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Here is a photo from an article, Hydrometallurgy 2016, 160, 129–136

enter image description here

This indicates the reaction mechanism as esterification. However, the written reaction equation ($\ce{H3BO3 + nROH -> H3BO3.nROH}$) suggests the mechanism as solvation.

Shouldn't the reaction be $\ce{H3BO3 + ROH -> H2RBO3 + H2O}$ or something like that based on the scheme?

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The research paper sighted in the question (Ref.1) is about the extraction of boron (as boric acid: $\ce{H3BO3}$) from salt lake brine using 2-ethylhexanol/kerosene as organic phase. It is true that the given diagram in this paper (as shown in the question) is showing an esterification, but the authors refer it to two references, one of them is Ref.2. However, the association used to calculate the distribution of boric acid between aqueous and organic phases in Ref.1 is not the esterification. Accordingly to the paper, the association reaction is as follows:

$$\ce{H3BO3 + nROH <=> H3BO3.nROH}$$

Since there are no water molecule elimination during the reaction, this is not an esterification. It is a solvolysis reaction as OP correctly recognized.

Extraction of boron from existing sources is a challenging problem (Ref.3). Boron can be extracted as neutral ester $(\ce{B(OR)3})$, as boric acid complexes $(\ce{(H3BO3)_x.(ROH)_y})$ or as tetrahydroxy borate $(\ce{R+B(OH)4-})$. However, the extraction of boric acid by monohydric alcohols is caused by purely physical actions and the amount of extracted boric acid is roughly proportional to the concentration of an extractant (Ref.3). Accordingly, it is safe to say the extraction process is based on complexation of boric acid with intended alcohol.

References:

  1. Ran Zhang, Yingming Xie, Jianfeng Song, Lixin Xing, Dingfeng Kong, Xue-Mei Li, Tao He, "Extraction of boron from salt lake brine using 2-ethylhexanol," Hydrometallurgy 2016, 160, 129–136 (DOI: https://doi.org/10.1016/j.hydromet.2016.01.001)(PDF).
  2. Jianhua LÜ, Jidong LIU, Yujie SUN, Chunli LI, "Kinetics of Forward Extraction of Boric Acid from Salt Lake Brine by 2-Ethyl-1,3-hexanediol in Toluene Using Single Drop Technique," Chinese Journal of Chemical Engineering 2014, 22(5), 496-502 (DOI: https://doi.org/10.1016/S1004-9541(14)60059-8).
  3. Adam Balinski, Volker Recksiek, Norman Kelly, "Solvent Extraction of Boric Acid: Comparison of Five Different Monohydric Alcohols and Equilibrium Modeling with Numerical Methods," Processes 2021, 9(2), 398 (15 pages) (DOI: https://doi.org/10.3390/pr9020398).
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    $\begingroup$ Many thanks for your comprehensive answer. Here are my following problems: 1. I know 2-ethyl-1-hexanol extract vanadium as vanadic acid properly and silicium as salicylic acid relatively. Please Check: sciencedirect.com/science/article/abs/pii/S1383586617317823 It seems 2-ethyl-1-hexanol tends to extract acidic complexes, which can happen via esterification because the reaction is between an alcohol and an acid. Does my argument seem valid to you? 2. What equation fits the scheme I shared? Is my suggestion an appropriate one? Thank you again. $\endgroup$
    – Reza Mousavi
    Commented Apr 27, 2021 at 9:28
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    $\begingroup$ Unfortunately, I don't have access to said reference at this time. Yet, I suggested that your suggestion is appropriate according to the given image. However, it is clear from multiple reports from various authors that monohydric alcohols give complexation under the reaction conditions (at least at room temperature) while diols and higher hydric alcohols tends to esterify the reactant. That need extra striping step(s) to recover intended materials (here boric acid). $\endgroup$
    – Mathew Mahindaratne
    Commented Apr 27, 2021 at 9:58

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