latin">Latin</a> language as "Similia similibus solventur".<a href="#cite_note-19">[19]</a> This statement indicates that a solute will dissolve best in a solvent that has a similar <a href="/wiki/Chemical_structure" title="Chemical structure">chemical structure</a> to itself, based on favorable <a href="/wiki/Entropy_of_mixing" title="Entropy of mixing">entropy of mixing</a>. This view is simplistic, but it is a useful rule of thumb. The overall solvation capacity of a solvent depends primarily on its <a href="/wiki/Chemical_polarity" title="Chemical polarity">polarity</a>.<a href="#cite_note-20">[a]</a> For example, a very polar (<a href="/wiki/Hydrophile" title="Hydrophile">hydrophilic</a>) solute such as <a href="/wiki/Urea" title="Urea">urea</a> is very soluble in highly polar water, less soluble in fairly polar <a href="/wiki/Methanol" title="Methanol">methanol</a>, and practically insoluble in non-polar solvents such as <a href="/wiki/Benzene" title="Benzene">benzene</a>. In contrast, a non-polar or <a href="/wiki/Lipophilicity" title="Lipophilicity">lipophilic</a> solute such as <a href="/wiki/Naphthalene" title="Naphthalene">naphthalene</a> is insoluble in water, fairly soluble in methanol, and highly soluble in non-polar benzene.<a href="#cite_note-21">[20]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Sodium_chloride_dissolution.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Sodium_chloride_dissolution.jpg/480px-Sodium_chloride_dissolution.jpg" decoding="async" width="480" height="223" class="mw-file-element" data-file-width="2279" data-file-height="1058"></noscript><span class="lazy-image-placeholder" style="width: 480px;height: 223px;" data-mw-src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Sodium_chloride_dissolution.jpg/480px-Sodium_chloride_dissolution.jpg" data-width="480" data-height="223" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Sodium_chloride_dissolution.jpg/720px-Sodium_chloride_dissolution.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Sodium_chloride_dissolution.jpg/960px-Sodium_chloride_dissolution.jpg 2x" data-class="mw-file-element"> </a><figcaption>Dissolution of sodium chloride in water</figcaption></figure> In even more simple terms a simple <a href="/wiki/Ionic_compound" class="mw-redirect" title="Ionic compound">ionic compound</a> (with positive and negative ions) such as <a href="/wiki/Sodium_chloride" title="Sodium chloride">sodium chloride</a> (common salt) is easily soluble in a highly <a href="/wiki/Chemical_polarity" title="Chemical polarity">polar</a> solvent (with some separation of positive (δ+) and negative (δ-) charges in the covalent molecule) such as <a href="/wiki/Water" title="Water">water</a>, as thus the sea is salty as it accumulates dissolved salts since early geological ages. The solubility is favored by <a href="/wiki/Entropy_of_mixing" title="Entropy of mixing">entropy of mixing</a> (ΔS) and depends on <a href="/wiki/Enthalpy_of_dissolution" class="mw-redirect" title="Enthalpy of dissolution">enthalpy of dissolution</a> (ΔH) and the <a href="/wiki/Hydrophobic_effect" title="Hydrophobic effect">hydrophobic effect</a>. The <a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">free energy</a> of dissolution (<a href="/wiki/Gibbs_energy" class="mw-redirect" title="Gibbs energy">Gibbs energy</a>) depends on temperature and is given by the relationship: ΔG = ΔH – TΔS. Smaller ΔG means greater solubility. Chemists often exploit differences in solubilities to separate and purify compounds from reaction mixtures, using the technique of <a href="/wiki/Liquid-liquid_extraction" class="mw-redirect" title="Liquid-liquid extraction">liquid-liquid extraction</a>. This applies in vast areas of chemistry from drug synthesis to <a href="/wiki/Spent_nuclear_fuel" title="Spent nuclear fuel">spent nuclear fuel</a> reprocessing. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"><h2 id="Rate_of_dissolution">Rate of dissolution</h2></div><section class="mf-section-7 collapsible-block" id="mf-section-7"> Dissolution is not an instantaneous process. The rate of solubilization (in kg/s) is related to the solubility product and the surface area of the material. The speed at which a solid dissolves may depend on its crystallinity or lack thereof in the case of <a href="/wiki/Amorphous" class="mw-redirect" title="Amorphous">amorphous</a> solids and the surface area (crystallite size) and the presence of <a href="/wiki/Polymorphism_(materials_science)" class="mw-redirect" title="Polymorphism (materials science)">polymorphism</a>. Many practical systems illustrate this effect, for example in designing methods for controlled <a href="/wiki/Drug_delivery" title="Drug delivery">drug delivery</a>. In some cases, solubility equilibria can take a long time to establish (hours, days, months, or many years; depending on the nature of the solute and other factors). The rate of dissolution can be often expressed by the <a href="/wiki/Noyes%E2%80%93Whitney_equation" class="mw-redirect" title="Noyes–Whitney equation">Noyes–Whitney equation</a> or the Nernst and Brunner equation<a href="#cite_note-22">[21]</a> of the form: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}=A{\frac {D}{d}}(C_{\mathrm {s} }-C_{\mathrm {b} })}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>m</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>D</mi> <mi>d</mi> </mfrac> </mrow> <mo stretchy="false">(</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}=A{\frac {D}{d}}(C_{\mathrm {s} }-C_{\mathrm {b} })}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bee3a800b12a99c26ac46163c068471e9de321f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.771ex; height:5.509ex;" alt="{\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}=A{\frac {D}{d}}(C_{\mathrm {s} }-C_{\mathrm {b} })}"></noscript><span class="lazy-image-placeholder" style="width: 21.771ex;height: 5.509ex;vertical-align: -2.