# solubility

Dissolving salt as an example of a soluble compound.

The solubility of a substance indicates the extent to which a pure substance can be dissolved in a solvent . It describes the property of the substance to mix with homogeneous distribution (as atoms , molecules or ions ) in the solvent, i.e. H. to solve. Mostly the solvent is a liquid . But there are also solid solutions , such as alloys , glasses , ceramic materials and doped semiconductors . In the case of the solution of gases in liquids, the term solubility denotes a coefficient which indicates the amount of gas dissolved in the liquid at a certain pressure of the gas when the gas is in diffusion equilibrium between the gas space and the liquid, i.e. H. just as much in as diffused out. The solubility also depends on the temperature, on the pressure (to a small extent also in the case of non-gaseous compounds) and, for some compounds, on the pH value.

## Different definitions

According to the European Pharmacopoeia , solubility is the ratio of the mass of dissolved substance to the volume of the solvent at room temperature at saturation . This definition differs from the definition of mass concentration, which (despite the same unit of g / l) indicates the ratio of substance mass to volume of the solution. The IUPAC, for example, defines the mass concentration as a possible quantitative indication of the solubility ( analytical composition of a saturated solution, expressed in the form of the proportion of a dissolved substance in a specific solvent ).

The well-known CRC Handbook of Chemistry and Physics gives the solubility as the mass of the compound (with the exception of the crystalline water of hydrates), which can be dissolved in 100 g of water.

In general one differentiates:

• Qualitative solubility: is the substance soluble to a recognizable degree in a certain solvent?
• Quantitative solubility: It indicates the exact amount of substance that dissolves in the unit volume of a certain solvent.

## Qualitative solubility

For thermodynamic reasons ( entropy ), at temperatures above absolute zero there is a certain solubility for every substance in every other substance, as described in the article Pure Substance . The increasing accuracy of the analytical methods confirms this. A distinction between “soluble” and “insoluble” depends on the chosen boundary conditions. It is a matter of relative determinations of how sparingly soluble, limitedly soluble or indefinitely soluble one substance is in another.

A common classification of solubilities is given by the amount of maximum dissolved substance. Less than 0.1 mol / l of dissolved substance is referred to as sparingly soluble, between 0.1 and 1 mol / l as moderately soluble and solubilities greater than 1 mol / l are considered to be slightly soluble.

The liquids in which a solid is readily soluble depends on the molecular properties of the substance and the liquid. Thus, salt-like substances ( ionic compounds) almost only in polar solvents such as water or, for example, hydrofluoric soluble (HF). Many lipophilic (“fat-loving”) substances, on the other hand, are only appreciably soluble in organic solvents such as gasoline [a non-polar (“apolar”) solvent]. "Polar" in this context means that the molecules of the solvent have a dipole moment and therefore interact with charged (ions) or polar molecules of the substance to be dissolved, but without a reaction occurring. The polarity of solvents is scalable. Different polarities and thus different solubilities are used in the chromatographic processes.

Some substances, for example ethanol or acetone , are miscible with both water and non-polar solvents in any proportion.

## Quantitative solubility

### Solubility and solubility product

The solubility of a substance in a solvent does not have to be limited. Sulfuric acid can be mixed with water in any proportions.

Liquid-liquid equilibrium in the phenol-water mixture

When phenol is mixed with water, there are two areas at room temperature, a solution of up to 8% phenol in water and a solution of up to 25% water in phenol. In between there is an area of ​​"prohibited" mixing ratios. If phenol and water are mixed together in these proportions, this leads to the formation of two liquid phases. The range of impossible mixing ratios is called the miscibility gap. Above a certain temperature, the upper critical temperature of the solution, in the case of phenol and water at approx. 340 K (67 ° C), the mixture is completely miscible in any ratio.

In systems with limited solubility , the quantitative solubility or solubility limit indicates the maximum concentration of one substance in the other at which the mixture is still single-phase under equilibrium conditions . The solubility limit is temperature dependent. If the solubility limit is exceeded, a second phase is eliminated. If the necessary activation energy or diffusion for the separation of the second phase is missing , the mixture remains in a single-phase, metastable , supersaturated state even above the solubility limit .

