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Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: pbuis on March 31, 2021, 11:07:31 AM

Title: Olivine dissolution reaction : discrepancy kinetic model with pH measurement
Post by: pbuis on March 31, 2021, 11:07:31 AM
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?
Title: Re: Olivine dissolution reaction : discrepancy kinetic model with pH measurement
Post by: Corribus on March 31, 2021, 11:44:40 AM
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.
Title: Re: Olivine dissolution reaction : discrepancy kinetic model with pH measurement
Post by: pbuis on April 01, 2021, 07:53:57 AM
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?