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 reaction with another constituent of the solvent, such as acid or alkali. Each type of equilibrium is characterized by a temperature-dependent equilibrium constant. Solubility equilibria are important in pharmaceutical, environmental and many other scenarios.
A solubility equilibrium exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The equilibrium is an example of dynamic equilibrium in that some individual molecules migrate between the solid and solution phases such that the rates of dissolution and precipitation are equal to one another. When equilibrium is established, the solution is said to be saturated. The concentration of the solute in a saturated solution is known as the solubility. Units of solubility may be molar (mol dm−3) or expressed as mass per unit volume, such as μg ml−1. Solubility is temperature dependent. A solution containing a higher concentration of solute than the solubility is said to be supersaturated. A supersaturated solution may be induced to come to equilibrium by the addition of a "seed" which may be a tiny crystal of the solute, or a tiny solid particle, which initiates precipitation.
There are three main types of solubility equilibria.
In each case an equilibrium constant can be specified as a quotient of activities. This equilibrium constant is dimensionless as activity is a dimensionless quantity. However, use of activities is very inconvenient, so the equilibrium constant is usually divided by the quotient of activity coefficients, to become a quotient of concentrations. See equilibrium chemistry#Equilibrium constant for details. Moreover, the concentration of solvent is usually taken to be constant and so is also subsumed into the equilibrium constant. For these reasons, the constant for a solubility equilibrium has dimensions related to the scale on which concentrations are measured. Solubility constants defined in terms of concentrations are not only temperature dependent, but also may depend on solvent composition when the solvent contains also species other than those derived from the solute.
Equilibria are defined for specific crystal phases. Therefore, the solubility product is expected to be different depending on the phase of the solid. For example, aragonite and calcite will have different solubility products even though they have both the same chemical identity (calcium carbonate). Under any given conditions one phase will be thermodynamically more stable than the other; therefore, this phase will form when thermodynamic equilibrium is established. However, kinetic factors may favor the formation the unfavorable precipitate (e.g. aragonite), which is then said to be in a metastable state.
In pharmacology, the metastable state is sometimes referred to as amorphous state. Amorphous drugs have higher solubility than their crystalline counterparts due to the absence of long-distance interactions inherent in crystal lattice. Thus, it takes less energy to solvate the molecules in amorphous phase. The effect of amorphous phase on solubility is widely used to make drugs more soluble. 
The thermodynamic solubility constant is defined for large monocrystals. Solubility will increase with decreasing size of solute particle (or droplet) because of the additional surface energy. This effect is generally small unless particles become very small, typically smaller than 1 μm. The effect of the particle size on solubility constant can be quantified as follows:
where *KA is the solubility constant for the solute particles with the molar surface area A, *KA→0 is the solubility constant for substance with molar surface area tending to zero (i.e., when the particles are large), γ is the surface tension of the solute particle in the solvent, Am is the molar surface area of the solute (in m2/mol), R is the universal gas constant, and T is the absolute temperature.
The salt effects (salting in and salting-out) refers to the fact that the presence of a salt which has no ion in common with the solute, has an effect on the ionic strength of the solution and hence on activity coefficients, so that the equilibrium constant, expressed as a concentration quotient, changes.
Solubility is sensitive to changes in temperature. For example, sugar is more soluble in hot water than cool water. It occurs because solubility constants, like other types of equilibrium constants, are functions of temperature. In accordance with Le Chatelier's Principle, when the dissolution process is endothermic (heat is absorbed), solubility increases with rising temperature. This effect is the basis for the process of recrystallization, which can be used to purify a chemical compound. When dissolution is exothermic (heat is released) solubility decreases with rising temperature.
Sodium sulfate shows increasing solubility with temperature below about 32.4 °C, but a decreasing solubility at higher temperature. This is because the solid phase is the decahydrate (Na
2O) below the transition temperature, but a different hydrate above that temperature.
