# Re:

```
> For exchange species activity is equivalent fractions which is explained
in page 12 of manual.

> {activity} = Gama*be*ne/Te

For the exchange species CaX2, the equation is

[CaX2] = Gamma*2*CaX2/CEC,

where [] indicates activity CaX2 is in moles, and CEC is in equivalents (or
CaX2 is in moles/L and CEC is eq/L).

> However, I could not understand it. I think it is not just matter of
mol/L
and mol/kg.

> The reason is I tried to simulate and could get the matching output with
significantly different Log K values.

For the reaction

Ca+2 + 2X- = CaX2

The mass action expression is

K = [CaX2]/([Ca+2][X-]^2)

The value of [X-] is arbitrary because in concept it will cancel when you
put to half reactions together and the number of moles of X- is assumed to
be zero (all sites are filled with cations). So substituting the definition
of activity,

K = (2*CaX2/CEC)/[Ca+2], and assuming 1 kg water (usually the case),

K = (2(CaX2)/CEC)/[Ca+2]. If you were try to generate similar results just
using molarity, then

K' = K*CEC/2 = (CaX2)/(Ca+2).

So you can see that K' using just molality has a dependence on CEC relative
to the mole fraction approach. It will be different for monovalent cations.
The combined Ca/Na exchange reaction also has a CEC dependence.

Ca+2 + 2NaX = CaX2 + 2Na+

K = [CaX2][Na+]^2/([Ca+2][NaX]^2)

K = ((CaX2)*2/CEC)[Na+]^2 /([Ca+2](NaX/CEC)^2)

K = CEC (2(CaX2)[Na+]^2/([Ca+2](NaX)^2)

K' = K/(2*CEC) = (CaX2)[Na+]^2 / ([Ca+2](NaX)^2)

This last equation may be what you are calculating by using molarity of
exchange species, I'm not sure. Note that for monovalent/monovalent
exchange and divalent/divalent exchange, the exchange constants would be
the same between the PHREEQC and the molarity approach.

David

David Parkhurst (dlpark@xxxxxxxx)
U.S. Geological Survey
Box 25046, MS 413
Denver Federal Center
Denver, CO 80225

Project web page: https://wwwbrr.cr.usgs.gov/projects/GWC_coupled

```

• References:
• Re:
• From: Tirtha Raj Gautam

Complete Water Resources Division Software