Sensitivity Analysis on the Comparison between the Gapon and Vanselow Exchange Coefficients1
- V. P. Evangelou and
- R. E. Phillips2
The traditional nonthermodynamic Gapon exchange selectivity coefficient (KG) for Na-Ca exchange has previously been shown in the literature to be in close agreement with the Vanselow coefficient (Kv) for Na equivalent fractions (NNa) in the exchange of <0.20. Furthermore, it has previously been shown for a heterogeneous group of soils that the traditional empirical ESP-SAR relation (ESP = NNa × 100; ESP = exchangeable sodium percentage and SAR = sodium adsorption ratio) is indistinguishable from the ESP-SAR relation predicted by the Vanselow equation for NNa <0.40. This study is a sensitivity analysis of the comparison between the Kv and KG for Na+ replacing Ca2+ in the exchange phase. It is carried out by mathematically deriving and graphically demonstrating the interrelationships between Kv and KG. These interrelationships are established on the basis that the Na-Ca exchange system obeys ideal solid solution theory and thus Kv is reduced to a thermodynamic exchange constant. The results point out that generally, the greater the Kv, the greater the NNa range for which an apparent linear relationship between NNa and SAR is observed. This relationship, however, does not ensure that for the same NNa range the condition KG ≃ Kv is also met. The results show that as NNa approaches 0, KG = 0.50 Kv, and as NNa approaches 1, KG approaches infinity. The results also demonstrate that the condition KG ≃ Kv is dependent on the magnitude of Kv or KG for a limited NNa range, and it is independent of the magnitude of the cation exchange capacity (CEC). The condition KG ≃ Kv appears to have the potential to be met experimentally for Kv values in the range of <0.015 and up to a NNa value of approximately 0.60. At the larger Kv values (≫0.015), the condition KG ≃ Kv is less likely to be met because the absolute difference between Kv and KG is significant even at NNa values <0.20. The Kv, however, is always equal to the KG at NNa = 0.60. This cross-over point is independent of the magnitude of Kv and CEC.Please view the pdf by using the Full Text (PDF) link under 'View' to the left.
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