Solubility

 ( Chemical Properties ) 

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 solubility of a substance in a specific solvent is generally measured as the concentration of the solute in a solution, one in which no more solute can be dissolved. At this point, the two substances are said to be at the solubility equilibrium. For some solutes and solvents, there may be no such limit, in which case the two substances are said to be "miscibility in all proportions" (or just "miscible").

The solute can be a solid, a liquid, or a gas, while the solvent is usually solid or liquid. Both may be pure substances, or may themselves be solutions. Gases are always miscible in all proportions, except in very extreme situations,J. de Swaan Arons and G. A. M. Diepen (1966): "Gas—Gas Equilibria". Journal of Chemical Physics, volume 44, issue 6, page 2322. and a solid or liquid can be "dissolved" in a gas only by passing into the gaseous state first.

The solubility mainly depends on the composition of solute and solvent (including their 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 (, , or ) of the two substances, and of thermodynamics concepts such as enthalpy and entropy.

Under certain conditions, the concentration of the solute can exceed its usual solubility limit. The result is a supersaturation, which is metastability 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 between the two substances, such as the reaction of calcium hydroxide with hydrochloric acid; even though one might say, informally, that one "dissolved" the other. The solubility is also not the same as the rate of solution, 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, biology, physics, and oceanography, as well as in engineering, medicine, agriculture, and even in non-technical activities like painting, cleaning, cooking, and brewing. Most chemical reactions of scientific, industrial, or practical interest only happen after the have been dissolved in a suitable solvent. Water is by far the most common such solvent.

The term "soluble" is sometimes used for materials that can form colloid 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.

Alternatively, the solubility of a solute can be expressed in moles instead of mass. For example, if the quantity of solvent is given in kilograms, the value is the molality of the solution (mol/kg).

In more specialized contexts the solubility may be given by the mole fraction (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 are dimensionless numbers between 0 and 1 which may be expressed as percentages (%).

Moreover, many solids (such as and salts) will dissociate in non-trivial ways when dissolved; conversely, the solvent may form coordination complexes 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.

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.

The term solubility is also used in some fields where the solute is altered by solvolysis. For example, many metals and their are said to be "soluble in hydrochloric acid", although in fact the aqueous acid irreversibly degrades the solid to give soluble products. Most ionic solids dissociate when dissolved in polar solvents. 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 solution of cobalt(II) chloride can afford , each of which interconverts.

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 () 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 (i.e. about ten times higher) when the redox potential is controlled using a highly oxidizing Fe₃O₄-Fe₂O₃ redox buffer than with a moderately oxidizing Nickel-NiO buffer.

• For most and liquids, their solubility increases with temperature because their dissolution reaction is endothermic (Δ H > 0).John W. Hill, Ralph H. Petrucci, General Chemistry, 2nd edition, Prentice Hall, 1999. In liquid water at high temperatures, (e.g. that approaching the critical temperature), the solubility of ionic solutes tends to decrease due to the change of properties and structure of liquid water; the lower dielectric constant results in a less polar solvent and in a change of hydration energy affecting the Δ G of the dissolution reaction.

• 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 liquid water (temperature is in degrees Celsius, i.e. minus 273.15). Many salts behave like barium nitrate and disodium hydrogen arsenate, and show a large increase in solubility with temperature (Δ H > 0). Some solutes (e.g. sodium chloride in water) exhibit solubility that is fairly independent of temperature (Δ H ≈ 0). A few, such as calcium sulfate (gypsum) and cerium(III) sulfate, become less soluble in water as temperature increases (Δ H < 0). This is also the case for calcium hydroxide (portlandite), whose solubility at 70 °C is about half of its value at 25 °C. The dissolution of calcium hydroxide in water is also an exothermic process (Δ H < 0). As dictated by the van 't Hoff equation and Le Chatelier's principle, low temperatures favor dissolution of Ca(OH)₂. Portlandite solubility increases at low temperature. This temperature dependence is sometimes referred to as "retrograde" or "inverse" solubility. Occasionally, a more complex pattern is observed, as with sodium sulfate, where the less soluble decahydrate crystal (mirabilite) loses water of crystallization at 32 °C to form a more soluble anhydrous phase (thenardite) with a smaller change in Gibbs free energy (Δ G) in the dissolution reaction.

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 .

$\backslash left(\backslash frac\{\backslash partial\; \backslash ln\; N\_i\}\{\backslash partial\; P\}\; \backslash right)\_T\; =\; -\backslash frac\{V\_\{i,aq\}-V\_\{i,cr\}\}\; \{RT\}$

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.

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.

$p\; =\; k\_\{\backslash rm\; H\}\backslash ,\; c$

The solubility of gases is sometimes also quantified using Bunsen solubility coefficient.

In the presence of small Liquid bubble, 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 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.

In even more simple terms a simple ionic compound (with positive and negative ions) such as sodium chloride (common salt) is easily soluble in a highly polar 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 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.

The rate of dissolution can be often expressed by the Noyes–Whitney equation or the Nernst and Brunner equation of the form:

$\backslash frac\; \{\backslash mathrm\{d\}m\}\; \{\backslash mathrm\{d\}t\}\; =\; A\; \backslash frac\; \{D\}\; \{d\}\; (C\_\backslash mathrm\{s\}-C\_\backslash mathrm\{b\})$

where:

• $m$ = mass of dissolved material
• $t$ = time
• $A$ = surface area of the interface between the dissolving substance and the solvent
• $D$ = diffusion coefficient
• $d$ = thickness of the boundary layer of the solvent at the surface of the dissolving substance
• $C\_s$ = mass concentration of the substance on the surface
• $C\_b$ = mass concentration of the substance in the bulk of the solvent

For dissolution limited by diffusion (or mass transfer if mixing is present), $C\_s$ is equal to the solubility of the substance. When the dissolution rate of a pure substance is normalized to the surface area of the solid (which usually changes with time during the dissolution process), then it is expressed in kg/m²s and referred to as "intrinsic dissolution rate". The intrinsic dissolution rate is defined by the United States Pharmacopeia.

Dissolution rates vary by orders of magnitude between different systems. Typically, very low dissolution rates parallel low solubilities, and substances with high solubilities exhibit high dissolution rates, as suggested by the Noyes-Whitney equation.

The octanol-water partition coefficient, usually expressed as its logarithm (Log P), is a measure of differential solubility of a compound in a hydrophobe solvent (1-octanol) and a hydrophile 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.

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".El-Mansy, Mohamed & Yahia, Ibrahim S. & Alfaify, Sa. (2015). Conformational and Vibrational Properties of Indigo Dye: DFT Approach. Organo Opto-Electronics An International Journal. 3. 1-9.

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. Recycling is used to ensure maximum extraction.

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.

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⁺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 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.

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.

.

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 .

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 .

\log_{10} (S) = 0.8 - \log_{10} (P) - 0.01(\text{melting point} -25)
     
     

\log_{10} (S) = 0.5 - \log_{10} (P) - 0.01(\text{melting point} -25)