Self-ionization of water
The self-ionization of water (also autoionization of water, and autodissociation of water) is an ionization reaction in pure water or in an aqueous solution, in which a water molecule, H2O, deprotonates (loses the nucleus of one of its hydrogen atoms) to become a hydroxide ion, OH−. The hydrogen nucleus, H+, immediately protonates another water molecule to form hydronium, H3O+. It is an example of autoprotolysis, and exemplifies the amphoteric nature of water.
History and notation
The self-ionization of water was first proposed in 1884 by Svante Arrhenius as part of the theory of ionic dissociation which he proposed to explain the conductivity of electrolytes including water. Arrhenius wrote the self-ionization as . At that time, nothing was yet known of atomic structure or subatomic particles, so he had no reason to consider the formation of an ion from a hydrogen atom on electrolysis as any less likely than, say, the formation of a ion from a sodium atom.
In 1923 Johannes Nicolaus Brønsted and Martin Lowry proposed that the self-ionization of water actually involves two water molecules: . By this time the electron and the nucleus had been discovered and Rutherford had shown that a nucleus is very much smaller than an atom. This would include a bare ion which would correspond to a proton with zero electrons. Brønsted and Lowry proposed that this ion does not exist free in solution, but always attaches itself to a water (or other solvent) molecule to form the hydronium ion (or other protonated solvent).
Later spectroscopic evidence has shown that many protons are actually hydrated by more than one water molecule. The most descriptive notation for the hydrated ion is , where aq (for aqueous) indicates an indefinite or variable number of water molecules. However the notations and are still also used extensively because of their historical importance. This article mostly represents the hydrated proton as , corresponding to hydration by a single water molecule.
Chemically pure water has an electrical conductivity of 0.055 μS/cm. According to the theories of Svante Arrhenius, this must be due to the presence of ions. The ions are produced by the water self-ionization reaction, which applies to pure water and any aqueous solution:
- H2O + H2O ⇌ H3O+ + OH−
which is numerically equal to the more traditional thermodynamic equilibrium constant written as:
under the assumption that the sum of the chemical potentials of H+ and H3O+ is formally equal to twice the chemical potential of H2O at the same temperature and pressure.
Because most acid–base solutions are typically very dilute, the activity of water is generally approximated as being equal to unity, which allows the ionic product of water to be expressed as:
In dilute aqueous solutions, the activities of solutes (dissolved species such as ions) are approximately equal to their concentrations. Thus, the ionization constant, dissociation constant, self-ionization constant, water ion-product constant or ionic product of water, symbolized by Kw, may be given by:
where [H3O+] is the molarity (≈ molar concentration) of hydrogen or hydronium ion, and [OH−] is the concentration of hydroxide ion. When the equilibrium constant is written as a product of concentrations (as opposed to activities) it is necessary to make corrections to the value of depending on ionic strength and other factors (see below).
At 24.87 °C and zero ionic strength, Kw is equal to 1.0×10−14. Note that as with all equilibrium constants, the result is dimensionless because the concentration is in fact a concentration relative to the standard state, which for H+ and OH− are both defined to be 1 molal (or nearly 1 molar). For many practical purposes, the molal (mol solute/kg water) and molar (mol solute/L solution) concentrations can be considered as nearly equal at ambient temperature and pressure if the solution density remains close to one (i.e., sufficiently diluted solutions and negligible effect of temperature changes). The main advantage of the molal concentration unit (mol/kg water) is to result in stable and robust concentration values which are independent of the solution density and volume changes (density depending on the water salinity (ionic strength), temperature and pressure); therefore, molality is the preferred unit used in thermodynamic calculations or in precise or less-usual conditions, e.g., for seawater with a density significantly different from that of pure water, or at elevated temperatures, like those prevailing in thermal power plants.
We can also define pKw −log10 Kw (which is approximately 14 at 25 °C). This is analogous to the notations pH and pKa for an acid dissociation constant, where the symbol p denotes a cologarithm. The logarithmic form of the equilibrium constant equation is pKw = pH + pOH.
