Solubility

"Soluble" redirects here. For the algebraic object called a soluble group, see Solvable group.

Solubility is the property of a solid, liquid, or gaseous chemical substance called solute to dissolve in a liquid solvent to form a homogeneous solution. The solubility of a substance strongly depends on the used solvent as well as on temperature and pressure. 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.
The solvent is generally a liquid, which can be a pure substance or a mixture.^[1] One also speaks of solid solution, but rarely of solution in a gas (see vapor-liquid equilibrium instead)
The extent of solubility ranges widely, from infinitely soluble (fully miscible^[2] ) such as ethanol in water, to poorly soluble, such as silver chloride in water. The term insoluble is often applied to poorly or very poorly soluble compounds.
Under certain conditions the equilibrium solubility can be exceeded to give a so-called supersaturated solution, which is metastable.^[3]

Molecular view

Solubility occurs under dynamic equilibrium, which means that solubility results from the simultaneous and opposing processes of dissolution and phase separation (e.g. precipitation of solids). The solubility equilibrium occurs when the two processes proceed at a constant rate.
The term solubility is also used in some fields where the solute is altered by solvolysis. For example, many metals and their oxides are said to be "soluble in hydrochloric acid," whereas the aqueous acid degrades the solid to irreversibly give soluble products. It is also true that most ionic solids are degraded by polar solvents, but such processes are reversible. In those cases where the solute is not recovered upon evaporation of the solvent, the process is referred to as solvolysis. The thermodynamic concept of solubility does not apply straightforwardly to solvolysis.
When a solute dissolves, it may form several species in the solution. For example, an aqueous suspension of ferrous hydroxide, Fe(OH)₂, will contain the series [Fe(H₂O)_6 − x(OH)_x]^(2 − x)+ as well as other oligomeric species. Furthermore, the solubility of ferrous hydroxide and the composition of its soluble components depends on pH. In general, solubility in the solvent phase can be given only for a specific solute which 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).^{[citation needed]}

Factors affecting solubility

Solubility is defined for specific phases. For example, the solubility of aragonite and calcite in water are expected to differ, even though they are both polymorphs of calcium carbonate and have the same chemical formula.
The solubility of one substance in another is determined by the balance of intermolecular forces between the solvent and solute, and the entropy change that accompanies the solvation. Factors such as temperature and pressure will alter this balance, thus changing the solubility.
Solubility may also strongly depend on the presence of other species dissolved in the solvent, for example, complex-forming anions (ligands) in liquids. Solubility will also depend on the excess or deficiency of a common ion in the solution, a phenomenon known as the common-ion effect. To a lesser extent, solubility will depend on the ionic strength of solutions. The last two effects can be quantified using the equation for solubility equilibrium.
For a solid that dissolves in a redox reaction, solubility is expected to depend on the potential (within the range of potentials under which the solid remains the thermodynamically stable phase). For example, solubility of gold in high-temperature water is observed to be almost an order of magnitude higher when the redox potential is controlled using a highly-oxidizing Fe₃O₄-Fe₂O₃ redox buffer than with a moderately-oxidizing Ni-NiO buffer.^[4]
Solubility (metastable) also depends on the physical size of the crystal or droplet of solute (or, strictly speaking, on the specific or molar surface area of the solute). For quantification, see the equation in the article on solubility equilibrium. For highly defective crystals, solubility may increase with the increasing degree of disorder. Both of these effects occur because of the dependence of solubility constant on the Gibbs energy of the crystal. The last two effects, although often difficult to measure, are of practical importance.^{[citation needed]} 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 typically depends on temperature. For many solids dissolved in liquid water, the solubility increases with temperature up to 100 °C.^[5] 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.
Gaseous solutes exhibit more complex behavior with temperature. As the temperature is raised, gases usually become less soluble in water (to minimum which is below 120 °C for most permanent gases^[6]), but more soluble in organic solvents.^[5]
The chart shows solubility curves for some typical solid inorganic salts.^[7] Many salts behave like barium nitrate and disodium hydrogen arsenate, and show a large increase in solubility with temperature. Some solutes (e.g. NaCl in water) exhibit solubility which is fairly independent of temperature. A few, such as cerium(III) sulfate, become less soluble in water as temperature increases. This temperature dependence is sometimes referred to as "retrograde" or "inverse" solubility. Occasionally, a more complex pattern is observed, as with sodium sulfate, where the less soluble decahydrate crystal loses water of crystallization at 32 °C to form a more soluble anhydrous phase.^{[citation needed]}
The solubility of organic compounds nearly always increases with temperature. The technique of recrystallization, used for purification of solids, depends on a solute's different solubilities in hot and cold solvent. A few exceptions exist, such as certain cyclodextrins.^[8]

