Editing Solubility (section)

==Factors affecting solubility==
Solubility is defined for specific [[phase (matter)|phases]]. For example, the solubility of [[aragonite]] and [[calcite]] in water are expected to differ, even though they are both [[Polymorphism (materials science)|polymorphs]] of [[calcium carbonate]] and have the same [[chemical formula]].{{clarify|are the solutions different in any way? if not, how can the solubility differ?|date=September 2023}}

The solubility of one substance in another is determined by the balance of [[intermolecular force]]s between the solvent and solute, and the [[entropy]] 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, [[complex (chemistry)|complex-]]forming anions ([[ligand]]s) in liquids. Solubility will also depend on the excess or deficiency of a common ion in the solution{{clarify|what is a common ion?|date=September 2023}}, a phenomenon known as the [[common-ion effect]]. To a lesser extent, solubility will depend on the [[ionic strength]] of solutions. The last two effects can be quantified using the equation for [[solubility equilibrium]].

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 Fe<sub>3</sub>O<sub>4</sub>-Fe<sub>2</sub>O<sub>3</sub> [[redox buffer]] than with a moderately oxidizing [[Nickel|Ni]]-[[Nickel(II) oxide|NiO]] buffer.<ref>{{cite book|author=I.Y. Nekrasov| title=Geochemistry, Mineralogy and Genesis of Gold Deposits|publisher=Taylor & Francis| year= 1996|pages=135–136 |url=https://books.google.com/books?id=HUWRZecignoC&pg=PA135|isbn=978-90-5410-723-1}}</ref>
[[File:SolubilityVsTemperature.svg|border|right|400x400px]]
Solubility (metastable, at concentrations approaching saturation) also depends on the physical size of the crystal or droplet of solute (or, strictly speaking, on the [[specific surface area]] or molar surface area of the solute).<ref name=hefter>{{cite book|editor-last1=Hefter|editor-first1=G. T. |editor-last2=Tomkins|editor-first2=R. P. T.|title=The Experimental Determination of Solubilities |year=2003|publisher=Wiley-Blackwell |isbn= 978-0-471-49708-0}}</ref> For quantification, see the equation in the article on [[Solubility equilibrium#Particle size effect|solubility equilibrium]]. 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.{{Citation needed|date=July 2008}} For example, they provide the driving force for [[Ostwald ripening|precipitate aging]] (the crystal size spontaneously increasing with time).

===Temperature===
The solubility of a given solute in a given solvent is function of temperature. Depending on the change in [[enthalpy]] (Δ''H'') of the dissolution reaction, ''i.e.'', on the [[Endothermic process|endothermic]] (Δ''H''&nbsp;>&nbsp;0) or [[Exothermic process|exothermic]] (Δ''H''&nbsp;<&nbsp;0) character of the dissolution reaction, the solubility of a given compound may increase or decrease with temperature.  The [[van 't Hoff equation]] relates the change of solubility [[equilibrium constant]] (''K''<sub>sp</sub>) to temperature change and to reaction [[enthalpy]] change. 

*For most [[solid]]s and liquids, their solubility increases with temperature because their dissolution reaction is endothermic (Δ''H''&nbsp;>&nbsp;0).<ref name = hill>John W. Hill, Ralph H. Petrucci, ''General Chemistry'', 2nd edition, Prentice Hall, 1999.</ref> In liquid water at high temperatures, (e.g. that approaching the [[critical temperature]]), the solubility of ionic solutes tends to decrease due to the change of properties and structure of liquid water; the lower [[dielectric constant]] results in a less [[polar solvent]] and in a change of hydration energy affecting the Δ''G'' of the dissolution reaction.

