Editing Solubility equilibrium (section)

==Effects of conditions==
=== Temperature effect ===
[[File:SolubilityVsTemperature.png|thumb|300px]]

Solubility is sensitive to changes in [[temperature]]. For example, sugar is more soluble in hot water than cool water. It occurs because solubility products, like other types of equilibrium constants, are functions of temperature. In accordance with [[Le Chatelier's Principle]], when the dissolution process is [[endothermic reaction|endothermic]] (heat is absorbed), solubility increases with rising temperature. This effect is the basis for the process of [[Recrystallization (chemistry)|recrystallization]], which can be used to purify a chemical compound. When dissolution is [[exothermic]] (heat is released) solubility decreases with rising temperature.<ref name="pauling450">{{cite book|author-link=Linus Pauling| last=Pauling|first= Linus| title=General Chemistry|publisher= Dover Publishing |date= 1970 |page=450}}</ref>
[[Sodium sulfate]] shows increasing solubility with temperature below about 32.4&nbsp;°C, but a decreasing solubility at higher temperature.<ref>{{cite book|first1 = W.F.|last1 = Linke|first2=A.|last2= Seidell |title = Solubilities of Inorganic and Metal Organic Compounds|edition = 4th |publisher = Van Nostrand|year = 1965| isbn = 0-8412-0097-1}}</ref> This is because the solid phase is the decahydrate ({{Chem|Na|2|S|O|4|·10H|2|O}}) below the transition temperature, but a different hydrate above that temperature.{{cn|date=April 2023}}

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, Δ<sub>''m''</sub>''H'', and the mole fraction <math>x_i</math> of the solute at saturation:
<math display="block"> \left(\frac{\partial \ln x_i}{\partial T} \right)_P = \frac{\bar{H}_{i,\mathrm{aq}}-H_{i,\mathrm{cr}}}{RT^2}</math>
where <math> \bar{H}_{i,\mathrm{aq}}</math> is the [[partial molar enthalpy]] of the solute at infinite dilution and <math> H_{i,\mathrm{cr}}</math> the enthalpy per mole of the pure crystal.<ref>[[Kenneth Denbigh]], ''The Principles of Chemical Equilibrium'', 1957, p. 257</ref>

This differential expression for a non-electrolyte can be integrated on a temperature interval to give:<ref>[[Peter Atkins]], ''Physical Chemistry'', p. 153 (8th edition)</ref>
<math display="block"> \ln x_i=\frac{\Delta _m H_i}{R}  \left(\frac 1 {T_f} - \frac{1}{T} \right)</math>

For nonideal solutions activity of the solute at saturation appears instead of mole fraction solubility in the derivative with respect to temperature:
<math display="block"> \left(\frac{\partial \ln a_i}{\partial T} \right)_P= \frac{H_{i,\mathrm{aq}}-H_{i,\mathrm{cr}}}{RT^2}</math>

=== Common-ion effect ===
The [[common-ion effect]] is the effect of decreased solubility of one salt when another salt that 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.<ref>{{Housecroft3rd}} Section 6.10.</ref>
<math display="block">\mathrm{AgCl(s) \leftrightharpoons Ag^+ (aq) + Cl^- (aq) }</math>
The solubility, ''S'', in the absence of a common ion can be calculated as follows. The concentrations [Ag<sup>+</sup>] and [Cl<sup>−</sup>] are equal because one mole of AgCl would dissociate into one mole of Ag<sup>+</sup> and one mole of Cl<sup>−</sup>. Let the concentration of [Ag<sup>+</sup>(aq)] be denoted by ''x''. Then
<math display="block">K_\mathrm{sp}=\mathrm{[Ag^+] [Cl^-]}= x^2</math>
<math display="block"> \text{Solubility} = \mathrm{[Ag^+]=[Cl^-]} = x = \sqrt{K_\mathrm{sp}}  </math>
''K''<sub>sp</sub> for AgCl is equal to {{val|1.77|e=-10|u=mol<sup>2</sup> dm<sup>−6</sup>}} at 25&nbsp;°C, so the solubility is {{val|1.33|e=-5|u=mol dm<sup>−3</sup>}}.

