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In
chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in the real world. T ...

chemistry
, solubility is ability of a
substance Substance may refer to: * Substance (Jainism), a term in Jain ontology to denote the base or owner of attributes * Chemical substance, a material with a definite chemical composition * Matter, anything that has mass and takes up space * Substance th ...
, the
solute upMaking a table salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of Salt (chemistry), salts; salt in its natural form as a crystallinity, crystalline mineral is known ...
, to form a
solution Solution may refer to: * Solution (chemistry) Image:SaltInWaterSolutionLiquid.jpg, upMaking a saline water solution by dissolving Salt, table salt (sodium chloride, NaCl) in water. The salt is the solute and the water the solvent. In chemistry ...
with another substance, the
solvent A solvent (from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the ...

solvent
. 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 Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...

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 equilibriumSolubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entity, molecular entities) composed of atoms from more t ...
. 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 substances to mix in all proportions (that is, to fully dissolve in each other at any concentration In chemistry Chemistry is the study of the properties and behavior of . It is a that covers ...
in all proportions" (or just "miscible"). The solute can be a
solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied ...

solid
, a
liquid A liquid is a nearly incompressible In fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, ...

liquid
, or a
gas Gas is one of the four fundamental states of matter In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...

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 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 An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of ato ...

atom
s,
molecule A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon ...

molecule
s, or
ion An ion () is an atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ...
s) of the two substances, and of
thermodynamic Thermodynamics is a branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related ent ...

thermodynamic
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 ...

enthalpy
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 thermodynamics ...

entropy
. Under certain conditions, the concentration of the solute can exceed its usual solubility limit. The result is a
supersaturated solution Supersaturation occurs with a chemical solution when the concentration of a solute Making a table salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of Salt (chemistry ...
, which is
metastable In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds composed of atoms ...

metastable
and will rapidly exclude the excess solute if a suitable
nucleation Nucleation is the first step in the formation of either a new or a new structure via or . Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appear ...

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 chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...

chemical reaction
between then 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 ...

calcium hydroxide
with
hydrochloric acid Hydrochloric acid +(aq) Cl−(aq) or H3O+ Cl− also known as muriatic acid, is an aqueous solution An aqueous solution is a solution Solution may refer to: * Solution (chemistry) Image:SaltInWaterSolutionLiquid.jpg, upMaking a salin ...

hydrochloric acid
; even though one might say, informally, that one "dissolved" the other. The solubility is also not the same as the
rate of solution Solubility is the property of a solid, liquid or gaseous chemical substance called ''solution, solute'' to dissolve in a solid, liquid or gaseous solvent. The solubility of a substance fundamentally depends on the Physical property, physical an ...
, 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 (from the Ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek ...

geology
,
biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechanisms, Development ...

biology
,
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

physics
, and
oceanography Oceanography (from the Ancient Greek Ancient Greek includes the forms of the used in and the from around 1500 BC to 300 BC. It is often roughly divided into the following periods: (), Dark Ages (), the period (), and the period ...
, 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 speciali ...

engineering
,
medicine Medicine is the science Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts ( descriptive knowledge), skills (proced ...

medicine
,
agriculture Agriculture is the science, art and practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary Image:Family watching television 1958.jpg, Exercise trends, Increases in sedentary behaviors su ...

agriculture
, and even in non-technical activities like
painting Painting is the practice of applying paint Paint is any pigmented liquid, liquefiable, or solid mastic composition that, after application to a substrate in a thin layer, converts to a solid film. It is most commonly used to protect, ...

painting
,
cleaning Cleaning is the process of removing unwanted substances, such as dirt, infectious agents, and other impurities, from an object or environment. Cleaning occurs in many different contexts, and uses many different methods. Several occupations are de ...

cleaning
,
cooking Cooking, cookery, or culinary arts is the art, science, and craft of using heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy ...

cooking
, and
brewing Brewing is the production of beer Beer is one of the oldest and most widely consumed alcoholic drink An alcoholic drink is a drink A drink (or beverage) is a liquid A liquid is a nearly incompressible fluid In ph ...
. Most chemical reactions of scientific, industrial, or practical interest only happen after the
reagent A reagent is a substance or compound added to a system to cause a chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter ...
s have been dissolved in a suitable solvent.
Water Water (chemical formula H2O) 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 li ...