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bee3a800b12a99c26ac46163c068471e9de321f8" data-alt="{\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}=A{\frac {D}{d}}(C_{\mathrm {s} }-C_{\mathrm {b} })}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> where: <ul><li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></noscript><span class="lazy-image-placeholder" style="width: 2.04ex;height: 1.676ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" data-alt="{\displaystyle m}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  = mass of dissolved material</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></noscript><span class="lazy-image-placeholder" style="width: 0.84ex;height: 2.009ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" data-alt="{\displaystyle t}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  = time</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></noscript><span class="lazy-image-placeholder" style="width: 1.743ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" data-alt="{\displaystyle A}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  = surface area of the interface between the dissolving substance and the solvent</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}"></noscript><span class="lazy-image-placeholder" style="width: 1.924ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" data-alt="{\displaystyle D}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  = <a href="/wiki/Diffusion_coefficient" class="mw-redirect" title="Diffusion coefficient">diffusion coefficient</a></li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></noscript><span class="lazy-image-placeholder" style="width: 1.216ex;height: 2.176ex;vertical-align: -0.338ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" data-alt="{\displaystyle d}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  = thickness of the boundary layer of the solvent at the surface of the dissolving substance</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{s}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b6d160c0ac08478db6e852c204a78cd9bc2e14d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.665ex; height:2.509ex;" alt="{\displaystyle C_{s}}"></noscript><span class="lazy-image-placeholder" style="width: 2.665ex;height: 2.509ex;vertical-align: -0.671ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b6d160c0ac08478db6e852c204a78cd9bc2e14d" data-alt="{\displaystyle C_{s}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  = mass concentration of the substance on the surface</li> <li><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{b}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cf365bf59c72d2c4836aaadcda126759f293318" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.599ex; height:2.509ex;" alt="{\displaystyle C_{b}}"></noscript><span class="lazy-image-placeholder" style="width: 2.599ex;height: 2.509ex;vertical-align: -0.671ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cf365bf59c72d2c4836aaadcda126759f293318" data-alt="{\displaystyle C_{b}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  = mass concentration of the substance in the bulk of the solvent</li></ul> For dissolution limited by <a href="/wiki/Diffusion" title="Diffusion">diffusion</a> (or <a href="/wiki/Mass_transfer" title="Mass transfer">mass transfer</a> if mixing is present), <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{s}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b6d160c0ac08478db6e852c204a78cd9bc2e14d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.665ex; height:2.509ex;" alt="{\displaystyle C_{s}}"></noscript><span class="lazy-image-placeholder" style="width: 2.665ex;height: 2.509ex;vertical-align: -0.671ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b6d160c0ac08478db6e852c204a78cd9bc2e14d" data-alt="{\displaystyle C_{s}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is equal to the solubility of the substance. When the dissolution rate of a pure substance is normalized to the surface area of the solid (which usually changes with time during the dissolution process), then it is expressed in kg/m2s and referred to as "intrinsic dissolution rate". The intrinsic dissolution rate is defined by the <a href="/wiki/United_States_Pharmacopeia" title="United States Pharmacopeia">United States Pharmacopeia</a>. Dissolution rates vary by orders of magnitude between different systems. Typically, very low dissolution rates parallel low solubilities, and substances with high solubilities exhibit high dissolution rates, as suggested by the Noyes-Whitney equation. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(8)"><h2 id="Theories_of_solubility">Theories of solubility</h2></div><section class="mf-section-8 collapsible-block" id="mf-section-8"> <div class="mw-heading mw-heading3"><h3 id="Solubility_product">Solubility product</h3></div> <a href="/wiki/Solubility_constant" class="mw-redirect" title="Solubility constant">Solubility constants</a> are used to describe saturated solutions of ionic compounds of relatively low solubility (see <a href="/wiki/Solubility_equilibrium" title="Solubility equilibrium">solubility equilibrium</a>). The solubility constant is a special case of an <a href="/wiki/Equilibrium_constant" title="Equilibrium constant">equilibrium constant</a>. Since it is a product of ion concentrations in equilibrium, it is also known as the <a href="/wiki/Solubility_product" class="mw-redirect" title="Solubility product">solubility product</a>. It describes the balance between dissolved ions from the salt and undissolved salt. The solubility constant is also "applicable" (i.e. useful) to <a href="/wiki/Precipitation_(chemistry)" title="Precipitation (chemistry)">precipitation</a>, the reverse of the dissolving reaction. As with other equilibrium constants, <a href="/wiki/Temperature" title="Temperature">temperature</a> can affect the numerical value of solubility constant. While the solubility constant is not as simple as solubility, the value of this constant is generally independent of the presence of other species in the solvent. <div class="mw-heading mw-heading3"><h3 id="Other_theories">Other theories</h3></div> The <a href="/wiki/Flory%E2%80%93Huggins_solution_theory" title="Flory–Huggins solution theory">Flory–Huggins solution theory</a> is a theoretical model describing the solubility of polymers. The <a href="/wiki/Hansen_solubility_parameters" class="mw-redirect" title="Hansen solubility parameters">Hansen solubility parameters</a> and the <a href="/wiki/Hildebrand_solubility_parameter" title="Hildebrand solubility parameter">Hildebrand solubility parameters</a> are empirical methods for the prediction of solubility. It is also possible to predict solubility from other physical constants such as the <a href="/wiki/Enthalpy_of_fusion" title="Enthalpy of fusion">enthalpy of fusion</a>. The <a href="/wiki/Octanol-water_partition_coefficient" title="Octanol-water partition coefficient">octanol-water partition coefficient</a>, usually expressed as its <a href="/wiki/Logarithm" title="Logarithm">logarithm</a> (Log P), is a measure of differential solubility of a compound in a <a href="/wiki/Hydrophobe" title="Hydrophobe">hydrophobic</a> solvent (<a href="/wiki/1-octanol" class="mw-redirect" title="1-octanol">1-octanol</a>) and a <a href="/wiki/Hydrophile" title="Hydrophile">hydrophilic</a> solvent (water). The logarithm of these two values enables compounds to be ranked in terms of hydrophilicity (or hydrophobicity). The energy change associated with dissolving is usually given per mole of solute as the <a href="/wiki/Enthalpy_of_solution" class="mw-redirect" title="Enthalpy of solution">enthalpy of solution</a>. