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Water dissociation

 

Water dissociation to give hydrogen ions and hydroxide ions

Water dissociation and pH

A remarkable property of pure water is that it dissociates to form hydrogen ions (H3O+) and hydroxide (OH-) ions

 

V The ionic product, Kw

V pH

V Variation in Kw with temperature and pressure

V Acidity, basicity and the pKa of water
link; Hydrogen ions
link; Hydroxide ions
link; Grotthuss mechanism

 

'I will employ the name “hydrogen ion exponent” and

the symbol pH for the numerical value of the exponent of this power'

Søren Sørensen, 1909                  

The ionic product, Kw

Water dissociation (autoionization; self-ionization) occurs endothermically d due to electric field fluctuations between neighboring molecules. Dipole librations [191], resulting from thermal effects and favorable localized hydrogen bonding, [567] together with nuclear quantum effects [2025], cause these fluctuations. The process may be facilitated by exciting the O-H stretch overtone vibration [393]. Once formed (at an average concentration of about 1 M H2O-H+···OH- [1984]),h the ions may separate by means of the Grotthuss mechanism but normally (>99.9%) rapidly recombine (~20 ps [2171]) with a frequency in the terahertz range. Rarely (about once every eleven hours per molecule at 25 °C, or less than once a week at 0 °C) the localized hydrogen bonding arrangement breaks before allowing the separated ions to return [191]. The pair of ions (H+, OH-)g hydrate independently and continue their separate existence a for about 70 μs (this lifetime also dependent on the extent of hydrogen bonding, being shorter at lower temperatures). They tend to recombine when separated by only one or two water molecules.

H2O equilibrium arrows  H+ + OH-
Kw = [H+] ˣ [OH-]

 

This low occurrence of the ions means that at neutrality (pH 7 at 25 °C) c, similarly charged ions are, on average, separated by vast distances (~0.255 μm) in molecular terms and (for example) bacteria contain only a few tens of free hydrogen ions. Contributing to this effect are the high dielectric constant (encouraging charge separation) and high concentration of H2O (~55.5 M; increasing the absolute amount dissociated). The mean lifetime of a hydroxonium ion (1 ps; about the same as that of a hydrogen bond) is such that the charge could be associated with over 107 molecules of water before neutralization.

 

Although the extent of dissociation is tiny ([H+]/[H2O] = 2.8 x 10-9 at 37 °C), the dissociation and consequential changes in the tiny concentrations of hydrogen ions have absolute importance to living processes. Hydrogen and hydroxyl ions are produced already hydrated.

 

H2O (liq) equilibrium arrows  H+(aq) + OH- (aq)

 

Hydration enthalpies of protons and hydroxides, from [1938b]

Hydration enthalpies of protons and hydroxides, from [1938b]

The protons (H+) initially hydrate as hydroxonium ions, H3O+ (also called oxonium or hydronium ions) and do not exist as naked protons in liquid or solid water, where they interact extremely strongly with electron clouds. All three hydrogen atoms in the hydroxonium ion are held by strong covalent bonds and are equivalent (that is, C3v symmetry in a vacuum). The thermodynamic properties of the dissociation at 25 °C and 0.1 MPa are ΔU° = 59.5 kJ ˣ mol-1, ΔV° = 22.13 cm3 ˣ mol-1, ΔH° = 55.8 kJ ˣ mol-1, ΔG° = 79.9 kJ ˣ mol-1, ΔS° = -80.8 J ˣ K-1 ˣ mol-1 [1938]. The proton is never found unhydrated in aqueous solution and the hydroxonium ions, H3O+, also has negligible independent existence in an aqueous environment [2134]. All the hydroxonium ion protons are predominantly hydrogen-bonded causing further hydration to H3O+(H2O)n, where n depends on the conditions such as temperature, solutes, pressure and method of determination.

 

To avoid the misleading presumption of the existence of bare protons similar to other bare cations (but see [2132] for an alternative view), the above equations are better written as:

2 H2O(aq) equilibrium arrows  H3O+(aq) + OH-(aq)
Kw = [H3O+] ˣ [OH-]

 

Change in volume on water dissociation, from [1946]

Change in volume on water dissociation, data from [1946]

Both ions are ionic kosmotropes, hydrating and creating order in forming stronger hydrogen bonds with surrounding water molecules than the water molecules form between themselves, and creating short chains of hydrogen-bonded water molecules [2025]. Remarkably, the volume change in this reaction

 

2 H2O(aq) ->  H3O+(aq) + OH-(aq)  ΔV = -22.3 cm3 mol-1

 

at 25 °C and infinite dilution, [1946], see Figure right,

due to the change in the hydration strength plus electrostriction, is about the same as one molecule of water (18.1 cm3 ˣ mol-1); when one water molecule ionizes, its volume effectively disappears.

