View source for Metal ions in aqueous solution

{{short description|Properties and behavior of hydrated cations in aqueous solution}}
A '''metal ion in aqueous solution''' or '''aqua ion''' is a [[cation]], dissolved in [[water]], of [[chemical formula]] [M(H<sub>2</sub>O)<sub>n</sub>]<sup>z+</sup>. The [[hydration number|solvation number]], ''n'', determined by a variety of experimental methods is 4 for Li<sup>+</sup> and Be<sup>2+</sup> and 6 for most elements in periods 3 and 4 of the [[periodic table]]. [[Lanthanide]] and [[actinide]] aqua ions have higher solvation numbers (often 8 to 9), with the highest known being 11 for [[actinium|Ac]]<sup>3+</sup>. The strength of the bonds between the metal ion and water molecules in the primary [[solvation shell]] increases with the electrical charge, ''z'', on the metal ion and decreases as its [[ionic radius]], ''r'', increases. Aqua ions are subject to hydrolysis. The logarithm of the first hydrolysis constant is proportional to ''z''<sup>2</sup>/''r'' for most aqua ions.

The aqua ion is associated, through [[hydrogen bond]]ing with other water molecules in a secondary solvation shell. Water molecules in the first hydration shell exchange with molecules in the second solvation shell and molecules in the bulk liquid. The residence time of a molecule in the first shell varies among the [[chemical element]]s from about 100 [[picosecond]]s to more than 200 years. Aqua ions are prominent in [[electrochemistry]].

== Introduction to metal aqua ions ==
:{| class=wikitable style=text-align:center
|+Elements that form aqua cations
|-
| [[hydrogen|H]] || colspan=30 |
|{{font color|red|He}}
|-
| [[Lithium|Li]]|| [[Beryllium|Be]] ||colspan=24|
||{{font color|red|B}} ||{{font color|red|C}} ||{{font color|red|N}} ||{{font color|red|O}} ||{{font color|red|F}} ||{{font color|red|Ne}}
|-
| [[Sodium|Na]]|| [[Magnesium|Mg]]  ||colspan=24| 
|  [[Aluminium|Al]]
||{{font color|red|Si}} ||{{font color|red|P}} ||{{font color|red|S}} ||{{font color|red|Cl}} ||{{font color|red|Ar}}
|-
| [[Potassium|K]]|| [[Calcium|Ca]]|| colspan=14|
|[[Scandium|Sc]]||[[titanium|Ti]]||[[vanadium|V]]||[[chromium|Cr]]||[[manganese|Mn]]||[[iron|Fe]]||[[cobalt|Co]]||[[nickel|Ni]]||[[copper|Cu]]
|[[zinc|Zn]]||[[gallium|Ga]] ||[[germanium|Ge*]]||{{font color|red|As}} ||{{font color|red|Se}} ||{{font color|red|Br}} ||{{font color|red|Kr}}
|-
| [[Rubidium|Rb]]|| [[Strontium|Sr]]|| colspan=14|
||[[Yttrium|Y]]||[[zirconium|Zr]]||{{font color|red|Nb}}||[[molybdenum|Mo]]||{{font color|red|Tc}}||[[ruthenium|Ru]]||[[rhodium|Rh]]||[[palladium|Pd]]||[[silver|Ag]]
|[[cadmium|Cd]]||[[indium|In]]||[[tin|Sn]]||[[antimony|Sb*]] 
||{{font color|red|Te}} ||{{font color|red|I}} ||{{font color|red|Xe}}
|-
|[[Caesium|Cs]]|| [[Barium|Ba]]|| [[lanthanum|La]]
|[[cerium|Ce]]||[[Praseodymium|Pr]]||[[Neodymium|Nd]]|| [[Promethium|Pm]] ||[[Samarium|Sm]]||[[Europium|Eu]]||[[Gadolinium|Gd]]||[[Terbium|Tb]]||[[Dysprosium|Dy]]||[[Holmium|Ho]]||[[Erbium|Er]]||[[Thulium|Tm]]||[[Ytterbium|Yb]]||[[lutetium|Lu]] 
|[[hafnium|Hf]]||{{font color|red|Ta}}||{{font color|red|W}}||{{font color|red|Re}}||{{font color|red|Os}}||[[iridium|Ir]]||[[platinum|Pt]]||[[gold|Au]]
|[[mercury (element)|Hg]]||[[thallium|Tl]]||[[lead|Pb]]||[[bismuth|Bi]]||[[polonium|Po*]]||[[astatine|At*]]

||{{font color|red|Rn}}
|-
|[[francium|Fr*]]||[[radium|Ra*]]||[[actinium|Ac]]
| [[thorium|Th]]||[[protactinium|Pa]]||[[uranium|U]]||[[neptunium|Np]]||[[Plutonium|Pu]]
|[[americium|Am]]||[[curium|Cm]]||[[berkelium|Bk]]
|[[californium|Cf]]||[[einsteinium|Es*]]||[[Fermium|Fm*]]||[[Mendelevium|Md*]]||[[Nobelium|No*]]||[[lawrencium|Lr*]]||{{font color|grey|Rf}}||{{font color|grey|Db}}||{{font color|grey|Sg}}||{{font color|grey|Bh}}||{{font color|grey|Hs}}||{{font color|grey|Mt}}||{{font color|grey|Ds}}||{{font color|grey|Rg}}||{{font color|grey|Cn}}||{{font color|grey|Nh}}||{{font color|grey|Fl}}||{{font color|grey|Mc}}||{{font color|grey|Lv}}||{{font color|grey|Ts}}||{{font color|grey|Og}}
|}
:<nowiki>*</nowiki> No experimental information regarding aqua ion structures
Most [[chemical element]]s are [[metal]]lic. Compounds of the metallic elements usually form simple aqua ions with the formula [M(H<sub>2</sub>O)<sub>n</sub>]<sup>z+</sup> in low [[oxidation state]]s. With the higher oxidation states the simple aqua ions [[dissociation (chemistry)|dissociate]] losing [[hydrogen ion]]s to yield complexes that contain both water molecules and hydroxide or oxide ions, such as the [[vanadium]](IV) species [VO(H<sub>2</sub>O)<sub>5</sub>]<sup>2+</sup>. In the highest oxidation states only [[oxyanion]]s, such as the [[permanganate]](VII) ion, {{chem|MnO|4|-}}, are known. A few metallic elements that are commonly found only in high oxidation states, such as [[niobium]] and [[tantalum]], are not known to form aqua cations; near the metal–nonmetal boundary, [[arsenic]] and [[tellurium]] are only known as hydrolysed species. Some elements, such as [[tin]] and [[antimony]], are clearly metals, but form only covalent compounds in the highest oxidation states: their aqua cations are restricted to their lower oxidation states.<ref>Burgess, Section 1.2.</ref> [[Germanium]] is a semiconductor rather than a metal, but appears to form an aqua cation; similarly, [[hydrogen]] forms an aqua cation like metals, despite being a gas. The [[transactinide]]s have been greyed out due to a lack of experimental data. For some highly radioactive elements, experimental chemistry has been done, and aqua cations may have been formed, but no experimental information is available regarding the structure of those putative aqua ions.

[[File:Na+H2O.svg|thumb|left|Schematic representation of the aqua ion [Na(H<sub>2</sub>O)<sub>6</sub>]<sup>+</sup>. The oxygen atoms are arranged at the vertices of a regular [[octahedron]] centered on the sodium ion.]]
[[File:Secondary solvation.svg|thumb|First and second solvation shells of an octahedral aqua ion. Up to 12 water molecules may be present in the second shell (only two are shown in this diagram) linked by hydrogen bonds to the molecules in the first shell.]]

In aqueous solution the water molecules directly attached to the metal ion are said to belong to the [[first coordination sphere]], also known as the first, or primary, solvation shell. The bond between a water molecule and the metal ion is a [[dative covalent bond]], with the oxygen atom donating both electrons to the bond. Each coordinated water molecule may be attached by [[hydrogen bond]]s to other water molecules. The latter are said to reside in the second coordination sphere. The second coordination sphere is not a well defined entity for ions with charge 1 or 2. In dilute solutions it merges into the water structure in which there is an irregular network of hydrogen bonds between water molecules.<ref>Burgess, p. 20.</ref> With tripositive ions the high charge on the cation polarizes the water molecules in the first solvation shell to such an extent that they form strong enough hydrogen bonds with molecules in the second shell to form a more stable entity.<ref>Richens, p. 25.</ref>

The strength of the metal-oxygen bond can be estimated in various ways. The hydration enthalpy, though based indirectly on experimental measurements, is the most reliable measure. The scale of values is based on an arbitrarily chosen zero, but this does not affect differences between the values for two metals. Other measures include the M–O vibration frequency and the M–O bond length. The strength of the M-O bond tends to increase with the charge and decrease as the size of the metal ion increases. In fact there is a very good linear correlation between hydration enthalpy and the ratio of charge squared to ionic radius, z<sup>2</sup>/r.<ref>Burgess, p. 181.</ref> For ions in solution Shannon's "effective ionic radius" is the measure most often used.<ref>{{cite journal|last=Shannon|first=R.D.|year=1976|title=Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides|journal=Acta Crystallogr. A|volume=32|issue=5|pages=751–767|doi=10.1107/S0567739476001551|bibcode=1976AcCrA..32..751S|doi-access=}}. Richens, Appendix 2.</ref>

Water molecules in the first and second solvation shells can exchange places. The rate of exchange varies enormously, depending on the metal and its oxidation state. Metal aqua ions are always accompanied in solution by solvated anions, but much less is known about anion solvation than about cation solvation.<ref>Burgess, chapter 11.</ref>

Understanding of the nature of aqua ions is helped by having information on the nature of solvated cations in mixed solvents<ref>Burgess, Chapter 6.</ref> and non-aqueous [[solvent]]s, such as [[liquid ammonia]], [[methanol]], [[dimethyl formamide]] and [[dimethyl sulfoxide]] to mention a few.<ref>{{cite book|last=Chipperfield|first=John|title=Non-Aqueous Solvents|year=1999|publisher=OUP|location=Oxford|isbn= 978-0-19-850259-3}}</ref>

== Occurrence in nature ==
Aqua ions are present in most natural waters.<ref name=sm>Stumm&Morgan</ref> Na<sup>+</sup>, K<sup>+</sup>, Mg<sup>2+</sup> and Ca<sup>2+</sup> are major constituents of [[seawater]].
:{| class="wikitable" style=text-align:center
|+ Aqua ions in seawater ([[salinity]] = 35)                                          
|-
! Ion  
| [[Sodium|{{chem|Na|+}}]]
| [[Potassium|{{chem|K|+}}]] 
| [[Magnesium|{{chem|Mg|2+}}]]
| [[Calcium|{{chem|Ca|2+}}]]
|-
!Concentration <br />(mol kg<sup>−1</sup>)
| 0.469 
| 0.0102 
| 0.0528 
| 0.0103
|}

Many other aqua ions are present in seawater in concentrations ranging from [[Parts per million|ppm]] to [[Parts per trillion|ppt]].<ref name=sm/> The concentrations of sodium, potassium, magnesium and calcium in [[blood]] are similar to those of seawater. Blood also has lower concentrations of [[Dietary mineral|essential element]]s such as iron and zinc. [[Sports drink]] is designed to be [[Isotonicity|isotonic]] and also contains the minerals which are lost in [[perspiration]].