Dependence on temperature, pressure and ionic strength
The dependence of the water ionization on temperature and pressure has been investigated thoroughly. The value of pKw decreases as temperature increases from the melting point of ice to a minimum at c. 250 °C, after which it increases up to the critical point of water c. 374 °C. It decreases with increasing pressure.
|0 °C||0.10 MPa||14.95|
|25 °C||0.10 MPa||13.99|
|50 °C||0.10 MPa||13.26|
|75 °C||0.10 MPa||12.70|
|100 °C||0.10 MPa||12.25|
|150 °C||0.47 MPa||11.64|
|200 °C||1.5 MPa||11.31|
|250 °C||4.0 MPa||11.20|
|300 °C||8.7 MPa||11.34|
|350 °C||17 MPa||11.92|
With electrolyte solutions, the value of pKw is dependent on ionic strength of the electrolyte. Values for sodium chloride are typical for a 1:1 electrolyte. With 1:2 electrolytes, MX2, pKw decreases with increasing ionic strength.
Comparison of pKw values for liquid water, superheated steam, and supercritical water.Temp.Pressure 350 °C 400 °C 450 °C 500 °C 600 °C 800 °C 0.1 MPa 47.961b 47.873b 47.638b 46.384b 40.785b 17 MPa 11.920 (liquid)a 25 MPa 11.551 (liquid)c 16.566 18.135 18.758 19.425 20.113 100 MPa 10.600 (liquid)c 10.744 11.005 11.381 12.296 13.544 1000 MPa 8.311 (liquid)c 8.178 8.084 8.019 7.952 7.957
- Notes to the table. The values are for supercritical fluid except those marked: a at saturation pressure corresponding to 350 °C. b superheated steam. c compressed or subcooled liquid.
Heavy water, D2O, self-ionizes less than normal water, H2O;
- D2O + D2O ⇌ D3O+ + OD−
This is due to the equilibrium isotope effect, a quantum mechanical effect attributed to oxygen forming a slightly stronger bond to deuterium because the larger mass of deuterium results in a lower zero-point energy.
Expressed with activities a, instead of concentrations, the thermodynamic equilibrium constant for the heavy water ionization reaction is:
Assuming the activity of the D2O to be 1, and assuming that the activities of the D3O+ and OD− are closely approximated by their concentrations
The following table compares the values of pKw for H2O and D2O.
pKw values for pure water T/°C 10 20 25 30 40 50 H2O 14.535 14.167 13.997 13.830 13.535 13.262 D2O 15.439 15.049 14.869 14.699 14.385 14.103
Ionization equilibria in water–heavy water mixtures
In water–heavy water mixtures equilibria several species are involved: H2O, HDO, D2O, H3O+, D3O+, H2DO+, HD2O+, HO−, DO−.
The rate of reaction for the ionization reaction
- 2 H2O → H3O+ + OH−
where k is the Boltzmann constant. Thus some dissociation can occur because sufficient thermal energy is available. The following sequence of events has been proposed on the basis of electric field fluctuations in liquid water. Random fluctuations in molecular motions occasionally (about once every 10 hours per water molecule) produce an electric field strong enough to break an oxygen–hydrogen bond, resulting in a hydroxide (OH−) and hydronium ion (H3O+); the hydrogen nucleus of the hydronium ion travels along water molecules by the Grotthuss mechanism and a change in the hydrogen bond network in the solvent isolates the two ions, which are stabilized by solvation. Within 1 picosecond, however, a second reorganization of the hydrogen bond network allows rapid proton transfer down the electric potential difference and subsequent recombination of the ions. This timescale is consistent with the time it takes for hydrogen bonds to reorientate themselves in water.
The inverse recombination reaction
- H3O+ + OH− → 2 H2O
is among the fastest chemical reactions known, with a reaction rate constant of 1.3×1011 M−1 s−1 at room temperature. Such a rapid rate is characteristic of a diffusion-controlled reaction, in which the rate is limited by the speed of molecular diffusion.
