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 a

HCO

_{3}- b

CO

_{3}2- c

H+

Mg

_{2}+ d

H

_{4}SiO

_{4}e

Si02 f

H

_{3}SiO

_{4}- g

H

_{2}SiO

_{42}- 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}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 atm

HCO

_{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 unknown

H

_{4}SiO

_{4}e =g/2 based on (5)

Si02 f can be neglected based on (4)

H

_{3}SiO

_{4}- g unknown

H

_{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