Magnesium and calcium ions are common constituents of [[domestic water]] and are responsible for permanent and temporary [[hard water|hardness]], respectively. They are often found in [[mineral water]].

== Experimental methods ==
Information obtained on the nature of ions in solution varies with the nature of the experimental method used. Some methods reveal properties of the cation directly, others reveal properties that depend on both cation and anion. Some methods supply information of a static nature, a kind of snapshot of average properties, others give information about the dynamics of the solution.

=== Nuclear magnetic resonance (NMR) ===
Ions for which the water-exchange rate is slow on the [[Relaxation (NMR)|NMR time-scale]] give separate peaks for molecules in the first solvation shell and for other water molecules. The [[hydration number|solvation number]] is obtained as a ratio of peak areas. Here it refers to the number of water molecules in the first solvation shell. Molecules in the second solvation shell exchange rapidly with solvent molecules, giving rise to a small change in the chemical shift value of un-coordinated water molecules from that of water itself. The main disadvantage of this method is that it requires fairly concentrated solutions, with the associated risk of [[ion-pair]] formation with the anion.
{| class="wikitable" style="text-align:center"
|+Solvation numbers determined by NMR<ref>Burgess, p. 53.</ref>
!Ion
|Be<sup>2+</sup>||Mg<sup>2+</sup>||Al<sup>3+</sup>||Ga<sup>3+</sup>||In<sup>3+</sup>
|Fe<sup>2+</sup>||Co<sup>2+</sup>||Ni<sup>2+</sup>||Zn<sup>2+</sup>||Th<sup>4+</sup>
|-
!Number
|4||6||6||6||6||6||6||6||6||9
|-
!Nucleus
|<sup>1</sup>H <sup>17</sup>O||<sup>1</sup>H ||<sup>1</sup>H ||<sup>1</sup>H <sup>17</sup>O
|<sup>1</sup>H||<sup>17</sup>O||<sup>1</sup>H||<sup>1</sup>H <sup>17</sup>O||<sup>1</sup>H||<sup>1</sup>H
|}

===X-ray diffraction (XRD)===

A solution containing an aqua ion does not have the long-range order that would be present in a crystal containing the same ion, but there is short-range order. X-ray diffraction on solutions yields a [[radial distribution function]] from which the coordination number of the metal ion and metal-oxygen distance may be derived. With aqua ions of high charge some information is obtained about the second solvation shell.<ref>{{cite book|editor-last1=Sykes|editor-first1=A.G. |last1=Johansson|first1=Georg|title=Structures of Compexes in Solution Derived from X-ray Diffraction Measurements|series=Advances in Inorganic Chemistry|volume=39|year=1992|publisher=Academic Press|location=San Diego|isbn=978-0-12-023639-8|pages=161–232}}</ref><ref>{{cite journal|last=Ohtaki|first=H.|author2=Radnai, T.|year=1993|title=Structure and dynamics of hydrated ions|journal=Chem. Rev.|volume=93|issue=3|pages=1157–1204|doi=10.1021/cr00019a014}}</ref>

This technique requires the use of relatively concentrated solutions. X-rays are scattered by electrons, so scattering power increases with atomic number. This makes hydrogen atoms all but invisible to X-ray scattering.

Large angle X-ray scattering has been used to characterize the second solvation shell with trivalent ions such as Cr<sup>3+</sup> and Rh<sup>3+</sup>. The second hydration shell of Cr<sup>3+</sup> was found to have {{val|13|1}} molecules at an average distance of {{val|402|20|u=pm}}. This implies that every molecule in the first hydration shell is hydrogen bonded to two molecules in the second shell.<ref>{{cite book| last1=Magini| first1=M.| last2=Licheri| first2=G.| last3=Paschina|first3=G. |author4=Piccaluga,G. |author5=Pinna, G. | title=X-ray diffraction of ions in aqueous solutions : hydration and complex formation |year=1988|publisher=CRC Press|location=Boca Raton, Fla|isbn=978-0-8493-6945-2}}</ref>

=== Neutron diffraction ===
Diffraction by neutrons also give a [[radial distribution function]]. In contrast to X-ray diffraction, neutrons are scattered by nuclei and there is no relationship with atomic number.<ref>{{cite book|editor-last=Sykes|editor-first=A.G.|last1=Enderby|first1=J.E.|last2=Nielson|first2=G.W.|title=The Coordination of Metal Aquaions|series=Advances in Inorganic Chemistry|volume=34|year=1989|publisher=Academic Press|location=San Diego|isbn=978-0-12-023634-3|doi=10.1016/S0898-8838(08)60017-3|pages=195–218}}</ref> Indeed, use can be made of the fact that different isotopes of the same element can have widely different scattering powers. In a classic experiment, measurements were made on four [[nickel chloride]] solutions using the combinations of <sup>58</sup>Ni, <sup>60</sup>Ni, <sup>35</sup>Cl and <sup>37</sup>Cl isotopes to yield a very detailed picture of cation and anion solvation.<ref name=nickelchloride>{{cite journal|last=Neilson|first=G.W.|author2=Enderby, J.E.|year=1983|title=The Structure of an Aqueous Solution of Nickel Chloride|journal=[[Proceedings of the Royal Society A]]|volume=390|issue=1799|pages=353–371|doi=10.1098/rspa.1983.0136|bibcode = 1983RSPSA.390..353N |s2cid=95824687}}</ref> Data for a number of metal salts show some dependence on the salt concentration.
{| class="wikitable" style=text-align:center
|+Cation hydration in solution, determined by neutron diffraction<ref>{{cite book|last=Enderby|first=J.E.|editor=Bellisent-Funel, M-C. |editor2=Neilson, G.W.|title=The Physics and Chemistry of Aqueous Solutions|series=NATO ASI Series| publisher=Reidel| year=1987| isbn=978-90-277-2534-9| pages=129–145|chapter=Diffraction Studies of Aqueous Ionic Solutions}} p. 138.</ref>
!Salt||colspan="3" |LiCl!!colspan="3" |CaCl<sub>2</sub>!!colspan="4" |NiCl<sub>2</sub>
|-
!Molality of salt
||27.77||9.95||3.57||4.49||2.80||1.0||3.05 ||0.85 ||0.46||0.086           
|-
!Cation hydration number<sup>†</sup>
|2.3 (2)||3.0 (5)||5.5 (3)||6.4 (3)||7.2 (2) ||10.0 (6)||5.8 (2)||6.6 (5)||6.8 (8)||6.8 (8)        
|-
!θ /deg<sup>‡</sup>  
|75 (5)||52 (5)||40 (5)||34 (9)||34 (9)||38 (9)|| 42 (8)|| 27 (10)||17 (10)||0 (20)         
|-
|}
{| class="wikitable" style=text-align:center
|+(continued)
!Salt||Ni(ClO<sub>4</sub>)<sub>2</sub>!!Cu(ClO<sub>4</sub>)<sub>2</sub>!!Fe(NO<sub>3</sub>)<sub>3</sub>!!NdCl<sub>3</sub>||DyCl<sub>3</sub>
|-
!Molality of salt
|3.80||2.00||2.0||2.85||2.38     
|-
!Cation hydration number<sup>†</sup>
|5.8 (2)||4.9 (3)||5.0 (2)||8.5 (2)||7.4 (5)         
|-
!θ /deg<sup>‡</sup> 
|42 (8)||38 (6)||22 (4)||24 (4)||17 (3)    
|-
|}
: <sup>†</sup>Figures in brackets are [[standard deviation]]s on the last significant figure of the value.<sup>‡</sup> angle between a M-OH<sub>2</sub> bond and the plane of the water molecule.
Most of these data refer to concentrated solutions in which there are very few water molecules that are not in the primary hydration spheres of the cation or anion, which may account for some of the variation of solvation number with concentration even if there is no contact ion pairing. The angle θ gives the angle of tilt of the water molecules relative to a plane in the aqua ion. This angle is affected by the hydrogen bonds formed between water molecules in the primary and secondary solvation shells.

The measured solvation number is a time-averaged value for the solution as a whole. When a measured primary solvation number is fractional there are two or more species with integral solvation numbers present in equilibrium with each other. This also applies to solvation numbers that are integral numbers, within experimental error. For example, the solvation number of 5.5 for a [[lithium chloride]] solution could be interpreted as being due to presence of two different aqua ions with equal concentrations.
: [Li(H<sub>2</sub>O)<sub>6</sub>]<sup>+</sup> {{eqm}} [Li(H<sub>2</sub>O)<sub>5</sub>]<sup>+</sup> + H<sub>2</sub>O
Another possibility is that there is interaction between a solvated cation and an anion, forming an [[ion pair]]. This is particularly relevant when measurements are made on concentrated salt solutions. For example, a solvation number of 3 for a lithium chloride solution could be interpreted as being due to the equilibrium
: [Li(H<sub>2</sub>O)<sub>4</sub>]<sup>+</sup> + Cl<sup>−</sup> {{eqm}} [Li(H<sub>2</sub>O)<sub>3</sub>Cl] + H<sub>2</sub>O
lying wholly in favour of the ion pair.

