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WATER DISSOCIATION

1.  Equilibrium equation

In its simplest form, the dissociation of water is written as:

−−++

++↔↔ OHHOH2

(1)

although it is known that the actual reaction (or autoprotolysis) involves up to 4 hydrationmolecules, leading to the formation of the hydronium ion H3O

+and more hydrated hydrogen ions.

The general form of the equilibrium constant for reaction (1) is:

[[ ]] [[ ]]

[[ ]]OH

OHHK 

2OH

OHHw

2γ 

γ γ −−++

−−++

== (2)

where H+

stands for all forms of hydrated protons.

Rearranging this expression leads to the commonly used ion product:

[[ ]][[ ]] [[ ]]−−++

====

−−++

OH.HOH

K K 

OHH

2OH

w'w

2

γ γ 

γ 

(3)

'w

K includes the values of the various activity coefficients and the concentration of water which

can be considered as a constant. In the above expression, the terms between brackets [ ] are in

mole/kg of solution (molality). Although it is quite easy to convert molarity (mole/l) into molality(mole/kg) by taking into account the density of water as a function of temperature and salinity, wehave used the above expression with molarity instead of molality in CONTRASTE, becauseconcentration are expressed in terms of mass per unit volume in the model. Density variations andtheir departure from the value of pure water are therefore neglected.

2. Ion product of water

The formulation used for  'wK is the one proposed by Millero (1995) and recommended by the U.S.

Department of Energy (DOE, 1994). It is based on the results of Hansson (1973), Culberson andPytkowicz (1973), and Dickson and Riley (1979) which are all in good agreement when adjusted tothe same pH scale.

The general expression when using molality (including for H+, i.e. using the free hydrogen ion

concentration) is given by:

(( )) (( )) S.gS).T(f )T(K ln)S,T(K ln 2

1

'w

'w ++++==

(4)

where T refers to the absolute temperature and S to the salinity. It includes a function (( )))T(K ln 'w

giving the natural logarithm of the ion product at zero salinity, a temperature functions f(T) and aconstant g. These functions are detailed in the following table.

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a0 = −1.384726 104

a1 = 1.489652 102(( )) )Tln(aa

T

a)T(K ln 21

0'w ++++==

a2 = −2.36521 101

 b0 = 1.1867 102

 b1 = -5.977)Tln( b bT

 b

)T(f  210

++++==

 b2 = 1.0495

210615.1g −−

−−==

This equation can be used for temperature between 0 to 45 °C and salinity in the range 0 to 45.

Control values:'wK ln = –34.08927 at 0°C (273.15 K), salinity 0 ( 8.14 pK 'w == 05)

'w

K ln = −30.89083 at 20°C (293.15 K), salinity 35 ( 416.13 pK 'w == )

 Note that 'w

'w K log pK  −−== = − 0.43429 '

wK ln .

3. Model entries for computing water dissociation

1. Number of species: 22. Number of reactions: 03. Number of equilibrium conditions: 1

4. Variables:−−++

OH,H5.  Reaction:

R 1:

−−++

++↔↔

OHHOH2

6. Rate: -7. Equilibrium:

  [[ ]] [[ ]]−−++

== OH.HK 'w

8. Model parameters: 'w

K  (depends on temperature and salinity)

References

Culbertson, C. and Pytkowicz, R.M., 1973. Ionization of water in seawater. Mar. Chem., 1, 309-316.

Dickson, A.G. and Riley, J.P., 1979. The estimation of acid dissociation constants in seawater from potentiometric titrations with strong base. I. The ion product of water – Kw. Mar. Chem., 7, 101-109.

DOE, 1994. Handbook of methods for the analysis of the various parameters of the carbon dioxidesystem in sea water. Version 2,A. A.C. Dickson and C. Goyet, eds. ORNL/CDIAC-74.

Hansson, I., 1973. A new set of acidity constants for carbonic acid dissociation constants inseawater as a function of temperature and salinity. Deep-Sea Res., 20, 461-478.

Millero, F.J., 1995. Thermodynamics of the carbon dioxide system in the oceans. Geochim.

Cosmoch. Acta, 59, 661-677.

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