Water
is by far the most common such solvent. The term "soluble" is sometimes used for materials that can form 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 the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
,
volume Volume is a scalar quantity expressing the amount Quantity or amount is a property that can exist as a multitude Multitude is a term for a group of people who cannot be classed under any other distinct category, except for their shared fact ...

volume
, 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
handbook A German 1874 handbook for mechanics, millwrights, engineers, technicians, trades people and technical schools A handbook is a type of reference work, or other collection of instructions, that is intended to provide ready reference. The term or ...
s will often express the solubility of a substance in a liquid as
gram The gram (alternative spelling: gramme; SI unit symbol: g) is a metric system The metric system is a that succeeded the decimalised system based on the introduced in France in the 1790s. The historical development of these systems culm ...
s of solute per
decilitre The litre (British English British English (BrE) is the standard dialect of the English language English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, early medieval Englan ...
(100 mL) of solvent (g/dL); or, less commonly, as grams per
litre The litre (British English British English (BrE) is the standard dialect A standard language (also standard variety, standard dialect, and standard) is a language variety that has undergone substantial codification of grammar and ...

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 kilogram (also kilogramme) is the SI base unit, base unit of mass in the International System of Units (SI), the metric system, having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is oft ...
, the value is the
molality Molality is a measure of number of moles of solute present in 1 kg of solvent. This contrasts with the definition of molarity Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the conce ...
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 Titration (also known as titrimetry and volumetric analysis) is a common laboratory method of quantitative chemical analysis Analytical chemistry studies and uses instruments and methods used to separate, identify, and quantify matter. In pr ...

titration
, it may be expressed as moles of solute per litre of solution (mol/L), the
molarity Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types ...
of the latter. In more specialized contexts the solubility may be given by the
mole fraction In chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they underg ...
(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 or capable of donating a (hydrogen ion H+) (a ), or, alternatively, capable of forming a with an (a ). The first category of acids are the proton donors, or s. In the special case of , proton donors form the H3O+ and are ...
s and
salts In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...
) will
dissociate Dissociation in chemistry and biochemistry is a general process in which molecules (or ionic compounds such as salt (chemistry), salts, or coordination complex, complexes) separate or split into smaller particles such as atoms, ions, or radical (c ...
in non-trivial ways when dissolved; conversely, the solvent may form
coordination complex A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of chemical bond, bound molecules or ions, that are in turn known as ''ligands'' or complexing ...
es 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 substances to mix in all proportions (that is, to fully dissolve in each other at any concentration In chemistry Chemistry is the study of the properties and behavior of . It is a that covers ...
) such as
ethanol Ethanol (also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic Organic may refer to: * Organic, of or relating to an organism, a living entity * Organic, of or relating to an anatomical organ (anatomy), ...

ethanol
in water, to essentially insoluble, such as
titanium dioxide Titanium dioxide, also known as titanium(IV) oxide or titania , is the inorganic compound In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical ...
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, accoding 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 Dissolution may refer to: Arts and entertainment Books * Dissolution (Forgotten Realms novel), ''Dissolution'' (''Forgotten Realms'' novel), a 2002 fantasy novel by Richard Lee Byers * Dissolution (Sansom novel), ''Dissolution'' (Sansom novel), a 2 ...

dissolution
and phase joining (e.g.
precipitation In meteorology Meteorology is a branch of the (which include and ), with a major focus on . The study of meteorology dates back , though significant progress in meteorology did not begin until the 18th century. The 19th century saw mod ...
of
solids Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric process, isochoric flow) re ...
). The solubility equilibrium occurs when the two processes proceed at a constant rate. The term ''solubility'' is also used in some fields where the solute is altered by
solvolysisSolvolysis is a type of nucleophilic substitution (SN1/SN2) or elimination where the nucleophile In chemistry, a nucleophile is a chemical species that forms bonds with Electrophile, electrophiles by donating an electron pair. All molecules and io ...
. For example, many metals and their
oxide An oxide () is a chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entity, molecular entities) composed of atoms from more than one chemical element, element held together by che ...
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 An aqueous solution is a solution Image:SaltInWaterSolutionLiquid.jpg, Making a saline water solution by dissolving Salt, table salt (sodium chloride, NaCl) in water. The salt is the solute and the water the solvent. In chemistry, a solution ...
suspension Suspension or suspended may refer to: Science and engineering * Suspension (topology), in mathematics * Suspension (dynamical systems), in mathematics * Suspension of a ring, in mathematics * Suspension (chemistry), small solid particles suspende ...
of
ferrous hydroxide Iron(II) hydroxide or ferrous hydroxide is an inorganic compound with the formula Fe(OH)2. It is produced when iron(II) salts, from a compound such as iron(II) sulfate, are treated with hydroxide Hydroxide is a polyatomic ion, diatomic anion wi ...
, , will contain the series as well as other species. Furthermore, the solubility of ferrous hydroxide and the composition of its soluble components depend on . 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 Aragonite is a , one of the three most common naturally occurring of , (the other forms being the s and ). It is formed by biological and physical processes, including precipitation from marine and freshwater environments. The of aragonite d ...

aragonite
and
calcite Calcite is a carbonate mineral Carbonate minerals are those mineral In geology Geology (from the Ancient Greek γῆ, ''gē'' ("earth") and -λoγία, ''-logia'', ("study of", "discourse")) is an Earth science concerned with the solid E ...

calcite
in water are expected to differ, even though they are both polymorphs of
calcium carbonate Calcium carbonate is a chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entity, molecular entities) composed of atoms from more than one chemical element, element held together ...

calcium carbonate
and have the same
chemical formula A chemical formula is a way of presenting information about the chemical proportions of s that constitute a particular or molecule, using symbols, numbers, and sometimes also other symbols, such as parentheses, dashes, brackets, commas and ...
. 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 neighboring pa ...

intermolecular force
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 thermodynamics ...