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(9)"><h2 id="Applications">Applications</h2></div><section class="mf-section-9 collapsible-block" id="mf-section-9"> Solubility is of fundamental importance in a large number of scientific disciplines and practical applications, ranging from ore processing and nuclear reprocessing to the use of medicines, and the transport of pollutants. Solubility is often said to be one of the "characteristic properties of a substance", which means that solubility is commonly used to describe the substance, to indicate a substance's polarity, to help to distinguish it from other substances, and as a guide to applications of the substance. For example, <a href="/wiki/Indigo_dye#Chemical_properties" title="Indigo dye">indigo</a> is described as "insoluble in water, alcohol, or ether but soluble in chloroform, nitrobenzene, or concentrated <a href="/wiki/Sulfuric_acid" title="Sulfuric acid">sulfuric acid</a>".<a href="#cite_note-23">[22]</a> Solubility of a substance is useful when separating mixtures. For example, a mixture of salt (<a href="/wiki/Sodium_chloride" title="Sodium chloride">sodium chloride</a>) and silica may be separated by dissolving the salt in water, and filtering off the undissolved silica. The synthesis of chemical compounds, by the milligram in a laboratory, or by the ton in industry, both make use of the relative solubilities of the desired product, as well as unreacted starting materials, byproducts, and side products to achieve separation. Another example of this is the synthesis of <a href="/wiki/Benzoic_acid" title="Benzoic acid">benzoic acid</a> from <a href="/wiki/Phenylmagnesium_bromide" title="Phenylmagnesium bromide">phenylmagnesium bromide</a> and <a href="/wiki/Dry_ice" title="Dry ice">dry ice</a>. Benzoic acid is more soluble in an organic solvent such as <a href="/wiki/Dichloromethane" title="Dichloromethane">dichloromethane</a> or <a href="/wiki/Diethyl_ether" title="Diethyl ether">diethyl ether</a>, and when shaken with this organic solvent in a <a href="/wiki/Separatory_funnel" title="Separatory funnel">separatory funnel</a>, will preferentially dissolve in the organic layer. The other reaction products, including the magnesium bromide, will remain in the aqueous layer, clearly showing that separation based on solubility is achieved. This process, known as <a href="/wiki/Liquid%E2%80%93liquid_extraction" title="Liquid–liquid extraction">liquid–liquid extraction</a>, is an important technique in <a href="/wiki/Synthetic_chemistry" class="mw-redirect" title="Synthetic chemistry">synthetic chemistry</a>. Recycling is used to ensure maximum extraction. <div class="mw-heading mw-heading3"><h3 id="Differential_solubility">Differential solubility</h3></div> In flowing systems, differences in solubility often determine the dissolution-precipitation driven transport of species. This happens when different parts of the system experience different conditions. Even slightly different conditions can result in significant effects, given sufficient time. For example, relatively low solubility compounds are found to be soluble in more extreme environments, resulting in geochemical and geological effects of the activity of hydrothermal fluids in the Earth's crust. These are often the source of high quality economic mineral deposits and precious or semi-precious gems. In the same way, compounds with low solubility will dissolve over extended time (geological time), resulting in significant effects such as extensive cave systems or Karstic land surfaces. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(10)"><h2 id="Solubility_of_ionic_compounds_in_water">Solubility of ionic compounds in water</h2></div><section class="mf-section-10 collapsible-block" id="mf-section-10"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Solubility_chart" title="Solubility chart">Solubility chart</a> and <a href="/wiki/Solubility_table" title="Solubility table">Solubility table</a></div> Some ionic compounds (<a href="/wiki/Salts" class="mw-redirect" title="Salts">salts</a>) dissolve in water, which arises because of the attraction between positive and negative charges (see: <a href="/wiki/Solvation" title="Solvation">solvation</a>). For example, the salt's positive ions (e.g. Ag+) attract the partially negative oxygen atom in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">H2O. Likewise, the salt's negative ions (e.g. Cl−) attract the partially positive hydrogens in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">H2O. Note: the oxygen atom is partially negative because it is more <a href="/wiki/Electronegativity" title="Electronegativity">electronegative</a> than hydrogen, and vice versa (see: <a href="/wiki/Chemical_polarity" title="Chemical polarity">chemical polarity</a>). <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">AgCl(s) ⇌ Ag+(aq) + Cl−(aq)</dd></dl> However, there is a limit to how much salt can be dissolved in a given volume of water. This concentration is the solubility and related to the <a href="/wiki/Solubility_product" class="mw-redirect" title="Solubility product">solubility product</a>, Ksp. This equilibrium constant depends on the type of salt (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">AgCl vs. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">NaCl, for example), temperature, and the common ion effect. One can calculate the amount of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">AgCl that will dissolve in 1 liter of pure water as follows: <dl><dd>Ksp = [Ag+] × [Cl−] / M2 (definition of solubility product; M = mol/L)</dd> <dd>Ksp = 1.8 × 10−10 (from a table of solubility products)</dd></dl> [Ag+] = [Cl−], in the absence of other silver or chloride salts, so <dl><dd>[Ag+]2 = 1.8 × 10−10 M2</dd> <dd>[Ag+] = 1.34 × 10−5 mol/L</dd></dl> The result: 1 liter of water can dissolve 1.34 × 10−5 <a href="/wiki/Mole_(unit)" title="Mole (unit)">moles</a> of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">AgCl at room temperature. Compared with other salts, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">AgCl is poorly soluble in water. For instance, table salt (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">NaCl) has a much higher Ksp = 36 and is, therefore, more soluble. The following table gives an overview of solubility rules for various ionic compounds. <table class="wikitable" style="margin:0.5em auto"> <tbody><tr> <th style="width:50%">Soluble </th> <th style="width:50%">Insoluble<a href="#cite_note-24">[23]</a> </th></tr> <tr> <td><a href="/wiki/Alkali_metal" title="Alkali metal">Group I</a> and <a href="/wiki/Ammonium" title="Ammonium">NH4+</a> compounds (except <a href="/w/index.php?title=Lithium_phosphate&action=edit&redlink=1" class="new" title="Lithium phosphate (page does not exist)">lithium phosphate</a>)</td> <td><a