=== Vibrational spectra ===
[[infrared spectroscopy|Infrared spectra]] and [[raman spectroscopy|Raman spectra]] can be used to measure the M-O stretching frequency in metal aqua ions. Raman spectroscopy is particularly useful because the Raman spectrum of water is weak whereas the infrared spectrum of water is intense. Interpretation of the vibration frequencies is somewhat complicated by the presence, in octahedral and tetrahedral ions, of two vibrations, a symmetric one measured in the Raman spectrum and an anti-symmetric one, measured in the infrared spectrum.
{| class="wikitable" style="text-align:center"
|+Symmetric M-O stretching vibrations of some aqua ions in solution <ref>{{cite book|last=Adams|first=D.M.|title=Metal-Ligand and Related Vibrations|url=https://archive.org/details/metalligandrelat0000adam|url-access=registration|year=1967|publisher=Edward Arnold|location=London}} p.254.</ref><ref>Burgess, p. 85.</ref>
! metal ion
|[[beryllium|Be<sup>2+</sup>]]|||[[magnesium|Mg]]<sup>2+</sup>||[[manganese|Mn]]<sup>2+</sup>
|[[iron|Fe]]<sup>2+</sup>||[[nickel|Ni]]<sup>2+</sup>||[[copper|Cu]]<sup>2+</sup> 
|[[zinc|Zn]]<sup>2+</sup>||[[Mercury (element)|Hg]]<sup>2+</sup>
|[[aluminium|Al]]<sup>3+</sup>||[[gallium|Ga]]<sup>3+</sup>||[[indium|In]]<sup>3+</sup>        
|-
! wavenumber /cm<sup>−1</sup>
|530-543||360-365|| 395|| 389|||405|| 440
| 385-400||380||520-526|| 475|| 400
|}
Although the relationship between vibration frequency and [[molecular vibration|force constant]] is not simple, the general conclusion that can be taken from these data is that the strength of the M-O bond increases with increasing ionic charge and decreasing ionic size. The M-O stretching frequency of an aqua ion in solution may be compared with its counterpart in a crystal of known structure. If the frequencies are very similar it can be concluded that the coordination number of the metal ion is the same in solution as it is in a compound in the solid state.

===Dynamic methods===
Data such as [[Conductivity (electrolytic)|conductivity]], [[electrical mobility]] and [[diffusion]] relate to the movement of ions through a solution. When an ion moves through a solution it tends to take both first and second solvation shells with it. Hence solvation numbers measured from dynamic properties tend to be much higher that those obtained from static properties.
:{| class="wikitable"
|+[[Hydration number]]s measured by dynamic methods<ref>Richens, p. 40.</ref>
|-
! !! [[lithium|Li]]<sup>+</sup>!! [[sodium|Na]]<sup>+</sup>!![[cesium|Cs]]<sup>+</sup>!![[magnesium|Mg]]<sup>2+</sup>!![[calcium|Ca]]<sup>2+</sup>!![[barium|Ba]]<sup>2+</sup>!![[zinc|Zn]]<sup>2+</sup>!![[chromium|Cr]]<sup>3+</sup>||[[aluminium|Al]]<sup>3+</sup>
|-
| [[Ion transport number]]||13-22||7-13||4||12-14||8-12||3-5||10-13|| ||
|-
| Ion mobility||3-21||2-10|| ||10-13||7-11||5-9||10-13|| ||
|-
| Diffusion||5||3||1||9||9||8||11||17||13
|}

== Solvation numbers and structures ==

=== Hydrogen ===
{{main|Hydronium#Solvation}}
[[Image:Zundel-cation.JPG|thumb|Zundel cation]]
[[Hydrogen]] is not a metal, but like them it tends to lose its valence electron in chemical reactions, forming a cation H<sup>+</sup>. In aqueous solution, this immediately attaches itself to a water molecule,<ref>{{Greenwood&Earnshaw2nd|pages=36–37}}</ref> forming a species generally symbolised as [[hydronium|H<sub>3</sub>O<sup>+</sup>]] (sometimes loosely written H<sup>+</sup>). Such hydration forms cations that can in essence be considered as [H(OH<sub>2</sub>)<sub>''n''</sub>]<sup>+</sup>.<ref>Richens, p. 123</ref>

The solvation of H<sup>+</sup> in water is not fully characterised and many different structures have been suggested. Two well-known structures are the ''Zundel cation'' and the ''Eigen cation''. The Eigen solvation structure has the hydronium ion at the center of an {{chem2|H9O4(+)}} complex in which the hydronium is strongly [[hydrogen bond|hydrogen-bonded]] to three neighbouring water molecules. In the Zundel {{chem2|H5O2(+)}} complex the proton is shared equally by two water molecules in a [[symmetric hydrogen bond]].<ref>{{cite journal |last1=Zavitsas |first1=A. A. |date=2001 |title=Properties of water solutions of electrolytes and nonelectrolytes |journal=[[The Journal of Physical Chemistry B]] |volume=105 |issue=32 |pages=7805–7815 |doi=10.1021/jp011053l}}</ref><ref>{{cite journal |last1=Hulthe |first1=G. |last2=Stenhagen |first2=G. |last3=Wennerström |first3=O. |last4=Ottosson |first4=C-H. |date=1997 |title=Water cluster studied by electrospray mass spectrometry |doi=10.1016/S0021-9673(97)00486-X |journal=[[Journal of Chromatography A]] |volume=512 |pages=155–165}}</ref><ref>{{cite journal|last1=Zundel|first1=G. |last2= Metzger|first2=H. |date=1968|title= Energiebänder der tunnelnden Überschuß-Protonen in flüssigen Säuren. Eine IR-spektroskopische Untersuchung der Natur der Gruppierungen H5O2+ |journal=[[Zeitschrift für Physikalische Chemie]]|volume=58|issue= 5_6 |pages=225–245|doi=10.1524/zpch.1968.58.5_6.225|s2cid=101048854 }}</ref><ref>{{cite journal |last1=Wicke |first1=E. |last2=Eigen |first2=M. |last3=Ackermann |first3=Th |year=1954 |title=Über den Zustand des Protons (Hydroniumions) in wäßriger Lösung |journal=[[Zeitschrift für Physikalische Chemie]] |volume=1 |issue=5_6 |pages=340–364 |doi=10.1524/zpch.1954.1.5_6.340}}</ref><ref>{{Cite journal | doi = 10.1021/ja9101826|pmc=2946644|pmid=20078058| title = The Structure of the Hydrogen Ion ({{chem|H|aq|+}}) in Water| journal = [[Journal of the American Chemical Society]]| volume = 132| issue = 5| pages = 1484–1485| date = January 15, 2010| last1 = Stoyanov | first1 = Evgenii S. | last2 = Stoyanova | first2 = Irina V. | last3 = Reed | first3 = Christopher A. }}</ref>

=== Alkali metals ===

The hydrated [[lithium]] cation in water is probably tetrahedral and four-coordinated.<ref name=Persson2022>{{cite journal |last1=Persson |first1=Ingmar |date=2022 |title=Structures of Hydrated Metal Ions in Solid State and Aqueous Solution |journal=Liquids |volume=2 |issue=3 |pages=210–242 |doi=10.3390/liquids2030014 |doi-access=free }}</ref> There are most probably six water molecules in the primary solvation sphere of the octahedral [[sodium]] ion.<ref name=Persson2022/><ref>Richens, p. 127</ref> [[Potassium]] is seven-coordinate, and [[rubidium]] and [[caesium]] are probably eight-coordinate square antiprismatic.<ref name=Persson2022/> No data is available for [[francium]].

=== Alkaline earth metals ===
{| class=wikitable style=text-align:center
|+ Group 2 cations in aqueous solution
! ||[Be(H<sub>2</sub>O)<sub>4</sub>]<sup>2+</sup>||[Mg(H<sub>2</sub>O)<sub>6</sub>]<sup>2+</sup>||Ca<sup>2+</sup>(aq)||Sr<sup>2+</sup>(aq)||Ba<sup>2+</sup>(aq)
|-
!M-O distance (pm) 
|167||209||242<sup>§</sup>||263<sup>§</sup>||281<sup>§</sup>       
|-
|<math>\Delta H^\ominus </math> solvation (kJ mol<sup>−1</sup>)
|2494||1921||1577||1443||1305       
<!-- |-
!<math>\Delta V^\ominus</math> (cm<sup>3</sup> mol<sup>−1</sup>)
|−12.0||−21.2||−17.9||−18.2||−12.5  
 -->|}
:§ Values extrapolated from data for solid-state crystal structures

The [[beryllium]] cation [Be(H<sub>2</sub>O)<sub>4</sub>]<sup>2+</sup> has a very well-defined primary solvation shell with a tetrahedral BeO<sub>4</sub> core.<ref name=R129>Richens, p. 129.</ref> For [[magnesium]], [Mg(H<sub>2</sub>O)<sub>6</sub>]<sup>2+</sup> is also a well-characterized species, with an octahedral MgO<sub>6</sub> core.<ref name=R129/> The situation for [[calcium]] is more complicated. Neutron diffraction data gave a solvation number for calcium chloride, CaCl<sub>2</sub>, which is strongly dependent on concentration: {{val|10.0|0.6}} at 1&nbsp;mol·dm<sup>−3</sup>, decreasing to {{val|6.4|0.3}} at 2.8&nbsp;mol·dm<sup>−3</sup>. The enthalpy of solvation decreases  with increasing ionic radius. Various solid hydrates are known with 8-coordination in [[square antiprism]] and [[dodecahedral]] geometry.<ref>Richens, section 2.3.</ref> In water, calcium and [[strontium]] are most probably eight-coordinate square antiprismatic (although seven-coordination for calcium cannot presently be excluded). [[Barium]] is not as well-studied: it seems to have a coordination number of either eight or nine. Theoretical simulation of [[radium]] suggests that its aqua cation is ten-coordinate.<ref name=Persson2022/>

===Group 3 metals, lanthanides and actinides===
[[File:Tri-capped prism.png|thumb|face-capped trigonal prism structure]]
[[Scandium]](III) and [[yttrium]](III) are both eight-coordinate, but have different structures: scandium has an unusual dicapped triangular prismatic structure (with one cap location empty), while yttrium is square antiprismatic. [[Lutetium]](III) is tricapped triangular prismatic, but has a significant water deficit: one of the capping water molecules is significantly closer to the lutetium than the remaining ones and the average coordination number is only 8.2 rather than 9. Based on its ionic radius, [[lawrencium]](III) is probably nine-coordinate tricapped triangular prismatic with no water deficit.<ref name=Persson2022/>

The trivalent lanthanide ions decrease steadily in size from [[lanthanum]] to [[lutetium]], an effect known as the [[lanthanide contraction]].<ref>Richens, p. 185.</ref> From lanthanum to [[dysprosium]], the coordination number is maintained at 9 with a tricapped trigonal prismatic structure, although starting from [[samarium]] the capping water molecules are no longer equally strongly bounded. A water deficit then appears for [[holmium]] through lutetium with the average coordination number dropping to 8.2 at lutetium(III). The configuration is maintained despite the small size of the cations and the water deficit, probably due to strong hydrogen bonding.<ref name=Persson/> [[Europium]](II) is seven-coordinate, and [[cerium]](IV) is hydrolysed to the oxygen-bridged dimer [(H<sub>2</sub>O)<sub>7</sub>Ce–O–Ce(OH<sub>2</sub>)<sub>7</sub>]<sup>6+</sup>.<ref name=Persson2022/>

[[Actinium]](III) is eleven-coordinate in aqueous solution. [[Thorium]](IV) is nine-coordinate tricapped trigonal prismatic, and it is assumed that the same is true for the other actinide(IV) cations in aqueous solutions (as that is also their solid-state configuration). Studies on coordination number and/or structure for actinides(III) to date stretch only to [[californium]].<ref name=Persson/><ref name=Ac>{{cite journal |last1=Thierer |first1=Laura M. |last2=Tomson |first2=Neil C. |title=The Actinium Aqua Ion: A Century in the Making |journal=ACS Cent. Sci. |date=2017 |volume=3 |issue=3 |pages=153–155 |doi=10.1021/acscentsci.7b00074|pmid=28386590 |pmc=5364445 |doi-access=free }}</ref> However, since lawrencium(III) has a similar ionic radius to dysprosium(III), it is likely that [[uranium]](III) through lawrencium(III) are all nine-coordinate tricapped triangular prismatic with the capping positions fully occupied.<ref name=Persson/><ref name=Persson2022/> No data is available for [[fermium]](II), [[mendelevium]](II), or [[nobelium]](II).