*[[Gas]]eous 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&nbsp;°C for most permanent gases<ref>{{cite book|editor=P. Cohen|title=The ASME Handbook on Water Technology for Thermal Power Systems|publisher=The American Society of Mechanical Engineers|year=1989| page =442}}</ref>), but more soluble in organic solvents (endothermic dissolution reaction related to their solvation).<ref name=hill/>

The chart shows solubility curves for some typical solid inorganic [[salt (chemistry)|salts]] in liquid water (temperature is in degrees [[Celsius]], i.e. [[kelvin]]s minus 273.15).<ref>{{cite book|title=Handbook of Chemistry and Physics| edition= 27th|location= Cleveland, Ohio|year=1943 |publisher= Chemical Rubber Publishing Co.}}</ref> Many salts behave like [[barium nitrate]] and [[disodium hydrogen arsenate]], and show a large increase in solubility with temperature (Δ''H''&nbsp;>&nbsp;0). Some solutes (e.g. [[sodium chloride]] in water) exhibit solubility that is fairly independent of temperature (Δ''H''&nbsp;≈&nbsp;0). A few, such as [[calcium sulfate]] ([[gypsum]]) and [[cerium(III) sulfate]], become less soluble in water as temperature increases (Δ''H''&nbsp;<&nbsp;0).<ref name="Scientific American">{{cite web|title=What substances, such as cerium sulfate, have a lower solubility when they are heated?|website=[[Scientific American]] |url=http://www.scientificamerican.com/article/what-substances-such-as-c/|access-date=28 May 2014}}</ref> This is also the case for [[calcium hydroxide]] ([[portlandite]]), whose solubility at 70&nbsp;°C is about half of its value at 25&nbsp;°C. The dissolution of calcium hydroxide in water is also an exothermic process (Δ''H''&nbsp;<&nbsp;0). As dictated by the [[van 't Hoff equation]] and [[Le Chatelier's principle]], low temperatures favor dissolution of Ca(OH)<sub>2</sub>. Portlandite solubility increases at low temperature. This temperature dependence is sometimes referred to as "retrograde" or "inverse" solubility.{{cn|date=June 2024}} Occasionally, a more complex pattern is observed, as with [[sodium sulfate]], where the less soluble deca[[hydrate]] crystal ([[mirabilite]]) loses [[water of crystallization]] at 32&nbsp;°C to form a more soluble [[anhydrous]] phase ([[thenardite]]) with a smaller change in [[Gibbs free energy]] (Δ''G'') in the dissolution reaction.{{Citation needed|date=July 2008}}

[[File:Temperature dependence solublity of solid in liquid water high temperature.svg|right|400px]]

The solubility of [[organic compounds]] nearly always increases with temperature. The technique of [[Recrystallization (chemistry)|recrystallization]], used for purification of solids, depends on a solute's different solubilities in hot and cold solvent. A few exceptions exist, such as certain [[cyclodextrin]]s.<ref>{{cite journal|title=A highly water-soluble 2+1 b-cyclodextrin–fullerene conjugate|author=Salvatore Filippone, Frank Heimanna and André Rassat|journal=[[Chem. Commun.]]|volume=2002|pages=1508–1509|doi=10.1039/b202410a|year=2002|issue=14|pmid=12189867}}</ref>

===Pressure===
For condensed phases (solids and liquids), the pressure dependence of solubility is typically weak and usually neglected in practice. Assuming an [[ideal solution]], the dependence can be quantified as:

:<math> \left(\frac{\partial \ln N_i}{\partial P} \right)_T = -\frac{V_{i,aq}-V_{i,cr}} {RT} </math>

where the index <math>i</math> iterates the components, <math>N_i</math> is the mole fraction of the <math>i</math>-th component in the solution, <math>P</math> is the pressure, the index <math>T</math> refers to constant temperature, <math>V_{i,aq}</math> is the [[partial molar volume]] of the <math>i</math>-th component in the solution, <math>V_{i,cr}</math> is the partial molar volume of the <matH>i</math>-th component in the dissolving solid, and <math>R</math> is the [[universal gas constant]].<ref>{{cite book|author=E.M. Gutman| title=Mechanochemistry of Solid Surfaces|publisher= World Scientific Publishing Co.|year=1994}}</ref>

The pressure dependence of solubility does occasionally have practical significance. For example, [[Fouling#Precipitation fouling|precipitation fouling]] of oil fields and wells by [[calcium sulfate]] (which decreases its solubility with decreasing pressure) can result in decreased productivity with time.