solubility

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In
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties ...
, solubility is the ability of a
substance Substance may refer to: * Matter, anything that has mass and takes up space Chemistry * Chemical substance, a material with a definite chemical composition * Drug substance ** Substance abuse, drug-related healthcare and social policy diagnosis o ...
, the solute, to form a solution with another substance, the
solvent A solvent (s) (from the Latin language, Latin ''wikt:solvo#Latin, solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a Solution (chemistry), solution. A solvent is usually a liquid but can also be a solid, a ...
. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubility of a substance in a specific solvent is generally measured as the
concentration In chemistry, concentration is the Abundance (chemistry), abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: ''mass concentration (chemistry), mass concentration'', ...
of the solute in a saturated solution, one in which no more solute can be dissolved. At this point, the two substances are said to be at the solubility equilibrium. For some solutes and solvents, there may be no such limit, in which case the two substances are said to be "
miscible Miscibility () is the property of two chemical substance, substances to mix in all mixing ratio, proportions (that is, to fully dissolution (chemistry), dissolve in each other at any concentration), forming a homogeneity and heterogeneity, homoge ...
in all proportions" (or just "miscible"). The solute can be a
solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
, a
liquid A liquid is a nearly Compressibility, incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of State of matter#Four fundamental states, the four fund ...
, or a gas, 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,J. de Swaan Arons and G. A. M. Diepen (1966): "Gas—Gas Equilibria". ''Journal of Chemical Physics'', volume 44, issue 6, page 2322. 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 pH 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 (
atom Every atom is composed of a atomic nucleus, nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, l ...
s,
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
s, or ions) of the two substances, and of
thermodynamic Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
concepts such as
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant p ...
and
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
. Under certain conditions, the concentration of the solute can exceed its usual solubility limit. The result is a supersaturated solution, which is metastable and will rapidly exclude the excess solute if a suitable nucleation site appears. The concept of solubility does not apply when there is an irreversible
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
between the two substances, such as the reaction of
calcium hydroxide Calcium hydroxide (traditionally called slaked lime) is an inorganic compound with the chemical formula calcium, Ca(Hydroxide, OH)2. It is a colorless crystal or white powder and is produced when quicklime (calcium oxide) is mixed or slaking (ge ...
with
hydrochloric acid Hydrochloric acid, also known as muriatic acid, is an aqueous solution of hydrogen chloride. It is a colorless solution with a distinctive pungency, pungent smell. It is classified as a acid strength, strong acid. It is a component of the gas ...
; even though one might say, informally, that one "dissolved" the other. The solubility is also not the same as the rate of solution, 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
geology Geology () is a branch of natural science concerned with Earth and other Astronomical object, astronomical objects, the features or rock (geology), rocks of which it is composed, and the processes by which they change over time. Modern geology ...
,
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of Cell (biology), cells that proce ...
,
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...
, and oceanography, as well as in
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...
,
medicine Medicine is the science and Praxis (process), practice of caring for a patient, managing the diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliation of their injury or disease, and Health promotion ...
,
agriculture Agriculture or farming is the practice of cultivating Plant, plants and livestock. Agriculture was the key development in the rise of Sedentism, sedentary human civilization, whereby farming of Domestication, domesticated species created food ...
, and even in non-technical activities like
painting Painting is the practice of applying paint, pigment, color or other medium to a solid surface (called the "matrix" or "support"). The medium is commonly applied to the base with a brush, but other implements, such as knives, sponges, and ai ...
, cleaning, cooking, and
brewing Brewing is the production of beer by steeping a starch source (commonly cereal grains, the most popular of which is barley) in water and #Fermenting, fermenting the resulting sweet liquid with Yeast#Beer, yeast. It may be done in a brewery ...
. Most chemical reactions of scientific, industrial, or practical interest only happen after the reagents have been dissolved in a suitable solvent.
Water Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...
is by far the most common such solvent. The term "soluble" is sometimes used for materials that can form colloidal suspensions of very fine solid particles in a liquid.Claudius Kormann, Detlef W. Bahnemann, and Michael R. Hoffmann (1988): "Preparation and characterization of quantum-size titanium dioxide". ''Journal of Physical Chemistry'',volume 92, issue 18, pages 5196–5201. The quantitative solubility of such substances is generally not well-defined, however.