===Group 4-12 metals===
{{see also|Metal aquo complex}}
[[File:Hexaaquacopper(II)-3D-balls.png|thumb|upright=0.8|Jahn-Teller distorted octahedral structure of [Cu(H<sub>2</sub>O)<sub>6</sub>]<sup>2+</sup> found in the solid state and possibly also in solution<ref name="Persson" />]]
[[File:Cu water.png|thumb|upright=0.8|Proposed square pyramidal structure of [Cu(H<sub>2</sub>O)<sub>5</sub>]<sup>2+</sup> in aqueous solution<ref>{{cite journal | last1 = Frank | first1 = Patrick | last2 = Benfatto | first2 = Maurizio | last3 = Szilagyi | first3 = Robert K. | last4 = D'Angelo | first4 = Paola | last5 = Della Longa | first5 = Stefano | last6 = Hodgson | first6 = Keith O. | date = 2005 | title = The Solution Structure of [Cu(aq)]<sup>2+</sup> and Its Implications for Rack-Induced Bonding in Blue Copper Protein Active Sites | journal = [[Inorganic Chemistry (journal)|Inorganic Chemistry]] | volume = 44 | issue = 6| pages = 1922–1933 | doi = 10.1021/ic0400639 | pmid = 15762718 }}</ref>]]

The ions of these metals in the +2 and +3 [[oxidation state]]s have a solvation number of 6. All have a regular octahedral structure except the aqua ions of [[chromium]](II) and [[copper]](II) which are subject to [[Jahn-Teller]] distortion. In the copper case the two axial Cu−O distances are 238 pm, whereas the four equatorial Cu−O distances are 195 pm in the solid state.<ref>Richens, chapters 4-12</ref> However, it is unclear whether Cu<sup>2+</sup> has a solvation number of 5 or 6 in aqueous solution, with conflicting experimental reports.<ref name="Persson">{{ cite journal | first1 = Ingmar | last1 = Persson | title = Hydrated metal ions in aqueous solution: How regular are their structures? | journal = [[Pure and Applied Chemistry]] | year = 2010 | volume = 82 | issue = 10 | pages = 1901–1917 | doi = 10.1351/PAC-CON-09-10-22 | doi-access = free }}</ref> The structure of [[cobalt]](III) in aqueous solution has not been determined.<ref name=Persson2022/> Copper(I) is estimated to be four-coordinate tetrahedral.<ref name=Persson2022/>

A solvation number of 6 with an octahedral structure is well established for [[zinc]](II) and [[cadmium]](II) in dilute solutions. In concentrated solutions the Zn<sup>2+</sup> ion may adopt a 4-coordinate, tetrahedral, structure, but the evidence is not conclusive because of the possibility of ion pairing and/or hydrolysis.<ref>Richens, p. 544.</ref> The solvation number of [[mercury (element)|mercury]](II) is most likely to be 6.<ref>Richens, p. 555.</ref> [[Zinc]](II) is six-coordinate octahedral, but [[cadmium]](II) may be in equilibrium between six- and seven-coordination. [[Mercury (element)|Mercury]](II) is a pseudo-Jahn-Teller-distorted octahedron.<ref name=Persson2022/> The bis aqua structure of the mercury(I) ion, [(H<sub>2</sub>O)-Hg-Hg-(OH<sub>2</sub>)]<sup>+</sup>, found in solid compounds,<ref>Richens, p. 551</ref> is not the same as that found in solution which involves three water molecules coordinated to each mercury completing a distorted tetrahedral arrangement.<ref name=Persson2022/> Another aqua species in which there is a metal-metal bond is the [[molybdenum]](II) species formulated as [(H<sub>2</sub>O)<sub>4</sub>Mo≣Mo(H<sub>2</sub>O)<sub>4</sub>]<sup>4+</sup>.<ref>{{cite journal |last1=Finholt |first1=James E. |last2=Leupin |first2=Peter |last3=Sykes |first3=A. Geoffrey |title=Kinetics and mechanism of substitution of the quadruply bonded molybdenum(II) aqua dimer with thiocyanate and oxalate |journal= Inorganic Chemistry|date=1983 |volume=22 |issue=22 |pages=3315–3333 |doi=10.1021/ic00164a027}}</ref> Each molybdenum is surrounded by four water molecules in a square-planar arrangement, in a structure similar to that of the known structure of the chloro complex [Mo<sub>2</sub>Cl<sub>8</sub>]<sup>4−</sup>.<ref>Richens, p. 282.</ref>

There are a few divalent and trivalent aqua ions of transition metals in the second and third transition series: [[ruthenium]](II) and (III), [[rhodium]](III), and [[iridium]](III), all octahedral. (Ruthenium and iridium structures have only been examined in the solid state, but it is assumed that they are the same in aqueous solution.)<ref name=Persson2022/> [[Molybdenum]](III) is questionable (and may be strongly hydrolyzed in aqueous solution), and molybdenum(II) dimerises with each molybdenum binding four water molecules.<ref name=Persson2022/><ref name=Persson/> [[Palladium]](II) and [[platinum]](II) aqua ions were originally thought to be square planar, but are actually strongly tetragonally elongated square-pyramidal or octahedral with the extra one or two water molecules extremely loosely bound.<ref name=Persson2022/> The structure of [[silver]](I) is disputed: it may be two-coordinate, or it may be four-coordinate with two extra very loosely bound water molecules.<ref name=Persson2022/> [[Gold]](III) is four-coordinate square planar in the solid state, and it is assumed to have the same structure in aqueous solution.<ref name=Persson2022/> Distortion occurs for low-coordinate metals with strong covalent tendencies due to the second-order Jahn-Teller effect. With oxidation state 4, however, the only unhydrolyzed species are the square antiprismatic [[zirconium]](IV), [Zr(H<sub>2</sub>O)<sub>8</sub>]<sup>4+</sup>, and [[hafnium]](IV), [Hf(H<sub>2</sub>O)<sub>8</sub>]<sup>4+</sup>, and even they are extremely prone to hydrolysis.<ref name=Persson/> Such a zirconium cation is only formed in dilute solutions of Zr<sup>IV</sup> in strong acid, and in practice the cationic species encountered of zirconium and hafnium are polynuclear.<ref>Richens, pp. 215–220</ref>

=== Group 13-18 elements ===

[[Boron]] is not a metal, and boron(III) is too acidic for an aqua ion to exist: deprotonation proceeds as far as [[boric acid]], [[borate]]s, and hydroxyborates.<ref>Richens, pp. 141–143</ref> The [[aluminium]](III) aqua ion, [Al(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup> is very well characterized in solution and the solid state. The AlO<sub>6</sub> core has octahedral symmetry, [[molecular point group|point group]] O<sub>h</sub>. The aqua ions of [[gallium]](III), [[indium]](III) and [[thallium]](III) are also six-coordinate octahedral.<ref name=Persson2022/> The coordination geometry of thallium(I) is not experimentally known, but it is likely to be hemidirected with a large gap in the coordination sphere.<ref name=Persson2022/>

[[Silicon]] is likewise not a metal, and silicon(IV) is a strong enough acid to deprotonate bound OH<sup>−</sup>. Thus various forms of hydrated [[silica]] ([[silicic acid]]) form.<ref name=SiGe>Richens, pp. 151–152</ref> There is some evidence that [[germanium]](II) aqua ions can form in [[perchloric acid]] media.<ref>
{{cite journal |last1=Pan |first1=Kuan |last2=Fu |first2=Yi-Chang |last3=Huang |first3=Teh-Shoon |date=December 1964 |title=Polarographic Behavior of Germanium(II)‐Perchlorate in Perchloric Acid Solutions |journal=Journal of the Chinese Chemical Society |volume=11 |issue=4 |pages=176–184 |doi=10.1002/jccs.196400020}}</ref> Quantum mechanical calculations suggests that the germanium(II) aqua ion shows extreme distortion of the first coordination sphere due to the high charge density and the stereochemically active lone pairs. The first shell is calculated to usually have a solvation number of 6, but numbers 4–7 are also possible and the shell splits into two with differing distances from the central Ge<sup>2+</sup>.<ref>{{cite journal |last1=Azam |first1=S. S. |last2=Lim |first2=L. |first3=T. S. |last3=Hofer |first4=B. R. |last4=Randolf |first5=B. M. |last5=Rode |date=2009 |title=Hydrated Germanium (II): Irregular Structural and Dynamical Properties Revealed by a Quantum Mechanical Charge Field Molecular Dynamics Study |journal=Journal of Computational Chemistry |volume=31 |issue=2 |pages=278–285 |doi=10.1002/jcc.21315|pmid=19479764 |s2cid=22766649 }}</ref> However, germanium(II) is readily oxidised to germanium(IV),<ref name=Richens152>Richens, p. 152–4</ref> for which only hydrolyzed species are expected.<ref name=core/> The important germanium(IV) species are anionic oxo-hydroxo mixed species, thus displaying intermediate behaviour between silicon and tin: the major species appear to be [GeO(OH)<sub>3</sub>]<sup>−</sup> and the octameric [Ge<sub>8</sub>O<sub>16</sub>(OH)<sub>3</sub>]<sup>3−</sup>, with [GeO<sub>2</sub>(OH)<sub>2</sub>]<sup>2−</sup> occurring in smaller quantities.<ref name=SiGe/> [[Tin]](II) is 3-coordinate hemidirected<ref>{{Cite journal|doi=10.1002/chem.201603904|title=Hydrated and Solvated Tin(II) Ions in Solution and the Solid State, and a Coordination Chemistry Overview of the d10s2Metal Ions|year=2016|last1=Persson|first1=Ingmar|last2=d'Angelo|first2=Paola|last3=Lundberg|first3=Daniel|journal=Chemistry - A European Journal|volume=22|issue=51|pages=18583–18592|pmid=27862415|url=https://pub.epsilon.slu.se/14039/1/persson_et_al_160223.pdf}}</ref><ref>{{Cite journal|doi = 10.1021/ic1017714|title = Coordination Chemistry Study of Hydrated and Solvated Lead(II) Ions in Solution and Solid State|year = 2011|last1 = Persson|first1 = Ingmar|last2 = Lyczko|first2 = Krzysztof|last3 = Lundberg|first3 = Daniel|last4 = Eriksson|first4 = Lars|last5 = Płaczek|first5 = Anna|journal = Inorganic Chemistry|volume = 50|issue = 3|pages = 1058–1072|pmid = 21226482}}</ref> with a very large gap in the coordination sphere of tin(II).<ref name=Persson2022/> The hydration number of [[lead]](II) is not well-established and could be anywhere from five to seven.<ref name=Persson2022/> In practice these cations tend to be polynuclear.<ref name=Richens152/> For tin(IV) and lead(IV) there are only hydrolyzed species.<ref name=core/>