The dependence on temperature of solubility for an ideal solution (achieved for low solubility substances) is given by the following expression containing the enthalpy of melting ΔmH and mole fraction of the solute at saturation:
This differential expression for a non-electrolyte can be integrated on a temperature interval to give:
For nonideal solutions activity of the solute at saturation appears instead of mole fraction solubility in the derivative w.r.t. temperature:
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 i iterates the components, xi is the mole fraction of the ith component in the solution, P is the pressure, the index T refers to constant temperature, -Vi,aq is the partial molar volume of the ith component in the solution, Vi,cr is the partial molar volume of the ith component in the dissolving solid, and R is the universal gas constant.
The pressure dependence of solubility does occasionally have practical significance. For example, precipitation fouling of oil fields and wells by calcium sulfate (which decreases its solubility with decreasing pressure) can result in decreased productivity with time.
Dissolution of an organic solid can be described as an equilibrium between the substance in its solid and dissolved forms. For example, when sucrose (table sugar) forms a saturated solution
An equilibrium expression for this reaction can be written, as for any chemical reaction (products over reactants):
o is called the thermodynamic solubility constant. The braces indicate activity. The activity of a pure solid is, by definition, unity. Therefore
The activity of a substance, A, in solution can be expressed as the product of the concentration, [A], and an activity coefficient, γ. When K
o is divided by γ, the solubility constant, Ks,
is obtained. This is equivalent to defining the standard state as the saturated solution so that the activity coefficient is equal to one. The solubility constant is a true constant only if the activity coefficient is not affected by the presence of any other solutes that may be present. The unit of the solubility constant is the same as the unit of the concentration of the solute. For sucrose K = 1.971 mol dm−3 at 25 °C. This shows that the solubility of sucrose at 25 °C is nearly 2 mol dm−3 (540 g/l). Sucrose is unusual in that it does not easily form a supersaturated solution at higher concentrations, as do most other carbohydrates.
The expression for the equilibrium constant for this reaction is:
where is the thermodynamic equilibrium constant and braces indicate activity. The activity of a pure solid is, by definition, equal to one.
When the solubility of the salt is very low the activity coefficients of the ions in solution are nearly equal to one. By setting them to be actually equal to one this expression reduces to the solubility product expression:
For 2:2 and 3:3 salts, such as CaSO4 and FePO4, the general expression for the solubility product is the same as for a 1:1 electrolyte
The equilibrium expression for an unsymmetrical salt like CaCl2 or Na2(SO4) is given by
A solute like Sn(SO4)2 is a 1:2 electrolyte like CaCl2, so a more complicated expression is needed for the solution equilibrium as the ionic charges are Sn4+ and SO42-. The solubility product, however, depends only on stoichiometry and is given by
When the product dissociates the concentration of B is equal to q/ times the concentration of A.
The solubility, S is 1/[A]. One may incorporate 1/ and insert it under the root to obtain
Solubility products are often expressed in logarithmic form. Thus, for calcium sulfate, Ksp = 4.93×10−5, log Ksp = −4.32. The smaller the value, or the more negative the log value, the lower the solubility.
Some salts are not fully dissociated in solution. Examples include MgSO4, famously discovered by Manfred Eigen to be present in seawater as both an inner sphere complex and an outer sphere complex. The solubility of such salts is calculated by the method outlined in dissolution with reaction.
For hydroxides solubility products are often given in a modified form, K*sp, using hydrogen ion concentration in place of hydroxide ion concentration. The two concentrations are related by the self-ionization constant for water, Kw.
log Ksp for Ca(OH)2 is about −5 at ambient temperatures; log K*sp = −5 + 2 × 14 = 23, approximately.
The common-ion effect is the effect of decreasing the solubility of one salt, when another salt, which has an ion in common with it, is also present. For example, the solubility of silver chloride, AgCl, is lowered when sodium chloride, a source of the common ion chloride, is added to a suspension of AgCl in water.
The solubility, S, in the absence of a common ion can be calculated as follows. The concentrations [Ag+] and [Cl−] are equal because one mole of AgCl dissociates into one mole of Ag+ and one mole of Cl−. Let the concentration of [Ag+](aq) be denoted by x.
