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In chemistry, solubility is the ability of a substance, the
solute In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent ...
, to form a
solution Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Soluti ...
with another substance, the
solvent A solvent (s) (from the 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 fluid. Water is a solvent for ...
. 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 of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', '' number concentration'', ...
of the solute in a
saturated Saturation, saturated, unsaturation or unsaturated may refer to: Chemistry * Saturation, a property of organic compounds referring to carbon-carbon bonds ** Saturated and unsaturated compounds **Degree of unsaturation ** Saturated fat or fatty ac ...
solution, one in which no more solute can be dissolved. At this point, the two substances are said to be at the
solubility equilibrium Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical react ...
. For some solutes and solvents, there may be no such limit, in which case the two substances are said to be " miscible 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, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural ...
, a liquid, or a
gas Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
, 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 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, liquid, gas, ...
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
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
s) of the two substances, and of
thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
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 ...
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 In physical chemistry, supersaturation occurs with a solution when the concentration of a solute exceeds the concentration specified by the value of solubility at equilibrium. Most commonly the term is applied to a solution of a solid in a liqu ...
, which is
metastable In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball i ...
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 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 pungent smell. It is classified as a strong acid Acid strength is the tendency of an acid, symbol ...
; even though one might say, informally, that one "dissolved" the other. The solubility is also not the same as the
rate of solution In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubi ...
, 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 objects, the features or rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Ea ...
,
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 cells that process hereditary i ...
,
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, 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 speciali ...
,
medicine Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...
,
agriculture Agriculture or farming is the practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that enabled people t ...
, 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 Cleaning is the process of removing unwanted substances, such as dirt, infectious agents, and other impurities, from an object or environment. Cleaning is often performed for aesthetic, hygienic, functional, environmental, or safety purposes ...
, cooking, and brewing. 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 property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
,
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). Th ...
, 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 handbook is a type of reference work, or other collection of instructions, that is intended to provide ready reference. The term originally applied to a small or portable book containing information useful for its owner, but the ''Oxford Engl ...
s 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 of pure water equal to th ...
s of solute per decilitre (100 mL) of solvent (g/dL); or, less commonly, as grams per
litre The litre (international spelling) or liter (American English spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3 ...
(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 unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
, the value is the
molality Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution. A commonly used unit for molali ...
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 to determine the concentration of an identified analyte (a substance to be analyzed). A reagent, termed the ''titrant'' ...
, 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 of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solu ...
of the latter. In more specialized contexts the solubility may be given by the
mole fraction In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This ex ...
(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 acids and
salts In chemistry, a salt is a chemical compound consisting of an ionic assembly of positively charged cations and negatively charged anions, which results in a compound with no net electric charge. A common example is table salt, with positively c ...
) will
dissociate Dissociation in chemistry is a general process in which molecules (or ionic compounds such as salts, or complexes) separate or split into other things such as atoms, ions, or radicals, usually in a reversible manner. For instance, when an acid ...
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 bound molecules or ions, that are in turn known as '' ligands'' or complexing agents. ...
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) 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 with the chemical formula . Its formula can be also written as or (an ethyl group linked to a ...
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 CI 77891. It is a white solid that is insolub ...
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 Dissolution may refer to: Arts and entertainment Books * ''Dissolution'' (''Forgotten Realms'' novel), a 2002 fantasy novel by Richard Lee Byers * ''Dissolution'' (Sansom novel), a 2003 historical novel by C. J. Sansom Music * Dissolution, in mu ...
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, sleet, snow, ice pellets, graupel and hail. ...
of
solids 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 kinetic energy. A solid is characterized by structural ...
). 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 In chemistry, solvolysis is a type of nucleophilic substitution (S1/S2) or elimination reaction, elimination where the nucleophile is a solvent molecule. Characteristic of S1 reactions, solvolysis of a chirality (chemistry), chiral reactant affor ...
. For example, many metals and their oxides 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 in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be re ...