[[Arsenic]](III) is calculated to form hydrolyzed species only.<ref name=core>{{cite journal|doi=10.1016/j.cplett.2011.05.060|url=https://core.ac.uk/download/pdf/82115185.pdf|title=Hydration of highly charged ions|year=2011|last1=Hofer|first1=Thomas S.|last2=Weiss|first2=Alexander K.H.|last3=Randolf|first3=Bernhard R.|last4=Rode|first4=Bernd M.|journal=Chemical Physics Letters|volume=512|issue=4–6|pages=139–145|pmid=22298911|pmc=3268562|bibcode=2011CPL...512..139H }}</ref> The stable cationic arsenic(III) species in water is calculated to be [As(OH)<sub>2</sub>]<sup>+</sup>,<ref>{{Cite journal|doi=10.1016/j.cplett.2009.03.011|title=Hydrolysis of As(III): A femtosecond process|year=2009|last1=Bhattacharjee|first1=Anirban|last2=Hofer|first2=Thomas S.|last3=Pribil|first3=Andreas B.|last4=Randolf|first4=Bernhard R.|last5=Rode|first5=Bernd M.|journal=Chemical Physics Letters|volume=473|issue=1–3|pages=176–178|bibcode=2009CPL...473..176B}}</ref> though hydrolysis usually proceeds further to neutral and anionic species.<ref name=Richens155/> [[Antimony]](III) aqua ions may exist in dilute solutions of antimony(III) in concentrated acids.<ref name=Richens155>Richens, p. 155</ref><ref>{{cite journal |last1=Jander |first1=G. |last2=Hartmann |first2=H.-J. |date=1965 |title=Über Reaktionen von Antimon(III) in wäßriger Lösung. III: Polarographische Messungen |lang=de |url= |journal=Zeitschrift für anorganische und allgemeine Chemie |volume=339 |issue=5–6 |pages=256–261 |doi=10.1002/zaac.19653390505 |access-date=}}</ref> Quantum mechanical calculations reveal a solvation number of 8, with the first coordination sphere splitting into two hydration hemispheres with 4 water molecules each.<ref>{{Cite journal|doi = 10.1021/ic901737y|title = Structural and Dynamical Aspects of the Unsymmetric Hydration of Sb(III): An ab initio Quantum Mechanical Charge Field Molecular Dynamics Simulation|year = 2010|last1 = Lim|first1 = Len Herald V.|last2 = Bhattacharjee|first2 = Anirban|last3 = Asam|first3 = S. Sikander|last4 = Hofer|first4 = Thomas S.|last5 = Randolf|first5 = Bernhard R.|last6 = Rode|first6 = Bernd M.|journal = Inorganic Chemistry|volume = 49|issue = 5|pages = 2132–2140|pmid = 20121188}}</ref> [[Bismuth]](III) is eight-coordinate square antiprismatic in aqueous solution, though in the solid state it is nine-coordinate tricapped triangular prismatic.<ref name=Persson2022/> Although the structures for thallium(I), germanium(II), tin(II), lead(II), and antimony(III) are affected by the lone pairs, this is not so for bismuth(III).<ref name=Persson/>

[[Selenium]](IV) is mostly present as [[selenous acid]] (H<sub>2</sub>SeO<sub>3</sub>) below pH 2; at higher pH this deprotonates to HSeO<sub>3</sub><sup>−</sup> and then SeO<sub>3</sub><sup>2−</sup>.<ref>Baes and Mesmer, p. 385</reF> Cationic [[tellurium]](IV) appears to be [Te(OH)<sub>3</sub>]<sup>+</sup>; it predominates in dilute solutions below pH 2. Above pH 4, the dominating species becomes TeO(OH)<sub>3</sub><sup>−</sup>, and above pH 8 it becomes TeO<sub>2</sub>(OH)<sub>2</sub><sup>2−</sup>.<ref>Richens, pp. 159–160</ref> [[Polonium]](IV) should be similar to tellurium(IV), though a little weaker, in its tendency towards hydrolysis.<ref>{{cite journal |last1=Ayala |first1=Regla |last2=Martínez |first2=José Manuel |first3=Rafael R. |last3=Pappalardo |first4=Enrique |last4=Sánchez Marcos |date=2012 |title=Quantum-Mechanical Study on the Aquaions and Hydrolyzed Species of Po(IV), Te(IV), and Bi(III) in Water |url= |journal=The Journal of Physical Chemistry B |volume=116 |issue=51 |pages=14903–14914 |doi=10.1021/jp309439f |access-date=}}</ref> The structure of polonium(II) does not appear to have been studied.

The [[halogen]]s, being strongly nonmetallic, prefer to form anions rather than cations in aqueous solution.<ref>Richens, pp. 161–162</ref> Anion solvation is complicated because the water molecules point the other way: cations bind to the oxygen atom of water, with the hydrogens facing away, while anions prefer to bond asymmetrically to only one of the hydrogen atoms in a nearby water molecule. This results in significant water–water [[hydrogen bond]]ing and network formation already within the first hydration shell, to an extent that does not occur for cation solvation. Such interactions are larger for the heavier and larger halides; the hydrogen bonding decreases in strength as one proceeds from [[iodide]] to [[fluoride]], because of increasing negative charge on the water molecules, the increasing [[inductive effect]] stemming from the higher electric fields, and increasing geometrical strain for the hydrogen bonding.<ref>{{cite journal |last1=Robertson |first1=William H. |last2=Johnson |first2=Mark A. |date=2003 |title=Molecular Aspects of Halide Ion Hydration: The Cluster Approach |url= |journal=Annual Review of Physical Chemistry |volume=54 |issue=1 |pages=173–213 |doi=10.1146/annurev.physchem.54.011002.103801 |access-date=}}</ref> The rare and extremely radioactive [[astatine]] seems to be more metallic: a cationic astatine(I) species is inferred from trace-scale experiments in acidic solutions, and sometimes symbolised At<sup>+</sup>, but its structure has not been determined.<ref>{{cite book | series = Gmelin Handbook of Inorganic and Organometallic Chemistry | title = 'At, Astatine', System No. 8a | edition=8th | year = 1985 | publisher = Springer-Verlag | isbn = 978-3-540-93516-2 | last1 = Kugler | first1 = H. K. | last2 = Keller | first2 = C. | volume = 8 |pages=220–221}}</ref>

The [[noble gas]]es do not react with water, but their solubility in water increases when going down the group. [[Argon]] atoms in water appear to have a first hydration shell composed of 16±2 water molecules at a distance of 280–540&nbsp;pm, and a weaker second hydration shell is found out to 800&nbsp;pm. Similar hydration spheres have been found for [[krypton]] and [[xenon]] atoms in water.<ref>Richens, p. 163</ref>

=== Oxo-aqua-cations ===
Some elements in oxidation states higher than 3 form stable, aquated, oxo ions. Well known examples are the [[vanadyl]](IV) and [[uranyl]](VI) ions. They can be viewed as particularly stable hydrolysis products in a hypothetical reaction such as
:[V(H<sub>2</sub>O)<sub>6</sub>]<sup>4+</sup> → [VO(H<sub>2</sub>O)<sub>5</sub>]<sup>2+</sup> + 2H<sup>+</sup>
The [[vanadium]] has a distorted octahedral environment ([[molecular point group|point group C<sub>4v</sub>]]) of one oxide ion and 5 water molecules.<ref>Richens, p. 236</ref> Titanyl, TiO<sup>2+</sup>, has a similar structure.<ref name=Persson/> Vanadium(V) is believed to exist as the dioxo-ion [VO<sub>2</sub>(H<sub>2</sub>O)<sub>4</sub>]<sup>+</sup> at pH less than 2, but the evidence for this ion depends on the formation of complexes, such as [[oxalate]] complexes which have been shown to have the {{chem|VO|2|+}} unit, with ''cis''-VO bonds, in the solid state.<ref>Richens, p. 240</ref> The [[chromium]](IV) ion [CrO(H<sub>2</sub>O)<sub>5</sub>]<sup>2+</sup>, similar to the vanadium ion has been proposed on the basis of indirect evidence.<ref>Richens, p. 278.</ref>

The uranyl ion, {{chem|UO|2|2+}}, has a ''trans'' structure. The aqua ion  {{chem|UO|2|2+}}(aq) has five water molecules in the plane perpendicular to the O-U-O axis in a [[pentagonal bipyramid]] structure, point group D<sub>5h</sub>. Neptunyl and [[plutonyl]] have the same structure. Nothing is known of actinide(V) structures.<ref name=Persson2022/>

== Thermodynamics ==

The main goal of thermodynamics in this context is to derive estimates of single-ion thermodynamic quantities such as hydration [[enthalpy]] and hydration [[entropy]]. These quantities relate to the reaction
:M<sup>z+</sup> (gas) + solvent → M<sup>z+</sup> (in solution)
The enthalpy for this reaction is not directly measurable, because all measurements use salt solutions that contain both cation and anion. Most experimental measurements relate to the [[enthalpy of dissolution|heat evolved when a salt dissolves]] in water, which gives the sum of cation and anion solvation enthalpies. Then, by considering the data for different anions with the same cation and different cations with the same anion, single ion values relative to an arbitrary zero, are derived.
[[File:CFSE DH.png|thumb|upright=1.2|Minus hydration enthalpy for (octahedral) divalent transition metal M<sup>2+</sup> ions<ref name=b182>Data from Burgess, p. 182.</ref>]]
[[File:Lanthanide HE.png|thumb|upright=1.2|Hydration enthalpies of trivalent lanthanide Ln<sup>3+</sup> ions<ref name = b182/>]]
:{| class="wikitable" style=text-align:center
|+Single ion standard hydration enthalpy /kJ mol<sup>−1</sup><ref name = b182/>
| Li<sup>+</sup><br />-514.6||Be<sup>2+</sup><br />-2487.0
|-
|Na<sup>+</sup><br />-404.6||Mg<sup>2+</sup><br />-1922.1|| || ||Al<sup>3+</sup><br />-4659.7
|-
|K<sup>+</sup><br />-320.9||Ca<sup>2+</sup><br />-1592.4||Sc<sup>3+</sup><br />-3960.2|| ...||Ga<sup>3+</sup><br />-4684.8
|-
|Rb<sup>+</sup><br />-296.2||Sr<sup>2+</sup><br />-1444.7||Y<sup>3+</sup><br />-3620.0||... ||In<sup>3+</sup><br />-4108.7||Sn<sup>2+</sup><br />-1554.4
|-
|Cs<sup>+</sup><br />-263.2||Ba<sup>2+</sup><br />-1303.7||La<sup>3+</sup><br />-3282.8||... ||Tl<sup>3+</sup><br />-4184.0||Pb<sup>2+</sup><br />-1479.9
|}
Other values include Zn<sup>2+</sup> -2044.3, Cd<sup>2+</sup> -1805.8 and Ag<sup>+</sup> -475.3 kJ mol<sup>−1</sup>.

