Effect of Temperature and Salinity on Equilibrium Constants
CO2 Partial Pressure and Fugacity
The Hydration of Carbon Dioxide (K_{0})
Kw, the Ionic Water Product due to H2O H3O^{+} + OH^{ }^{ }equilibrium
The First and Second Dissociation Constant of Carbon Dioxide
The solubility of Calcite and Aragonite
The Partial Hydrolysis of Ca and Mg Ions
The Dissociation of Boric Acid
The Second Dissociation of Sulphuric Acid
The Dissociation of Hydrofluoric Acid
The Three Dissociations of Phosphoric Acid H_{3}PO_{4}
CO2 Partial Pressure and Fugacity
Before dealing with chemical equations in seawater, we should first focus on the compound in air that starts a series of reactions when dissolved, namely carbon dioxide. Its partial pressure is continuously monitored, by different stations around the world, the most famous one being the Mauna Loa Observatory (Hawaii).
The partial pressure of a gas in a mixture of gases is simply the total pressure multiplied by its mole fraction. However, the activity of CO2 is not exactly equal to its partial pressure.
For accurate calculations, the
fugacity of CO2, fCO2, may be used instead of its partial pressure.
The fugacity of CO2
is
numerically very similar to CO2 partial pressure in atm,
and therefore corresponds
to CO2 ppm
in dry air by the Dalton law. The fugacity can be calculated from its
partial pressure (Koerzinger, 1999), requiring two virial
coefficients B
and d,
as explained here in the following (from Zeebe 2001)
where
fCO2 and
pCO2 are in
atm,
the total pressure, P,
is in Pa (1 atm = 101325 Pa), the first virial coefficient of CO2, B,
and the parameter
are in m^{3}
mol^{1}, R =
8.314 J K1 is the gas constant and the absolute temperature, T,
in in Kelvin.
B has been determined by Weiss, (1974):
The
parameter
is the cross virial coefficient, (m^{3}
mol^{1})
= (57.7 – 0.118 • T)•10^{6}
Here below is the simple code needed to calculate fugacity from ppm (parts per million) of CO2.
T = 25 + 275 ' temperature in K R = 8.314 fCO2 = ppmCO2*exp(101325*((1636.75 + 12.0408*T  3.27957e2*T^2 + 3.16528e5*T^3)*1e6 + 2*(57.7  0.118*T)*1e6)/R/T) H2CO3 = K0*fCO2*1e6 
The last line of the code shows how the concentration of H2CO3^{*} (which comprises the true acid form H2CO3 and hydrated CO2) can be calculated, knowing the K_{0} value, as shown in the next topic.
The Hydration of Carbon Dioxide (K_{0})
CO2 + H2O H2CO3 K_{0} = [H_{2}CO_{3}^{*}]/f(CO_{2})
LnK0 = 9345.17/T  60.2409 + 23.3585*log(T/100) + S*(0.023517  0.00023656*T + 0.0047036*(T/100)^2) K0 = exp(LnK0) 
f(CO2)
is the fugacity of CO2, which is numerically very similar to CO2
partial pressure in milli
atm and therefore corresponds
to CO2 ppm in
dry air by the Dalton law. For further insight see Section
5.1. Because we have to calculate various combinations of equilibrium
relationships, we have to use the consistent set of constants
provided by DOE (1994) which is based on measurements in artificial
seawater.
Kw, the Ionic Water Product due to H2O
H3O^{+} + OH^{ }
Equilibrium
K_{w} = [H^{+}]·[OH^{}]
As explained in Section 3.4, water itself is a weak electrolyte whose dissociation must be carefully taken into account. In seawater the following expression is used to represent its dependence on temperature and salinity. As is the case for the following expressions, it should not be extrapolated to zero or near zero salinity, as it results from experiments with salinity from 25 to 45 (gramsofsalts/Kgofsolution).