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:

$\left(\frac{\partial \ln N_i}{\partial P} \right)_T = -\frac{V_{i,aq}-V_{i,cr}} {RT}$

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_i,aq is the partial molar volume of the i^th component in the solution, V_i,cr is the partial molar volume of the i^th component in the dissolving solid, and R is the universal gas constant^[9].
The pressure dependence of solubility does occasionally have practical significance. For example, precipitation fouling of oil fields and wells by calcium sulfate (which decreases its solubility with decreasing pressure) can result in decreased productivity with time.

Solubility of gases

Henry's law is used to quantify the solubility of gases in solvents. The solubility of a gas in a solvent is directly proportional to the partial pressure of that gas above the solvent. This relationship is written as:

$p = kc \,$

where k is a temperature-dependent constant (for example, 769.2 L•atm/mol for dioxygen (O₂) in water at 298 K), p is the partial pressure (atm), and c is the concentration of the dissolved gas in the liquid (mol/L).

Polarity

A popular aphorism used for predicting solubility is "like dissolves like".^[10] This statement indicates that a solute will dissolve best in a solvent that has a similar polarity to itself. This view is rather simplistic, since it ignores many solvent-solute interactions, but it is a useful rule of thumb. For example, a very polar (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 lipophilic solute such as naphthalene is insoluble in water, fairly soluble in methanol, and highly soluble in non-polar benzene.^[11]
Liquid solubilities also generally follow this rule. Lipophilic plant oils, such as olive oil and palm oil, dissolve in non-polar solvents such as alkanes, but are less soluble in polar liquids such as water.
Synthetic chemists often exploit differences in solubilities to separate and purify compounds from reaction mixtures, using the technique of liquid-liquid extraction.
Insolubility and spontaneous phase separation does not mean that dissolution is disfavored by enthalpy. Quite the contrary, in the case of water and hydrophobic substances, hydrophobic hydration is reasonably exothermic and enthalpy alone should be favor it. It appears that entropic factors — the reduced freedom of movement of water molecules around hydrophobic molecules — lead to an overall hydrophobic effect.

Rate of dissolution

Dissolution is not always an instantaneous process. It is fast when salt and sugar dissolve in water but much slower for a tablet of aspirin or a large crystal of hydrated copper(II) sulfate. These observations are the consequence of two factors: the rate of solubilization 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. Critically, the dissolution rate depends on the presence of mixing and other factors that determine the degree of undersaturation in the liquid solvent film immediately adjacent to the solid solute crystal. 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). In practice, it means that the amount of solute in a solution is not always determined by its thermodynamic solubility, but may depend on kinetics of dissolution (or precipitation).
The rate of dissolution and solubility should not be confused as they are different concepts, kinetic and thermodynamic, respectively. The solubilization kinetics, as well as apparent solubility can be improved after complexation of an active ingredient with cyclodextrin. This can be used in the case of drug with poor solubility.^[12]

