I am studying the dissolution of Forsterite (olivine). I used the assumptions hereunder to predict the concentration in Mg 2+ but the result is completely inconsistent with prediction from kinetics. Could someone tell me what is wrong in the assumptions I used? See the attached file.

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

Based on experimental data, the pH is 9,8, at 20°C after 1 day. I used extra pure water to conduct the experiment. According to the kinetic model , based on the particles size, I expect to reach a concentration of 2,40E-04 in Mg 2+. This is an order of magnitude as there is a large uncertainty on the kinetic model.

I have the following chemical elements to consider (“a” = concentration in CO2 aq, etc…)

CO2 aq a Mg2+ d H2SiO4 2- h

HCO3- b H4SiO4 e OH- k

CO3 2- c Si02 f CT a + b + c

H+ H3SiO4 - g Tot Si =e + f + g + h

In addition I have the following equilibrium (1 to

plus relation Mg to Si from (reaction A) (9):

(1) CO2 aq with CO2 g in the atmosphere (provides “a” concentration in CO2 aq / K0 = 0, 0396)

(2) CO2 aq with HCO3 - / K1 = 4,2E-07 (provides “b” concentration in HCO3- knowing “a”)

(3) HCO3 – with CO3 2- / K2 = 4,3E-11 (provides “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) The equilibrium of electrical charges b + 2c + g + 2h + k = [H+] + 2d

(

[H+] * [OH -] = Kw = 1E-14

(9) And based on reaction (A) I know that d= 2Tot Si = 2(e+f+g+h) as (A) produces 2 Mg2+ for one H4 SiO4

I am not sure how I can use the fact that I produced 4 HCO3- for 2 Mg 2+

Based on the equations above 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 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 (

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

Using the assumptions hereabove I obtain a concentration “d” in Mg2+ which is well above the concentration predicted by the kinetic model (3,4E-02 based on these equations vs 2,40E-04 using the kinetic model). It seems that the concentration in carbonate and bicarbonate ions is overestimated, but why? Equations 1, 2 and 3 are not valid in this context? What is wrong in the assumptions I used?