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 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.

Equilibrium constant

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 self-ionization reaction

H₂O + H₂O ⇌ H₃O⁺ + OH⁻

This equilibrium applies to pure water and any aqueous solution.

Expressed with activities a, instead of concentrations, the thermodynamic equilibrium constant for the water ionization reaction is:

$K_{\rm eq} = \frac{a_{\rm{H_3O^+}} \cdot a_{\rm{OH^-}}}{a_{\rm{H_2O}}^2}$

which is numerically equal to the more traditional thermodynamic equilibrium constant written as:

$K_{\rm eq} = \frac{a_{\rm{H^+}} \cdot a_{\rm{OH^-}}}{a_{\rm{H_2O}}}$

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.^[1]

Because most acid–base solutions are typically very dilute, the activity of water is generally approximated as being equal to be unity, which allows the ionic product of water to be expressed as:^[2]

$K_{\rm eq}=a_{\rm{H_3O^+}} \cdot a_{\rm{OH^-}}$

In dilute aqueous solutions, the activities of the solute particles are approximately equal to their concentrations. Thus, the ionization constant, dissociation constant, self-ionization constant, or ionic product of water, symbolized by K_w, may be given by:

$K_{\rm w}=[{\rm{H_3O^+}}][{\rm{OH^-}}]$

where [H₃O⁺] is the concentration of hydrogen or hydronium ion, and [OH⁻] is the concentration of hydroxide ion.

At 25 °C K_w 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 Molar.

We can also define pK_w = −log₁₀ K_w = 14 at 25 °C. This is analogous to the notations pH and pK_a for an acid dissociation constant, where the symbol p denotes a cologarithm. The logarithmic form of the equilibrium constant equation is pK_w = pH + pOH.

Dependence on temperature, pressure and ionic strength

Temperature dependence of the water ionization constant at 25 MPa

Pressure dependence of the water ionization constant at 25 °C

Variation of pKw with ionic strength of NaCl solutions at 25 °C

The dependence of the water ionization on temperature and pressure has been investigated thoroughly.^[3] The value of pK_w 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.

pK_w values for liquid water.^[4]

Temperature	Pressure[5]	pKw
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 pK_w is dependent on ionic strength of the electrolyte. Values for sodium chloride are typical for a 1:1 electrolyte. With 1:2 electrolytes, MX₂, pK_w decreases with increasing ionic strength.^[6]

The value of K_w is usually of interest in the liquid phase. Example values for superheated steam (gas) and supercritical water fluid are given in the table.

Comparison of pK_w values for liquid water, superheated steam, and supercritical water.^[1]

Temp. Pressure	350 °C	400 °C	450 °C	500 °C	600 °C	800 °C
0.1 MPa	11.920 (liquid)^a	47.961^b	47.873^b	47.638^b	46.384^b	40.785^b
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 subcooled liquid.

Isotope effects

Heavy water, D₂O, self-ionizes less than normal water, H₂O;

D₂O + D₂O ⇌ D₃O⁺ + OD⁻

This is attributed to oxygen forming a slightly stronger bond to deuterium because the larger mass of deuterium results in a lower zero-point energy, a quantum mechanical effect analogous to the kinetic isotope effect.

Expressed with activities a, instead of concentrations, the thermodynamic equilibrium constant for the heavy water ionization reaction is:

$K_{\rm eq} = \frac{a_{\rm{D_3O^+}} \cdot a_{\rm{OD^-}}}{a_{\rm{D_2O}}^2}$

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

$K_{\rm w}=[{\rm{D_3O^+}}][{\rm{OD^-}}]$

The following table compares the values of pK_w for H₂O and D₂O.^[7]

pK_w 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⁻.

Mechanism

The rate of reaction for the ionization

2 H₂O → H₃O⁺ + OH⁻

depends on the activation energy, ΔE^‡. According to the Boltzmann distribution the proportion of water molecules that have sufficient energy, due to thermal population, is given by

$\frac{N}{N_0} = e^{-\frac{\Delta E^\ddagger}{kT}}$

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.^[8] Random fluctuations in molecular motions occasionally (about once every 10 hours per water molecule^[9]) 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.^[10][11][12]

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.^[13]

Relationship with the neutral point of water

Water molecules dissociate into equal amounts of H₃O⁺ and OH⁻, so their concentrations are equal to 1.00×10⁻⁷ mol dm⁻³ at 25 °C. 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 1/2pK_w.

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 which are exposed to air will absorb the acid carbon dioxide and the concentration of H₃O⁺ will increase. 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.

See also

• Chemical equilibrium
• Acid–base reaction
• Standard hydrogen electrode

References

1. "Release on the Ionization Constant of H₂O" (PDF). Lucerne: The International Association for the Properties of Water and Steam. August 2007.
2. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "autoprotolysis constant".
3. International Association for the Properties of Water and Steam (IAPWS)
4. 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. doi:10.1063/1.1928231.
5. 0.1 MPa for T < 100 °C. Saturation pressure for T > 100 °C.
6. Harned, H. S.; Owen,, B. B. (1958). The Physical Chemistry of Electrolytic Solutions (3rd ed.). New York: Reinhold. pp. 634–649, 752–754.
7. Lide, D. R., ed. (1990). CRC Handbook of Chemistry and Physics (70th ed.). Boca Raton (FL):CRC Press.
8. 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. doi:10.1126/science.1056991. PMID 11251111.
9. Eigen, M.; De Maeyer, L. (1955). "Untersuchungen über die Kinetik der Neutralisation I" [Investigations on the kinetics of neutralization I]. Z. Elektrochem. 59: 986.
10. Stillinger, F. H. (1975). "Theory and Molecular Models for Water". Adv. Chem. Phys. 31: 1. doi:10.1002/9780470143834.ch1.
11. Rapaport, D. C. (1983). "Hydrogen bonds in water". Mol. Phys. 50 (5): 1151. Bibcode:1983MolPh..50.1151R. doi:10.1080/00268978300102931.
12. Chen, S.-H.; Teixeira, J. (1986). "Structure and Dynamics of Low-Temperature Water as Studied by Scattering Techniques". Adv. Chem. Phys. 64: 1. doi:10.1002/9780470142882.ch1.
13. Tinoco, I.; Sauer, K.; Wang, J. C. (1995). Physical Chemistry: Principles and Applications in Biological Sciences (3rd ed.). Prentice-Hall. p. 386.

External links

• General Chemistry – Autoionization of Water