### Forsterite (olivine) dissolution reaction / assumptions

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

Mg

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 CO

CO

HCO

CO

H+

Mg

H

Si02 f

H

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) CO

(2) CO

(3) HCO

(4) SiO

(5) H

(6) H

(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 Mg

I am not sure how I can use the fact that (A) produces 4 HCO

c/ results: based on these equations / equilibrium (1) to (9) I obtain the following :

CO

HCO

CO

H+ 1,6E-10 based on measured pH

Mg

H

Si02 f can be neglected based on (4)

H

H

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 HCO

NB : I used extra pure water to conduct the experiment therefore the initial concentration in Mg 2+ in the water was extremely low.

Thanks for your help / advices

Mg

_{2}SiO_{4}+ 4H_{2}O + 4 CO_{2}------ H_{4}SiO_{4}+ 4 HCO_{3}- + 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 CO

_{2}aq, etc…).CO

_{2}aq aHCO

_{3}- bCO

_{3}2- cH+

Mg

_{2}+ dH

_{4}SiO_{4}eSi02 f

H

_{3}SiO_{4}- gH

_{2}SiO_{42}- hTot 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) CO

_{2}aq with atmospheric CO_{2}g (allows to obtain “a” concentration in CO_{2}aq / K0 = 0, 0396)(2) CO

_{2}aq with HCO_{3}- / K_{1}= 4,2E-07 (allows to obtain “b” concentration in HCO_{3}- knowing “a”)(3) HCO

_{3}– with CO_{3}2- / K_{2}= 4,3E-11 (allows to obtain “c” concentration in CO_{3}2- knowing “b”)(4) SiO

_{2}(s) + 2H_{2}O = H_{4}SiO_{4}(aq) ; K_{1}a = 10-2,7(5) H

_{4}SiO_{4}(aq) + H_{2}O = H_{3}SiO_{4}- (aq) + H_{3}O+(aq) K_{2}a = 3,162E-10(6) H

_{3}SiO_{4}- (aq) + H_{2}O = H_{2}SiO_{4}2- + H_{3}O+(aq) / K_{3}a = 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 Mg

_{2}+ for 1 H_{4}SiO_{4}I am not sure how I can use the fact that (A) produces 4 HCO

_{3}- for 2 Mg 2+ ???c/ results: based on these equations / equilibrium (1) to (9) I obtain the following :

CO

_{2}aq a 1,4E-05 based on (1) with PCO_{2}=0,00035 atmHCO

_{3}- b 3,6E-02 based on (2)CO

_{3}2- c 9,9E-03 based on (3)H+ 1,6E-10 based on measured pH

Mg

_{2}+ d unknownH

_{4}SiO_{4}e =g/2 based on (5)Si02 f can be neglected based on (4)

H

_{3}SiO_{4}- g unknownH

_{2}SiO_{42}- 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 HCO

_{3}– et CO_{3}2- ?NB : I used extra pure water to conduct the experiment therefore the initial concentration in Mg 2+ in the water was extremely low.

Thanks for your help / advices