href="/wiki/Carbonate" title="Carbonate">Carbonates</a> (except <a href="/wiki/Alkali_metal" title="Alkali metal">Group I</a>, <a href="/wiki/Ammonium" title="Ammonium">NH4+</a> and <a href="/wiki/Uranyl" title="Uranyl">uranyl</a> compounds) </td></tr> <tr> <td><a href="/wiki/Nitrate" title="Nitrate">Nitrates</a></td> <td><a href="/wiki/Sulfite" title="Sulfite">Sulfites</a> (except <a href="/wiki/Alkali_metal" title="Alkali metal">Group I</a> and <a href="/wiki/Ammonium" title="Ammonium">NH4+</a> compounds) </td></tr> <tr> <td><a href="/wiki/Acetate" title="Acetate">Acetates</a> (ethanoates) (except <a href="/wiki/Silver" title="Silver">Ag+</a> compounds)</td> <td><a href="/wiki/Phosphate" title="Phosphate">Phosphates</a> (except <a href="/wiki/Alkali_metal" title="Alkali metal">Group I</a> and <a href="/wiki/Ammonium" title="Ammonium">NH4+</a> compounds (excluding <a href="/wiki/Lithium" title="Lithium">Li</a>+)) </td></tr> <tr> <td><a href="/wiki/Chloride" title="Chloride">Chlorides</a> (chlorates and perchlorates), <a href="/wiki/Bromide" title="Bromide">bromides</a> and <a href="/wiki/Iodide" title="Iodide">iodides</a> (except <a href="/wiki/Silver" title="Silver">Ag+</a>, <a href="/wiki/Lead" title="Lead">Pb2+</a>, <a href="/wiki/Copper" title="Copper">Cu+</a> and <a href="/wiki/Mercury_(element)" title="Mercury (element)">Hg22+</a>)</td> <td><a href="/wiki/Hydroxide" title="Hydroxide">Hydroxides</a> and <a href="/wiki/Oxide" title="Oxide">oxides</a> (except <a href="/wiki/Alkali_metal" title="Alkali metal">Group I</a>, <a href="/wiki/Ammonium" title="Ammonium">NH4+</a>, <a href="/wiki/Barium" title="Barium">Ba2+</a>, <a href="/wiki/Strontium" title="Strontium">Sr2+</a> and <a href="/wiki/Thallium" title="Thallium">Tl+</a>) </td></tr> <tr> <td><a href="/wiki/Sulfate" title="Sulfate">Sulfates</a> (except <a href="/wiki/Silver" title="Silver">Ag+</a>, <a href="/wiki/Lead" title="Lead">Pb2+</a>, <a href="/wiki/Barium" title="Barium">Ba2+</a>, <a href="/wiki/Strontium" title="Strontium">Sr2+</a> and <a href="/wiki/Calcium" title="Calcium">Ca2+</a>)</td> <td><a href="/wiki/Sulfide" title="Sulfide">Sulfides</a> (except <a href="/wiki/Alkali_metal" title="Alkali metal">Group I</a>, <a href="/wiki/Alkaline_earth_metal" title="Alkaline earth metal">Group II</a> and <a href="/wiki/Ammonium" title="Ammonium">NH4+</a> compounds) </td></tr></tbody></table> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(11)"><h2 id="Solubility_of_organic_compounds">Solubility of organic compounds</h2></div><section class="mf-section-11 collapsible-block" id="mf-section-11"> The principle outlined above under <a href="#Polarity">polarity</a>, that like dissolves like, is the usual guide to solubility with organic systems. For example, <a href="/wiki/Petroleum_jelly" title="Petroleum jelly">petroleum jelly</a> will dissolve in <a href="/wiki/Gasoline" title="Gasoline">gasoline</a> because both petroleum jelly and gasoline are non-polar hydrocarbons. It will not, on the other hand, dissolve in <a href="/wiki/Ethyl_alcohol" class="mw-redirect" title="Ethyl alcohol">ethyl alcohol</a> or water, since the polarity of these solvents is too high. Sugar will not dissolve in gasoline, since sugar is too polar in comparison with gasoline. A mixture of gasoline and sugar can therefore be separated by <a href="/wiki/Filtration" title="Filtration">filtration</a> or <a href="/wiki/Solvent_extraction" class="mw-redirect" title="Solvent extraction">extraction</a> with water. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(12)"><h2 id="Solid_solution">Solid solution</h2></div><section class="mf-section-12 collapsible-block" id="mf-section-12"> This term is often used in the field of <a href="/wiki/Metallurgy" title="Metallurgy">metallurgy</a> to refer to the extent that an <a href="/wiki/Alloy" title="Alloy">alloying</a> element will dissolve into the <a href="/wiki/Base_metal" title="Base metal">base metal</a> without forming a separate <a href="/wiki/Phase_(matter)" title="Phase (matter)">phase</a>. The <a href="/wiki/Solvus" class="mw-redirect" title="Solvus">solvus</a> or solubility line (or curve) is the line (or lines) on a <a href="/wiki/Phase_diagram" title="Phase diagram">phase diagram</a> that give the limits of solute addition. That is, the lines show the maximum amount of a component that can be added to another component and still be in <a href="/wiki/Solid_solution" title="Solid solution">solid solution</a>. In the solid's crystalline structure, the 'solute' element can either take the place of the matrix within the lattice (a substitutional position; for example, chromium in iron) or take a place in a space between the lattice points (an interstitial position; for example, carbon in iron). In microelectronic fabrication, solid solubility refers to the maximum concentration of impurities one can place into the substrate. In solid compounds (as opposed to elements), the solubility of a solute element can also depend on the phases separating out in equilibrium. For example, amount of Sn soluble in the ZnSb phase can depend significantly on whether the phases separating out in equilibrium are (Zn4Sb3+Sn(L)) or (ZnSnSb2+Sn(L)).<a href="#cite_note-25">[24]</a> Besides these, the ZnSb compound with Sn as a solute can separate out into other combinations of phases after the solubility limit is reached depending on the initial <a href="/wiki/Chemical_composition" title="Chemical composition">chemical composition</a> during synthesis. Each combination produces a different solubility of Sn in ZnSb. Hence solubility studies in compounds, concluded upon the first instance of observing secondary phases separating out might underestimate solubility.<a href="#cite_note-26">[25]</a> While the maximum number of phases separating out at once in equilibrium can be determined by the Gibb's <a href="/wiki/Phase_rule" title="Phase rule">phase rule</a>, for chemical compounds there is no limit on the number of such phase separating combinations itself. Hence, establishing the "maximum solubility" in solid compounds experimentally can be difficult, requiring equilibration of many samples. If the dominant <a href="/wiki/Crystallographic_defect" title="Crystallographic defect">crystallographic defect</a> (mostly interstitial or substitutional point defects) involved in the solid-solution can be chemically intuited beforehand, then using some simple thermodynamic guidelines can considerably reduce the number of samples required to establish maximum solubility.