Editing Solubility equilibrium (section)

==Quantitative aspects==
===Simple dissolution===
Dissolution of an '''organic solid''' can be described as an equilibrium between the substance in its solid and dissolved forms. For example, when [[sucrose]] (table sugar) forms a saturated solution
<math display="block">\mathrm { C_{12} H_{22} O_{11}(s) \leftrightharpoons  C_{12} H_{22} O_{11} (aq)}</math>
An equilibrium expression for this reaction can be written, as for any chemical reaction (products over reactants):
<math display="block">K^\ominus = \frac{\left\{\mathrm{{C}_{12}{H}_{22}{O}_{11}(aq)}\right\}}{ \left \{\mathrm{{C}_{12}{H}_{22}{O}_{11}(s)}\right\}}</math>
where ''K''<sup><s>o</s></sup> is called the thermodynamic solubility constant. The braces indicate [[Activity (chemistry)|activity]]. The activity of a pure solid is, by definition, unity. Therefore
<math display="block">K^\ominus = \left\{\mathrm{{C}_{12}{H}_{22}{O}_{11}(aq)}\right\}</math>
The activity of a substance, A, in solution can be expressed as the product of the concentration, [A], and an [[activity coefficient]], ''γ''. When ''K''<sup><s>o</s></sup> is divided by ''γ'', the solubility constant, ''K''<sub>s</sub>,
<math display="block">K_\mathrm{s} = \left[\mathrm{{C}_{12}{H}_{22}{O}_{11}(aq)}\right]</math>
is obtained. This is equivalent to defining the [[standard state]] as the saturated solution so that the activity coefficient is equal to one. The solubility constant is a true constant only if the activity coefficient is not affected by the presence of any other solutes that may be present. The unit of the solubility constant is the same as the unit of the concentration of the solute. For [[sucrose]] ''K''<sub>s</sub>&nbsp;=&nbsp;1.971&nbsp;mol&nbsp;dm<sup>−3</sup> at 25&nbsp;°C. This shows that the solubility of sucrose at 25&nbsp;°C is nearly 2&nbsp;mol&nbsp;dm<sup>−3</sup> (540&nbsp;g/L). Sucrose is unusual in that it does not easily form a supersaturated solution at higher concentrations, as do most other [[carbohydrate]]s.

===Dissolution with dissociation===
'''Ionic compounds''' normally [[Dissociation (chemistry)|dissociate]] into their constituent ions when they dissolve in water. For example, for [[silver chloride]]:
<chem display="block">AgCl_{(s)} <=> Ag^+_{(aq)}{} + Cl^-_{(aq)}  </chem>
The expression for the equilibrium constant for this reaction is:
<math chem display="block">K^\ominus
= \frac{\left\{\ce{Ag+}_\ce{(aq)}\right\}\left\{\ce{Cl-}_\ce{(aq)}\right\}}{ \left\{\ce{AgCl_{(s)}}\right\}}
=\left\{\ce{Ag+}_\ce{(aq)}\right\}\left\{\ce{Cl-}_\ce{(aq)}\right\}
</math>
where <math>K^\ominus</math> is the thermodynamic equilibrium constant and braces indicate activity. The activity of a pure solid is, by definition, equal to one.

When the solubility of the salt is very low the activity coefficients of the ions in solution are nearly equal to one. By setting them to be actually equal to one this expression reduces to the '''solubility product''' expression:
<math chem display="block">K_\ce{sp} = [\ce{Ag+}] [\ce{Cl-}]= [\ce{Ag+}]^2= [\ce{Cl-}]^2.</math>