In the case of salts, the solubility follows from the solubility product under the condition that the salt divides into and ions. ${\ displaystyle L}$${\ displaystyle K_ {L}}$${\ displaystyle A_ {m} B_ {n}}$${\ displaystyle m {\ text {}} A ^ {+}}$${\ displaystyle n {\ text {}} B ^ {-}}$

${\ displaystyle K_ {L} = c_ {eq} ^ {m} \ mathrm {(A ^ {+})} \ cdot c_ {eq} ^ {n} \ mathrm {(B ^ {-})}}$

If none of the ions involved is also present from a mixture, the solubility of the salt in question can be calculated. The solubility of the salt is: ${\ displaystyle A_ {m} B_ {n}}$

${\ displaystyle L = {\ frac {c_ {eq} \ mathrm {(} A ^ {+})} {m}} = {\ frac {c_ {eq} \ mathrm {(} B ^ {-})} {n}} = {\ sqrt [{n + m}] {\ frac {K_ {L}} {n ^ {n} \ cdot m ^ {m}}}}}$

In mixed solutions , as in natural water with a large number of ions, the concentrations of anions and cations do not match stoichiometrically in pairs (as would correspond to the solution of individual salts). An example of this is dissolved lime , which dissolves as calcium hydrogen carbonate through dissolved carbon dioxide and makes the essential contribution to water hardness . Via the dissociation equilibrium of the carbonic acid , with the changing carbon dioxide content of the water (through respiration and photosynthesis of the aquatic organisms), the concentrations of the carbonate and hydrogen carbonate anions also shift, the concentration of the calcium cations remains unaffected. In this case, the product of the non-equivalent concentrations of calcium and carbonate ions decides whether and to what extent calcium carbonate will precipitate (as scale or sea ​​chalk ) due to exceeding the solubility product .

The quantitative solubility, like the general concentration of solutions, is given in different units (also supplemented by the temperature):

### Determination by conductivity measurements

For salts that are very sparingly soluble in water (e.g. BaSO 4 , PbS, HgS, AgCl), the solubility product can be determined from conductivity measurements with sensitive conductometers . The limit conductivity of the salt at infinite dilution is also required for the calculation .

Friedrich Kohlrausch and Arnold F. Holleman developed this determination method.

### Temperature dependence

Solubility of some salts in water at different temperatures

As a first approximation, the solubility of one substance in another depends on the enthalpy of solution : If the solution reaction is endothermic (positive enthalpy of solution), the solubility increases when heated. In the case of an exothermic dissolution reaction, the solubility decreases when heated. If the enthalpy of solution is almost zero, as is the case with table salt , for example, the solubility hardly changes when heated.

How high the solubility is depends not only on the enthalpy of solution, but also on the entropy of solution . A negative enthalpy of solution thus contributes to good solubility, but a salt can still be sparingly soluble if the entropy of solution is also negative.

### Example of calculating the concentration of the saturated solution of a salt

Calculation of the concentration c for a saturated solution of aluminum sulfate in water, if K L is known

${\ displaystyle \ mathrm {Al_ {2} (SO_ {4}) _ {3} \ \ rightleftharpoons \ 2 \ Al ^ {3 +} + 3 \ SO_ {4} ^ {2-}}}$
${\ displaystyle K_ {L} = c_ {eq} ^ {2} \ mathrm {(Al ^ {3+})} \ cdot c_ {eq} ^ {3} \ mathrm {(SO_ {4} ^ {2- })}}$

This means that every mole of aluminum sulfate in the solution produces 2 moles of aluminum and 3 moles of sulfate ions. The following relationships also apply:

${\ displaystyle c_ {eq} \ mathrm {(Al ^ {3 +}) = 2} \; c \ quad {\ text {and}} \ quad c_ {eq} \ mathrm {(SO_ {4} ^ {2 -}) = 3} \; c}$

The factors before c, like the exponents in the previous equation, are the stoichiometric factors. Inserted into the equation for K L , we get:

${\ displaystyle K_ {L} = (2 \; c) ^ {2} \ cdot (3 \; c) ^ {3}}$

by which:

${\ displaystyle c = {\ sqrt [{5}] {\ frac {K_ {L}} {2 ^ {2} \ cdot 3 ^ {3}}}}}$

The numerical values ​​for the solubility products are obtained from the standard free enthalpies .