# Quantification of solubility

The solubility of a specific solute in a specific solvent is generally expressed as the concentration of a saturated solution of the two. Any of the several ways of expressing concentration of solutions can be used, such as the
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
,
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
, or amount in moles of the solute for a specific mass, volume, or mole amount of the solvent or of the solution.

## Per quantity of solvent

In particular, chemical handbooks will often express the solubility of a substance in a liquid as
gram The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume Volume is a measure ...
s of solute per decilitre (100 mL) of solvent (g/dL); or, less commonly, as grams per litre (g/L). The quantity of solvent can instead be expressed in mass, as in g/100g" or 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".Abler (2021):
W/W (Weight/Weight)
. Online page a
Abler.com website
Accessed on 2021-11-26.
(The values in g/L and g/kg are practically the same for water, but not for other solvents.) Alternatively, the quantity of solute can be expressed in moles instead of mass; if the quantity of solvent is given in kilograms, the value is the molality of the solution (mol/kg).

## Per quantity of solution

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 titration, it may be expressed as moles of solute per litre of solution (mol/L), the molarity of the latter. In more specialized contexts the solubility may be given by the mole fraction (moles of solute per total moles of solute plus solvent) or by the mass fraction at equilibrium (mass of solute per mass of solute plus solvent), both adimensional numbers between 0 and 1 which may be expressed as percentages.

## Liquid and gaseous solutes

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.

## Conversion of solubility values

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.I. Lee and J. Lee (2012): "Measurement of mixing ratio and volume change of ethanol-water binary mixtures using suspended microchannel resonators." ''SENSORS'', volume 2012, pages 1-3. . Moreover, many solids (such as
acid An acid is a molecule or ion capable of either donating a proton (i.e. hydrogen ion, H+), known as a Brønsted–Lowry acid, or forming a covalent bond with an electron pair, known as a Lewis acid A Lewis acid (named for the American p ...
s and salts) will dissociate in non-trivial ways when dissolved; conversely, the solvent may form coordination complexes 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.

# Qualifiers used to describe extent of solubility

The extent of solubility ranges widely, from infinitely soluble (without limit, i. e.
miscible Miscibility () is the property of two chemical substance, substances to mix in all mixing ratio, proportions (that is, to fully dissolution (chemistry), dissolve in each other at any concentration), forming a homogeneity and heterogeneity, homoge ...
) such as
ethanol Ethanol (abbr. EtOH; also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound. It is an Alcohol (chemistry), alcohol with the chemical formula . Its formula can be also written as or (an ethyl ...
in water, to essentially insoluble, such as
titanium dioxide Titanium dioxide, also known as titanium(IV) oxide or titania , is the inorganic compound with the chemical formula . When used as a pigment, it is called titanium white, Pigment White 6 (PW6), or Colour Index International, CI 77891. It is a w ...
in water. A number of other descriptive terms are also used to qualify the extent of solubility for a given application. For example, U.S. Pharmacopoeia gives the following terms, according to the mass ''m''sv of solvent required to dissolve one unit of mass ''m''su of solute: (The solubilities of the examples are approximate, for water at 20-25 °C.) 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.

# Molecular view

Solubility occurs under dynamic equilibrium, which means that solubility results from the simultaneous and opposing processes of dissolution and phase joining (e.g.
precipitation In meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls under gravitational pull from clouds. The main forms of precipitation include drizzle, rain, Rain and snow mixed, sleet, snow, ice pellets, ...
of solids). The solubility equilibrium occurs when the two processes proceed at equal and opposite rates. The term ''solubility'' is also used in some fields where the solute is altered by solvolysis. For example, many metals and their
oxide An oxide () is a chemical compound that contains at least one oxygen atom and one other chemical element, element in its chemical formula. "Oxide" itself is the dianion of oxygen, an O2– (molecular) ion. with oxygen in the oxidation state of ...
s are said to be "soluble in hydrochloric acid", although in fact the aqueous acid irreversibly degrades the solid to give soluble products. It is also true that most ionic solids are dissolved by polar solvents, but such processes are reversible. 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 aqueous suspension of ferrous hydroxide, , will contain the series as well as other species. Furthermore, the solubility of ferrous hydroxide and the composition of its soluble components depend on pH. In general, solubility in the solvent phase can be given only for a specific solute that is thermodynamically stable, and the value of the solubility will include all the species in the solution (in the example above, all the iron-containing complexes).