For 2:2 and 3:3 salts, such as CaSO<sub>4</sub> and FePO<sub>4</sub>, the general expression for the solubility product is the same as for a 1:1 electrolyte
<math display="block"> \mathrm{AB} \leftrightharpoons  \mathrm{A}^{p+} +  \mathrm{B}^{p-}</math>
:<math>K_{sp}= \mathrm{[A] [B]} = \mathrm{[A]^2}= \mathrm{[B]^2}</math> (electrical charges are omitted in general expressions, for simplicity of notation)
With an unsymmetrical salt like Ca(OH)<sub>2</sub> the solubility expression is given by
<math chem display="block"> \ce{ Ca(OH)_2 <=>  {Ca}^{2+} +  2OH^- }</math>
<math chem display="block">K_{sp} =  \ce{[Ca]}  \ce{[OH]}^2 </math>
Since the concentration of hydroxide ions is twice the concentration of calcium ions this reduces to <math>\mathrm{K_{sp} =  4[Ca]^3 }</math>

In general, with the chemical equilibrium
<math chem display="block"> \ce{A}_p \ce{B}_q ~\ce{\leftrightharpoons}~ p\ce{A}^{n+} +  q\ce{B}^{m-}</math>
<math chem display="block"> \ce{[B]} = \frac{q}{p}\ce{[A] }  </math>
and the following table, showing the relationship between the solubility of a compound and the value of its solubility product, can be derived.<ref>{{Cite book|title=Fundamentals of Analytical Chemistry|last=Skoog|first=Douglas A| last2=West|first2=Donald M| last3=Holler|first3=F James| publisher=Brooks/Cole| year=2004| edition=8th| pages=238–242| chapter=9B-5|ISBN = 0030355230}}</ref>
:{| class="wikitable"
!Salt  ||p||q||Solubility, S
|-
!AgCl<br>Ca(SO<sub>4</sub>)<br>Fe(PO<sub>4</sub>)
| 1|| 1|| {{math|1={{sqrt|''K''<sub>sp</sub>}}}}
|-
!Na<sub>2</sub>(SO<sub>4</sub>)<br>Ca(OH)<sub>2</sub>
| 2<br>1|| 1<br>2|| <math chem>\sqrt[3]{K_\ce{sp}\over4}</math>
|-
!Na<sub>3</sub>(PO<sub>4</sub>)<br>FeCl<sub>3</sub>
|3<br>1|| 1<br>3 || <math chem>\sqrt[4]{K_\ce{sp}\over27}</math>
|-
!Al<sub>2</sub>(SO<sub>4</sub>)<sub>3</sub><br>Ca<sub>3</sub>(PO<sub>4</sub>)<sub>2</sub>
|2<br>3||3<br>2||<math chem>\sqrt[5]{K_\ce{sp}\over 108}</math>
|-
!M<sub>p</sub>(An)<sub>q</sub>
|p
|q
|<math chem="">\sqrt[p+q]{K_\ce{sp}\over p^p q^q}</math>
|}
Solubility products are often expressed in logarithmic form. Thus, for calcium sulfate, with {{math|1=''K''<sub>sp</sub> = {{val|4.93|e=-5}} mol<sup>2</sup> dm<sup>−6</sup>}}, {{math|1=log ''K''<sub>sp</sub> = −4.32}}. The smaller the value of ''K''<sub>sp</sub>, or the more negative the log value, the lower the solubility.

Some salts are not fully dissociated in solution. Examples include [[magnesium sulfate|MgSO<sub>4</sub>]], famously discovered by [[Manfred Eigen]] to be present in [[seawater]] as both an [[inner sphere complex]] and an [[ion association|outer sphere complex]].<ref>{{cite web|url=http://nobelprize.org/nobel_prizes/chemistry/laureates/1967/eigen-lecture.pdf |first=Manfred |last=Eigen|author-link=Manfred Eigen |title=Nobel lecture|date=1967|website=Nobel Prize}}</ref> The solubility of such salts is calculated by the method outlined in [[#Dissolution with reaction|dissolution with reaction]].