 

The concentrations of H3O+ and OH- are normally taken as the total concentrations of all the singly charged small clusters including these species. As other water molecules are required to promote the hydrolysis, the equations below includes the most important. None of these hydrated ions should be considered as 'fixed' structures, with further water molecules constantly coming and going in aqueous solution with timescales of picoseconds. No bare protons occur, however.

 

4 H2O equilibrium arrows  H5O2+ + H3O2-

10 H2O equilibrium arrows  H13O6+ + H7O4-

 

The concentration of hydroxonium and hydroxide ions produced is therefore equal to the square root of the dissociation constant (Kw).

 

A wide range of values for Kw have been calculated using Quantum Cluster Equilibrium (QCE) theory with a variety of ab initio and density functional methods [3025].

 

Aqueous OH- does not ionize further as (O2- + H2O -> 2OH-, K > 1022). H3O+ does not protonate further to the tetrahedral H4O2+ ion as although H4O2+ may be metastable in the gas phase, it is thermodynamically unstable to loss of a proton [2133] and would immediately dissociate in aqueous solution. [Back to Top to top of page]

pH

pH of common materials

 

Approximate pH of common materials

The hydronium (oxonium) ion concentration (commonly called 'hydrogen ion concentration') is often given in terms of the pH, where

pH = Log10(1/[H3O+]) = -Log10([H3O+])

 

(that is, [H3O+] = 10-pH)f with the concentration of H3O+ in mol ˣ L-1. More precisely pH = -Log10(aH) = -Log10(mH ˣ λH/m°) where aH, mH, λH and m° are the relative (molality based) activity, molality, molal activity coefficient j and standard molality (1 mol kg-1) of the hydrogen ions. Water can thus support acid-base equilibria over a range of about 16 pH units (see right). At the low concentrations normally found, the molarity-based hydrogen ion concentration is close enough to the relative (molality based) activity for its use in most circumstances. The presence of salts and other solutes will generally reduce this activity and the activity varies with temperature. The molal activity of hydrogen ions cannot be determined directly but may be determined using a glass electrode relative to the response of standard buffer solutions of comparable ionic strength. Glass electrode-determined pH values are error-prone and calculated hydrogen ion concentrations should be treated with caution, particularly at the extremes of pH [1890]. For more information and a list of primary pH standards see [813]. Proof that the use of the equation pH = -Log10([H+]) may give misleading results (and pH = -Log10(aH) is preferred) is easily shown as the pH of 0.1 M HCl decreases when it is diluted with 5% M LiCl [1107].

 

Typical pH electrode

 

typical pH electrode

 

The pH scale was first introduced by Sørensen (as p) in 1909 [1036] using colorimetric measurements and the hydrogen electrode, which gives an electrode potential proportional to pH. pH electrodes are now commonly used to determine the pH (see right). i The pH scale extends to negative numbers (for example, concentrated HCl has a pH of about -1.1) and to greater than 14 (for example, saturated NaOH has a pH of about 15.0) [1187]. There is a recent review of the pH of natural water [1712]. [Back]

 

In a similar manner, pKw is defined by pKw = Log10(1/Kw) = -Log10(Kw), utilizing concentrations in mol L-1.

 

Where the solution contains significant amounts of heavy water (D2O) the measured pH will differ slightly from that expected from the amounts of protonated species H3O+ + H2DO+ + HD2O+ + D3O+ [2953].

 

[Back to Top to top of page]

 

pKw versus temperature

PKw versus temperature at 0.1MPa or saturated pressure (>100C)
pKw = -log10(Kw ) [IAPWS]

Variation in Kw with T and P

Kw is very temperature dependent, increasing with temperature (that is, from 0.001 ˣ 10-14 mol2 ˣ L-2 at -35 °C (pH 8.5) [112], 0.112 ˣ 10-14 mol2 ˣ L-2 at 0 °C (pH 7.5), to 0.991 ˣ 10-14 mol2 ˣ L-2 at 25 °C (pH 7.0), to 9.311 ˣ 10-14 ˣ mol2 ˣ L-2 at 60 °C (pH 6.5) [87]), to 10-12 ˣ mol2 ˣ L-2 at 300 °C (pH 6.0, ~50 MPa) [456] in agreement with the high positive standard free energy. b There is a minimum at about 249 °C along the saturated pressure line for H2O and at about 257 °C for D2O (see right [1865]). The pKw H2O minimum is about 0.74 lower than that for D2O [1865]. (see also conductivity maximum).

 

A theoretical treatment of this temperature dependence is available [763].

