Effect of Temperature and Salinity on Equilibrium Constants


CO2 Partial Pressure and Fugacity

The Hydration of Carbon Dioxide (K0

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 H3PO4

 


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 inatm, the total pressure, P, is in Pa (1 atm = 101325 Pa), the first virial coefficient of CO2, B, and the parameter are in m3 mol-1, R = 8.314 J K-1 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,
 (m3 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 - 3.27957e-2*T^2 + 3.16528e-5*T^3)*1e-6 + 2*(57.7 - 0.118*T)*1e-6)/R/T)

H2CO3 = K0*fCO2*1e-6

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 K0 value, as shown in the next topic.


The Hydration of Carbon Dioxide (K0

CO2 + H2O H2CO3                  K0 = [H2CO3*]/f(CO2)

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

Kw = [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 (grams-of-salts/Kg-of-solution).



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

(K1)

H2CO3   H+ + HCO3-                  K1 = [HCO3-]·[H+]/[H2CO3*]


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



(K2

HCO3 -   H+ + HCO3--             K2 = [CO3-- ]·[H+]/[HCO3- ]


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  

CaCO3(calcite) Ca+ + CO3 --                 Ksp(cal) = [Ca++]·[CO3--]


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)

CaCO3(aragonite) Ca+ + CO3--               Ksp(arg) = [Ca++]·[CO3--]


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


LnKspAra = LogKspAra*log(10)


The Partial Hydrolysis of Ca and Mg Ions 

Ca++ + OH- Ca(OH)+-                   K7 = [Ca(OH)+]/([Ca++]·[OH-])

deltaG = -7576 'Joule

K7 = exp(-1*deltaG/(R*T))

Mg++ + OH- Mg(OH)+                  K8 = [Mg(OH)+]/([Mg++]·[OH-])

deltaG = -14656 'Joule

K8 = exp(-1*deltaG/(R*T))



The Dissociation of Boric Acid

B(OH)3 + H2O B(OH)4- + H+             KB = [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 

HSO4- SO4- - + H+                KS = [H+]·[SO4--]/[HSO4-]



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-                 KF = [H+]·[F-]/[HF]


where ST (total concentration of sulphate) = 0.02824*S/35 : [H+] = [H+] Total scale


The Three Dissociations of Phosphoric Acid H3PO4

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)  H3PO4 H+ + H2PO4-                   K1P = [H+]·[H2PO4-]/[H3PO4]



II)  H2PO4- H+ + HPO4--
                    K2P = [H+]·[HPO4--]/[H2PO4-]



III)   HPO4-- H+ + PO4---
                      K3P = [H+]·[PO4---]/[HPO4--]