<a href="#cite_note-27">[26]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(13)"><h2 id="Incongruent_dissolution">Incongruent dissolution</h2></div><section class="mf-section-13 collapsible-block" id="mf-section-13"> Many substances dissolve congruently (i.e. the composition of the solid and the dissolved solute stoichiometrically match). However, some substances may dissolve <a href="/wiki/Incongruent_transition" title="Incongruent transition">incongruently</a>, whereby the composition of the solute in solution does not match that of the solid. This solubilization is accompanied by alteration of the "primary solid" and possibly formation of a secondary solid phase. However, in general, some primary solid also remains and a complex solubility equilibrium establishes. For example, dissolution of <a href="/wiki/Albite" title="Albite">albite</a> may result in formation of <a href="/wiki/Gibbsite" title="Gibbsite">gibbsite</a>.<a href="#cite_note-28">[27]</a> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1123817410">NaAlSi3O8(s) + H+ + 7H2O ⇌ Na+ + Al(OH)3(s) + 3H4SiO4.</dd></dl> In this case, the solubility of albite is expected to depend on the solid-to-solvent ratio. This kind of solubility is of great importance in geology, where it results in formation of <a href="/wiki/Metamorphic_rock" title="Metamorphic rock">metamorphic rocks</a>. In principle, both congruent and incongruent dissolution can lead to the formation of secondary solid phases in equilibrium. So, in the field of <a href="/wiki/Materials_Science" class="mw-redirect" title="Materials Science">Materials Science</a>, the solubility for both cases is described more generally on <a href="/wiki/Chemical_composition" title="Chemical composition">chemical composition</a> <a href="/wiki/Phase_diagram" title="Phase diagram">phase diagrams</a>. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(14)"><h2 id="Solubility_prediction">Solubility prediction</h2></div><section class="mf-section-14 collapsible-block" id="mf-section-14"> Solubility is a property of interest in many aspects of science, including but not limited to: environmental predictions, biochemistry, pharmacy, drug-design, agrochemical design, and protein ligand binding. Aqueous solubility is of fundamental interest owing to the vital biological and transportation functions played by water.<a href="#cite_note-Skyner_et_al-29">[28]</a><a href="#cite_note-Tomasi_et_al-30">[29]</a><a href="#cite_note-Cramer_et_al-31">[30]</a> In addition, to this clear scientific interest in water solubility and solvent effects; accurate predictions of solubility are important industrially. The ability to accurately predict a molecule's solubility represents potentially large financial savings in many chemical product development processes, such as pharmaceuticals.<a href="#cite_note-Abramov_et_al-32">[31]</a> In the pharmaceutical industry, solubility predictions form part of the early stage lead optimisation process of drug candidates. Solubility remains a concern all the way to formulation.<a href="#cite_note-Abramov_et_al-32">[31]</a> A number of methods have been applied to such predictions including <a href="/wiki/Quantitative_structure%E2%80%93activity_relationship" title="Quantitative structure–activity relationship">quantitative structure–activity relationships</a> (QSAR), quantitative structure–property relationships (QSPR) and <a href="/wiki/Data_mining" title="Data mining">data mining</a>. These models provide efficient predictions of solubility and represent the current standard. The draw back such models is that they can lack physical insight. A method founded in physical theory, capable of achieving similar levels of accuracy at an sensible cost, would be a powerful tool scientifically and industrially.<a href="#cite_note-McDonagh_et_al_book-33">[32]</a><a href="#cite_note-Palmer_et_al-34">[33]</a><a href="#cite_note-McDonagh_et_al-35">[34]</a><a href="#cite_note-Lusci_et_al-36">[35]</a> Methods founded in physical theory tend to use thermodynamic cycles, a concept from classical <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>. The two common thermodynamic cycles used involve either the calculation of the free energy of <a href="/wiki/Sublimation_(phase_transition)" title="Sublimation (phase transition)">sublimation</a> (solid to gas without going through a liquid state) and the free energy of solvating a gaseous molecule (gas to solution), or the <a href="/wiki/Enthalpy_of_fusion" title="Enthalpy of fusion">free energy of fusion</a> (solid to a molten phase) and the free energy of mixing (molten to solution). These two process are represented in the following diagrams. <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Sublimation_sol_cycle3.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Sublimation_sol_cycle3.png/220px-Sublimation_sol_cycle3.png" decoding="async" width="220" height="146" class="mw-file-element" data-file-width="4283" data-file-height="2846"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 146px;" data-mw-src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Sublimation_sol_cycle3.png/220px-Sublimation_sol_cycle3.png" data-width="220" data-height="146" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Sublimation_sol_cycle3.png/330px-Sublimation_sol_cycle3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Sublimation_sol_cycle3.png/440px-Sublimation_sol_cycle3.png 2x" data-class="mw-file-element"> </a><figcaption>Thermodynamic cycle for calculating solvation via sublimation</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Fusion_sol_cycle3.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Fusion_sol_cycle3.png/220px-Fusion_sol_cycle3.png" decoding="async" width="220" height="187" class="mw-file-element" data-file-width="4283" data-file-height="3647"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 187px;" data-mw-src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Fusion_sol_cycle3.png/220px-Fusion_sol_cycle3.png" data-width="220" data-height="187" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Fusion_sol_cycle3.png/330px-Fusion_sol_cycle3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Fusion_sol_cycle3.png/440px-Fusion_sol_cycle3.png 2x" data-class="mw-file-element"> </a><figcaption>Thermodynamic cycle for calculating solvation via fusion</figcaption></figure> These cycles have been used for attempts at first principles predictions (solving using the fundamental physical equations) using physically motivated <a href="/wiki/Solvent_models" class="mw-redirect" title="Solvent models">solvent models</a>,<a href="#cite_note-Palmer_et_al-34">[33]</a> to create parametric equations and QSPR models<a href="#cite_note-Ran-37">[36]</a><a href="#cite_note-McDonagh_et_al-35">[34]</a> and combinations of the two.<a href="#cite_note-McDonagh_et_al-35">[34]</a> The use of these cycles enables the calculation of the solvation free energy indirectly via either gas (in the sublimation cycle) or a melt (fusion cycle). This is helpful as calculating the free energy of solvation directly is extremely difficult. The free energy of solvation can be converted to a solubility value using various formulae, the most general case being shown below, where the numerator is the free energy of solvation, R is the <a href="/wiki/Gas_constant" title="Gas constant">gas constant</a> and T is the temperature in <a href="/wiki/Kelvin" title="Kelvin">kelvins</a>.