There is an excellent linear correlation between hydration enthalpy and the ratio of charge squared, z<sup>2</sup>, to M-O distance, r<sub>eff</sub>.<ref>Richens, Figure 1.2.</ref>
:<math>\Delta H^\ominus = - 69500 \ \mathrm{z^2 / r_{eff}}</math>

Values for transition metals are affected by [[crystal field]] stabilization. The general trend is shown by the magenta line which passes through Ca<sup>2+</sup>, Mn<sup>2+</sup> and Zn<sup>2+</sup>, for which there is no stabilization in an octahedral crystal field. Hydration energy increases as size decreases. Crystal field splitting confers extra stability on the aqua ion. The maximum crystal field stabilization energy occurs at Ni<sup>2+</sup>. The agreement of the hydration enthalpies with predictions provided one basis for the general acceptance of crystal field theory.<ref>{{cite book|last=Orgel|first=Lesie E.|title=An introduction to transition-metal chemistry. Ligand field theory|edition=2nd.|year=1966|publisher=Methuen|location=London|page=76}}</ref>

The hydration enthalpies of the trivalent [[lanthanide]] ions show an increasingly negative values at atomic number increases, in line with the decrease in ionic radius known as the [[lanthanide contraction]].

Single ion hydration entropy can be derived. Values are shown in the following table. The more negative the value, the more there is ordering in forming the aqua ion. It is notable that the heavy alkali metals have rather small entropy values which suggests that both the first and second solvation shells are somewhat indistinct.

:{| class="wikitable" style=text-align:center
|+Single ion standard hydration entropy at 25&nbsp;°C /J deg<sup>−1</sup> mol<sup>−1</sup><ref>Burgess, p. 187.</ref>
| Li<sup>+</sup><br />-118.8||
|-
|Na<sup>+</sup><br />-87.4||Mg<sup>2+</sup><br />-267.8|| || ||Al<sup>3+</sup><br />-464.4
|-
|K<sup>+</sup><br />-51.9||Ca<sup>2+</sup><br />-209.2|| || ...||Ga<sup>3+</sup><br />-510.4
|-
|Rb<sup>+</sup><br />-40.2||Sr<sup>2+</sup><br />-205.0|| ||... ||In<sup>3+</sup><br />-426.8
|-
|Cs<sup>+</sup><br />-36.8||Ba<sup>2+</sup><br />-159.0
||La<sup>3+</sup><br />-368.2||... ||
|}

==Hydrolysis of aqua ions==
{{See also|Hydrolysis}}
There are two ways of looking at an equilibrium involving hydrolysis of an aqua ion. Considering the dissociation equilibrium
:[M(H<sub>2</sub>O)<sub>n</sub>]<sup>z+</sup> - H<sup>+</sup>{{eqm}} [M(H<sub>2</sub>O)<sub>n-1</sub>(OH)]<sup>(z-1)+</sup>
the [[Thermodynamic activity|activity]] of the hydrolysis product, omitting the water molecules, is given by
:<math chem>\{ [\ce{M(OH)}]^{(z-1)+} \} = K_{1,-1}\{ \ce M^{z+}\} \{\ce H^+\} ^{-1}</math>
The alternative is to write the equilibrium as a complexation or substitution reaction
:[M(H<sub>2</sub>O)<sub>n</sub>]<sup>z+</sup> +OH<sup>−</sup> {{eqm}} :[M(H<sub>2</sub>O)<sub>n-1</sub>(OH)]<sup>(z-1)+</sup> + H<sub>2</sub>O
In which case
:<math chem>\{ [\ce{M(OH)}]^{(z-1)+} \} = K_{1,1}\{\ce M^{z+}\} \{\ce{OH}^-\} </math>
The concentration of hydrogen and hydroxide ions are related by the [[self-ionization of water]], K<sub>w</sub> = {H<sup>+</sup>} {OH<sup>−</sup>} so the two equilibrium constants are related as
:<math>K_{1,-1} = K_{1,1} \times K_w</math>
In practice the first definition is more useful because equilibrium constants are determined from measurements of hydrogen ion concentrations. In general,
:<math chem>[\ce M_x(\ce{OH})_y] = \beta_{x,-y}* [\ce M]^x [\ce H]^{-y} </math>
charges are omitted for the sake of generality and activities have been replaced by concentrations. <math>\beta*</math> are [[equilibrium constant|cumulative]] hydrolysis constants.

Modeling the hydrolysis reactions that occur in solution is usually based on the [[determination of equilibrium constants]] from potentiometric (pH) titration data. The process is far from straightforward for a variety of reasons.<ref>Baes&Mesmer, chapter 3.</ref> Sometimes the species in solution can be precipitated as salts and their structure confirmed by X-ray crystallography. In other cases, precipitated salts bear no relation to what is postulated to be in solution, because a particular crystalline substances may have both low solubility and very low concentration in the solutions.

=== First hydrolysis constant ===

The logarithm of hydrolysis constant, K<sub>1,-1</sub>, for the removal of one proton from an aqua ion
:[M(H<sub>2</sub>O)<sub>n</sub>]<sup>z+</sup> - H<sup>+</sup> {{eqm}} [M(H<sub>2</sub>O)<sub>n-1</sub>(OH)]<sup>(z-1)+</sup>
:[ [M(OH)]<sup>{(z-1)+</sup> ] = K<sub>1,-1</sub> [M<sup>z+</sup>] [H<sup>+</sup>] <sup>−1</sup>
shows a linear relationship with the ratio of charge to M-O distance, z/d. Ions fall into four groups. The slope of the straight line is the same for all groups, but the intercept, A, is different.<ref name=bm1>Baes&Mesmer, p407</ref>
:{| class="wikitable"
|+log K<sub>1,-1</sub> = A + 11.0 z/d
!cation||A
|-
|Mg<sup>2+</sup>, Ca<sup>2+</sup>, Sr<sup>2+</sup>, Ba<sup>2+</sup> <br /> Al<sup>3+</sup>, Y<sup>3+</sup>, La<sup>3+</sup>||{{val|-22.0|0.5}}
|-
| Li<sup>+</sup>, Na<sup>+</sup>, K<sup>+</sup><br />Be<sup>2+</sup>, Mn<sup>2+</sup>, Fe<sup>2+</sup>, Co<sup>2+</sup>, Ni<sup>2+</sup>, Cu<sup>2+</sup>, Zn<sup>2+</sup>, Cd<sup>2+</sup><br />Sc<sup>3+</sup>, Ti<sup>3+</sup>, V<sup>3+</sup>, Cr<sup>3+</sup>, Fe<sup>3+</sup>, Rh<sup>3+</sup>, Ga<sup>3+</sup>, In<sup>3+</sup><br /> Ce<sup>4+</sup>, Th<sup>4+</sup>, Pa<sup>4+</sup>, U<sup>4+</sup>, Np<sup>4+</sup>, Pu<sup>4+</sup>,   ||{{val|-19.8|1}}
|-
| Ag<sup>+</sup>, Tl<sup>+</sup><br /> Pb<sup>2+</sup><br /> Ti<sup>3+</sup>, Bi<sup>3+</sup>,   ||{{val|-15.9|1}}
|-
| Sn<sup>2+</sup>, Hg<sup>2+</sup>, Pd<sup>2+</sup> ||ca. 12
|}
The cations most resistant to hydrolysis for their size and charge are [[hsab theory|hard]] pre-transition metal ions or lanthanide ions. The slightly less resistant group includes the transition metal ions. The third group contains mostly [[hsab theory|soft]] ions ion of post-transition metals. The ions which show the strongest tendency to hydrolyze for their charge and size are Pd<sup>2+</sup>, Sn<sup>2+</sup> and  Hg<sup>2+</sup>.<ref name=bm1/> This is because of the low coordination numbers of ions in this part of the periodic table (also including Ag<sup>+</sup> and Au<sup>+</sup>), so that fewer water molecules are present around the cation and they experience more electrostatic force than normal. A similar situation affects Be<sup>2+</sup>, the smallest aqua cation, which is also more acidic than would normally be expected.<ref>{{cite book |last=Wulfsberg |first=Gary |author-link= |date=2000 |title=Inorganic Chemistry |url= |location= |publisher=University Science Books |page=68 |isbn=9781891389016}}</ref>

The standard enthalpy change for the first hydrolysis step is generally not very different from that of the dissociation of pure water. Consequently, the standard enthalpy change for the substitution reaction
:[M(H<sub>2</sub>O)<sub>n</sub>]<sup>z+</sup> +OH<sup>−</sup> {{eqm}} :[M(H<sub>2</sub>O)<sub>n-1</sub>(OH)]<sup>(z-1)+</sup> + H<sub>2</sub>O
is close to zero. This is typical of reactions between a hard cation and a hard anion, such as the hydroxide ion.<ref>Baes&Mesmer, p 409.</ref> It means that the standard entropy charge is the major contributor to the standard free energy change and hence the equilibrium constant.
:<math>\Delta G^\ominus = -RT \ln K = \Delta H^\ominus - T \Delta S^\ominus</math>
The change in ionic charge is responsible for the effect as the aqua ion has a greater ordering effect on the solution than the less highly charged hydroxo complex.