Quantification of solubility

Solubility is commonly expressed as a concentration, either by mass (g of solute per kg of solvent, g per dL (100 mL) of solvent), molarity, molality, mole fraction or other similar descriptions of concentration. The maximum equilibrium amount of solute that can dissolve per amount of solvent is the solubility of that solute in that solvent under the specified conditions. The advantage of expressing solubility in this manner is its simplicity, while the disadvantage is that it can strongly depend on the presence of other species in the solvent (for example, the common ion effect).
Solubility constants are used to describe saturated solutions of ionic compounds of relatively low solubility (see solubility equilibrium). The solubility constant is a special case of an equilibrium constant. It describes the balance between dissolved ions from the salt and undissolved salt. The solubility constant is also "applicable" (i.e. useful) to precipitation, the reverse of the dissolving reaction. As with other equilibrium constants, temperature can affect the numerical value of solubility constant. The solubility constant is not as simple as solubility, however the value of this constant is generally independent of the presence of other species in the solvent.
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 partition coefficient (Log P) is a measure of differential solubility of a compound in a hydrophobic solvent (octanol) and a hydrophilic solvent (water). The logarithm of these two values enables compounds to be ranked in terms of hydrophilicity (or hydrophobicity).

Applications

Solubility is of fundamental importance in a large number of scientific disciplines and practical applications, ranging from ore processing, 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 is described as "insoluble in water, alcohol, or ether but soluble in chloroform, nitrobenzene, or concentrated sulfuric acid".^{[citation needed]}
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 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.

Solubility of ionic compounds in water

Some ionic compounds (salts) dissolve in water, which arises because of the attraction between positive and negative charges (see: solvation). For example, the salt's positive ions (e.g. Ag⁺) attract the partially-negative oxygens in H₂O. Likewise, the salt's negative ions (e.g. Cl⁻) attract the partially-positive hydrogens in H₂O. Note: oxygen is partially-negative because it is more electronegative than hydrogen, and vice-versa (see: chemical polarity).

AgCl_(s) $\overrightarrow{\leftarrow}$ Ag⁺_(aq) + Cl⁻_(aq)

However, there is a limit to how much salt can be dissolved in a given volume of water. This amount is given by the solubility product, K_sp. This value depends on the type of salt (AgCl vs. NaCl, for example), temperature, and the common ion effect.
One can calculate the amount of AgCl that will dissolve in 1 liter of water, some algebra is required.

K_sp = [Ag⁺] × [Cl⁻] (definition of solubility product)

K_sp = 1.8 × 10⁻¹⁰ (from a table of solubility products)

[Ag⁺] = [Cl⁻], in the absence of other silver or chloride salts,

[Ag⁺]² = 1.8 × 10⁻¹⁰

[Ag⁺] = 1.34 × 10⁻⁵

The result: 1 liter of water can dissolve 1.34 × 10⁻⁵ moles of AgCl_(s) at room temperature. Compared with other types of salts, AgCl is poorly soluble in water. In contrast, table salt (NaCl) has a higher K_sp and is, therefore, more soluble.

Main article: Solubility chart

Soluble	Insoluble
Group I and NH₄⁺ compounds	carbonates (except Group I, NH₄⁺ and uranyl compounds)
nitrates	sulfites (except Group I and NH₄⁺ compounds)
acetates (ethanoates) (except Ag⁺ compounds)	phosphates (except Group I and NH₄⁺ compounds)
chlorides, bromides and iodides (except Ag⁺, Pb²⁺, Cu⁺ and Hg₂²⁺)	hydroxides and oxides (except Group I, NH₄⁺, Ba²⁺, Sr²⁺ and Tl⁺)
sulfates (except Ag⁺, Pb²⁺, Ba²⁺, Sr²⁺ and Ca²⁺)	sulfides (except Group I, Group II and NH₄⁺ 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 because both petroleum jelly and gasoline are hydrocarbons. It will not, on the other hand, dissolve in alcohol or water, since the polarity of these solvents is too high. Sugar will not dissolve in gasoline, since sugar is too polar in comparison with gasoline. A mixture of gasoline and sugar can therefore be separated by filtration, or extraction with water.

Solubility in non-aqueous solvents

Most publicly available solubility values are those for solubility in water.^[13] The reference also lists some for non-aqueous solvents. Solubility data for non-aqueous solvents is currently being collected via an open notebook science crowdsourcing project.^[14]^[15]

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 solubility line (or curve) is the line (or lines) on a phase diagram which 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 subtitutional position, for example: chromium in iron) or can 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.