Ksp for AgCl is equal to 1.77×10−10 mol2 dm−6 at 25 °C, so the solubility is 1.33×10−5 mol dm−3.
Now suppose that sodium chloride is also present, at a concentration of 0.01 mol dm−3. The solubility, ignoring any possible effect of the sodium ions, is now calculated by
This is a quadratic equation in x, which is also equal to the solubility.
In the case of silver chloride x2 is very much smaller than 0.01x, so this term can be ignored. Therefore
a considerable reduction. In gravimetric analysis for silver, the reduction in solubility due to the common ion effect is used to ensure "complete" precipitation of AgCl.
A typical reaction with dissolution involves a weak base, B, dissolving in an acidic aqueous solution.
This reaction is very important for pharmaceutical products. Dissolution of weak acids in alkaline media is similarly important.
The uncharged molecule usually has lower solubility than the ionic form, so solubility depends on pH and the acid dissociation constant of the solute. The term "intrinsic solubility" is used to describe the solubility of the un-ionized form in the absence of acid or alkali.
Leaching of aluminium salts from rocks and soil by acid rain is another example of dissolution with reaction: alumino-silicates are bases which react with the acid to form soluble species, such as Al3+(aq).
Formation of a chemical complex may also change solubility. A well-known example, is the addition of a concentrated solution of ammonia to a suspension of silver chloride, in which dissolution is favoured by the formation of an ammine complex.
Another example involves the addition of water softeners to washing powders to inhibit the precipitation of salts of magnesium and calcium ions, which are present in hard water, by forming complexes with them.
The calculation of solubility in these cases requires two or more simultaneous equilibria to be considered. For example,
|Intrinsic solubility equilibrium||B(s) ⇌ B(aq)||Ks = [B(aq)]|
|Acid–base equilibrium||B(aq) + H+(aq) ⇌ BH+(aq)||Ka = [B(aq)][H+(aq)]/[BH+(aq)]|
The determination of solubility is fraught with difficulties. First and foremost is the difficulty in establishing that the system is in equilibrium at the chosen temperature. This is because both precipitation and dissolution reactions may be extremely slow. If the process is very slow solvent evaporation may be an issue. Supersaturation may occur. With very insoluble substances, the concentrations in solution are very low and difficult to determine. The methods used fall broadly into two categories, static and dynamic.
In static methods a mixture is brought to equilibrium and the concentration of a species in the solution phase is determined by chemical analysis. This usually requires separation of the solid and solution phases. In order to do this the equilibration and separation should be performed in a thermostatted room. Very low concentrations can be measured if a radioactive tracer is incorporated in the solid phase.
A variation of the static method is to add a solution of the substance in a non-aqueous solvent, such as dimethyl sulfoxide, to an aqueous buffer mixture.  Immediate precipitation may occur giving a cloudy mixture. The solubility measured for such a mixture is known as "kinetic solubility". The cloudiness is due to the fact that the precipitate particles are very small resulting in Tyndall scattering. In fact the particles are so small that the particle size effect comes into play and kinetic solubility is often greater than equilibrium solubility. Over time the cloudiness will disappear as the size of the crystallites increases, and eventually equilibrium will be reached in a process known as precipitate ageing.
Solubility values of organic acids, bases, and ampholytes of pharmaceutical interest may be obtained by a process called "Chasing equilibrium solubility". In this procedure, a quantity of substance is first dissolved at a pH where it exists predominantly in its ionized form and then a precipitate of the neutral (un-ionized) species is formed by changing the pH. Subsequently, the rate of change of pH due to precipitation or dissolution is monitored and strong acid and base titrant are added to adjust the pH to discover the equilibrium conditions when the two rates are equal. The advantage of this method is that it is relatively fast as the quantity of precipitate formed is quite small. However, the performance of the method may be affected by the formation supersaturated solutions.