=== Multiple hydrolysis reactions ===
[[File:BeHydrolysis.png|thumb|Beryllium hydrolysis as a function of pH. Water molecules attached to Be are omitted]]
[[File:Be3OHW6.svg|thumb|trimeric hydrolysis product of beryllium]]
[[File:Mo3O4.png|thumb|The [[molybdenum]](IV) oxo-aqua ion [Mo<sub>3</sub>O<sub>4</sub>(H<sub>2</sub>O)<sub>9</sub>]<sup>4+</sup>]]
The hydrolysis of beryllium shows many of the characteristics typical of multiple hydrolysis reactions. The concentrations of various species, including polynuclear species with bridging hydroxide ions, change as a function of pH up to the precipitation of an insoluble hydroxide. Beryllium hydrolysis is unusual in that the concentration of [Be(H<sub>2</sub>O)<sub>3</sub>(OH)]<sup>+</sup> is too low to be measured. Instead a trimer ([Be<sub>3</sub>(H<sub>2</sub>O)<sub>6</sub>(OH<sub>3</sub>))<sup>3+</sup> is formed, whose structure has been confirmed in solid salts. The formation of polynuclear species is driven by the reduction in charge density within the molecule as a whole. The local environment of the beryllium ions approximates to [Be(H<sub>2</sub>O)<sub>2</sub>(OH)<sub>2</sub>]<sup>+</sup>. The reduction in effective charge releases free energy in the form of a decrease of the entropy of ordering at the charge centers.<ref>Baes&Mesmer, section 18.2.</ref>
:{| class="wikitable"
|+Some polynuclear hydrolysis products<ref>Baes&Mesmer, Table 18.3.</ref>
! Species formula!! cations!! ! scope="col" width="300" |structure
|-
| M<sub>2</sub>(OH)<sup>+</sup>|| Be<sup>2+</sup>, Mn<sup>2+</sup>, Co<sup>2+</sup>, Ni<sup>2+</sup> <br /> Zn<sup>2+</sup>, Cd<sup>2+</sup>, Hg<sup>2+</sup>, Pb<sup>2+</sup> ||single hydroxide bridge between two cations
|-
|M<sub>2</sub>(OH){{su|b=2|p=(2z-2)+}} ||Cu<sup>2+</sup>, Sn<sup>2+</sup> <br /> Al<sup>3+</sup>, Sc<sup>3+</sup>, Ln<sup>3+</sup>, Ti<sup>3+</sup>, Cr<sup>3+</sup> <br /> Th<sup>4+</sup> <br />VO<sup>2+</sup>, {{chem|UO|2|2+}}, {{chem|NpO|2|2+}}, {{chem|PuO|2|2+}} || double hydroxide bridge between two cations
|-
|{{chem|M|3|(OH)|3|3+}}  ||Be<sup>2+</sup>, Hg<sup>2+</sup> || six-membered ring with alternate M<sup>n+</sup> and OH<sup>−</sup> groups
|-
|{{chem|M|3}}(OH){{su|b=4|p=(3z-4)+}} ||Sn<sup>2+</sup>, Pb<sup>2+</sup> <br /> Al<sup>3+</sup>, Cr<sup>3+</sup>, Fe<sup>3+</sup>, In<sup>3+</sup> || Cube with alternate vertices of M<sup>n+</sup> and OH<sup>−</sup> groups, one vertex missing
|-
|{{chem|M|4|(OH)|4|4+}} ||Mg<sup>2+</sup>, Co<sup>2+</sup>, Ni<sup>2+</sup>, Cd<sup>2+</sup>, Pb<sup>2+</sup> ||Cube with alternate vertices of M<sup>n+</sup> and OH<sup>−</sup> groups
|-
|{{chem|M|4|(OH)|8|8+}} || Zr<sup>4+</sup>, Th<sup>4+</sup> || Square of M<sup>n+</sup> ions with double hydroxide bridges on each side of the square
|}
The hydrolysis product of [[aluminium]] formulated as [Al<sub>13</sub>O<sub>4</sub>(OH)<sub>24</sub>(H<sub>2</sub>O)<sub>12</sub>]<sup>7+</sup> is very well characterized and may be present in nature in water at pH ca. 5.4.<ref>Richens, p. 145.</ref>

The overall reaction for the loss of two protons from an aqua ion can be written as
:[M(H<sub>2</sub>O)<sub>n</sub>]<sup>z+</sup> - 2 H<sup>+</sup>{{eqm}} [M(H<sub>2</sub>O)<sub>n-2</sub>(OH)<sub>2</sub>]<sup>(z-2)+</sup>
However, the equilibrium constant for the loss of two protons applies equally well to the equilibrium
:[M(H<sub>2</sub>O)<sub>n</sub>]<sup>z+</sup> - 2 H<sup>+</sup>{{eqm}} [MO(H<sub>2</sub>O)<sub>n-2</sub>]<sup>(z-2)+</sup> + H<sub>2</sub>O
because the concentration of water is assumed to be constant. This applies in general: any equilibrium constant is equally valid for a product with an oxide ion as for the product with two hydroxyl ions. The two possibilities can only be distinguished by determining the structure of a salt in the solid state. Oxo bridges tend to occur when the metal oxidation state is high.<ref>Baes&Mesmer, p. 420.</ref> An example is provided by the [[molybdenum]](IV) complex [Mo<sub>3</sub>O<sub>4</sub>(H<sub>2</sub>O)<sub>9</sub>]<sup>4+</sup> in which there is a triangle of molybdenum atoms joined by [[sigma bond|σ- bonds]] with an oxide bridge on each edge of the triangle and a fourth oxide which bridges to all three Mo atoms.<ref>Richens, Figure 6.26, p. 295</ref>

=== Oxyanions ===
{{main|oxyanion}}

There are very few oxo-aqua ions of metals in the oxidation state +5 or higher. Rather, the species found in aqueous solution are monomeric and polymeric oxyanions. Oxyanions can be viewed as the end products of hydrolysis, in which there are no water molecules attached to the metal, only oxide ions.

== Exchange kinetics ==
A water molecule in the first solvation shell of an aqua ion may exchange places with a water molecule in the bulk solvent.  It is usually assumed that the [[rate-determining step]] is a [[dissociation (chemistry)|dissociation reaction]].
:[M(H<sub>2</sub>O)<sub>n</sub>]<sup>z+</sup> → [M(H<sub>2</sub>O)<sub>n-1</sub>]<sup>z+</sup><span style="font-size:190%;">*</span> + H<sub>2</sub>O
The <span style="font-size:190%;">*</span> symbol signifies that this is the [[transition state]] in a chemical reaction. The rate of this reaction is proportional to the concentration of the aqua ion, [A].
: <math> \mathrm {rate} = - \left( \frac{d[A]}{dt} \right) _T = k[A]</math>.
The proportionality constant, ''k'', is called a first-order [[rate constant]] at temperature T. The unit of the [[reaction rate]] for water exchange is usually taken as mol dm<sup>−3</sup>s<sup>−1</sup>.

The [[half-life]] for this reaction is equal to log<sub>e</sub>2 / k. This quantity with the dimension of time is useful because it is independent of concentration. The quantity 1/k, also with dimension of time, equal to the half life divided by 0.6932, is known as the [[residence time distribution|residence time]] or [[time constant]].<ref>*{{cite book |title=Physical Chemistry |last=Atkins |first=P.W. |author2=de Paula, J. |year=2006 | publisher=Oxford University Press |edition=8th. |isbn=978-0-19-870072-2}} Chapter 22.</ref>

The residence time for water exchange varies from about 10<sup>−10</sup> [[second|s]] for Cs<sup>+</sup> to about 10<sup>+10</sup> s (more than 200 [[year|y]]) for Ir<sup>3+</sup>. It depends on factors such as the size and charge on the ion and, in the case of transition metal ions, [[crystal field]] effects. Very fast and very slow reactions are difficult to study. The most information on the kinetics a water exchange comes from systems with a residence time between about 1 μs and 1 s. The enthalpy and entropy of activation, ΔH<sup>‡</sup> and  ΔS<sup>‡</sup> can be obtained by observing the variation of rate constant with temperature.

:{| class="wikitable" style="text-align:center"
|+ Kinetic parameters (at 25&nbsp;°C) for water exchange: divalent ions, M<sup>2+</sup> (aq)  <ref name=Burgess>Adapted from Burgess, Tables 11.4 and 11.5</ref>
|-
! !!Be||Mg||V||Cr!!Mn!!Fe!!Co	!!Ni!!Cu!!Zn||UO<sub>2</sub>
|-
!Residence time  (μs)
|	0.001	||2	||0.00013	||0.0032	||0.0316	||0.32	 ||0.79	||40	||0.0005	||0.032||1.3 
|-
!ΔH<sup>‡</sup> (kJ mol<sup>−1</sup>)
| ||		43	||69	||13	||34	||32	||33	||43	||23 || ||		
|-
!ΔS<sup>‡</sup> (J deg<sup>−1</sup>mol<sup>−1</sup>)
| ||		8	||21	||-13	||12	||-13	||-17	||-22	||25 || ||
|}
Note the general increase in the residence time from vanadium to nickel, which mirrors the decrease in ion size with increasing atomic number, which is a general trend in the [[periodic table]], though given a specific name only in the case of the [[lanthanide contraction]]. The effects of [[crystal field]] stabilization energy are superimposed on the periodic trend.

:{| class="wikitable" style="text-align:center"
|+ Kinetic parameters (at 25&nbsp;°C) for water exchange - trivalent ions, M<sup>3+</sup> (aq)<ref name=Burgess/>
|-
! ||	Al||	Ti||	Cr||	Fe||	Ga||	Rh||	In||	La
|-
!  residence	time (μs)
| 6.3×10<sup>6</sup>	||16	||2.0×10<sup>12</sup>	||316	||501	||3.2×10<sup>13</sup>	||50	||0.050		
|-
!ΔH<sup>‡</sup>	(kJ mol<sup>−1</sup>)
|		11	||26	||109	||37	||26	||134	||17 ||			
|-
!ΔS<sup>‡</sup>	(J deg<sup>−1</sup>mol<sup>−1</sup>)
|		117	||-63	||0	||-54	||-92	||59 || ||	
|}
Solvent exchange is generally slower for trivalent than for divalent ions, as the higher electrical charge on the cation makes for stronger M-OH<sub>2</sub> bonds and, in consequence, higher activation energy for the dissociative reaction step, [M(H<sub>2</sub>O)<sub>n</sub>]<sup>3+</sup> → [M(H<sub>2</sub>O)<sub>n-1</sub>]<sup>3+</sup> + H<sub>2</sub>O. The values in the table show that this is due to both activation enthalpy and entropy factors.<ref>Burgess, p. 326.</ref>

The ion [Al(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup> is relatively inert to substitution reactions because its electrons are effectively in a closed shell electronic configuration, [Ne]3s<sup>2</sup>3p<sup>6</sup>, making dissociation an energy-expensive reaction. Cr<sup>3+</sup>, which has an octahedral structure and a d<sup>3</sup> electronic configuration is also relatively inert, as are Rh<sup>3+</sup> and Ir<sup>3+</sup> which have a low-spin d<sup>6</sup> configuration.

