Difference between Van't Hoff and analytical expression provided in LLNL.DAT

[Jeonghwan Hwang]

Hello, this is Jeonghwan Hwang.
I am recently studying to check the change of the equilibrium constant (log K) with temperature (T).

PHREEQC has various databases, and among them, information about Cs+ that I want is in LLNL.dat and Sit.dat.
In PHREEQC, the equilibrium constant (log K) for temperature (T) can be obtained in two ways, van't Hoff and analytical expression, respectively. They are represented in the database as'log_k','delta_H' for van't Hoff equation and 'analytic' for analytical expression (https://water.usgs.gov/water-resources/software/PHREEQC/documentation/phreeqc3-html/phreeqc3-50.htm).

There are three reactions I have looked at as an example.
Cs+ + Br- = CsBr
Cs+ + I- = CsI
Cs+ + Cl- = CsCl

In LLNL.dat and Sit.dat, all of 'log_k', 'delta_H', and 'analytic' were provided.

===============================LLNL.DAT============================
1.0000 Cs+ + 1.0000 Br-  =  CsBr
        -llnl_gamma           3.0   
        log_k           -0.2712
   -delta_H   10.9621   kJ/mol   # Calculated enthalpy of reaction   CsBr
#   Enthalpy of formation:   -88.09 kcal/mol
        -analytic 1.2064e+002 3.2000e-002 -3.8770e+003 -4.7458e+001 -6.0533e+001
#       -Range:  0-300

1.0000 Cs+ + 1.0000 Cl-  =  CsCl
        -llnl_gamma           3.0   
        log_k           -0.1385
   -delta_H   2.73215   kJ/mol   # Calculated enthalpy of reaction   CsCl
#   Enthalpy of formation:   -100.95 kcal/mol
        -analytic 1.2472e+002 3.3730e-002 -3.9130e+003 -4.9212e+001 -6.1096e+001
#       -Range:  0-300

1.0000 I- + 1.0000 Cs+  =  CsI
        -llnl_gamma           3.0   
        log_k           +0.2639
   -delta_H   -6.56888   kJ/mol   # Calculated enthalpy of reaction   CsI
#   Enthalpy of formation:   -76.84 kcal/mol
        -analytic 1.1555e+002 3.1419e-002 -3.3496e+003 -4.5828e+001 -5.2302e+001
#       -Range:  0-300
===================================================================

=============================Sit.dat===============================
1.000Cs+     + 1.000Br-     = CsBr
     log_k     0.090     
     delta_h   5.922     #kJ/mol       
     # Enthalpy of formation:           -373.488        #kJ/mol       
     -analytic 1.12749E+0 0E+0 -3.09327E+2 0E+0 0E+0

1.000Cs+     + 1.000Cl-     = CsCl
     log_k    -0.090     
     delta_h   7.523     #kJ/mol       
     # Enthalpy of formation:           -417.557        #kJ/mol       
     -analytic 1.22797E+0 0E+0 -3.92953E+2 0E+0 0E+0

1.000Cs+     + 1.000I-     = CsI
     log_k     1.050     
     delta_h  -0.055     #kJ/mol       
     # Enthalpy of formation:           -314.835        #kJ/mol       
     -analytic 1.04036E+0 0E+0 2.87285E+0 0E+0 0E+0
===================================================================

So, I calculated the log K with both expressions, respectively, to comparing values.
The Sit.dat was confirmed to show similar values ??between van't Hoff and analytical expression when calculated with Excel.
However, in LLNL.dat, the log K values ??were very different according to the two approaches.

My first question is "what formula is applied preferentially when calculating the equilibrium constant according to temperature in LLNL.dat in PHREEQC if van't Hoff and analytical results represent the different value".

In addition, the thermodynamic database of LLNL.dat is expressed as applicable to 0-300 cel. I wonder that both expressions can be applied to 0-300 cel.

Thank you for reading.
Sincerely,

Jeonghwan Hwang.

[dlparkhurst]

The analytical expression is used, if it is defined; if it is not defined, then the Van't Hoff expression is used.

Sit.dat appears to have created analytical expressions that exactly match the Van't Hoff expressions, so there is not advantage to using one or the other.

llnl.dat was created from a database labeled thermo.com.V8.R6.230 formerly distributed from Lawrence Livermore National Lab. The values for CsBr, CsCl, and CsI appear to be the same as distributed for Geochemist's Workbench in a database labeled thermo.com.V8.R6.full
(generated by GEMBOCHS.V2-Jewel.src.R6 03-dec-1996 16:55:04). These databases have a temperature grid for log K, and the analytical expression for log K in llnl.dat matches the grid, and the delta H matches calculated from delta H of formation given in the databases.

The Van't Hoff and analytical expressions appears to be consistent for CsBr. However, the delta H and analytical expressions for CsCl and CsI are inconsistent. CsI seems to have conflicting signs for the temperature dependence, and the analytical expression for CsCl implies a delta H of about 10 rather than 2.7.

So, the inconsistency is caused by the original database from which llnl.dat was translated. I don't know whether the analytical expressions or the delta H is correct. The analytical expressions seem to be more consistent between the electrolytes. You could try to go back to Supcrt or Gembochs (the programs used to produce the original databases) to reevaluate these species. I've never used these programs, so I don't know how difficult it would be.

Alternatively, you could try to track down references used for sit.dat. Here is the web site: www.thermochimie-tdb.com. You also can look in the literature for any experimental data from which you could calculate a delta H or analytical expression.

Taking a step back, I suspect these ion pairs do not have much influence on calculations. My guess is that they are strong electrolytes and the pairing would be minimal.

One final option is to use the Pitzer approach, where ion pairing is not calculated explicitly. It would be difficult for mixed electrolytes, but I suspect you could find parameters for single-electrolyte solutions.

[Jeonghwan Hwang]

Thank you for advising.

I understand the difference between analytical and Vant Hoff expressions.

In addition, I found the base data for sit.dat at 'www.thermochimie-tbd.com', as you suggested.
Unfortunately, I could not find the information about Supcrt and Gembochs,
but I could find the method to apply and compare the database from attached phreeqc file.

Thank you.
Sincerely,

Jeonghwan Hwang