 

Variation in pKw ( pKa)

Water ionization; variation in pKw and pKa with respect to temperature and pressure
supercritical conditions

pKw versus pressure

pKw (and pKa) versus pressure at 25 °C
Temperature and density dependence of dissociation have been examined [1321]. Dissociation depends on the pressure, with Kw doubling at about 100 MPa; unsurprising in view of the negative ΔV associated with the dissociation, -18.1 cm3 mol-1.

 

Dissociation also varies with solute concentration and ionic strength; for example, Kw goes through a maximum of about 2 ˣ 10-14 mol2 ˣ L-2 at about 0.25 M ionic strength (using tetramethylammonium chloride, where possibly the change in hydrogen bonding caused by clathrate formation encourages dissociation) before dropping to a value of about 1 ˣ 10-16 mol2 ˣ L-2at 5 M (with higher concentrations disrupting the hydrogen bonding). Similar maxima occur with other salts such as NaCl (~0.6 M), KCl (~0.45 M), KNO3 (~0.5 M) and NaClO4 (~0.5 M) [2234]. Dissociation will also be different at interfaces; for example, it is greater at lipid membrane surfaces [1964].

 

In ice, where the local hydrogen bonding rarely breaks to separate the constantly forming and re-associating ions, the dissociation constant is much lower (for example at -4 °C, Kw = 2 x 10-20 mol2 ˣ L-2 ). [Back to Top to top of page]

Acidity, basicity and the pKa of water

There has been controversy and confusion for the last 90 years over the acidity e of water and its pKa; a confusion that is yet to be fully clarified. Does the pKa of H2O equal 15.74 [2966] or 14.00 [2965]? The answer depends on the standard state used for the solvent water.

 

The acidity constant (Ka) of weak acid HA, d

 HA (aq)+ H2O (l)equilibrium arrows A- (aq) + H3O+(aq)

is defined by

Ka= [H3O+][A-]/[HA]

pKa=  -Log10(Ka)

Together with its conjugate base A-, we get,

   HA (aq) + H2O (l) equilibrium arrows A- (aq)+ H3O+ (aq)         ΔGa°  = - RT Ln( Ka)           

    A- (aq)+ H2O (l) equilibrium arrows HA (aq) + OH- (aq)          ΔGb° = - RT Ln( Kb)          

_________________________________________________________

                                      H2O (l) + H2O (l) equilibrium arrows H3O+(aq) + OH- (aq)      ΔGw° = - RT Ln( Kw) = 79.89 kJ ˣ mol-1 [2967]

 

Where the ΔG° values are the standard Gibbs free energies for the equilibria.

Therefore, as ΔGw° = ΔGa° + ΔGb° , Ln( Kw) = Ln( Ka) + Ln( Kb) and

pKa+ pKb = pKw      and      Kw = Ka ˣ Kb

 

H2O, as a weak acid, may be treated in the same way

H2O (l) + H2O (l)equilibrium arrowsH3O+(aq) + OH- (aq)

Its pKa has been (mistakenly) derived as Ka= [H3O+][OH-]/[H2O] = Kw/[H2O] = Kw/55.345 (at 25 °C) and pKa = pKw +1.743 (= 15.738 at 25 °C). However, in this derivation the H2O is treated both as an acid ([H2O] in the denominator, equaling about 55.345 mol ˣ L-1) and the solvent (internalized in the Ka definition with a value of unity). This disparity in values introduces conflict.

 

The alternative (and correct) derivation utilizes the activity of water (equals unity) in the denominator [2965]

                             Ka (H2O)= [H3O+][OH-] = Kw = 10-13.995           (a number without units)

                           pKa = pKw = 13.995                            (H2O, 25 °C)

 

H2O is a very weak acid; compare with the pKas of H2Te, H2Se, and H2S that are 2.6, 3.89 and 7.04 respectively. The pKb (= pKw - pKa = 0.00) related to this Ka concerns the conjugate base (OH-) not H2O as commonly mistakenly cited. OH- is a strong base whereas H2O is a very weak base. The pKb of H2O is derived exactly as pKa (above, as the equation generates both an acid and a base) and gives the same value (= 13.995 at 25 °C).

 

H3O+ is a strong acid with associated Ka (H3O+) equaling unity exactly (see the equation below). pKa (H3O+) equals zero exactly and is invariant with temperature, as ΔG° is necessarily zero.