# Factors affecting solubility

Solubility is defined for specific phases. For example, the solubility of aragonite and
calcite Calcite is a Carbonate minerals, carbonate mineral and the most stable Polymorphism (materials science), polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on ...
in water are expected to differ, even though they are both polymorphs of
calcium carbonate Calcium carbonate is a chemical compound with the Chemical formula, formula . It is a common substance found in Rock (geology), rocks as the minerals calcite and aragonite (most notably as limestone, which is a type of sedimentary rock consisti ...
and have the same
chemical formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
. The solubility of one substance in another is determined by the balance of
intermolecular force An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the Electromagnetism, electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring ...
s between the solvent and solute, and the
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
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-forming anions ( ligands) in liquids. Solubility will also depend on the excess or deficiency of a common ion in the solution, 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 Fe3O4-Fe2O3 redox buffer than with a moderately oxidizing Ni-NiO buffer. 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). For quantification, see the equation in the article on 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. For example, they provide the driving force for 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 Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant p ...
(Δ''H'') of the dissolution reaction, ''i.e.'', on the endothermic (Δ''H'' > 0) or
exothermic In thermodynamics, an exothermic process () is a thermodynamic process or Chemical reaction, reaction that releases energy from the system to its Environment (systems), surroundings, usually in the form of heat, but also in a form of light (e.g. ...
(Δ''H'' < 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''sp) to temperature change and to reaction
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant p ...
change. For most solids and liquids, their solubility increases with temperature because their dissolution reaction is endothermic (Δ''H'' > 0).John W. Hill, Ralph H. Petrucci, ''General Chemistry'', 2nd edition, Prentice Hall, 1999. 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. Gaseous 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), but more soluble in organic solvents (endothermic dissolution reaction related to their solvation). The chart shows solubility curves for some typical solid inorganic salts in liquid water (temperature is in degrees Celsius, i.e. kelvins minus 273.15). Many salts behave like barium nitrate and disodium hydrogen arsenate, and show a large increase in solubility with temperature (Δ''H'' > 0). Some solutes (e.g.
sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salt (chemistry), salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of ...
in water) exhibit solubility that is fairly independent of temperature (Δ''H'' ≈ 0). A few, such as calcium sulfate (
gypsum Gypsum is a soft sulfate mineral composed of calcium sulfate Hydrate, dihydrate, with the chemical formula . It is widely mined and is used as a fertilizer and as the main constituent in many forms of plaster, blackboard or sidewalk chalk, and ...
) and cerium(III) sulfate, become less soluble in water as temperature increases (Δ''H'' < 0). This is also the case for
calcium hydroxide Calcium hydroxide (traditionally called slaked lime) is an inorganic compound with the chemical formula calcium, Ca(Hydroxide, OH)2. It is a colorless crystal or white powder and is produced when quicklime (calcium oxide) is mixed or slaking (ge ...
( portlandite), 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 (Δ''H'' < 0) and obeys the van 't Hoff equation and Le Chatelier's principle. A lowering of temperature favors the removal of dissolution heat from the system and thus favors dissolution of Ca(OH)2: so portlandite solubility increases at low temperature. This temperature dependence is sometimes referred to as "retrograde" or "inverse" solubility. 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 °C to form a more soluble
anhydrous A substance is anhydrous if it contains no water. Many processes in chemistry can be impeded by the presence of water; therefore, it is important that water-free reagents and techniques are used. In practice, however, it is very difficult to achie ...
phase ( thenardite) with a smaller change in Gibbs free energy (Δ''G'') in the dissolution reaction. The solubility of
organic compounds In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon chemical bond, bonds. Due to carbon's ability to Catenation, catenate (form chains with other carbon atoms), millions of organic c ...
nearly always increases with temperature. The technique of 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 cyclodextrins.

## 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: :$\left\left(\frac \right\right)_T = -\frac$ where the index $i$ iterates the components, $N_i$ is the mole fraction of the $i$-th component in the solution, $P$ is the pressure, the index $T$ refers to constant temperature, $V_$ is the partial molar volume of the $i$-th component in the solution, $V_$ is the partial molar volume of the $i$-th component in the dissolving solid, and $R$ is the universal gas constant. The pressure dependence of solubility does occasionally have practical significance. For example, precipitation fouling of oil fields and wells by calcium sulfate (which decreases its solubility with decreasing pressure) can result in decreased productivity with time.