Now suppose that sodium chloride is also present, at a concentration of 0.01&nbsp;mol dm<sup>−3</sup> = 0.01 M. The solubility, ignoring any possible effect of the sodium ions, is now calculated by
<math display="block">K_\mathrm{sp}=\mathrm{[Ag^+] [Cl^-]}=x(0.01 \,\text{M} + x)</math>
This is a quadratic equation in ''x'', which is also equal to the solubility.
<math display="block"> x^2 + 0.01 \, \text{M}\, x - K_{sp} = 0</math>
In the case of silver chloride, ''x''<sup>2</sup> is very much smaller than 0.01 M ''x'', so the first term can be ignored. Therefore
<math display="block">\text{Solubility}=\mathrm{[Ag^+]} = x = \frac{K_\mathrm{sp}}{0.01 \,\text{M}} = \mathrm{1.77 \times 10^{-8} \, mol \, dm^{-3}}</math>
a considerable reduction from {{val|1.33|e=-5|u=mol dm<sup>−3</sup>}}. In [[gravimetric analysis]] for silver, the reduction in solubility due to the common ion effect is used to ensure "complete" precipitation of AgCl.

=== Particle size effect ===
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:
<math display="block">\log(^*K_{A}) = \log(^*K_{A \to 0}) + \frac{\gamma A_\mathrm{m}} {3.454RT}</math>
where *''K<sub>A</sub>'' is the solubility constant for the solute particles with the molar surface area ''A'', *''K''<sub>''A''→0</sub> 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, ''A''<sub>m</sub> is the molar surface area of the solute (in m<sup>2</sup>/mol), ''R ''is the [[universal gas constant]], and ''T'' is the [[absolute temperature]].<ref name=hefter>{{cite book|editor1-last=Hefter|editor1-first=G. T.|editor2-last=Tomkins|editor2-first=R. P. T.| title=The Experimental Determination of Solubilities |year=2003|publisher=Wiley-Blackwell |isbn= 0-471-49708-8 }}</ref>

=== Salt effects ===
The salt effects<ref>{{VogelQuantitative}} Section 2.14</ref> ([[salting in]] and [[salting-out]]) refers to the fact that the presence of a salt which has [[common ion effect|no ion in common]] with the solute, has an effect on the [[ionic strength]] of the solution and hence on [[activity coefficient]]s, so that the equilibrium constant, expressed as a concentration quotient, changes.

=== Phase effect ===
Equilibria are defined for specific crystal [[Phase (matter)|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.{{cn|date=April 2023}}

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. [[In vivo supersaturation|The effect]] of amorphous phase on solubility is widely used to make drugs more soluble.<ref>{{Cite journal|last1=Hsieh|first1=Yi-Ling|last2=Ilevbare|first2=Grace A.|last3=Van Eerdenbrugh|first3=Bernard|last4=Box|first4=Karl J.|last5=Sanchez-Felix|first5=Manuel Vincente|last6=Taylor|first6=Lynne S.| date=2012-05-12|title=pH-Induced Precipitation Behavior of Weakly Basic Compounds: Determination of Extent and Duration of Supersaturation Using Potentiometric Titration and Correlation to Solid State Properties|journal=Pharmaceutical Research|language=en|volume=29|issue=10|pages=2738–2753|doi=10.1007/s11095-012-0759-8|pmid=22580905|s2cid=15502736|issn=0724-8741}}</ref><ref>{{Cite journal|last1=Dengale|first1=Swapnil Jayant| last2=Grohganz|first2=Holger| last3=Rades|first3=Thomas| last4=Löbmann|first4=Korbinian| date=May 2016|title=Recent advances in co-amorphous drug formulations|journal=Advanced Drug Delivery Reviews|volume=100|pages=116–125|doi=10.1016/j.addr.2015.12.009|pmid=26805787|issn=0169-409X}}</ref>

===Pressure effect===
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:
<math display="block"> \left(\frac{\partial \ln x_i}{\partial P} \right)_T = -\frac{\bar{V}_{i,\mathrm{aq}}-V_{i,\mathrm{cr}}} {RT} </math>
where <math>x_i</math> is the mole fraction of the <math>i</math>-th component in the solution, <math>P</math> is the pressure, <math>T</math> is the absolute temperature, <math>\bar{V}_{i,\text{aq}}</math> is the [[partial molar volume]] of the <math>i</math>th component in the solution, <math>V_{i,\text{cr}}</math> is the partial molar volume of the <math>i</math>th component in the dissolving solid, and <math>R</math> is the [[universal gas constant]].<ref>{{cite book|first=E. M.|last=Gutman| title=Mechanochemistry of Solid Surfaces|publisher=World Scientific Publishing|date=1994}}</ref>

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]] (which decreases its solubility with decreasing pressure) can result in decreased productivity with time.