Analytical Expressions


Hi all,

I hope that everyone is doing well!

I have a question that is simple, but I am not able to find the answer on the forum, databases, or the manual about analytical expressions.

From what I understand analytical expressions consist of six unique constants for a given chemical reaction (i.e. b1 b2 b3 b4 b5 b6). These constants then go in to a formula - logK = b1 + b2*T + b3/T + b4*log(T) + b5/T2 + b6*T2 - to tell us how log k varies with temperature for a given chemical reaction.

I am trying to model boron adsorption/desorption on a generic surface (HFO), as the surface and solution are progressively heated. I need to know how log k changes for each of my species (both solution and surface) with temperature. However, I am not able to find the analytical expressions for any of the Hfo reactions (i.e.   "Hfo_wOH = Hfo_wOH
      log_k   0
   Hfo_wOH   + H+ = Hfo_wOH2+
      log_k   7.29
   Hfo_wOH = Hfo_wO- + H+
      log_k   -8.93"). Seeing as this is one of the most basic surfaces/surface species - I am confused as to why there is no analytical expression listed in the databases. Are analytical expressions not used for surface species?

I have posted my code below for reference:

   H3BO3 + H2O = H4BO4- + H+ 
      log_k -9.24 #Dickson 1990 using salinity = 0
       -analytical 24.3919    0.012078   -1343.9    -13.2258   

   #25.0 100.0 in 75 steps

   Hfo_w   Hfo_wOH

# log_k is reported at 25C, 1 bar, used if no -delta_H or -analytic
# -delta_H molar enthalpy of reaction, used if no -analytic
# -analytic b1 b2 b3 b4 b5 b6 / logK = b1 + b2*T + b3/T + b4*log(T) + b5/T2 + b6*T2

   Hfo_wOH = Hfo_wOH
      log_k   0
   Hfo_wOH   + H+ = Hfo_wOH2+
      log_k   7.29
   Hfo_wOH = Hfo_wO- + H+
      log_k   -8.93   
   Hfo_wOH + H3BO3 = Hfo_wH3BO4- + H+
      log_k   -8.44"   


The sorption log Ks in the PHREEQC database come from Dzombak and Morel. They do not provide temperature dependence of these reactions. Their monograph was written 30 years ago; I have not kept up with the literature, but my guess is that data other than at 20 or 25 C is rare. Dzombak and Morel would be an entry into the literature. Any work on HFO would certainly reference them.

I think there is a recipe for making HFO, but it only persists for hours or days. I am not sure HFO is well defined at higher temperatures. If you are doing experimental work, I suspect that anything you can do with temperature dependence would be a useful contribution.

Hi Parkhurst,

Thank you! I will look into the literature and see if there is existing data out there.



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