# Solubility of gases

Henry's law is used to quantify the solubility of gases in solvents. The solubility of a gas in a solvent is directly proportional to the partial pressure of that gas above the solvent. This relationship is similar to Raoult's law and can be written as: :$p = k_\, c$ where $k_$ is a temperature-dependent constant (for example, 769.2 L· atm/ mol for dioxygen (O2) in water at 298 K), $p$ is the partial pressure (in atm), and $c$ is the
concentration In chemistry, concentration is the Abundance (chemistry), abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: ''mass concentration (chemistry), mass concentration'', ...
of the dissolved gas in the liquid (in mol/L). The solubility of gases is sometimes also quantified using Bunsen solubility coefficient. In the presence of small bubbles, 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 Δ''p'' = 2γ/''r''; see Young–Laplace equation). Henry's law is valid for gases that do not undergo change of chemical speciation on dissolution. Sieverts' law shows a case when this assumption does not hold. The
carbon dioxide Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon Carbon () is a chemical element with the chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetraval ...
solubility in
seawater Seawater, or salt water, is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% (35 g/L, 35 ppt, 600 mM). This means that every kilogram (roughly one liter by volume) of seawater has approx ...
is also affected by temperature, pH of the solution, and by the carbonate 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 climate changes as observed in ice cores from the Vostok site in
Antarctica Antarctica () is Earth's southernmost and least-populated continent. Situated almost entirely south of the Antarctic Circle and surrounded by the Southern Ocean, it contains the geographic South Pole. Antarctica is the fifth-largest contine ...
. At the geological time scale, because of the Milankovich cycles, when the astronomical parameters of the Earth orbit and its rotation axis progressively change and modify the solar irradiance 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
greenhouse effect The greenhouse effect is a process that occurs when energy from a planet's host star goes through the planet's atmosphere and heats the planet's surface, but greenhouse gases in the atmosphere prevent some of the heat from returning directly ...
and carbon dioxide acts as an amplifier of the general warming.

# Polarity

A popular aphorism used for predicting solubility is "''like dissolves like''" also expressed in the ''Latin'' language as "''Similia similibus solventur''". This statement indicates that a solute will dissolve best in a solvent that has a similar chemical structure to itself, based on favorable entropy of mixing. This view is simplistic, but it is a useful rule of thumb. The overall solvation capacity of a solvent depends primarily on its polarity. For example, a very polar (
hydrophilic A hydrophile is a molecule or other molecular entity that is intermolecular force, attracted to water molecules and tends to be dissolution (chemistry), dissolved by water.Liddell, H.G. & Scott, R. (1940). ''A Greek-English Lexicon'' Oxford: Clar ...
) solute such as
urea Urea, also known as carbamide, is an organic compound with chemical formula . This amide has two Amine, amino groups (–) joined by a carbonyl functional group (–C(=O)–). It is thus the simplest amide of carbamic acid. Urea serves an impor ...
is very soluble in highly polar water, less soluble in fairly polar
methanol Methanol (also called methyl alcohol and wood spirit, amongst other names) is an organic chemical and the simplest aliphatic alcohol, with the formula CH3OH (a methyl group In organic chemistry, a methyl group is an alkyl derived from m ...
, and practically insoluble in non-polar solvents such as
benzene Benzene is an Organic compound, organic chemical compound with the Chemical formula#Molecular formula, molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar Ring (chemistry), ring with one hydrogen atom ...
. In contrast, a non-polar or lipophilic solute such as
naphthalene Naphthalene is an organic compound with formula . It is the simplest polycyclic aromatic hydrocarbon, and is a white Crystal, crystalline solid with a characteristic odor that is detectable at concentrations as low as 0.08 Parts-per notation ...
is insoluble in water, fairly soluble in methanol, and highly soluble in non-polar benzene. In even more simple terms a simple ionic compound (with positive and negative ions) such as
sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salt (chemistry), salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of ...
(common salt) is easily soluble in a highly polar solvent (with some separation of positive (δ+) and negative (δ-) charges in the covalent molecule) such as
water Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...
, as thus the sea is salty as it accumulates dissolved salts since early geological ages. The solubility is favored by entropy of mixing (Δ''S'') and depends on enthalpy of dissolution (Δ''H'') and the hydrophobic effect. The free energy of dissolution ( Gibbs energy) depends on temperature and is given by the relationship: Δ''G'' = Δ''H'' – TΔ''S''. Smaller Δ''G'' means greater solubility. Chemists often exploit differences in solubilities to separate and purify compounds from reaction mixtures, using the technique of liquid-liquid extraction. This applies in vast areas of chemistry from drug synthesis to spent nuclear fuel reprocessing.