LnKw = 148.96502  13847.26/T  23.6521*log(T) + (118.67/T  5.977 + 1.0495*log(T))*S^0.5  0.01615*S Kw = exp(LnKwP) ' [H+]Total scale 
The First and Second Dissociation Constants of Carbon Dioxide
(K_{1})
H_{2}CO_{3} H^{+} + HCO_{3}^{} K_{1} = [HCO_{3}^{}]·[H^{+}]/[H_{2}CO_{3}^{*}]
LnK1 = 2.83655  2307.1266/T  1.5529413*log(T)  (4.0484/T + 0.20760841)*S^0.5 + 0.08468345*S  0.00654208*S^1.5 + log(1  0.001005*S) K1 = exp(LnK1) '[H+] = [H+]Total scale 
(K_{2})
HCO_{3} ^{} H^{+} + HCO_{3}^{} K_{2} = [CO_{3}^{ }]·[H^{+}]/[HCO_{3}^{ }]
LnK2 = 9.226508  3351.6106/T  0.2005743*log(T)  (23.9722/T + 0.106901773)*S^0.5 + 0.1130822*S  0.00846934*S^1.5 + log(1  0.001005*S) K2 = exp(LnK2) '[H+] = [H+]Total scale 
The solubility of Calcite and Aragonite
CaCO_{3(calcite)} Ca^{+} + CO_{3} ^{} K_{sp}(cal) = [Ca^{++}]·[CO_{3}^{}]
LogKspCal = 171.9065  0.077993*T + 2839.319/T + 71.595*log(T)/a1 + (0.77712 + 0.0028426*T + 178.34/T)*S^0.5  0.07711*S + 0.0041249*S^1.5 LnKspCal = LogKspCal*log(10) 
CaCO_{3(aragonite)} Ca^{+} + CO_{3}^{} K_{sp}(arg) = [Ca^{++}]·[CO_{3}^{}]
LogKspAra = 171.945  0.077993*T + 2903.293/T + 71.595*log(T)/a1 + (0.068393 + 0.0017276*T + 88.135/T)*S^0.5  0.10018*S + 0.0059415*S^1.5

The Partial Hydrolysis of Ca and Mg Ions
Ca^{++} + OH^{ } Ca(OH)^{+} K_{7} = [Ca(OH)^{+}]/([Ca^{++}]·[OH^{}])
deltaG = 7576 'Joule K7 = exp(1*deltaG/(R*T)) 
Mg^{++} + OH^{ } Mg(OH)^{+} K_{8} = [Mg(OH)^{+}]/([Mg^{++}]·[OH^{}])
deltaG = 14656 'Joule K8 = exp(1*deltaG/(R*T)) 
The Dissociation of Boric Acid
B(OH)_{3 }+ H_{2}O^{ } B(OH)_{4}^{} + H^{+} K_{B} = [H^{+}]·[B(OH)_{4}^{}]/[B(OH)_{3}]
LnKB = (8966.9  2890.53*S^0.5  77.942*S + 1.728*S^1.5  0.0996*S^2)/T + 148.0248 + 137.1942*S^0.5 + 1.62142*S  (24.4344 + 25.085*S^0.5 + 0.2474*S)*log(T) + 0.053105*S^0.5*T KB = exp(LnKB) ' [H+] = [H+]Total scale 
The Second Dissociation of Sulphuric Acid
HSO_{4}^{ } SO_{4}^{ } + H^{+} K_{S} = [H^{+}]·[SO_{4}^{}]/[HSO_{4}^{}]
where
I (ionic strength)
= 19.924*S/(1000  1.005*S)
Here it is imperative to use the [H+] free concentration, as we are dealing with acid sulphate dissociation. Therefore the [H+] concentration does not include the [HSO4^{}] concentration participating to equilibrium.The first dissociation of sulphuric acid is 100% complete, being a strong acid.
The Dissociation of Hydrofluoric Acid
HF H^{+ } + F^{} K_{F} = [H+]·[F^{}]/[HF]
where
S_{T}
(total concentration of sulphate) = 0.02824*S/35 : [H+] = [H+] Total
scale
The Three Dissociations of Phosphoric Acid H_{3}PO_{4}
For the three dissociation reactions of phosphoric acid and the following of silicic acid, the formulae for empiric constants are reported, but these are not used at the present for the calculation in the 'SeaWaterCalc' code. The concentration of the two acids is very low in seawater and locally variable. They could easily be implemented by inserting them in the code.
I) H_{3}PO_{4} H^{+ } + H_{2}PO_{4}^{} K_{1P} = [H^{+}]·[H_{2}PO_{4}^{}]/[H_{3}PO_{4}]
II)
H_{2}PO_{4}^{
} H^{+}
+ HPO_{4}^{}
K_{2P}
= [H^{+}]·[HPO_{4}^{}]/[H_{2}PO_{4}^{}]
III)
HPO_{4}^{
} H^{+
}
+ PO_{4}^{}
K_{3P}
= [H^{+}]·[PO_{4}^{}]/[HPO_{4}^{}]