A number of computer programs are available to do the calculations. They include:
Acetylene (systematic name: ethyne) is the chemical compound with the formula C2H2. It is a hydrocarbon and the simplest alkyne. This colorless gas is widely used as a fuel and a chemical building block. It is unstable in its pure form and thus is usually handled as a solution. Pure acetylene is odorless, but commercial grades usually have a marked odor due to impurities.As an alkyne, acetylene is unsaturated because its two carbon atoms are bonded together in a triple bond. The carbon–carbon triple bond places all four atoms in the same straight line, with CCH bond angles of 180°.Acetylide
Acetylide refers to chemical compounds with the chemical formulas MC≡CH and MC≡CM, where M is a metal. The term is used loosely and can refer to substituted acetylides having the general structure RC≡CM (where R is an organic side chain). Acetylides are reagents in organic synthesis. The calcium acetylide commonly called calcium carbide is a major compound of commerce.Bacterioplankton
Bacterioplankton refers to the bacterial component of the plankton that drifts in the water column. The name comes from the Ancient Greek word πλανκτος (planktos), meaning "wanderer" or "drifter", and bacterium, a Latin term coined in the 19th century by Christian Gottfried Ehrenberg. They are found in both seawater and freshwater.
Bacterioplankton occupy a range of ecological niches in marine and aquatic ecosystems. They are both primary producers and primary consumers in these ecosystems and drive global biogeochemical cycling of elements essential for life (e.g., carbon and nitrogen). Many bacterioplankton species are autotrophic, and derive energy from either photosynthesis or chemosynthesis. Photosynthetic bacterioplankton are often categorized as picophytoplankton, and include major cyanobacterial groups such as Prochlorococcus and Synechococcus. Other heterotrophic bacterioplankton are saprotrophic, and obtain energy by consuming organic material produced by other organisms. This material may be dissolved in the medium and taken directly from there, or bacteria may live and grow in association with particulate material such as marine snow. Bacterioplankton play critical roles in global nitrogen fixation, nitrification, denitrification, remineralisation and methanogenesis.
Bacterioplankton abundance depends on environmental variables like temperature, nutrient availability and predation. Like other small plankton, the bacterioplankton are preyed upon by zooplankton (usually protozoans), and their numbers are also controlled through infection by bacteriophages.College Scholastic Ability Test
College Scholastic Ability Test or CSAT (Korean: 대학수학능력시험, hanja: 大學修學能力試驗; also abbreviated as Suneung (Korean: 수능, hanja: 修能) is a type of standardized test accepted by South Korean universities. KICE, Korea Institute of Curriculum and Evaluation, offers and manages the test every November. Though first designed to just assess scholastic ability required for education in college, it nowadays functions as a national graduation test which asks all the contents students learnt in high school. Determining which university the student can enter, the CSAT plays an important role in education in South Korea. It has been praised for its efficiency, meritocratic factors and high international results. Of the students taking the test, the percentage of re-takers is about 20%.On the test day, the stock markets open late, buses and subways are increased to avoid traffic jams that could prevent students from getting to testing sites, and planes are grounded so the noise does not disturb the students. In some cases, when some students are running late to the test, they are escorted by police officers. Younger students and the members of the students' families gather outside testing sites to cheer on the students.Common-ion effect
The common-ion effect states that in a chemical solution in which several species reversibly associate with each other by an equilibrium process, increasing the concentration of any one of its dissociated components by adding another chemical that also contains it will cause an increased amount of association. This result is a consequence of Le Chatelier's principle for the equilibrium reaction of the association/dissociation. The effect is commonly seen as an effect on the solubility of salts and other weak electrolytes. Adding an additional amount of one of the ions of the salt generally leads to increased precipitation of the salt, which reduces the concentration of both ions of the salt until the solubility equilibrium is reached. The effect is based on the fact that both the original salt and the other added chemical have one ion in common with each other.Dissociation (chemistry)
Dissociation in chemistry and biochemistry is a general process in which molecules (or ionic compounds such as salts, or complexes) separate or split into smaller particles such as atoms, ions, or radicals, usually in a reversible manner. For instance, when an acid dissolves in water, a covalent bond between an electronegative atom and a hydrogen atom is broken by heterolytic fission, which gives a proton (H+) and a negative ion. Dissociation is the opposite of association or recombination.Enthalpy change of solution
The enthalpy of solution, enthalpy of dissolution, or heat of solution is the enthalpy change associated with the dissolution of a substance in a solvent at constant pressure resulting in infinite dilution.