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 ions. Iron(II) hydroxide is a white solid, but eve ...
, , 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 Aragonite is a carbonate mineral, one of the three most common naturally occurring crystal forms of calcium carbonate, (the other forms being the minerals calcite and vaterite). It is formed by biological and physical processes, including pre ...
and calcite in water are expected to differ, even though they are both polymorphs of calcium carbonate 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 symbol ...
. 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 electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. ...
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 (
ligand In coordination chemistry, a ligand is an ion or molecule ( functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's elec ...
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 The common-ion effect refers to the decrease in solubility of an ionic precipitate by the addition to the solution of a soluble compound with an ion in common with the precipitate. This behaviour is a consequence of Le Chatelier's principle for the ...
. 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 Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical react ...
. 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 In geology, a redox buffer is an assemblage of minerals or compounds that constrains oxygen fugacity as a function of temperature. Knowledge of the redox conditions (or equivalently, oxygen fugacities) at which a rock forms and evolves can be im ...
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 solids defined as the total surface area of a material per unit of mass, (with units of m2/kg or m2/g) or solid or bulk volume (units of m2/m3 or m−1). It is a physical value that can be used to dete ...
or molar surface area of the solute). For quantification, see the equation in the article on
solubility equilibrium Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical react ...
. 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 ...
(Δ''H'') of the dissolution reaction, ''i.e.'', on the
endothermic In thermochemistry, an endothermic process () is any thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, H.P., Butler, L. J. (2015).''Principle of Modern Chemistry'', Brooks Cole. ...
(Δ''H'' > 0) or exothermic (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 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 change, , for the process. It was proposed by Dutch chemist Jacobus Henricus van ' ...
relates the change of solubility
equilibrium constant The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
(''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 ...
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 A solvent (s) (from the 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 fluid. Water is a solvent for p ...
and in a change of hydration energy affecting the Δ''G'' of the dissolution reaction.
Gas Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
eous solutes exhibit more complex behavior with temperature. As the temperature is raised, gases usually become less soluble in water (exothermic dissolution reaction related to their hydration) (to a minimum, which is below 120 °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 chemistry, a salt is a chemical compound consisting of an ionic assembly of positively charged cations and negatively charged anions, which results in a compound with no net electric charge. A common example is table salt, with positively c ...
in liquid water (temperature is in degrees Celsius, i.e.
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
s minus 273.15). Many salts behave like
barium nitrate Barium nitrate is the inorganic compound with the chemical formula Ba( NO3)2. It, like most barium salts, is colorless, toxic, and water-soluble. It burns with a green flame and is an oxidizer; the compound is commonly used in pyrotechnics. Man ...
and
disodium hydrogen arsenate Disodium hydrogen arsenate is the inorganic compound with the formula Na2HAsO4.7H2O. The compound consists of a salt and seven molecules of water of crystallization although for simplicity the formula usually omits the water component. The other ...
, and show a large increase in solubility with temperature (Δ''H'' > 0). Some solutes (e.g. sodium chloride in water) exhibit solubility that is fairly independent of temperature (Δ''H'' ≈ 0). A few, such as
calcium sulfate Calcium sulfate (or calcium sulphate) is the inorganic compound with the formula CaSO4 and related hydrates. In the form of γ-anhydrite (the anhydrous form), it is used as a desiccant. One particular hydrate is better known as plaster of Paris ...
(
gypsum Gypsum is a soft sulfate mineral composed of calcium sulfate 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 drywal ...
) and cerium(III) sulfate, become less soluble in water as temperature increases (Δ''H'' < 0). This is also the case for calcium hydroxide (
portlandite Portlandite is a hydroxide-bearing mineral typically included in the oxide mineral class. It is the naturally occurring form of calcium hydroxide (Ca(OH)2) and the calcium analogue of brucite (Mg(OH)2). Occurrence Portlandite occurs in a variety ...
), 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 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 change, , for the process. It was proposed by Dutch chemist Jacobus Henricus van ' ...
and
Le Chatelier's principle Le Chatelier's principle (pronounced or ), also called Chatelier's principle (or the Equilibrium Law), is a principle of chemistry used to predict the effect of a change in conditions on chemical equilibria. The principle is named after French c ...
. 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 Mirabilite, also known as Glauber's salt, is a hydrous sodium sulfate mineral with the chemical formula Na2SO4·10H2O. It is a vitreous, colorless to white monoclinic mineral that forms as an evaporite from sodium sulfate-bearing brines. It is fo ...
) loses
water of crystallization In chemistry, water(s) of crystallization or water(s) of hydration are water molecules that are present inside crystals. Water is often incorporated in the formation of crystals from aqueous solutions. In some contexts, water of crystallization i ...
at 32 °C to form a more soluble anhydrous phase ( thenardite) with a smaller change in
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and ...
(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 bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The s ...
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
cyclodextrin Cyclodextrins are a family of cyclic oligosaccharides, consisting of a macrocyclic ring of glucose subunits joined by α-1,4 glycosidic bonds. Cyclodextrins are produced from starch by enzymatic conversion. They are used in food, pharmaceutical ...
s.


