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### Forsterite (olivine) dissolution reaction / assumptions

Posted: Mon Apr 05, 2021 10:14 am
I am studying dissolution of forsterite (olivine) at ambient temperature and pressure:

Mg2SiO4 + 4H2O + 4 CO2 ------ H4 SiO4 + 4 HCO3- + 2 Mg 2+ (reaction A)

I used the assumptions listed hereunder to estimate the concentration in Mg 2+ based on pH measurement (9,8) but the result is completely inconsistent with the prediction based on the kinetic model. I assume the assumptions I used may not be valid. Could someone tell me which of the reactions (1) to (9) I used might not be valid ?
a/ In the table hereunder I listed the various chemical species I take into account and the associated concentrations (“a” = concentration in CO2 aq, etc…).
CO2 aq a
HCO3- b
CO3 2- c
H+
Mg2+ d
H4SiO4 e
Si02 f
H3SiO4- g
H2SiO42- h
Tot Si e + f + g + h
OH- k

b/ I used the equilibrium relations (1) to (8) and equation (9) (based on Mg 2+ to Si ratio resulting from reaction (A)):

(1) CO2 aq with atmospheric CO2 g (allows to obtain “a” concentration in CO2 aq / K0 = 0, 0396)
(2) CO2 aq with HCO3 - / K1 = 4,2E-07 (allows to obtain “b” concentration in HCO3- knowing “a”)
(3) HCO3 – with CO3 2- / K2 = 4,3E-11 (allows to obtain “c” concentration in CO3 2- knowing “b”)
(4) SiO2(s) + 2H2O = H4SiO4 (aq) ; K1a = 10-2,7
(5) H4SiO4 (aq) + H2O = H3SiO4- (aq) + H3O+(aq) K2a = 3,162E-10
(6) H3SiO4- (aq) + H2O = H2SiO4 2- + H3O+(aq) / K3a = 2,512E-13
(7) Electrical equilibrium : b + 2c + g + 2h + k = [H+] + 2d
(8) [H+] * [OH -] = Kw = 1E-14
(9) Based on reaction (A) we know that d= 2Tot Si = 2(e+f+g+h) since (A) produces 2 Mg2+ for 1 H4 SiO4

I am not sure how I can use the fact that (A) produces 4 HCO3- for 2 Mg 2+ ???

c/ results: based on these equations / equilibrium (1) to (9) I obtain the following :
CO2 aq a 1,4E-05 based on (1) with PCO2=0,00035 atm
HCO3- b 3,6E-02 based on (2)
CO3 2- c 9,9E-03 based on (3)
H+ 1,6E-10 based on measured pH
Mg2+ d unknown
H4SiO4 e =g/2 based on (5)
Si02 f can be neglected based on (4)
H3SiO4- g unknown
H2SiO42- h can be neglected based on (6)
OH- k 6,3E-05 based on pH and (8)
Tot Si e + f + g + h
from reaction A d=2(e+f+g+h)≈2(g+g/2)=3g based on (9)

electrical equilibrium 2d=b+2c+g+k then 6g=b+2c+g+k then 5g=b+2c+k
electrical equilibrium (contd) then g= 1,1E-02 and d= 3,4E-02

I obtain a concentration “d” in Mg 2+ (3,4E-02) which is much higher (by a factor 100) than what predicts the kinetic model. Could someone tell me if the equations (1) to (9) I used are valid in this context ? Particularly the equations allowing to compute concentration in HCO3 – et CO3 2- ?
NB : I used extra pure water to conduct the experiment therefore the initial concentration in Mg 2+ in the water was extremely low.