Editing Solubility equilibrium (section)

=== 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>