cantera


This is the classic problem of the solubility of NaCl in water.
The result is a saturated solution of Na+ and Cl- in water in equilibrium
with NaCl solid. This problem also has a gas phase consisting of N2, H2O,
H2, and O2. CO2 has been thrown in as well. However, the element abundance
of C is zero. So, CO2 should turn out to have a zero concentration.



The problem can be divided up into two parts: estimating the Gibbs
reaction delta for
        Na+ + Cl- = NaCl(solid)

 (so that Del(Gf) = G(NaCl(solid)) - G(Na+) - G(Cl-))

and estimating the activity coefficients for the electrolytes at
the solubility limit.

By far the most important as always is estimating the delta G
for the reaction above. Note the electrolytes are using the
molality basis.

Using the NASA basis we get
  NaCl(solid) :  Hf(298.15) = -411.1207 kJ/gmol
                 S(298.15)  = 72.1093    J/(gmol K)
      (from NIST Webbook)
                 Gf(298.15) = -432.6200 kJ/gmol

From Codata key values for Thermodynamics:
     Cl-        Hf(298.15) = -167.080  kJ/gmol
                S(298.15)  =   56.60    J/(gmol K)
                Gf(298.15) = -183.9552 kJ/gmol

     Na+        Hf(298.15) = -240.34 kJ/gmol
                 S(298.15) =   58.45   J/(gmol K)
             -> Gf(298.15) = -257.7668 kJ/gmol


           Del(Gf)(298.15) =  9.1020 kJ/gmol



In addition, the relative humidity of the salt solution may be compared
to the humidity above a pure water solution in order to understand
the effects of the lowering of the water activity.


If you run the equilibrium calculation without salt, you get the
equilibrium of water vapor above water, consistent with the
current thermo.
    X_H2O(g) = 0.03169 
   at 25C and 1atm

If you then run the calculation with a saturated salt solution you
get a smaller amount of water vapor in equilibrium with the water
electrolyte:

    X_H2O(g) = 0.023243
    at 25V and 1atm

The ratio of these two numbers is the relative humidity at which
the a saturated salt solution deliqueses from a salt particle.

  rel humidity = 0.733


This is a very important number in terms of its effect on aqueous
corrosion.




Next, let's compare the above calculation with the calculation presented 
in the current directory. First, getting Gabs from the cttables calculation:

   G(298.15) NaCl(solid)      = -432.6201 kJ/gmol

   G(298.15) Na+              = -257.7668  kJ/gmol

   G(298.15) Cl-              = -183.9552  kJ/gmol

         (note, Na+ and Cl- have screwed up H and S values. However, the
          G value seems to be correct).

Putting this together yields:
     Delta G = 9.1019 kJ / gmol

----------------------------------------------------------------------------
   H2O(l) = H+ + OH- Equilibrium Reaction
------------------------------------------------------------------------

  The equilibrium constant for water is given in Robinson and Stokes, p. 363 
and p.544.
 
      10^(-13.996) = actCoef(H+) actCoef(OH-) Molal(H+) Molal(OH-) / activity_H2O.

This works out to a value of
      DeltaG =  79.88936 kJ/gmol
      DeltaH =  56.576 kJ/gmol
      DeptaCp = -194.68 J/K gmol

In the current database:
      G(298, OH-)    = -226.7839 kJ / gmol
      G(298  H+)     =    0.0
      G(298, H2O(L)) = -306.6858.
          -------------------------
            DeltaG =     79.902

Therefore, there is a slight error of 0.013 kJ/gmol, but the database is roughly correct.



Silvestre & Pitzer
------------------------------------------------------------------------

The equilibrium condition for this simple system comes down to the
following equation
 
  Delta G = - 2 R T ln (m * actCoeff)

This is the basic test of the system.

Delta G = -2161 cal gmol-1 = -9.0416 kJ gmol-l
M_sat = 6.146
ActCoeff_mixed_molalityScale = 1.008


Using the given files and conditions, I calculate equilibrium as:

Delta G =  9.1019  kJ gmol-l
M_sat = 6.193
ActCoeff_mixed_molalityScale = 1.0132


Relative Humidity Lowering
------------------------------------------------------
from the saturated NaCl calculation using HMW 
          x_H2O = 0.0237641
From the pure water equilibrium case:
          x_H2O = 0.0316882

Therefore the relative humidity lowering is 0.7504