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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 ri ...
). 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 oxide
An oxide () is a chemical compound that contains at least one oxygen atom and one other element in its chemical formula. "Oxide" itself is the dianion of oxygen, an O2– (molecular) ion. with oxygen in the oxidation state of −2. Most of the E ...
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 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 rep ...
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 suspend ...
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 prec ...
and calcite
Calcite is a Carbonate minerals, carbonate mineral and the most stable Polymorphism (materials science), polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on ...
in water are expected to differ, even though they are both polymorphs of calcium carbonate and have the same chemical formula
In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
.
The solubility of one substance in another is determined by the balance of intermolecular force
An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction
or repulsion which act between atoms and other types of neighbouring particles, e.g. a ...
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 electr ...
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
The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as ...
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 det ...
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 reacti ...
. 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. p. ...
(Δ''H'' > 0) or exothermic
In thermodynamics, an exothermic process () is a thermodynamic process or reaction that releases energy from the system to its surroundings, usually in the form of heat, but also in a form of light (e.g. a spark, flame, or flash), electricity (e ...
(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
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 relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
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
The degree Celsius is the unit of temperature on the Celsius scale (originally known as the centigrade scale outside Sweden), one of two temperature scales used in the International System of Units (SI), the other being the Kelvin scale. The ...
, 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 phys ...
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
Sodium chloride , commonly known as salt (although sea salt also contains other chemical salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35.45 g ...
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 Pari ...
(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 drywall. ...
) and cerium(III) sulfate
Cerium(III) sulfate, also called cerous sulfate, is an inorganic compound with the formula Ce2(SO4)3. It is one of the few salts whose solubility in water decreases with rising temperature.
Cerium (III) sulfate ( anhydrous) is a hygroscopic wh ...
, 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
Sodium sulfate (also known as sodium sulphate or sulfate of soda) is the inorganic compound with formula Na2SO4 as well as several related hydrates. All forms are white solids that are highly soluble in water. With an annual production of 6 milli ...
, where the less soluble decahydrate
In chemistry, a hydrate is a substance that contains water or its constituent elements. The chemical state of the water varies widely between different classes of hydrates, some of which were so labeled before their chemical structure was understo ...
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 is ...
at 32 °C to form a more soluble anhydrous
A substance is anhydrous if it contains no water. Many processes in chemistry can be impeded by the presence of water; therefore, it is important that water-free reagents and techniques are used. In practice, however, it is very difficult to achie ...
phase ( thenardite) with a smaller change in Gibbs free energy
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 pr ...
(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:
:
where the index iterates the components, is the mole fraction of the -th component in the solution, is the pressure, the index refers to constant temperature, is the partial molar volume of the -th component in the solution, is the partial molar volume of the -th component in the dissolving solid, and 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 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 Pari ...
(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:
:
where 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), is the partial pressure (in atm), and 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 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 Δ''p'' = 2γ/''r''; see Young–Laplace equation).
Henry's law is valid for gases that do not undergo change of chemical speciation on dissolution. Sieverts' law shows a case when this assumption does not hold.
The carbon dioxide 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 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 and carbon dioxide acts as an amplifier of the general warming.
Polarity
A popular aphorism used for predicting solubility is "''like dissolves like''" also expressed in the ''Latin'' language as "''Similia similibus solventur''". This statement indicates that a solute will dissolve best in a solvent that has a similar chemical structure to itself, based on favorable entropy of mixing. This view is simplistic, but it is a useful rule of thumb. The overall solvation capacity of a solvent depends primarily on its 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 salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35.45 g ...
(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''. Smaller Δ''G'' means greater solubility.
Chemists often exploit differences in solubilities to separate and purify compounds from reaction mixtures, using the technique of liquid-liquid extraction. This applies in vast areas of chemistry from drug synthesis to spent nuclear fuel reprocessing.
Rate of dissolution
Dissolution is not an instantaneous process. The rate of solubilization (in kg/s) is related to the solubility product and the surface area of the material. The speed at which a solid dissolves may depend on its crystallinity or lack thereof in the case of amorphous 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:
:
where:
* = mass of dissolved material
* = time
* = surface area of the interface between the dissolving substance and the solvent
* = diffusion coefficient
* = thickness of the boundary layer of the solvent at the surface of the dissolving substance
* = mass concentration of the substance on the surface
* = mass concentration of the substance in the bulk of the solvent
For dissolution limited by diffusion (or mass transfer if mixing is present), is equal to the solubility of the substance. When the dissolution rate of a pure substance is normalized to the surface area of the solid (which usually changes with time during the dissolution process), then it is expressed in kg/m2s and referred to as "intrinsic dissolution rate". The intrinsic dissolution rate is defined by the United States Pharmacopeia.