The enthalpy of solution is most often expressed in kJ/mol at constant temperature. The energy change can be regarded as being made of three parts, the endothermic breaking of bonds within the solute and within the solvent, and the formation of attractions between the solute and the solvent. An ideal solution has a null enthalpy of mixing. For a non-ideal solution it is an excess molar quantity.Excess property
Excess properties are properties of mixtures which quantify the non-ideal behavior of real mixtures. They are defined as the difference between the value of the property in a real mixture and the value that would exist in an ideal solution under the same conditions. The most frequently used excess properties are the excess volume, excess enthalpy, and excess chemical potential. The excess volume, internal energy, and enthalpy are identical to the corresponding mixing properties; that is,
These relationships hold because the volume, internal energy, and enthalpy changes of mixing are zero for an ideal solution.Hydration number
The hydration number, or solvation number of a compound is defined as the average number of molecules bound to the compound more strongly (by 13.3 kcal/mol or more) than they are bound to other water molecules. The hydration number is dependent on the concentration of the compound in solution, and the identity of the compound. When compounds are dissolved in water, the water molecules form a solvation shell surrounding the solute. For charged species, the orientation of water molecules around the solute is dependent on its ionic charge, with cations attracting water’s electronegative oxygen and anions attracting the hydrogens. Uncharged compounds such as methane can also be solvated by water and also have a hydration number. Although solvation shells can contain inner and outer shell solvent-solute interactions, the hydration number generally focuses on the inner shell solvent molecules that most directly interact with the solute.Insulin analog
An insulin analog is an altered form of insulin, different from any occurring in nature, but still available to the human body for performing the same action as human insulin in terms of glycemic control. Through genetic engineering of the underlying DNA, the amino acid sequence of insulin can be changed to alter its ADME (absorption, distribution, metabolism, and excretion) characteristics. Officially, the U.S. Food and Drug Administration (FDA) refers to these as "insulin receptor ligands", although they are more commonly referred to as insulin analogs.
These modifications have been used to create two types of insulin analogs: those that are more readily absorbed from the injection site and therefore act faster than natural insulin injected subcutaneously, intended to supply the bolus level of insulin needed at mealtime (prandial insulin); and those that are released slowly over a period of between 8 and 24 hours, intended to supply the basal level of insulin during the day and particularly at nighttime (basal insulin). The first insulin analog approved for human therapy (insulin Lispro rDNA) was manufactured by Eli Lilly and Company.List of types of equilibrium
This is a list of various types of equilibrium, the condition of a system in which all competing influences are balanced.Ostwald ripening
Ostwald ripening is a phenomenon observed in solid solutions or liquid sols that describes the change of an inhomogeneous structure over time, i.e., small crystals or sol particles dissolve, and redeposit onto larger crystals or sol particles.Dissolution of small crystals or sol particles and the redeposition of the dissolved species on the surfaces of larger crystals or sol particles was first described by Wilhelm Ostwald in 1896. Ostwald ripening is generally found in water-in-oil emulsions, while flocculation is found in oil-in-water emulsions.Salt (chemistry)
In chemistry, a salt is a solid chemical compound consisting of an ionic assembly of cations and anions. Salts are composed of related numbers of cations (positively charged ions) and anions (negative ions) so that the product is electrically neutral (without a net charge). These component ions can be inorganic, such as chloride (Cl−), or organic, such as acetate (CH3CO−2); and can be monatomic, such as fluoride (F−), or polyatomic, such as sulfate (SO2−4).Solubility
Solubility is the property of a solid, liquid or gaseous chemical substance called solute to dissolve in a solid, liquid or gaseous solvent. The solubility of a substance fundamentally depends on the physical and chemical properties of the solute and solvent as well as on temperature, pressure and presence of other chemicals (including changes to the pH) of the solution. The extent of the solubility of a substance in a specific solvent is measured as the saturation concentration, where adding more solute does not increase the concentration of the solution and begins to precipitate the excess amount of solute.