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 In thermodynamics, a partial molar property is a quantity which describes the variation of an extensive property of a solution or mixture with changes in the molar composition of the mixture at constant temperature and pressure. It is the p ...
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 molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
. The pressure dependence of solubility does occasionally have practical significance. For example, 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 hydrates. In the form of γ-anhydrite (the anhydrous form), it is used as a desiccant. One particular hydrate is better known as plaster of Paris ...
(which decreases its solubility with decreasing pressure) can result in decreased productivity with time.


Solubility of gases

Henry's law In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formulate ...
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 There are several known allotropes of oxygen. The most familiar is molecular oxygen (O2), present at significant levels in Earth's atmosphere and also known as dioxygen or triplet oxygen. Another is the highly reactive ozone (O3). Others are: * ...
(O2) in water at 298 K), p is the partial pressure (in atm), and c is the
concentration In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', '' number 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
bubble Bubble, Bubbles or The Bubble may refer to: Common uses * Bubble (physics), a globule of one substance in another, usually gas in a liquid ** Soap bubble * Economic bubble, a situation where asset prices are much higher than underlying funda ...
s, 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 In physics, the Young–Laplace equation () is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or w ...
). Henry's law is valid for gases that do not undergo change of chemical speciation on dissolution.
Sieverts' law Sieverts' law, in physical metallurgy and in chemistry, is a rule to predict the solubility of gases in metals. It is named after German chemist Adolf Sieverts (1874–1947). The law states that the solubility of a diatomic gas in metal is propor ...
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 atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is trans ...
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 appr ...
is also affected by temperature, pH of the solution, and by the
carbonate A carbonate is a salt of carbonic acid (H2CO3), characterized by the presence of the carbonate ion, a polyatomic ion with the formula . The word ''carbonate'' may also refer to a carbonate ester, an organic compound containing 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 cont ...
. At the
geological time The geologic time scale, or geological time scale, (GTS) is a representation of time based on the rock record of Earth. It is a system of chronological dating that uses chronostratigraphy (the process of relating strata to time) and geochron ...
scale, because of the
Milankovich cycle Milankovitch cycles describe the collective effects of changes in the Earth's movements on its climate over thousands of years. The term was coined and named after Serbian geophysicist and astronomer Milutin Milanković. In the 1920s, he hypot ...
s, 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 An aphorism (from Greek ἀφορισμός: ''aphorismos'', denoting 'delimitation', 'distinction', and 'definition') is a concise, terse, laconic, or memorable expression of a general truth or principle. Aphorisms are often handed down by ...
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 A chemical structure determination includes a chemist's specifying the molecular geometry and, when feasible and necessary, the electronic structure of the target molecule or other solid. Molecular geometry refers to the spatial arrangement of ...
to itself, based on favorable
entropy of mixing In thermodynamics, the entropy of mixing is the increase in the total entropy when several initially separate systems of different composition, each in a thermodynamic state of internal equilibrium, are mixed without chemical reaction by the therm ...
. 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 attracted to water molecules and tends to be dissolved by water.Liddell, H.G. & Scott, R. (1940). ''A Greek-English Lexicon'' Oxford: Clarendon Press. In contrast, hydrophobes are ...
) solute such as
urea Urea, also known as carbamide, is an organic compound with chemical formula . This amide has two amino groups (–) joined by a carbonyl functional group (–C(=O)–). It is thus the simplest amide of carbamic acid. Urea serves an important ...
is very soluble in highly polar water, less soluble in fairly polar methanol, and practically insoluble in non-polar solvents such as
benzene Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms ...
. In contrast, a non-polar or
lipophilic Lipophilicity (from Greek λίπος "fat" and φίλος "friendly"), refers to the ability of a chemical compound to dissolve in fats, oils, lipids, and non-polar solvents such as hexane or toluene. Such non-polar solvents are themselves lipo ...
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 (common salt) is easily soluble in a highly
polar Polar may refer to: Geography Polar may refer to: * Geographical pole, either of two fixed points on the surface of a rotating body or planet, at 90 degrees from the equator, based on the axis around which a body rotates * Polar climate, the c ...