[edit] 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, generally, some primary solid also remains and a complex solubility equilibrium establishes. For example, dissolution of albite may result in formation of gibbsite.^[16]

NaAlSi₃O₈(s) + H⁺ + 7H₂O = Na⁺ + Al(OH)₃(s) + 3H₄SiO₄.

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.

Raoult's law

Once the components in the solution have reached equilibrium, the total vapor pressure p of the solution is:

$p = p^{\star}_{\rm A} x_{\rm A} + p^{\star}_{\rm B} x_{\rm B} + \cdots$

and the individual vapor pressure for each component is

$p_i = p^{\star}_i x_i$

where

p*_i is the vapor pressure of the pure component

x_i is the mole fraction of the component in solution

Consequently, as the number of components in a solution increases, the individual vapor pressures decrease, since the mole fraction of each component decreases with each additional component. If a pure solute which has zero vapor pressure (it will not evaporate) is dissolved in a solvent, the vapor pressure of the final solution will be lower than that of the pure solvent.
This law is strictly valid only under the assumption that the chemical interactions between the two liquids is equal to the bonding within the liquids: the conditions of an ideal solution. Therefore, comparing actual measured vapor pressures to predicted values from Raoult's law allows information about the relative strength of bonding between liquids to be obtained. If the measured value of vapor pressure is less than the predicted value, fewer molecules have left the solution than expected. This is put down to the strength of bonding between the liquids being greater than the bonding within the individual liquids, so fewer molecules have enough energy to leave the solution. Conversely, if the vapor pressure is greater than the predicted value more molecules have left the solution than expected, due to the bonding between the liquids being less strong than the bonding within each.
The vapor pressure and composition in equilibrium with a solution can yield valuable information regarding the thermodynamic properties of the liquids involved. Raoult’s law relates the vapor pressure of components to the composition of the solution. The law assumes ideal behavior. It gives a simple picture of the situation just as the ideal gas law does. The ideal gas law is very useful as a limiting law. As the interactive forces between molecules and the volume of the molecules approaches zero, so the behavior of gases approach the behavior of the ideal gas.
Raoult’s law is similar in that it assumes that the physical properties of the components are identical. The more similar the components are, the more their behavior approaches that described by Raoult’s law. For example, if the two components differ only in isotopic content, then the vapor pressure of each component will be equal to the vapor pressure of the pure substance

P 0

times the mole fraction in the solution. This is Raoult’s law.
Using the example of a solution of two liquids, A and B, if no other gases are present, then the total vapor pressure p above the solution is equal to the weighted sum of the "pure" vapor pressures of the two components, p_A and p_B. Thus the total pressure above solution of A and B would be

$p = p^{\star}_{\rm A} x_{\rm A} + p^{\star}_{\rm B} x_{\rm B}$

Derivation

We define an ideal solution as a solution for which the chemical potential of component

i

is:

$\mu _i = \mu_i^{\star} + RT\ln x_i\,$ ,

where µ*_i is the chemical potential of pure i.
If the system is at equilibrium, then the chemical potential of the component i must be the same in the liquid solution and in the vapor above it. That is,

$\mu _{i,{\rm liq}} = \mu _{i,{\rm vap}}\,$

Assuming the liquid is an ideal solution, and using the formula for the chemical potential of a gas, gives:

$\mu _{i,{\rm liq}}^{\star} + RT\ln x_i = \mu_{i,{\rm vap}}^\ominus + RT\ln \frac{{f_i }} {{p^\ominus }}$

where ƒ_i is the fugacity of the vapor of

i

.
The corresponding equation for pure

i

in equilibrium with its (pure) vapor is:

$\mu _{i,{\rm liq}}^{\star} = \mu _{i,{\rm vap}}^\ominus + RT\ln \frac{{f_i^{\star}}} {{p^\ominus }}$

where * indicates the pure component.
Subtracting both equations gives us

$RT\ln x_i = RT\ln \frac{{f_i }}{{f_i^{\star} }}$

which re-arranges to

$f_i = x_i f_i^{\star}$

The fugacities can be replaced by simple pressures if the vapor of the solution behaves ideally i.e.