== Formation of complexes ==
{{main|Coordination complex|Stability constants of complexes}}
Metal aqua ions are often involved in the formation of [[Coordination complex|complexes]]. The reaction may be written as
:pM<sup>x+</sup>(aq)  + qL<sup>y−</sup> → [M<sub>p</sub>L<sub>q</sub>]<sup>(px-qy)+</sup>
In reality this is a substitution reaction in which one or more water molecules from the first hydration shell of the metal ion are replaced by ligands, L. The complex is described as an inner-sphere complex. A complex such as [ML]<sup>(p-q)+</sup> may be described as a contact [[ion pair]].

When the water molecule(s) of the second hydration shell are replaced by ligands, the complex is said to be an outer-sphere complex, or solvent-shared ion pair. The formation of solvent-shared or contact ion pairs is particularly relevant to the determination of solvation numbers of aqua ions by methods that require the use of concentrated solutions of salts, as ion pairing is concentration-dependent. Consider, for example, the formation of the complex [MgCl]<sup>+</sup> in solutions of MgCl<sub>2</sub>. The formation constant ''K'' of the complex is about 1 but varies with ionic strength.<ref name=scdb>[http://www.acadsoft.co.uk/scdbase/scdbase.htm IUPAC SC-Database] A comprehensive database of published data on equilibrium constants of metal complexes and ligands</ref> The concentration of the rather weak complex increases from about 0.1% for a 10mM solution to about 70% for a 1M solution (1M = 1&nbsp;mol dm<sup>−3</sup>).

==Electrochemistry==
The [[standard electrode potential]] for the half-cell equilibrium M<sup>z+</sup> + z {{e-}} {{eqm}} M(''s'') has been measured for all metals except for the heaviest trans-uranium elements.

:{| class=wikitable style=text-align:center
|+Standard electrode potentials /V for couples M<sup>z+</sup>/M(s)<ref name = table81>Burgess, Table 8.1</ref><ref name="CRC">{{RubberBible87th}}</ref><ref name=van92>{{cite book |last=Vanýsek |first=Petr |chapter=Electrochemical Series |editor-first=William M. |editor-last=Haynes |title=CRC Handbook of Chemistry and Physics |chapter-url=https://books.google.com/books?id=pYPRBQAAQBAJ&pg=SA5-PA80 |date=2011 |publisher=CRC Press |isbn=978-1-4398-5512-6 |pages=5–80–9 |edition=92nd}}</ref><ref>[https://www.nist.gov/system/files/documents/2019/04/02/jpcrd355.pdf Standard Electrode Potentials and Temperature Coefficients in Water at 298.15 K], Steven G. Bratsch (NIST)</ref><ref>[http://www.dactari.toxcea.org/Local/dactari/dir/pdf/default/Sb.pdf Antimony - Physico-chemical properties - DACTARI]</ref>
|-
| [[Hydrogen|H]]{{+}}<br />0
|-
| [[Lithium|Li]]{{+}}<br />−3.040|| [[Beryllium|Be]]<sup>2+</sup><br /> −1.85
|-
| [[Sodium|Na]]{{+}}<br /> −2.71|| [[Magnesium|Mg]]<sup>2+</sup><br /> −2.372|| || || || [[Aluminium|Al]]<sup>3+</sup><br />−1.66
|-
| [[Potassium|K]]{{+}} <br /> −2.931|| [[Calcium|Ca]]<sup>2+</sup><br /> −2.868|| [[Scandium|Sc]]<sup>3+</sup><br />−2.90
|...||[[zinc|Zn<sup>2+</sup>]] <br /> −0.751||[[gallium|Ga<sup>3+</sup>]] <br /> −0.53||[[germanium|Ge<sup>2+</sup>]] <br />+0.1
|-
| [[Rubidium|Rb]]{{+}} <br /> −2.98|| [[Strontium|Sr]]<sup>2+</sup><br /> −2.899|| [[Yttrium|Y]]<sup>3+</sup><br />−2.37
|...||[[cadmium|Cd<sup>2+</sup>]] <br /> −0.403||[[indium|In<sup>3+</sup>]] <br /> −0.342||[[tin|Sn<sup>2+</sup>]] <br /> −0.136||[[antimony|Sb<sup>3+</sup>]] <br />+0.15
|-
|[[Caesium|Cs]]{{+}}<br /> −3.026|| [[Barium|Ba]]<sup>2+</sup><br /> −2.912||[[Lutetium|Lu<sup>3+</sup>]] <br /> −2.25
|...||[[mercury (element)|Hg<sup>2+</sup>]] <br /> −0.854||[[thallium|Tl<sup>3+</sup>]] <br /> +0.73||[[lead|Pb<sup>2+</sup>]] <br /> −0.126||[[bismuth|Bi<sup>3+</sup>]] <br /> +0.16||[[polonium|Po<sup>4+</sup>]] <br />+0.76
|-
| [[francium|Fr]]{{+}}<br />−2.9 || [[Radium|Ra]]<sup>2+</sup><br />−2.8||[[lawrencium|Lr<sup>3+</sup>]] <br />−1.96
|-
|
|-
| || ||[[Lanthanum|La]]<sup>3+</sup><br />−2.52  ||[[cerium|Ce<sup>3+</sup>]] <br /> −2.32 ||[[Praseodymium|Pr<sup>3+</sup>]] <br /> −2.34||[[Neodymium|Nd<sup>3+</sup>]] <br /> −2.32|| [[Promethium|Pm<sup>3+</sup>]]<br />−2.30 ||[[Samarium|Sm<sup>3+</sup>]] <br /> −2.28
|[[Europium|Eu<sup>3+</sup>]] <br /> −1.98||[[Gadolinium|Gd<sup>3+</sup>]] <br /> −2.27||[[Terbium|Tb<sup>3+</sup>]] <br /> −2.27
|[[Dysprosium|Dy<sup>3+</sup>]] <br /> −2.32||[[Holmium|Ho<sup>3+</sup>]] <br /> −2.37||[[Erbium|Er<sup>3+</sup>]] <br /> −2.33
|[[Thulium|Tm<sup>3+</sup>]] <br /> −2.30||[[Ytterbium|Yb<sup>3+</sup>]] <br /> −2.23
|-
| || || [[actinium|Ac<sup>3+</sup>]] <br /> −2.18||[[thorium|Th<sup>4+</sup>]] <br /> −1.83||[[protactinium|Pa<sup>4+</sup>]] <br /> −1.46||[[uranium|U<sup>4+</sup>]] <br /> −1.51||[[neptunium|Np<sup>4+</sup>]] <br /> −1.33||[[Plutonium|Pu<sup>4+</sup>]] <br /> −1.80
|[[americium|Am<sup>3+</sup>]] <br /> −2.06||[[curium|Cm<sup>3+</sup>]] <br /> −2.07||[[berkelium|Bk<sup>3+</sup>]] <br /> −2.03
|[[californium|Cf<sup>3+</sup>]] <br /> −2.01||[[einsteinium|Es<sup>3+</sup>]] <br /> −1.99||[[Fermium|Fm<sup>3+</sup>]] <br /> −1.97||[[Mendelevium|Md<sup>3+</sup>]] <br /> −1.65||[[nobelium|No<sup>3+</sup>]] <br /> −1.20
|}
:{| class=wikitable style=text-align:center
|+Standard electrode potentials /V for 1st. row transition metal ions<ref name = table81/>
!Couple!![[titanium|Ti]]!![[vanadium|V]]!![[chromium|Cr]]!![[manganese|Mn]]!![[iron|Fe]]!![[cobalt|Co]]!![[nickel|Ni]]!![[copper|Cu]]
|-
|M<sup>2+</sup> / M||−1.63||−1.18||−0.91||−1.18||−0.473||−0.28||−0.228||+0.345
|-
|M<sup>3+</sup> / M||−1.37||−0.87||−0.74||−0.28||−0.06||+0.41
|}
:{| class=wikitable style=text-align:center
|+Miscellaneous standard electrode potentials /V<ref name = table81/>
![[silver|Ag<sup>+</sup> / Ag]]!![[palladium|Pd<sup>2+</sup> / Pd]]!![[platinum|Pt<sup>2+</sup> / Pt]]!![[zirconium|Zr<sup>4+</sup> / Zr]]!![[hafnium|Hf<sup>4+</sup> / Hf]]!![[gold|Au<sup>3+</sup> / Au]]!![[cerium|Ce<sup>4+</sup> / Ce]]
|-
| +0.799||+0.915||+1.18||−1.53||−1.70|| +1.50||−1.32
|}

As the standard electrode potential is more negative the aqua ion is more difficult to [[reduction (chemistry)|reduce]]. For example, comparing the potentials for zinc (-0.75 V) with those of iron (Fe(II) -0.47 V, Fe(III) -0.06 V) it is seen that iron ions are more easily reduced than zinc ions. This is the basis for using zinc to provide [[anodic protection]] for large structures made of iron or to protect small structures by [[galvanization]].

== References ==
{{reflist|3}}

== Bibliography ==
*{{cite book |last1=Baes |first1=C.F. |last2=Mesmer |first2=R.E. |title=The Hydrolysis of Cations |year=1986 |orig-year=1976 |publisher=Robert E. Krieger |location=Malabar, FL |isbn=978-0-89874-892-5}}
*{{cite book |last=Burgess |first=John |title=Metal Ions in Solution |year=1978 |publisher=Ellis Horwood |location=Chichester |isbn=978-0-85312-027-8}}
*{{cite book |last=Richens |first=David. T. |title=The Chemistry of Aqua Ions |year=1997 |publisher=Wiley |isbn=978-0-471-97058-3}}
*{{cite book |last1=Stumm |first1=Werner |last2=Morgan |first2=James J. |title=Aquatic Chemistry - Chemical Equilibria and Rates in Natural Waters  |edition=3rd. |year=1995 |publisher=Wiley-Blackwell  |isbn=978-0-471-51185-4}}
*{{cite book|last1=Schweitzer|first1=George K. |last2=Pesterfield| first2=Lester L.| title=The Aqueous Chemistry of the Elements |year=2010|publisher=OUP|location=Oxford|isbn=978-0-19-539335-4 }}

== Further reading ==
* H. L. Friedman, F. Franks, ''Aqueous Solutions of Simple Electrolytes,'' Springer; reprint of the 1973 edition, 2012 {{ISBN|1468429574}}

[[Category:Solutions]]