Self-ionization of water

File:Autoprotolyse eau.svg

The self-ionization of water (also autoionization of water, and autodissociation of water) is the chemical reaction in which two water molecules react to produce a hydronium ion (H₃O⁺) and a hydroxide ion (OH⁻):

2 H₂O (l) 15px H₃O⁺ (aq) + OH⁻ (aq)

It is an example of autoprotolysis, and relies on the amphoteric nature of water.

Water, however pure, is not a simple collection of H₂O molecules. Even in "pure" water, sensitive equipment can detect a very slight electrical conductivity of 0.055 µS·cm⁻¹. According to the theories of Svante Arrhenius, this must be due to the presence of ions.

Concentration and frequency

The preceding reaction has a chemical equilibrium constant of K_eq = ([H₃O⁺] [OH⁻]) / [H₂O]² = 3.23 × 10⁻¹⁸. So the acidity constant which is K_a = K_eq × [H₂O] = ([H₃O⁺] [OH⁻]) / [H₂O] = 1.8 × 10⁻¹⁶. For reactions in water (or diluted aqueous solutions), the molarity (a unit of concentration) of water, [H₂O], is practically constant and is omitted from the acidity constant expression by convention. The resulting equilibrium constant is called the ionization constant, dissociation constant, or self-ionization constant, or ion product of water and is symbolized by K_w.

K_w = K_a [H₂O] = K_eq [H₂O]² = [H₃O⁺] [OH⁻]

where

[H₃O⁺] = molarity of hydrogen or hydronium ion, and

[OH⁻] = molarity of hydroxide ion.

At Standard Ambient Temperature and Pressure (SATP), about 25 °C (298 K), K_w = [H₃O⁺][OH⁻] = 1.0×10⁻¹⁴. Pure water ionizes or dissociates into equal amounts of H₃O⁺ and OH⁻, so their molarities are equal:

[H₃O⁺] = [OH⁻].

At SATP, the concentrations of hydroxide and hydronium are both very low at 1.0 × 10⁻⁷ mol/L and the ions are rarely produced: a randomly selected water molecule will dissociate within approximately 10 hours. Since the concentration of water molecules in water is largely unaffected by dissociation and [H₂O] equals approximately 56 mol/l, it follows that for every 5.6×10⁸ water molecules, one pair will exist as ions. Any solution in which the H₃O⁺ and OH⁻ concentrations equal each other is considered a neutral solution. Absolutely pure water is neutral, although even trace amounts of impurities could affect these ion concentrations and the water may no longer be neutral. K_w is sensitive to both pressure and temperature; it increases when either increases.

Deionized water (also called DI water) is water that has had most impurity ions common in tap water or natural water sources (such as Na⁺ and Cl⁻) removed by means of distillation or some other water purification method. Removal of all ions from water is next to impossible, since water self-ionizes quickly to reach equilibrium.

Dependence on temperature and pressure

File:Temperature dependence water ionization.svg

Temperature dependence of the water ionization constant at 25 MPa

File:Pressure dependence water ionization pKw on P.svg

Pressure dependence of the water ionization constant at 25 °C

By definition, pK_w = −log₁₀ K_w. At SATP, pK_w = −log₁₀ (1.0×10⁻¹⁴) = 14.0. The value of pK_w varies with temperature. As temperature increases, pK_w decreases; and as temperature decreases, pK_w increases (for temperatures up to about 250 °C). This means that ionization of water typically increases with temperature.

There is also a (usually small) dependence on pressure (ionization increases with increasing pressure). The dependence of the water ionization on temperature and pressure has been well investigated and a standard formulation exists.

Acidity

pH is a logarithmic measure of the acidity (or alkalinity) of an aqueous solution. By definition, pH = −log₁₀ [H₃O⁺]. Since [H₃O⁺] = [OH⁻] in a neutral solution, by mathematics, for a neutral aqueous solution pH = 7 at SATP.

Self-ionization is the process that determines the pH of water. Since the concentration of hydronium at SATP (25 °C) is approximately 1.0×10⁻⁷mol/l, the pH of pure liquid water at this temperature is 7. Since K_w increases as temperature increases, hot water has a higher concentration of hydronium than cold water, but this does not mean it is more acidic, as the hydroxide concentration is also higher by the same amount.

Mechanism

Geissler et al. have determined that electric field fluctuations in liquid water cause molecular dissociation. They propose the following sequence of events that takes place in about 150 fs: the system begins in a neutral state; 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 proton 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 reorient themselves in water.

Isotope effects

Heavy water, D₂O, self-ionizes less than normal water, H₂O; oxygen forms a slightly stronger bond to deuterium because the larger mass of deuterium difference results in a lower zero-point energy, a quantum mechanical effect. The following table compares the values of pK_w for H₂O and D₂O.

T (°C)	H2O	D2O
10	14.5346	15.439
20	14.1669	15.049
25	13.9965	14.869
30	13.8330	14.699
40	13.5348	14.385
50	13.2617	14.103

See also

• Chemical equilibrium
• Acid
• Base
• Acid-base reaction theories

External links

• General Chemistry—Autoionization of Waterca:Producte iònic de l'aigua