$p_i \approx x_i p_i^{\star}$

which is Raoult’s Law.

Ideal mixing

An ideal solution can be said to follow Raoult's Law but it must be kept in mind that in the strict sense ideal solutions do not exist. The fact that the vapor is taken to be ideal is the least of our worries. Interactions between gas molecules are typically quite small especially if the vapor pressures are low. The interactions in a liquid however are very strong. For a solution to be ideal we must assume that it does not matter whether a molecule A has another A as neighbor or a B molecule. This is only approximately true if the two species are almost identical chemically. We can see that from considering the Gibbs free energy change of mixing:

$\Delta_{\rm mix} G = nRT(x_1\ln x_1 + x_2\ln x_2)\,$

This is always negative, so mixing is spontaneous. However the expression is, apart from a factor –T, equal to the entropy of mixing. This leaves no room at all for an enthalpy effect and implies that Δ_mixH must be equal to zero and this can only be if the interactions U between the molecules are indifferent.
It can be shown using the Gibbs–Duhem equation that if Raoult's law holds over the entire concentration range x = 0–1 in a binary solution then, for the second component, the same must also hold.
If the deviations from ideality are not too strong, Raoult's law will still be valid in a narrow concentration range when approaching x = 1 for the majority phase (the solvent). The solute will also show a linear limiting law but with a different coefficient. This law is known as Henry's law.
The presence of these limited linear regimes has been experimentally verified in a great number of cases.
In a perfectly ideal system, where ideal liquid and ideal vapor are assumed, a very useful equation emerges if Raoult's law is combined with Dalton's Law.

$x_i = \frac{y_i p_{\rm total}}{p_{i,{\rm eqm}}}\,$

Non-ideal mixing

Raoult's Law may be adapted to non-ideal solutions by incorporating two factors that will account for the interactions between molecules of different substances. The first factor is a correction for gas non-ideality, or deviations from the ideal-gas law. It is called the fugacity coefficient (

φ

). The second, the activity coefficient (

γ

), is a correction for interactions in the liquid phase between the different molecules.
This modified or extended Raoult's law is then written:

$p_{i} \phi_i = p_i^{\star} \gamma_i x_i\,$

Real solutions

Many pairs of liquids are present in which there is no uniformity of attractive forces i.e. the adhesive & cohesive forces of attraction are not uniform between the two liquids, so that they show deviation from the raoult's law which is applied only to ideal solutions.

Negative deviation

When adhesive forces between molecules of A & B are greater than the cohesive forces between A & A or B & B, then the vapor pressure of the solution is less than the expected vapor pressure from Raoult's law. This is called as negative deviation from Raoult's law. These cohesive forces are lessened not only by dilution but also attraction between two molecules through formation of hydrogen bonds. This will further reduce the tendency of A and B to escape.

For example, chloroform & acetone show such an attraction by formation of an H-bond.

Positive deviation

When the cohesive forces between like molecules are greater than the adhesive forces, the dissimilarities of polarity or internal pressure will lead both components to escape solution more easily. Therefore, the vapor pressure will be greater than the expected from the Raoult's law, showing positive deviation. If the deviation is large, then the vapor pressure curve will show a maximum at a particular composition, e.g. benzene & ethyl alcohol, carbon disulfide & acetone, chloroform & ethanol.

Dühring's rule

Dühring's rule states that a linear relationship exists between the temperatures at which two solutions exert the same vapor pressure.^[1]^[2] The rule is often used to compare a pure liquid and a solution at a given concentration.
Dühring's plot is a graphical representation of such a relationship, typically with the pure liquid's boiling point along the x-axis and the mixture's boiling point along the y-axis; each line of the graph represents a constant concentration.

Dühring's plot for boiling point of NaCl solutions^[1]

Chemistry