Metal ions in aqueous solution

A metal ion in aqueous solution or aqua ion is a cation, dissolved in water, of chemical formula ^z+. The solvation number, n, determined by a variety of experimental methods is 4 for Li⁺ and Be²⁺ and 6 for most elements in periods 3 and 4 of the periodic table. Lanthanide and actinide aqua ions have higher solvation numbers, with the highest known being 11 for Ac³⁺. 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 z²/r for most aqua ions.
The aqua ion is associated, through hydrogen bonding 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 elements from about 100 picoseconds to more than 200 years. Aqua ions are prominent in electrochemistry.

Introduction to metal aqua ions

Most chemical elements are metallic. Compounds of the metallic elements usually form simple aqua ions with the formula ^z+ in low oxidation states. With the higher oxidation states the simple aqua ions dissociate losing hydrogen ions to yield complexes that contain both water molecules and hydroxide or oxide ions, such as the vanadium species ²⁺. In the highest oxidation states only oxyanions, such as the permanganate ion,, 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. 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 transactinides 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 ⁺. The oxygen atoms are arranged at the vertices of a regular octahedron centered on the sodium ion.
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 bonds 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. 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.
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, z²/r. For ions in solution Shannon's "effective ionic radius" is the measure most often used.
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.
Understanding of the nature of aqua ions is helped by having information on the nature of solvated cations in mixed solvents and non-aqueous solvents, such as liquid ammonia, methanol, dimethyl formamide and dimethyl sulfoxide to mention a few.

Occurrence in nature

Aqua ions are present in most natural waters. Na⁺, K⁺, Mg²⁺ and Ca²⁺ are major constituents of seawater.
Many other aqua ions are present in seawater in concentrations ranging from ppm to ppt. The concentrations of sodium, potassium, magnesium and calcium in blood are similar to those of seawater. Blood also has lower concentrations of essential elements such as iron and zinc. Sports drink is designed to be 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 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 NMR time-scale give separate peaks for molecules in the first solvation shell and for other water molecules. The 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.

Ion	Be²⁺	Mg²⁺	Al³⁺	Ga³⁺	In³⁺	Fe²⁺	Co²⁺	Ni²⁺	Zn²⁺	Th⁴⁺
Number	4	6	6	6	6	6	6	6	6	9
Nucleus	¹H ¹⁷O	¹H	¹H	¹H ¹⁷O	¹H	¹⁷O	¹H	¹H ¹⁷O	¹H	¹H

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.
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 Cr³⁺ and Rh³⁺. The second hydration shell of Cr³⁺ was found to have molecules at an average distance of. This implies that every molecule in the first hydration shell is hydrogen bonded to two molecules in the second shell.

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. 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 ⁵⁸Ni, ⁶⁰Ni, ³⁵Cl and ³⁷Cl isotopes to yield a very detailed picture of cation and anion solvation. Data for a number of metal salts show some dependence on the salt concentration.
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.
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
lying wholly in favour of the ion pair.