<a href="#cite_note-Palmer_et_al-34">[33]</a> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log S(V_{m})={\frac {\Delta G_{\text{solvation}}}{-2.303RT}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>log</mi> <mo>⁡</mo> <mi>S</mi> <mo stretchy="false">(</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>solvation</mtext> </mrow> </msub> </mrow> <mrow> <mo>−</mo> <mn>2.303</mn> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log S(V_{m})={\frac {\Delta G_{\text{solvation}}}{-2.303RT}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/104784b133fbd42919aef44c215a1bc7a6db2d6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:24.137ex; height:5.509ex;" alt="{\displaystyle \log S(V_{m})={\frac {\Delta G_{\text{solvation}}}{-2.303RT}}}"></noscript><span class="lazy-image-placeholder" style="width: 24.137ex;height: 5.509ex;vertical-align: -2.005ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/104784b133fbd42919aef44c215a1bc7a6db2d6f" data-alt="{\displaystyle \log S(V_{m})={\frac {\Delta G_{\text{solvation}}}{-2.303RT}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> Well known fitted equations for solubility prediction are the general solubility equations. These equations stem from the work of Yalkowsky et al.<a href="#cite_note-38">[37]</a><a href="#cite_note-JY_GSE-39">[38]</a> The original formula is given first, followed by a revised formula which takes a different assumption of complete miscibility in octanol.<a href="#cite_note-JY_GSE-39">[38]</a> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log _{10}(S)=0.8-\log _{10}(P)-0.01({\text{melting point}}-25)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.8</mn> <mo>−</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>P</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mn>0.01</mn> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>melting point</mtext> </mrow> <mo>−</mo> <mn>25</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log _{10}(S)=0.8-\log _{10}(P)-0.01({\text{melting point}}-25)}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2c469d9e9bc8a3321370ac550be32147bf1e5a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:52.92ex; height:2.843ex;" alt="{\displaystyle \log _{10}(S)=0.8-\log _{10}(P)-0.01({\text{melting point}}-25)}"></noscript><span class="lazy-image-placeholder" style="width: 52.92ex;height: 2.843ex;vertical-align: -0.838ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2c469d9e9bc8a3321370ac550be32147bf1e5a9" data-alt="{\displaystyle \log _{10}(S)=0.8-\log _{10}(P)-0.01({\text{melting point}}-25)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log _{10}(S)=0.5-\log _{10}(P)-0.01({\text{melting point}}-25)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.5</mn> <mo>−</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>P</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mn>0.01</mn> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>melting point</mtext> </mrow> <mo>−</mo> <mn>25</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log _{10}(S)=0.5-\log _{10}(P)-0.01({\text{melting point}}-25)}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44d026d80af2d02367296cd06a6364b26a2e2d3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:52.92ex; height:2.843ex;" alt="{\displaystyle \log _{10}(S)=0.5-\log _{10}(P)-0.01({\text{melting point}}-25)}"></noscript><span class="lazy-image-placeholder" style="width: 52.92ex;height: 2.843ex;vertical-align: -0.838ex;" data-mw-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44d026d80af2d02367296cd06a6364b26a2e2d3a" data-alt="{\displaystyle \log _{10}(S)=0.5-\log _{10}(P)-0.01({\text{melting point}}-25)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> These equations are founded on the principles of the fusion cycle. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(15)"><h2 id="See_also">See also</h2></div><section class="mf-section-15 collapsible-block" id="mf-section-15"> <ul><li><a href="/wiki/Apparent_molar_property" title="Apparent molar property">Apparent molar property</a> – Difference in properties of one mole of substance in a mixture vs. an ideal solution</li> <li><a href="/wiki/Biopharmaceutics_Classification_System" title="Biopharmaceutics Classification System">Biopharmaceutics Classification System</a> – System to differentiate drugs on the basis of their solubility and permeability</li> <li><a href="/wiki/D%C3%BChring%27s_rule" title="Dühring's rule">Dühring's rule</a> – Linear relationship between the temperatures at which two solutions exert the same vapour pressure</li> <li><a href="/wiki/Fajans%E2%80%93Paneth%E2%80%93Hahn_Law" title="Fajans–Paneth–Hahn Law">Fajans–Paneth–Hahn Law</a> – chemistry rule concerning co-precipitation and adsorptionPages displaying wikidata descriptions as a fallback</li> <li><a href="/wiki/Flexible_SPC_water_model" class="mw-redirect" title="Flexible SPC water model">Flexible SPC water model</a> – Aspect of computational chemistryPages displaying short descriptions of redirect targets</li> <li><a href="/wiki/Henry%27s_law" title="Henry's law">Henry's law</a> – Gas law regarding proportionality of dissolved gas</li> <li><a href="/wiki/Hot_water_extraction" title="Hot water extraction">Hot water extraction</a> – method of carpet cleaningPages displaying wikidata descriptions as a fallback</li> <li><a href="/wiki/Hydrotrope" title="Hydrotrope">Hydrotrope</a> – chemical substancePages displaying wikidata descriptions as a fallback</li> <li><a href="/wiki/Micellar_solubilization" title="Micellar solubilization">Micellar solubilization</a> – Process of incorporating the solubilizate into or onto micelles</li> <li><a href="/wiki/Raoult%27s_law" title="Raoult's law">Raoult's law</a> – Law of thermodynamics for vapour pressure of a mixture</li> <li><a href="/wiki/Rate_of_solution" class="mw-redirect" title="Rate of solution">Rate of solution</a> – Capacity of a substance to dissolve in a homogeneous wayPages displaying short descriptions of redirect targets</li> <li><a href="/wiki/Solubility_equilibrium" title="Solubility equilibrium">Solubility equilibrium</a> – Thermodynamic equilibrium between a solid and a solution of the same compound</li> <li><a href="/wiki/Van_%27t_Hoff_equation" title="Van 't Hoff equation">Van 't Hoff equation</a> – Relation between temperature and the equilibrium constant of a chemical reaction</li></ul> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(16)"><h2 id="Notes">Notes</h2></div><section class="mf-section-16 collapsible-block" id="mf-section-16"> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-20"><a href="#cite_ref-20">^</a> The solvent polarity is defined as its solvation power according to Reichardt. </li> </ol></div></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(17)"><h2 id="References">References</h2></div><section class="mf-section-17 collapsible-block" id="mf-section-17"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-iupac-1">^ <a href="#cite_ref-iupac_1-0">a</a> <a href="#cite_ref-iupac_1-1">b</a> <a href="/wiki/International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <a href="/wiki/IUPAC_books#Gold_Book" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a>, 2nd ed. 