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 In thermodynamics, the entropy of mixing is the increase in the total entropy when several initially separate systems of different composition, each in a thermodynamic state of internal equilibrium, are mixed without chemical reaction by the therm ...
(Δ''S'') and depends on
enthalpy of dissolution In thermochemistry, the enthalpy of solution ( heat of solution or enthalpy of solvation) is the enthalpy change associated with the dissolution of a substance in a solvent at constant pressure resulting in infinite dilution. The enthalpy of so ...
(Δ''H'') and the
hydrophobic effect The hydrophobic effect is the observed tendency of nonpolar substances to aggregate in an aqueous solution and exclude water molecules. The word hydrophobic literally means "water-fearing", and it describes the segregation of water and nonpolar ...
. The free energy of dissolution (
Gibbs energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pre ...
) 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 Spent nuclear fuel, occasionally called used nuclear fuel, is nuclear fuel that has been irradiated in a nuclear reactor (usually at a nuclear power plant). It is no longer useful in sustaining a nuclear reaction in an ordinary thermal reactor and ...
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. Many practical systems illustrate this effect, for example in designing methods for controlled
drug delivery Drug delivery refers to approaches, formulations, manufacturing techniques, storage systems, and technologies involved in transporting a pharmaceutical compound to its target site to achieve a desired therapeutic effect. Principles related to dr ...
. 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 Arthur Amos Noyes (September 13, 1866 – June 3, 1936) was an American chemist, inventor and educator. He received a PhD in 1890 from Leipzig University under the guidance of Wilhelm Ostwald. He served as the acting president of MIT between ...
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 Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is enco ...
* 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 chemica ...
(or
mass transfer Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration ...
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 The ''United States Pharmacopeia'' (''USP'') is a pharmacopeia (compendium of drug information) for the United States published annually by the United States Pharmacopeial Convention (usually also called the USP), a nonprofit organization that ...
. 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 constant Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical reacti ...
s are used to describe saturated solutions of ionic compounds of relatively low solubility (see
solubility equilibrium Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical react ...
). The solubility constant is a special case of an
equilibrium constant The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
. Since it is a product of ion concentrations in equilibrium, it is also known as the
solubility product Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical reacti ...
. 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, sleet, snow, ice pellets, graupel and hail. ...
, 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 Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing. The result is an equatio ...
is a theoretical model describing the solubility of polymers. The
Hansen solubility parameters Hansen solubility parameters were developed by Charles M. Hansen in his Ph.D thesis in 1967 as a way of predicting if one material will dissolve in another and form a solution. They are based on the idea that like dissolves like where one molecul ...
and the
Hildebrand solubility parameter The Hildebrand solubility parameter (δ) provides a numerical estimate of the degree of interaction between materials and can be a good indication of solubility, particularly for nonpolar materials such as many polymers. Materials with similar valu ...
s 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 In thermodynamics, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a s ...
. The
octanol-water partition coefficient The ''n''-octanol-water partition coefficient, ''K''ow is a partition coefficient for the two-phase system consisting of ''n''-octanol and water. ''K''ow is also frequently referred to by the symbol P, especially in the English literature. It is a ...
, 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 In chemistry, hydrophobicity is the physical property of a molecule that is seemingly repelled from a mass of water (known as a hydrophobe). In contrast, hydrophiles are attracted to water. Hydrophobic molecules tend to be nonpolar and, t ...
solvent (
1-octanol 1-Octanol, also known as octan-1-ol, is the organic compound with the molecular formula CH3(CH2)7OH. It is a fatty alcohol. Many other isomers are also known generically as octanols. 1-Octanol is manufactured for the synthesis of esters for us ...
) and a
hydrophilic A hydrophile is a molecule or other molecular entity that is attracted to water molecules and tends to be dissolved by water.Liddell, H.G. & Scott, R. (1940). ''A Greek-English Lexicon'' Oxford: Clarendon Press. In contrast, hydrophobes are ...
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 In thermochemistry, the enthalpy of solution ( heat of solution or enthalpy of solvation) is the enthalpy change associated with the dissolution of a substance in a solvent at constant pressure resulting in infinite dilution. The enthalpy of so ...
.