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-forming anions (
ligand In coordination chemistry A coordination complex consists of a central atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by havi ...
s) 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 The ionic strength of a solution Solution may refer to: * Solution (chemistry) Image:SaltInWaterSolutionLiquid.jpg, upMaking a saline water solution by dissolving Salt, table salt (sodium chloride, NaCl) in water. The salt is the solute and the ...
of solutions. The last two effects can be quantified using the equation for
solubility equilibriumSolubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entity, molecular entities) composed of atoms from more t ...
. 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 Specific surface area (SSA) is a property of solid Solid is one of the four fundamental states of matter (the others being liquid, gas and plasma). The molecules in a solid are closely packed together and contain the least amount of kin ...
or molar surface area of the solute). For quantification, see the equation in the article on
solubility equilibriumSolubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entity, molecular entities) composed of atoms from more t ...
. 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
Gibbs free energy In 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 quan ...
(ΔG) of the dissolution reaction, ''i.e.'', on the
endothermic In thermochemistry Thermochemistry is the study of the heat energy which is associated with chemical reactions and/or physical transformations. A reaction may release or absorb energy, and a phase change may do the same, such as in melting and bo ...
(ΔG > 0) or
exothermic In 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 qu ...
(ΔG < 0) character of the dissolution reaction, the solubility of a given compound may increase or decrease with temperature. The
van 't Hoff equation The Van 't Hoff equation relates the change in the equilibrium constant, , of a chemical reaction to the change in temperature, ''T'', given the Standard enthalpy of reaction, standard enthalpy change, , for the process. It was proposed by Dutch ch ...
relates the change of solubility equilibrium constant (Ksp) 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 ...

enthalpy
change (ΔH). For most solids and liquids, their solubility increases with temperature because their dissolution reaction is endothermic (ΔG > 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 Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine * Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in ...
), the solubility of ionic solutes tends to decrease due to the change of properties and structure of liquid water; the lower
dielectric constant The dielectric constant (or relative permittivity) is the permittivity, electric permeability of a material expressed as a ratio with the vacuum permittivity, electric permeability of a vacuum. A dielectric is an insulating material, and the diele ...
results in a less
polar solvent A solvent (from the Latin language, Latin ''wikt:solvo#Latin, solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical flui ...
and in a change of hydration energy affecting the ΔG of the dissolution reaction.
Gas Gas is one of the four fundamental states of matter In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...

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 minimum, which is below 120 °C for most permanent gases), but more soluble in organic solvents (endothermic dissolution reaction related to their solvatation). The chart shows solubility curves for some typical solid inorganic
salts In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...
(temperature is in degrees
Celsius The degree Celsius is a unit of temperature on the Celsius scale, a temperature scale Scale of temperature is a methodology of calibrating the physical quantity temperature in metrology. Empirical scales measure temperature in relation to conv ...

Celsius
i.e.
kelvin The kelvin is the base unit of temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal en ...

kelvin
s minus 273.15). Many salts behave like
barium nitrate Barium nitrate is the inorganic compound In chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, structure, proper ...

barium nitrate
and , and show a large increase in solubility with temperature (ΔG > 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 mass, molar ...
in water) exhibit solubility that is fairly independent of temperature (ΔG ≈ 0). A few, such as
calcium sulfate Calcium sulfate (or calcium sulphate) is the inorganic compound with the formula CaSO4 and related hydrate In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that cove ...

calcium sulfate
(
gypsum Gypsum is a soft sulfate mineral The sulfate minerals are a class of mineral In geology Geology (from the Ancient Greek γῆ, ''gē'' ("earth") and -λoγία, ''-logia'', ("study of", "discourse")) is an Earth science concerned with ...

gypsum
) and cerium(III) sulfate, become less soluble in water as temperature increases (ΔG < 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 ...

calcium hydroxide
(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 (ΔG < 0) and obeys the
van 't Hoff equation The Van 't Hoff equation relates the change in the equilibrium constant, , of a chemical reaction to the change in temperature, ''T'', given the Standard enthalpy of reaction, standard enthalpy change, , for the process. It was proposed by Dutch ch ...
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 decahydrate crystal (mirabilite) loses water of crystallization at 32 °C to form a more soluble anhydrous phase (thenardite) because the change in
Gibbs free energy In 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 quan ...
(ΔG), of the dissolution reaction. 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 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(\frac \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, Fouling#Precipitation fouling, precipitation fouling of oil fields and wells by
calcium sulfate Calcium sulfate (or calcium sulphate) is the inorganic compound with the formula CaSO4 and related hydrate In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that cove ...