# Rate of dissolution

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
amorphous In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid) is a solid that lacks the long-range order that is characteristic of a crystal. The terms "glass" and "glassy solid" are sometimes used synonymousl ...
solids and the surface area (crystallite size) and the presence of polymorphism. Many practical systems illustrate this effect, for example in designing methods for controlled drug delivery. 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 Noyes–Whitney equation or the Nernst and Brunner equation of the form: :$\frac = A \frac \left(C_\mathrm-C_\mathrm\right)$ where: * $m$ = mass of dissolved material * $t$ = time * $A$ = surface area of the interface between the dissolving substance and the solvent * $D$ = diffusion coefficient * $d$ = thickness of the boundary layer of the solvent at the surface of the dissolving substance * $C_s$ = mass concentration of the substance on the surface * $C_b$ = mass concentration of the substance in the bulk of the solvent For dissolution limited by
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
(or mass transfer if mixing is present), $C_s$ 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 United States Pharmacopeia. 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.

# Theories of solubility

## Solubility product

Solubility constants are used to describe saturated solutions of ionic compounds of relatively low solubility (see solubility equilibrium). The solubility constant is a special case of an equilibrium constant. Since it is a product of ion concentrations in equilibrium, it is also known as the solubility product. It describes the balance between dissolved ions from the salt and undissolved salt. The solubility constant is also "applicable" (i.e. useful) to
precipitation In meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls under gravitational pull from clouds. The main forms of precipitation include drizzle, rain, Rain and snow mixed, sleet, snow, ice pellets, ...
, the reverse of the dissolving reaction. As with other equilibrium constants,
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
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.

## Other theories

The Flory–Huggins solution theory is a theoretical model describing the solubility of polymers. The Hansen solubility parameters and the Hildebrand solubility parameters are empirical methods for the prediction of solubility. It is also possible to predict solubility from other physical constants such as the enthalpy of fusion. The octanol-water partition coefficient, usually expressed as its
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...
(Log P), is a measure of differential solubility of a compound in a hydrophobic solvent ( 1-octanol) and a
hydrophilic A hydrophile is a molecule or other molecular entity that is intermolecular force, attracted to water molecules and tends to be dissolution (chemistry), dissolved by water.Liddell, H.G. & Scott, R. (1940). ''A Greek-English Lexicon'' Oxford: Clar ...
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 enthalpy of solution.

# Applications

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,
indigo Indigo is a deep color close to the Shades of blue#Blue (RGB) (X11 blue), color wheel blue (a primary color in the RGB color space), as well as to some variants of ultramarine, based on the indigo dye, ancient dye of the same name. The word " ...
is described as "insoluble in water, alcohol, or ether but soluble in chloroform, nitrobenzene, or concentrated sulfuric acid". Solubility of a substance is useful when separating mixtures. For example, a mixture of salt (
sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salt (chemistry), salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of ...
) 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 benzoic acid from phenylmagnesium bromide and
dry ice Dry ice is the solid form of carbon dioxide. It is commonly used for temporary refrigeration as CO2 does not have a liquid state at normal atmospheric pressure and Sublimation (phase transition), sublimates directly from the solid state to the ga ...
. Benzoic acid is more soluble in an organic solvent such as
dichloromethane Dichloromethane (DCM or methylene chloride, methylene bichloride) is an organochlorine compound with the chemical formula, formula . This colorless, volatile liquid with a chloroform-like, sweet odour is widely used as a solvent. Although it is n ...
or
diethyl ether Diethyl ether, or simply ether, is an organic compound in the ether class with the formula , sometimes abbreviated as (see Skeletal formula#Pseudoelement symbols, Pseudoelement symbols). It is a colourless, highly Volatility (chemistry), volati ...
, and when shaken with this organic solvent in a separatory funnel, 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 liquid–liquid extraction, is an important technique in synthetic chemistry. Recycling is used to ensure maximum extraction.

## Differential solubility

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.