### Verbal classification according to the European Pharmacopoeia

The European Pharmacopoeia defines the following terms, at 15 ° C to 25 ° C:

designation V (solvent) in ml per g substance g · l −1 solvent
very easily soluble <1 > 1000
easily soluble 1 to 10 100 to 1000
soluble 10 to 30 33 to 100
sparingly soluble 30 to 100 10 to 33
poorly soluble 100 to 1000 1 to 10
very poorly soluble 1000 to 10000 0.1 to 1
practically (almost) insoluble > 10000 <0.1

## Dissolution of gases in liquids

At the interface between gases and liquids, diffusion leads to an exchange of gas molecules between the solution and the gas space. The entry of molecules into the solution is proportional to the partial pressure of the gas, and the exit is proportional to the concentration of the gas in the solution (see Henry's law ). At the so-called saturation concentration there is a dynamic equilibrium between the two diffusion directions. The saturation concentration is proportional to the partial pressure in the gas space. The connecting constant of proportionality is referred to here as solubility, more precisely as the solubility coefficient:

Gas solubility gas i = saturation concentration i / partial pressure i

The index i refers to the gas in possible mixed solutions, such as the solution of the gas mixture “air” in water.

As a rule, this solubility of gases in liquids decreases with increasing temperature. Solids dissolved in water also reduce the gas solubility. This is why, for example, less oxygen is soluble in sea water than in fresh water.

A deviation from the proportionality between gas pressure and equilibrium concentration is only noticeable at very high pressures (compared to atmospheric pressure).

## Solution in solids

The principles of solubility are in principle also retained for solids. Different phases can also be observed here. If a solid mixture is single-phase, it is a solution. Crystalline substances form mixed crystals or intermetallic compounds . Separate phases are often very finely divided. This is particularly the case when the cooling rate is higher than the rate of diffusion during formation or when the composition is eutectic . For this reason, it is usually not possible to assess the solubility with the naked eye, especially since single-phase systems are often crystalline, and intergranular phases can also arise. Aids are diagrams of the temperature profile of the cooling, where phase changes appear as breakpoints or kinks, and light microscopic and other crystallographic examinations with even greater effort.

In the case of solids, metastable solutions are significantly more common than in liquids. These arise particularly when the solubility in the already solidified mixture decreases with a decrease in temperature and there is no longer a sufficient diffusion rate.

The solubility of solids in one another or their multiphase nature and the change in this property with temperature is of great importance for the formation of technical alloys . A multi-phase approach is often desirable. Copper / nickel and silver / gold are examples of systems with complete solubility in any composition, the latter also occurring naturally as an electron . Steels , on the other hand, are predominantly multi-phase (ferrite, austenite, martensite, cementite); as single-phase alloys, only high-alloy ferritic chromium steels with 15% to 30% chromium and less than 0.1% carbon are of technical importance. The copper / zinc system has five different phases at room temperature, which are separated by miscibility gaps. Depending on the composition, there is only one of these or a mixture of these two in the miscibility gap between two phases. Two of these phases are in the technically relevant area ( brass : copper content min. 50%).

The copper / tin system , to which tin bronze belongs as the oldest technical alloy, is an example of metastable conditions: Between 520 ° C and 586 ° C, tin in copper is up to 15.8% of that which is already solid at this temperature Alloy soluble. Although the solubility of tin is close to zero in equilibrium at room temperature, material that has not exceeded such a tin concentration at the elevated temperature remains single-phase when it is cooled further, since diffusion hardly takes place. On the other hand, the melt already segregates during the previous solidification and the material solidified last can exceed the limit of 15.8% tin even with significantly lower tin contents of the alloy. Because of the great diffusion inertia of tin, these differences in concentration can only be compensated by prolonged annealing at approx. 750 ° C. Both effects together mean that, depending on the cooling rate, cast tin bronze is single-phase with tin contents of a maximum of 4% to 6% and even single-phase up to 15% can be achieved through annealing, although there is no significant solubility at room temperature.

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