Insolubility is the inability to dissolve in a solid, liquid or gaseous solvent.
Most often, the solvent is a liquid, which can be a pure substance or a mixture. One may also speak of solid solution, but rarely of solution in a gas (see vapor–liquid equilibrium instead).
Under certain conditions, the equilibrium solubility can be exceeded to give a so-called supersaturated solution, which is metastable. Metastability of crystals can also lead to apparent differences in the amount of a chemical that dissolves depending on its crystalline form or particle size. A supersaturated solution generally crystallises when 'seed' crystals are introduced and rapid equilibration occurs. Phenylsalicylate is one such simple observable substance when fully melted and then cooled below its fusion point.
Solubility is not to be confused with the ability to dissolve a substance, because the solution might also occur because of a chemical reaction. For example, zinc dissolves (with effervescence) in hydrochloric acid as a result of a chemical reaction releasing hydrogen gas in a displacement reaction. The zinc ions are soluble in the acid.
The solubility of a substance is an entirely different property from the rate of solution, which is how fast it dissolves. The smaller a particle is, the faster it dissolves although there are many factors to add to this generalization.
Crucially solubility applies to all areas of chemistry, geochemistry, inorganic, physical, organic and biochemistry. In all cases it will depend on the physical conditions (temperature, pressure and concentration) and the enthalpy and entropy directly relating to the solvents and solutes concerned.
By far the most common solvent in chemistry is water which is a solvent for most ionic compounds as well as a wide range of organic substances. This is a crucial factor in acidity and alkalinity and much environmental and geochemical work.Solution
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. The mixing process of a solution happens at a scale where the effects of chemical polarity are involved, resulting in interactions that are specific to solvation. The solution assumes the phase of the solvent when the solvent is the larger fraction of the mixture, as is commonly the case. The concentration of a solute in a solution is the mass of that solute expressed as a percentage of the mass of the whole solution. The term "aqueous solution" is used when one of the solvents is water.Solvation
Solvation describes the interaction of solvent with dissolved molecules. Ionized and uncharged molecules interact strongly with solvent, and the strength and nature of this interaction influence many properties of the solute, including solubility, reactivity, and color, as well as influencing the properties of the solvent such as the viscosity and density. In the process of solvation, ions are surrounded by a concentric shell of solvent. Solvation is the process of reorganizing solvent and solute molecules into solvation complexes. Solvation involves bond formation, hydrogen bonding, and van der Waals forces. Solvation of a solute by water is called hydration.Solubility of solid compounds depends on a competition between lattice energy and solvation, including entropy effects related to changes in the solvent structure.Solvation shell
A solvation shell is the solvent interface of any chemical compound or biomolecule that constitutes the solute. When the solvent is water it is often referred to as a hydration shell or hydration sphere. The number of solvent molecules surrounding each unit of solute is called the hydration number of the solute.
A classic example is when water molecules arrange around a metal ion. For example, if the latter were a cation, the electronegative oxygen atom of the water molecule would be attracted electrostatically to the positive charge on the metal ion. The result is a solvation shell of water molecules that surround the ion. This shell can be several molecules thick, dependent upon the charge of the ion, its distribution and spatial dimensions.
A number of molecules of solvent are involved in the solvation shell around anions and cations from a dissolved salt in a solvent. Metal ions in aqueous solutions form metal aquo complexes. This number can be determined by various methods like compressibility and NMR measurements among others.Van 't Hoff equation
The van 't Hoff equation relates the change in the equilibrium constant, Keq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, ΔH⊖, for the process. It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book Études de dynamique chimique (Studies in Dynamic Chemistry). This equation is sometimes also referred to as the Vukančić–Vuković equation.The van 't Hoff equation has been widely utilized to explore the changes in state functions in a thermodynamic system. The van 't Hoff plot, which is derived from this equation, is especially effective in estimating the change in enthalpy, or total energy, and entropy, or amount of disorder, of a chemical reaction.
and related quantities