 H3O+(aq) + H2O (l) equilibrium arrows H2O (l) + H3O+(aq)   ΔG°    = - RT Ln(Ka (H3O+))    = 0.00 kJ ˣ mol-1 [2967]

 

There is a difficulty that has been ignored in these definitions as Ka and Kb would normally be expressed in terms of activities rather than concentrations [1188] and the activity of pure H2O is defined as unity whereas that of solutes is defined relative to their standard state (1 mol ˣ kg-1) rather than the concentration of water (~55.345 mol ˣ L-1). It is important that the chosen value (pKa = 13.995 for H2O) fits in with the known acidity and basicity of water compared with other materials. Whilst older published materials reported methanol as being more acidic (pKa = 15.3) than water [2107] (and so mistakenly favoring a pKa for water of 15.74), a recent re-analysis [2965] shows that water is 35-fold more acidic than methanol, a value that fits well with the pKa of H2O being ~14.

 

This value (pKa = 14.00) may be separately determined from thermodynamic ΔG data [2967]. [Back to Top to top of page]

 


Footnotes

a It follows that pure water droplets containing less than about 108 water molecules (~0.1 μm radius) would usually (i.e. on average) contain no ions in the absence of surface effects. [Back]

 

b A bulk energy diagram for the dissociation in bulk water has been described [604]. [Back]

 

c Note that acid-base neutrality only occurs when the concentration of hydrogen ions equals the concentration of hydroxyl ions (whatever the pH). This only occurs at pH 7 in pure water when at 25 °C. A solution is acidic when the hydrogen ion concentration is greater than the hydroxide ion concentration, whatever the pH. The pH of a neutral solution is numerically equal to half the pKw of the solution. Therefore a pH of 7 at 0 °C indicates a slightly acid solution (neutrality is pH 7.5) whereas a pH of 7 at 50 °C indicates a slightly alkaline solution (neutrality is pH 6.6). [Back]

 

d In a vacuum the reaction

H2O (g) -> H+ (g) + OH- (g)

requires over three times more energy (1.66 MJ mol-1; Kw = 1 ˣ 10-285 mol2 ˣ L-2 [3025]) than dissociation

H2O (g)  -> H· (g) + ·OH (g)

(531 kJ ˣ mol-1). In liquid water, the hydration of the ions (H+ ΔG° hydration -1112.5 kJ ˣ mol-1, this includes H3O+ ΔG° hydration -461.1 kJ ˣ mol-1; OH- ΔG° hydration -437.6 kJ ˣ mol-1 [1067]) reduces the ΔG° of the reaction

2 H2O (l) equilibrium arrows H3O+ (aq) + OH- (aq)

to +99.78 kJ ˣ mol-1 (These calculations assume that the standard state of the solvent water is taken as 1.0 M. If the standard state of the solvent water is the unit activity or mole fraction (= 1.0), the ΔG° is +79.907 kJ ˣ mol-1 as given above). The dissociated radicals (H··OH) are also somewhat stabilized in liquid water, as shown by the occasional dissociation of water [1066, see equations]. [Back]

 

e Note that the 'acidity' of a material is commonly its pH and depends both on its pKa and its concentration. The 'acidity' of drinks and foodstuffs, however, also depends on the response of our taste buds. [Back]

 

f As Logarithms may only be taken of dimensionless numbers, all the concentrations (activities, partial pressures, etc.) in any Logarithmic expression are actually divided by unit values in the same units of that concentration (activity, partial pressure, etc.); thus, for example here [H3O+] (concentration of H3O+ in mol L-1) is actually [H3O+]/(1.0 mol L-1).

 

The p in pH originated as the arbitrary choice for the naming of the electrode solutions 'p' and 'q' by Sørensen [1036, 1891], but is now taken to mean the 'logarithm to the base 10 of the reciprocal of' (cologarithm) as in the function described above. [Back]

 

g Strictly speaking these equations should be expressed in terms of activities rather than concentrations; thus

Kw = [aH+] ˣ [aOH-]

The derivations are easier to follow as given and usually the concentrations are so small that the difference is inconsequential. [Back]

 

h Similar concentrations are found for ice [2171]. [Back]

 

i Different membrane glasses may be used dependent on the solution to be analyzed (e.g. high temperatures, strong alkali or HF).

 

The electrode reaction for the Ag/AgCl/saturated KCl reference electrode is

AgCl + e- --> Ag0 + Cl-                E = +0.197 V (in saturated KCl)

[Back]

 

j The activity coefficient of hydrogen ions depends on the acid concentration, temperature, ionic strength, the dielectric constant, the size of the ions and the density of the medium. [Back]

 

k The pH of a weak monoprotic acid of concentration c is: pH=-log[[-Ka + (Ka² + 4CKa)^½]/2]

so long as c ˣ Ka > Kw. [Back]

 

 

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This page was established in 2000 and last updated by Martin Chaplin on 14 November, 2017


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