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 litre, L·Atmosphere (unit), atm/Mole (unit), mol for Oxygen#Allotropes, dioxygen (O2) in water at 298 K), p is the partial pressure (atm), and c is the
concentration In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...

concentration
of the dissolved gas in the liquid (mol/L). The solubility of gases is sometimes also quantified using Bunsen solubility coefficient. In the presence of small Liquid bubble, 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 Δp = 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 solubility in seawater 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 change (general concept), climate changes as observed in ice cores from the Vostok site in Antarctica. 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 in the atmosphere because of its lower solubility in warmer sea water. On its turn, higher levels of CO2 in the atmosphere increase the greenhouse effect 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. This view is simplistic, but it is a useful rule of thumb. The overall solvation capacity of a solvent depends primarily on its Chemical polarity, polarity. For example, a very polar (hydrophile, hydrophilic) solute such as urea is very soluble in highly polar water, less soluble in fairly polar methanol, and practically insoluble in non-polar solvents such as benzene. In contrast, a non-polar or lipophilicity, lipophilic solute such as naphthalene 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 mass, molar ...
(common salt) is easily soluble in a highly Chemical polarity, polar solvent (with some separation of positive (δ+) and negative (δ-) charges in the covalent molecule) such as water, 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 Thermodynamic free energy, free energy of dissolution (Gibbs energy) depends on temperature and is given by the relationship: Δ''G'' = Δ''H'' – TΔ''S''. 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 solids and the surface area (crystallite size) and the presence of Polymorphism (materials science), 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 (C_\mathrm-C_\mathrm) 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 (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 equilibriumSolubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entity, molecular entities) composed of atoms from more t ...
). The solubility constant is a special case of an equilibrium constant. 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 Meteorology is a branch of the (which include and ), with a major focus on . The study of meteorology dates back , though significant progress in meteorology did not begin until the 18th century. The 19th century saw mod ...
, the reverse of the dissolving reaction. As with other equilibrium constants, temperature can affect the numerical value of solubility constant. The solubility constant is not as simple as solubility, however 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 (Log P) is a measure of differential solubility of a compound in a hydrophobe, hydrophobic solvent (1-octanol) and a hydrophile, hydrophilic 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 dye#Chemical properties, indigo 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 mass, molar ...
) 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. Benzoic acid is more soluble in an organic solvent such as dichloromethane or diethyl ether, 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). For example, the salt's positive ions (e.g. Ag+) attract the partially negative oxygens in . Likewise, the salt's negative ions (e.g. Cl) attract the partially positive hydrogens in . Note: oxygen is partially negative because it is more electronegativity, electronegative than hydrogen, and vice versa (see: chemical polarity). : However, there is a limit to how much salt can be dissolved in a given volume of water. This amount is given by the solubility product, Ksp. This value 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 water, some algebra is required. :Ksp = [Ag+] × [Cl] (definition of solubility product) :Ksp = 1.8 × 10−10 (from a table of solubility products) [Ag+] = [Cl], in the absence of other silver or chloride salts, :[Ag+]2 = 1.8 × 10−10 :[Ag+] = 1.34 × 10−5 The result: 1 liter of water can dissolve 1.34 × 10−5 mole (unit), moles of at room temperature. Compared with other types of salts, is poorly soluble in water. In contrast, table salt () has a higher Ksp and is, therefore, more soluble.


Solubility of organic compounds

The principle outlined above under #Polarity, polarity, that ''like dissolves like'', is the usual guide to solubility with organic systems. For example, petroleum jelly will dissolve in gasoline 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 solvent extraction, extraction with water.


Solid solution

This term is often used in the field of metallurgy to refer to the extent that an alloying 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.


Incongruent dissolution

Many substances dissolve congruently (i.e. the composition of the solid and the dissolved solute stoichiometrically match). However, some substances may dissolve Incongruent transition, 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.


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. The two common thermodynamic cycles used involve either the calculation of the free energy of Sublimation (phase transition), sublimation (solid to gas without going through a liquid state) and the free energy of solvating a gaseous molecule (gas to solution), or the enthalpy of fusion, 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
kelvin The kelvin is the base unit of temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal en ...

kelvin
s. :\log S(V_) = \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. These equations are founded on the principles of the fusion cycle. : \log_ (S) = 0.8 - \log_ (P) - 0.01(\text -25) : \log_ (S) = 0.5 - \log_ (P) - 0.01(\text -25)


See also

* * * * * * * * * * * * *


Notes


References


External links

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