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Journal of Chemical Theory and Computation. 8 (9): 3322–3337. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fct300345m">10.1021/ct300345m</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10023%2F25470">10023/25470</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26605739">26605739</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:26334468">26334468</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Chemical+Theory+and+Computation&rft.atitle=First-Principles+Calculation+of+the+Intrinsic+Aqueous+Solubility+of+Crystalline+Druglike+Molecules&rft.volume=8&rft.issue=9&rft.pages=%3Cspan+class%3D%22nowrap%22%3E3322-%3C%2Fspan%3E3337&rft.date=2012&rft_id=info%3Ahdl%2F10023%2F25470&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A26334468%23id-name%3DS2CID&rft_id=info%3Apmid%2F26605739&rft_id=info%3Adoi%2F10.1021%2Fct300345m&rft.aulast=Palmer&rft.aufirst=D.+S.&rft.au=McDonagh%2C+J.+L.&rft.au=Mitchell%2C+J.+B.+O.&rft.au=van+Mourik%2C+T.&rft.au=Fedorov%2C+M.+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASolubility" class="Z3988"> </li> <li id="cite_note-McDonagh_et_al-35">^ <a href="#cite_ref-McDonagh_et_al_35-0">a</a> <a href="#cite_ref-McDonagh_et_al_35-1">b</a> <a href="#cite_ref-McDonagh_et_al_35-2">c</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcDonaghNath,_N.De_Ferrari,_L.van_Mourik,_T.2014" class="citation journal cs1">McDonagh, J. 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</a> <div class="post-content footer-content"> <div id='mw-data-after-content'> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>Languages</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Oplosbaarheid" title="Oplosbaarheid – Afrikaans" lang="af" hreflang="af" data-title="Oplosbaarheid" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%86%D8%AD%D9%84%D8%A7%D9%84%D9%8A%D8%A9" title="انحلالية – Arabic" lang="ar" hreflang="ar" data-title="انحلالية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Solubilid%C3%A1" title="Solubilidá – Asturian" lang="ast" hreflang="ast" data-title="Solubilidá" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A6%E0%A7%8D%E0%A6%B0%E0%A6%BE%E0%A6%AC%E0%A7%8D%E0%A6%AF%E0%A6%A4%E0%A6%BE" title="দ্রাব্যতা – Bangla" lang="bn" hreflang="bn" data-title="দ্রাব্যতা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B7%D1%82%D0%B2%D0%BE%D1%80%D0%B8%D0%BC%D0%BE%D1%81%D1%82" title="Разтворимост – Bulgarian" lang="bg" hreflang="bg" data-title="Разтворимост" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Rastvorljivost" title="Rastvorljivost – Bosnian" lang="bs" hreflang="bs" data-title="Rastvorljivost" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Solubilitat" title="Solubilitat – Catalan" lang="ca" hreflang="ca" data-title="Solubilitat" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%98%D1%80%C4%95%D0%BB%D0%B5%D1%81%D0%BB%C4%95%D1%85" title="Ирĕлеслĕх – Chuvash" lang="cv" hreflang="cv" data-title="Ирĕлеслĕх" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Rozpustnost" title="Rozpustnost – Czech" lang="cs" hreflang="cs" data-title="Rozpustnost" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Hydoddedd" title="Hydoddedd – Welsh" lang="cy" hreflang="cy" data-title="Hydoddedd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Opl%C3%B8selighed" title="Opløselighed – Danish" lang="da" hreflang="da" data-title="Opløselighed" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/L%C3%B6slichkeit" title="Löslichkeit – German" lang="de" hreflang="de" data-title="Löslichkeit" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Lahustuvus" title="Lahustuvus – Estonian" lang="et" hreflang="et" data-title="Lahustuvus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%B1%CE%BB%CF%85%CF%84%CF%8C%CF%84%CE%B7%CF%84%CE%B1" title="Διαλυτότητα – Greek" lang="el" hreflang="el" data-title="Διαλυτότητα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Solubilidad" title="Solubilidad – Spanish" lang="es" hreflang="es" data-title="Solubilidad" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Solvebleco" title="Solvebleco – Esperanto" lang="eo" hreflang="eo" data-title="Solvebleco" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Disolbagarritasun" title="Disolbagarritasun – Basque" lang="eu" hreflang="eu" data-title="Disolbagarritasun" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%86%D8%AD%D9%84%D8%A7%D9%84%E2%80%8C%D9%BE%D8%B0%DB%8C%D8%B1%DB%8C" title="انحلال‌پذیری – Persian" lang="fa" hreflang="fa" data-title="انحلال‌پذیری" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Solubilit%C3%A9" title="Solubilité – French" lang="fr" hreflang="fr" data-title="Solubilité" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Intuaslagthacht" title="Intuaslagthacht – Irish" lang="ga" hreflang="ga" data-title="Intuaslagthacht" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Solubilidade" title="Solubilidade – Galician" lang="gl" hreflang="gl" data-title="Solubilidade" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9A%A9%ED%95%B4%EB%8F%84" title="용해도 – Korean" lang="ko" hreflang="ko" data-title="용해도" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BC%D5%B8%D6%82%D5%AE%D5%A5%D5%AC%D5%AB%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Լուծելիություն – Armenian" lang="hy" hreflang="hy" data-title="Լուծելիություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%B2%E0%A5%87%E0%A4%AF%E0%A4%A4%E0%A4%BE" title="विलेयता – Hindi" lang="hi" hreflang="hi" data-title="विलेयता" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Topljivost" title="Topljivost – Croatian" lang="hr" hreflang="hr" data-title="Topljivost" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kelarutan" title="Kelarutan – Indonesian" lang="id" hreflang="id" data-title="Kelarutan" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Solubilit%C3%A0" title="Solubilità – Italian" lang="it" hreflang="it" data-title="Solubilità" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%99%D7%A1%D7%95%D7%AA" title="מסיסות – Hebrew" lang="he" hreflang="he" data-title="מסיסות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%95%D1%80%D1%96%D0%B3%D1%96%D1%88%D1%82%D1%96%D0%BA" title="Ерігіштік – Kazakh" lang="kk" hreflang="kk" data-title="Ерігіштік" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Solibilite" title="Solibilite – Haitian Creole" lang="ht" hreflang="ht" data-title="Solibilite" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Tirpumas" title="Tirpumas – Lithuanian" lang="lt" hreflang="lt" data-title="Tirpumas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Oldhat%C3%B3s%C3%A1g" title="Oldhatóság – Hungarian" lang="hu" hreflang="hu" data-title="Oldhatóság" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A0%D0%B0%D1%81%D1%82%D0%B2%D0%BE%D1%80%D0%BB%D0%B8%D0%B2%D0%BE%D1%81%D1%82" title="Растворливост – Macedonian" lang="mk" hreflang="mk" data-title="Растворливост" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B2%E0%B5%87%E0%B4%AF%E0%B4%A4%E0%B5%8D%E0%B4%B5%E0%B4%82" title="ലേയത്വം – Malayalam" lang="ml" hreflang="ml" data-title="ലേയത്വം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Keterlarutan" title="Keterlarutan – Malay" lang="ms" hreflang="ms" data-title="Keterlarutan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A3%D1%83%D1%81%D0%B0%D0%BB%D1%82" title="Уусалт – Mongolian" lang="mn" hreflang="mn" data-title="Уусалт" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target">Монгол</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Oplosbaarheid" title="Oplosbaarheid – Dutch" lang="nl" hreflang="nl" data-title="Oplosbaarheid" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%BA%B6%E8%A7%A3%E5%BA%A6" title="溶解度 – Japanese" lang="ja" hreflang="ja" data-title="溶解度" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/L%C3%B8selighet" title="Løselighet – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Løselighet" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/L%C3%B8ysingsevne" title="Løysingsevne – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Løysingsevne" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%98%E0%A9%81%E0%A8%B2%E0%A8%A3%E0%A8%B8%E0%A8%BC%E0%A9%80%E0%A8%B2%E0%A8%A4%E0%A8%BE" title="ਘੁਲਣਸ਼ੀਲਤਾ – Punjabi" lang="pa" hreflang="pa" data-title="ਘੁਲਣਸ਼ੀਲਤਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%85%D9%86%D8%AD%D9%84_%DA%A9%DB%90%D8%AF%D9%84" title="منحل کېدل – Pashto" lang="ps" hreflang="ps" data-title="منحل کېدل" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rozpuszczalno%C5%9B%C4%87" title="Rozpuszczalność – Polish" lang="pl" hreflang="pl" data-title="Rozpuszczalność" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Solubilidade" title="Solubilidade – Portuguese" lang="pt" hreflang="pt" data-title="Solubilidade" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Solubilitate" title="Solubilitate – Romanian" lang="ro" hreflang="ro" data-title="Solubilitate" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D1%81%D1%82%D0%B2%D0%BE%D1%80%D0%B8%D0%BC%D0%BE%D1%81%D1%82%D1%8C" title="Растворимость – Russian" lang="ru" hreflang="ru" data-title="Растворимость" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Solubility" title="Solubility – Scots" lang="sco" hreflang="sco" data-title="Solubility" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Tretshm%C3%ABria" title="Tretshmëria – Albanian" lang="sq" hreflang="sq" data-title="Tretshmëria" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Solubility" title="Solubility – Simple English" lang="en-simple" hreflang="en-simple" data-title="Solubility" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Rozpustnos%C5%A5" title="Rozpustnosť – Slovak" lang="sk" hreflang="sk" data-title="Rozpustnosť" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Topnost" title="Topnost – Slovenian" lang="sl" hreflang="sl" data-title="Topnost" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%D9%88%D8%A7%D9%86%DB%95%D9%88%DB%95%DB%8C%DB%95%D8%AA%DB%8C" title="توانەوەیەتی – Central Kurdish" lang="ckb" hreflang="ckb" data-title="توانەوەیەتی" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A0%D0%B0%D1%81%D1%82%D0%B2%D0%BE%D1%80%D1%99%D0%B8%D0%B2%D0%BE%D1%81%D1%82" title="Растворљивост – Serbian" lang="sr" hreflang="sr" data-title="Растворљивост" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Topljivost" title="Topljivost – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Topljivost" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Liukoisuus" title="Liukoisuus – Finnish" lang="fi" hreflang="fi" data-title="Liukoisuus" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/L%C3%B6slighet" title="Löslighet – Swedish" lang="sv" hreflang="sv" data-title="Löslighet" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Solubilidad" title="Solubilidad – Tagalog" lang="tl" hreflang="tl" data-title="Solubilidad" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%B0%E0%AF%88%E0%AE%A4%E0%AE%BF%E0%AE%B1%E0%AE%A9%E0%AF%8D" title="கரைதிறன் – Tamil" lang="ta" hreflang="ta" data-title="கரைதிறன்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%A5%E0%B8%B0%E0%B8%A5%E0%B8%B2%E0%B8%A2" title="การละลาย – Thai" lang="th" hreflang="th" data-title="การละลาย" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%87%C3%B6z%C3%BCn%C3%BCrl%C3%BCk_(kimya)" title="Çözünürlük (kimya) – Turkish" lang="tr" hreflang="tr" data-title="Çözünürlük (kimya)" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%BE%D0%B7%D1%87%D0%B8%D0%BD%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Розчинність – Ukrainian" lang="uk" hreflang="uk" data-title="Розчинність" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AD%D9%84_%D9%BE%D8%B0%DB%8C%D8%B1%DB%8C" title="حل پذیری – Urdu" lang="ur" hreflang="ur" data-title="حل پذیری" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%99_h%C3%B2a_tan" title="Độ hòa tan – Vietnamese" lang="vi" hreflang="vi" data-title="Độ hòa tan" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%BA%B6%E8%A7%A3%E5%BA%A6" title="溶解度 – Wu" lang="wuu" hreflang="wuu" data-title="溶解度" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%BA%B6%E8%A7%A3%E5%BA%A6" title="溶解度 – Cantonese" lang="yue" hreflang="yue" data-title="溶解度" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%BA%B6%E8%A7%A3%E5%BA%A6" title="溶解度 – Chinese" lang="zh" hreflang="zh" data-title="溶解度" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li></ul> </section> </div> <div class="minerva-footer-logo"><img src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" alt="Wikipedia" width="120" height="18" style="width: 7.5em; height: 1.125em;"/> </div> <ul id="footer-info" class="footer-info hlist hlist-separated"> <li id="footer-info-lastmod"> This page was last edited on 15 January 2025, at 23:19 (UTC).</li> <li id="footer-info-copyright">Content is available under <a class="external" rel="nofollow" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">CC BY-SA 4.0</a> unless otherwise noted.</li> </ul> <ul id="footer-places" class="footer-places hlist hlist-separated"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li 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