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 color wheel blue (a primary color in the RGB color space), as well as to some variants of ultramarine, based on the ancient dye of the same name. The word "indigo" comes from the Latin word ''indicum'', m ...
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) 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 Benzoic acid is a white (or colorless) solid organic compound with the formula , whose structure consists of a benzene ring () with a carboxyl () substituent. It is the simplest aromatic carboxylic acid. The name is derived from gum benzoin, ...
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 sublimates directly from the solid state to the gas state. It is used primarily ...
. Benzoic acid is more soluble in an organic solvent such as dichloromethane or
diethyl ether Diethyl ether, or simply ether, is an organic compound in the ether class with the formula , sometimes abbreviated as (see Pseudoelement symbols). It is a colourless, highly volatile, sweet-smelling ("ethereal odour"), extremely flammable li ...
, and when shaken with this organic solvent in a
separatory funnel A separatory funnel, also known as a separation funnel, separating funnel, or colloquially sep funnel, is a piece of laboratory glassware used in liquid-liquid extractions to separate (''partition'') the components of a mixture into two immiscib ...
, 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 Liquid–liquid extraction (LLE), also known as solvent extraction and partitioning, is a method to separate compounds or metal complexes, based on their relative solubilities in two different immiscible liquids, usually water (polar) and an orga ...
, is an important technique in
synthetic chemistry As a topic of chemistry, chemical synthesis (or combination) is the artificial execution of chemical reactions to obtain one or several product (chemistry), products. This occurs by physics, physical and chemical manipulations usually involving o ...
. 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 In chemistry, a salt is a chemical compound consisting of an ionic assembly of positively charged cations and negatively charged anions, which results in a compound with no net electric charge. A common example is table salt, with positively c ...
) 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 dissolved molecules. Both ionized and uncharged molecules interact strongly with a solvent, and the strength and nature of this interaction influence many properties of the ...
). 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 , 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 atomic number and the d ...
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 concentration is the solubility and related to the
solubility product Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical reacti ...
, ''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 Moles can refer to: * Moles de Xert, a mountain range in the Baix Maestrat comarca, Valencian Community, Spain * The Moles (Australian band) *The Moles, alter ego of Scottish band Simon Dupree and the Big Sound People *Abraham Moles, French engin ...
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 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-ignited internal combustion engines (also known as petrol engines). It consists mostly of organi ...
because both petroleum jelly and gasoline are non-polar hydrocarbons. It will not, on the other hand, dissolve in
ethyl alcohol Ethanol (abbr. EtOH; also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound. It is an alcohol with the chemical formula . Its formula can be also written as or (an ethyl group linked to a hyd ...
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 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, ductilit ...
ing element will dissolve into the
base metal A base metal is a common and inexpensive metal, as opposed to a precious metal such as gold or silver. In numismatics, coins often derived their value from the precious metal content; however, base metals have also been used in coins in the past ...
without forming a separate phase. The
solvus In a physical or geochemical system, a solvus is a line (binary system) or surface (ternary system) on a phase diagram which separates a homogeneous solid solution from a field of several phases which may form by exsolution or incongruent melting. ...
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 A solid solution, a term popularly used for metals, is a homogenous mixture of two different kinds of atoms in solid state and have a single crystal structure. Many examples can be found in metallurgy, geology, and solid-state chemistry. The wor ...
. 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 In thermodynamics, the phase rule is a general principle governing "pVT" systems, whose thermodynamic states are completely described by the variables pressure (), volume () and temperature (), in thermodynamic equilibrium. If is the number of d ...
, 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 A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell para ...
(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 Albite is a plagioclase feldspar mineral. It is the sodium endmember of the plagioclase solid solution series. It represents a plagioclase with less than 10% anorthite content. The pure albite endmember has the formula . It is a tectosilicate ...
may result in formation of
gibbsite Gibbsite, Al(OH)3, is one of the mineral forms of aluminium hydroxide. It is often designated as γ-Al(OH)3 (but sometimes as α-Al(OH)3.). It is also sometimes called hydrargillite (or hydrargyllite). Gibbsite is an important ore of aluminiu ...
. : . 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 rock Metamorphic rocks arise from the transformation of existing rock to new types of rock in a process called metamorphism. The original rock ( protolith) is subjected to temperatures greater than and, often, elevated pressure of or more, caus ...
s. 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 relationship Quantitative structure–activity relationship models (QSAR models) are regression or classification models used in the chemical and biological sciences and engineering. Like other regression models, QSAR regression models relate a set of "predic ...
s (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, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
. 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 The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
and ''T'' is the temperature in
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
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. : \log_ (S) = 0.8 - \log_ (P) - 0.01(\text -25) : \log_ (S) = 0.5 - \log_ (P) - 0.01(\text -25) These equations are founded on the principles of the fusion cycle.


See also

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


Notes


References


External links

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