Relationship with the neutral point of water
Water molecules dissociate into equal amounts of H3O+ and OH−, so their concentrations are almost exactly 1.00×10−7 mol dm−3 at 25 °C and 0.1 MPa. A solution in which the H3O+ and OH− concentrations equal each other is considered a neutral solution. In general, the pH of the neutral point is numerically equal to 1/2pKw.
Pure water is neutral, but most water samples contain impurities. If an impurity is an acid or base, this will affect the concentrations of hydronium ion and hydroxide ion. Water samples that are exposed to air will absorb some carbon dioxide to form carbonic acid (H2CO3) and the concentration of H3O+ will increase due to the reaction H2CO3 + H2O = HCO3− + H3O+. The concentration of OH− will decrease in such a way that the product [H3O+][OH−] remains constant for fixed temperature and pressure. Thus these water samples will be slightly acidic. If a pH of exactly 7.0 is required, it must be maintained with an appropriate buffer solution.
- Acid–base reaction
- Chemical equilibrium
- Molecular autoionization (of various solvents)
- Standard hydrogen electrode
- "Release on the Ionization Constant of H2O" (PDF). Lucerne: The International Association for the Properties of Water and Steam. August 2007.
- IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "autoprotolysis constant". doi:10.1351/goldbook.A00532
- Stumm, Werner; Morgan, James (1996). Aquatic Chemistry. Chemical Equilibria and Rates in Natural Waters (3rd ed.). John Wiley & Sons, Inc. ISBN 9780471511847.
- Harned, H. S.; Owen, B. B. (1958). The Physical Chemistry of Electrolytic Solutions (3rd ed.). New York: Reinhold. pp. 635.
- International Association for the Properties of Water and Steam (IAPWS)
- Bandura, Andrei V.; Lvov, Serguei N. (2006). "The Ionization Constant of Water over Wide Ranges of Temperature and Density" (PDF). Journal of Physical and Chemical Reference Data. 35 (1): 15–30. Bibcode:2006JPCRD..35...15B. doi:10.1063/1.1928231.
- 0.1 MPa for T < 100 °C. Saturation pressure for T > 100 °C.
- Harned, H. S.; Owen, B. B. (1958). The Physical Chemistry of Electrolytic Solutions (3rd ed.). New York: Reinhold. pp. 634–649, 752–754.
- Lide, D. R., ed. (1990). CRC Handbook of Chemistry and Physics (70th ed.). Boca Raton (FL):CRC Press.
- Geissler, P. L.; Dellago, C.; Chandler, D.; Hutter, J.; Parrinello, M. (2001). "Autoionization in liquid water". Science. 291 (5511): 2121–2124. Bibcode:2001Sci...291.2121G. CiteSeerX 10.1.1.6.4964. doi:10.1126/science.1056991. PMID 11251111.
- Eigen, M.; De Maeyer, L. (1955). "Untersuchungen über die Kinetik der Neutralisation I" [Investigations on the kinetics of neutralization I]. Z. Elektrochem. 59: 986.
- Stillinger, F. H. (1975). Theory and Molecular Models for Water. Adv. Chem. Phys. Advances in Chemical Physics. Vol. 31. pp. 1–101. doi:10.1002/9780470143834.ch1. ISBN 9780470143834.
- Rapaport, D. C. (1983). "Hydrogen bonds in water". Mol. Phys. 50 (5): 1151–1162. Bibcode:1983MolPh..50.1151R. doi:10.1080/00268978300102931.
- Chen, S.-H.; Teixeira, J. (1986). Structure and Dynamics of Low-Temperature Water as Studied by Scattering Techniques. Adv. Chem. Phys. Advances in Chemical Physics. Vol. 64. pp. 1–45. doi:10.1002/9780470142882.ch1. ISBN 9780470142882.
- Tinoco, I.; Sauer, K.; Wang, J. C. (1995). Physical Chemistry: Principles and Applications in Biological Sciences (3rd ed.). Prentice-Hall. p. 386.
- General Chemistry – Autoionization of Water