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Sensitivity Analysis on the Comparison between the Gapon and Vanselow Exchange Coefficients¹

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 x 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 Ca²⁺ 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.

¹ Contribution from the Dep. of Agronomy, Univ. of Kentucky Agric. Exp. Stn., Lexington. The investigation reported in this paper (no. 86-3-205) is in connection with a project of the Kentucky Agric. Exp. Stn. and is published with the approval of the director.

² Associate Professor and Professor, respectively, Dep. of Agronomy, Univ. of Kentucky, Lexington, KY 40546-0091.

Received for publication September 22, 1986.