# Solubility of ionic compounds in water

Some ionic compounds ( salts) dissolve in water, which arises because of the attraction between positive and negative charges (see:
solvation Solvation (or dissolution) describes the interaction of a solvent with Solution (chemistry), dissolved molecules. Both ionized and uncharged molecules interact strongly with a solvent, and the strength and nature of this interaction influence ma ...
). For example, the salt's positive ions (e.g. Ag+) attract the partially negative oxygen atom in . Likewise, the salt's negative ions (e.g. Cl) attract the partially positive hydrogens in . Note: the oxygen atom is partially negative because it is more
electronegative Electronegativity, symbolized as ''Chi (letter), χ'', is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its ato ...
than hydrogen, and vice versa (see:
chemical polarity In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a negatively charged end and a positively charged end. Polar molecules must contain one or more polar ...
). : 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 solubility product, ''K''sp. This equilibrium constant depends on the type of salt ( vs. , for example), temperature, and the common ion effect. One can calculate the amount of that will dissolve in 1 liter of pure water as follows: :''K''sp = g+× l/ M2 (definition of solubility product; M = mol/L) :''K''sp = 1.8 × 10−10 (from a table of solubility products) g+= l in the absence of other silver or chloride salts, so : g+sup>2 = 1.8 × 10−10 M2 : g+= 1.34 × 10−5 mol/L The result: 1 liter of water can dissolve 1.34 × 10−5 moles of at room temperature. Compared with other salts, is poorly soluble in water. For instance, table salt () has a much higher ''K''sp = 36 and is, therefore, more soluble. The following table gives an overview of solubility rules for various ionic compounds.

# Solubility of organic compounds

The principle outlined above under polarity, that ''like dissolves like'', is the usual guide to solubility with organic systems. For example,
petroleum jelly Petroleum jelly, petrolatum, white petrolatum, soft paraffin, or multi-hydrocarbon, CAS number 8009-03-8, is a semi-solid mixture of hydrocarbons (with carbon numbers mainly higher than 25), originally promoted as a Topical medication, topical o ...
will dissolve in
gasoline Gasoline (; ) or petrol (; ) (see ) is a transparent, petroleum-derived flammable liquid that is used primarily as a fuel in most Spark-ignition engine, spark-ignited internal combustion engines (also known as petrol engines). It consists ...
because both petroleum jelly and gasoline are non-polar hydrocarbons. It will not, on the other hand, dissolve in ethyl alcohol 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 filtration or extraction with water.

# Solid solution

This term is often used in the field of
metallurgy Metallurgy is a domain of Materials science, materials science and engineering that studies the physical and chemical behavior of metallic Chemical element, elements, their Inter-metallic alloy, inter-metallic compounds, and their mixtures, which ...
to refer to the extent that an
alloy An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, ...
ing element will dissolve into the base metal without forming a separate phase. The solvus or solubility line (or curve) is the line (or lines) on a phase diagram 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 solid solution. 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)). 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 chemical composition 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. While the maximum number of phases separating out at once in equilibrium can be determined by the Gibb's phase rule, 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 crystallographic defect (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.

# Incongruent dissolution

Many substances dissolve congruently (i.e. the composition of the solid and the dissolved solute stoichiometrically match). However, some substances may dissolve incongruently, 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 albite may result in formation of gibbsite. : . 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 metamorphic rocks. In principle, both congruent and incongruent dissolution can lead to the formation of secondary solid phases in equilibrium. So, in the field of Materials Science, the solubility for both cases is described more generally on chemical composition phase diagrams.

# Solubility prediction

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. 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. 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 number of methods have been applied to such predictions including quantitative structure–activity relationships (QSAR), quantitative structure–property relationships (QSPR) and data mining. 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. Methods founded in physical theory tend to use thermodynamic cycles, a concept from classical
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
. The two common thermodynamic cycles used involve either the calculation of the free energy of sublimation (solid to gas without going through a liquid state) and the free energy of solvating a gaseous molecule (gas to solution), or the free energy of fusion (solid to a molten phase) and the free energy of mixing (molten to solution). These two process are represented in the following diagrams. These cycles have been used for attempts at first principles predictions (solving using the fundamental physical equations) using physically motivated solvent models, to create parametric equations and QSPR models and combinations of the two. 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 gas constant and ''T'' is the temperature in kelvins. :$\log S\left(V_\right) = \frac$ Well known fitted equations for solubility prediction are the general solubility equations. These equations stem from the work of Yalkowsky ''et al''. The original formula is given first, followed by a revised formula which takes a different assumption of complete miscibility in octanol. :$\log_ \left(S\right) = 0.8 - \log_ \left(P\right) - 0.01\left(\text -25\right)$ :$\log_ \left(S\right) = 0.5 - \log_ \left(P\right) - 0.01\left(\text -25\right)$ These equations are founded on the principles of the fusion cycle.