Dissolution rates vary by orders of magnitude between different systems. Typically, very low dissolution rates parallel low solubilities, and substances with high solubilities exhibit high dissolution rates, as suggested by the Noyes-Whitney equation.
Theories of solubility
Solubility product
Solubility constants are used to describe saturated solutions of ionic compounds of relatively low solubility (see solubility equilibrium 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. 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 can affect the numerical value of solubility constant. While the solubility constant is not as simple as solubility, the value of this constant is generally independent of the presence of other species in the solvent.
Other theories
The Flory–Huggins solution theory is a theoretical model describing the solubility of polymers. The Hansen solubility parameters and the Hildebrand solubility parameters are empirical methods for the prediction of solubility. It is also possible to predict solubility from other physical constants such as the enthalpy of fusion.
The octanol-water partition coefficient, usually expressed as its logarithm (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 salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35.45 g ...
) 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 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 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 concentration is the solubility and related to the solubility product, ''K''sp. This equilibrium constant depends on the type of salt ( vs. , for example), temperature, and the common ion effect.
One can calculate the amount of that will dissolve in 1 liter of pure water as follows:
:''K''sp = [Ag+] × [Cl−] / M2 (definition of solubility product; M = mol/L)
:''K''sp = 1.8 × 10−10 (from a table of solubility products)
[Ag+] = [Cl−], in the absence of other silver or chloride salts, so
:[Ag+]2 = 1.8 × 10−10 M2
:[Ag+] = 1.34 × 10−5 mol/L
The result: 1 liter of water can dissolve 1.34 × 10−5 mole (unit), moles of at room temperature. Compared with other salts, is poorly soluble in water. For instance, table salt () has a much higher ''K''sp = 36 and is, therefore, more soluble. The following table gives an overview of solubility rules for various ionic compounds.
Solubility of organic compounds
The principle outlined above under #Polarity, 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.
In solid compounds (as opposed to elements), the solubility of a solute element can also depend on the phases separating out in equilibrium. For example, amount of Sn soluble in the ZnSb phase can depend significantly on whether the phases separating out in equilibrium are (Zn4Sb3+Sn(L)) or (ZnSnSb2+Sn(L)). Besides these, the ZnSb compound with Sn as a solute can separate out into other combinations of phases after the solubility limit is reached depending on the initial chemical composition during synthesis. Each combination produces a different solubility of Sn in ZnSb. Hence solubility studies in compounds, concluded upon the first instance of observing secondary phases separating out might underestimate solubility. While the maximum number of phases separating out at once in equilibrium can be determined by the Gibb's phase rule, for chemical compounds there is no limit on the number of such phase separating combinations itself. Hence, establishing the "maximum solubility" in solid compounds experimentally can be difficult, requiring equilibration of many samples. If the dominant crystallographic defect (mostly interstitial or substitutional point defects) involved in the solid-solution can be chemically intuited beforehand, then using some simple thermodynamic guidelines can considerably reduce the number of samples required to establish maximum solubility.
Incongruent dissolution
Many substances dissolve congruently (i.e. the composition of the solid and the dissolved solute stoichiometrically match). However, some substances may dissolve 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.
In principle, both congruent and incongruent dissolution can lead to the formation of secondary solid phases in equilibrium. So, in the field of Materials Science, the solubility for both cases is described more generally on chemical composition phase diagrams.
Solubility prediction
Solubility is a property of interest in many aspects of science, including but not limited to: environmental predictions, biochemistry, pharmacy, drug-design, agrochemical design, and protein ligand binding. Aqueous solubility is of fundamental interest owing to the vital biological and transportation functions played by water. In addition, to this clear scientific interest in water solubility and solvent effects; accurate predictions of solubility are important industrially. The ability to accurately predict a molecule's solubility represents potentially large financial savings in many chemical product development processes, such as pharmaceuticals. In the pharmaceutical industry, solubility predictions form part of the early stage lead optimisation process of drug candidates. Solubility remains a concern all the way to formulation. A number of methods have been applied to such predictions including quantitative structure–activity relationships (QSAR), quantitative structure–property relationships (QSPR) and data mining. These models provide efficient predictions of solubility and represent the current standard. The draw back such models is that they can lack physical insight. A method founded in physical theory, capable of achieving similar levels of accuracy at an sensible cost, would be a powerful tool scientifically and industrially.
Methods founded in physical theory tend to use thermodynamic cycles, a concept from classical thermodynamics. 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, 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 phys ...
s.
:
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.
See also
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Notes
References
External links
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