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Sensitivity Analysis on the Comparison between the Gapon and Vanselow Exchange Coefficients
Author(s) -
Evangelou V. P.,
Phillips R. E.
Publication year - 1987
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1987.03615995005100060013x
Subject(s) - chemistry , analytical chemistry (journal) , sodium , phase (matter) , sensitivity (control systems) , activity coefficient , thermodynamics , physics , aqueous solution , chromatography , organic chemistry , electronic engineering , engineering
Abstract The traditional nonthermodynamic Gapon exchange selectivity coefficient ( K G ) for Na‐Ca exchange has previously been shown in the literature to be in close agreement with the Vanselow coefficient ( K v ) for Na equivalent fractions ( N Na ) 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 = N Na × 100; ESP = exchangeable sodium percentage and SAR = sodium adsorption ratio) is indistinguishable from the ESP‐SAR relation predicted by the Vanselow equation for N Na <0.40. This study is a sensitivity analysis of the comparison between the K v and K G for Na + replacing Ca 2+ in the exchange phase. It is carried out by mathematically deriving and graphically demonstrating the interrelationships between K v and K G . These interrelationships are established on the basis that the Na‐Ca exchange system obeys ideal solid solution theory and thus K v is reduced to a thermodynamic exchange constant. The results point out that generally, the greater the K v , the greater the N Na range for which an apparent linear relationship between N Na and SAR is observed. This relationship, however, does not ensure that for the same N Na range the condition K G ≃ K v is also met. The results show that as N Na approaches 0, K G = 0.50 K v , and as N Na approaches 1, K G approaches infinity. The results also demonstrate that the condition K G ≃ K v is dependent on the magnitude of K v or K G for a limited N Na range, and it is independent of the magnitude of the cation exchange capacity (CEC). The condition K G ≃ K v appears to have the potential to be met experimentally for K v values in the range of <0.015 and up to a N Na value of approximately 0.60. At the larger K v values (≫0.015), the condition K G ≃ K v is less likely to be met because the absolute difference between K v and K G is significant even at N Na values <0.20. The K v , however, is always equal to the K G at N Na = 0.60. This cross‐over point is independent of the magnitude of K v and CEC.