==== Hydroxides ====
The solubility product for the hydroxide of a metal ion, M<sup>''n''+</sup>, is usually defined,  as follows:
<math display="block">\mathrm{M(OH)_n \leftrightharpoons \mathrm{M^{n+} + n OH^-}}</math>
<math display="block">K_{sp} = \mathrm{[M^{n+}] [OH^-]^n} </math>
However, general-purpose computer programs are designed to use hydrogen ion concentrations with the alternative definitions.
<math display="block">\mathrm{M(OH)_n + nH^+ \leftrightharpoons M^{n+} + n H_2O }</math>
<math display="block">K^*_\text{sp} = \mathrm{[M^{n+}] [H^+]^{-n}} </math>

For hydroxides, solubility products are often given in a modified form, ''K''*<sub>sp</sub>, using hydrogen ion concentration in place of hydroxide ion concentration. The two values are related by the [[Self-ionization of water|self-ionization]] constant for water, ''K''<sub>w</sub>.<ref name="bm">{{cite book|last1=Baes |first1=C. F.|last2= Mesmer |first2=R. E. |title=The Hydrolysis of Cations |date=1976|publisher=Wiley|location= New York}}</ref>
<math display="block">K_\mathrm{w} = [\mathrm{H^+}] [\mathrm{OH^-}]</math>
<math display="block">K^*_\text{sp} =  \frac{K_\text{sp}}{(K_\text{w})^n}</math>
<math display="block">\log K^*_\text{sp} = \log K_\text{sp} - n \log K_\text{w}</math>
For example, at ambient temperature, for calcium hydroxide, Ca(OH)<sub>2</sub>, lg ''K''<sub>sp</sub> is ca. −5 and lg ''K''*<sub>sp</sub> ≈ −5 + 2 × 14 ≈ 23.

=== Dissolution with reaction ===
[[File:Silver Chloride dissolution.png|thumb|220px| When a concentrated solution of ammonia is added to a suspension of silver chloride dissolution occurs because a complex of Ag<sup>+</sup> is formed]]
A typical reaction with dissolution involves a [[weak base]], B, dissolving in an acidic [[aqueous solution]].
<math display="block">\mathrm {B} \mathrm{(s)} + \mathrm H^+ \mathrm {(aq)} \leftrightharpoons \mathrm {BH}^+ (\mathrm{aq)}</math>
This reaction is very important for pharmaceutical products.<ref>{{cite web|url=http://www.pharmainfo.net/reviews/potential-solubility-drug-discovery-and-development |title=Potential Of Solubility In Drug Discovery And development |last=Payghan |first=Santosh |year=2008 |publisher=Pharminfo.net |access-date=5 July 2010 |url-status=dead |archive-url=https://web.archive.org/web/20100330171700/http://www.pharmainfo.net/reviews/potential-solubility-drug-discovery-and-development |archive-date=March 30, 2010 }}</ref> Dissolution of weak acids in alkaline media is similarly important.
<math display="block">\mathrm{ HA(s) + OH^-(aq) \leftrightharpoons A^- (aq) + H_2O}</math>
The uncharged molecule usually has lower solubility than the ionic form, so solubility depends on pH and the [[acid dissociation constant]] of the solute. The term "intrinsic solubility" is used to describe the solubility of the un-ionized form in the absence of acid or alkali.

Leaching of [[aluminium salt]]s from rocks and soil by [[acid rain]] is another example of dissolution with reaction: [[alumino-silicate]]s are bases which react with the acid to form soluble species, such as Al<sup>3+</sup>(aq).

Formation of a chemical [[Complex (chemistry)|complex]] may also change solubility. A well-known example is the addition of a concentrated solution of [[ammonia]] to a suspension of [[silver chloride]], in which dissolution is favoured by the formation of an ammine complex.
<math display="block">\mathrm{AgCl(s) + 2 NH_3(aq) \leftrightharpoons [Ag(NH_3)_2]^+(aq) + Cl^- (aq)}</math>
When sufficient ammonia is added to a suspension of silver chloride, the solid dissolves. The addition of [[water softener]]s to washing powders to inhibit the formation of [[soap scum]] provides an example of practical importance.