April 13, 2021, 03:05:05 AM
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Topic: Olivine dissolution reaction : discrepancy kinetic model with pH measurement  (Read 208 times)

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Offline pbuis

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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 8) 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
(8)   [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 (8)         
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?

Offline Corribus

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Your post is really hard to read. You should get in the habit of using subscripts where appropriate, formatting your tables to aligned columns and rows, , including units with numerical values, correcting emojis that are all over the place, etc. If you expect to get quality help, take some care in how you present your questions.

I don't know what "According to the kinetic models, based on particle size" means. "This is an order of magnitude as there is a large uncertainty on the kinetic model" is unclear. What kinetic model are you referring to, and order of magnitude of what?

As a general note, if you solute includes small particles, you may have to consider particle surface energy and particle surface effects in both kinetic and thermodynamic models.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

Offline pbuis

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Thanks for your comment, I apologize for the poor quality of the text, I am not familiar with this forum , next time I’ll do it better.
To reply to your question: for the dissolution rate (in mole/m2 s), I am using a plot which shows the dissolution rate as a function of pH, and I made a minor adjustment for temperature. Regarding the particles I used an estimate of the total surface of the particles. Using the surface and the dissolution rate I could calculate the quantity of Mg 2+ produced daily.
Regarding the uncertainty: the range of uncertainty on the dissolution rate is a factor 20 between the mini and the maxi values. It’s quite large but it’s not sufficient to explain the discrepancy I observed ((3,4E-02 based on the equations vs 2,40E-04 using the kinetic model)
Would you have any advice on the validity of using the various reactions (1) to (9) in this context?

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