Gapon equation

Evangelou, V. P. and A. D. Karathanasis. 1986. Evaluation of potassium quantity-intensity relationships by a computer model employing the Gapon equation. Soil Sci. Soc. Am. Proc. 50 58-62. 

The exchange is between equivalents of charge. Strictly, ionic activity, not concentration, should be considered, but as ionic concentration in soil solution is so low, it is commonly used. This is known as the Gapon equation. This approach stresses the importance of the ion activity ratio, which tends to remain constant. As a result, monovalent ions are lost from a soil by leaching in preference to divalent and tri-valent ions. A consequence is the acidifcation of soil by leaching (see Section 5.4). 

The Gapon equation is widely recognized as empirical in nature and thermodynamically dubious (e.g., see references 7 and 24) but has nonetheless often been used successfully to fit cation-exchange data. We will demonstrate later that the Gapon equation can indeed describe monovalent-divalent exchange under conditions in which sorption in the diffuse layer is minor in comparison with chemisorption. 

With an arbitrary definition of KNaX as equal to unity, thus establishing a reference half reaction, the equilibrium constant for any other half reaction can be determined from measured selectivity coefficients. The Gapon equation can be readily implemented in this manner. Implementation of the Vanselow equation, however, requires modification of the general equilibrium models to account for the more complex dependence of mole fractions on the molar concentrations. An example ion-exchange calculation using the half reaction approach to represent the Gapon equation is presented in Appendix 2. 

The Gapon equation also uses concentrations rather than activities for the soluble ions, and writes the mass action equation with chemically equivalent quantities both... 

Workers at the U.S. Salinity Laboratory substituted the sum of Ca plus Mg for the exchangeable and bulk-solution Ca concentrations in the Gapon equation (8.10). This yields... 

This is equivalent to the Gapon equation, with an exchange constant of 0.015, except for the small negative intercept. For many applications, the intercept is negligible. Soils outside the principal irrigated portions of the western United States, such as the irrigated tropics, may have Gapon constants appreciably different from 0.015. 

Table 8.5 compares different exchange coefficients calculated from the data for ammonium-calcium exchange in Table 8.2. The simple Gapon equation (8.10) yields the most uniform exchange coefficient for this set of data the Eriksson equation s predictions also agree well with the measured values. Bond and Verburg (1997) applied the various ion equations to the more complicated case of ternary (Ca-K-Na). Their slight modifications of the 1918 work by Rothmund and Kornfeld yielded the most consistent exchange coefficients in their study. Snyder and Cavallaro (1997) applied a single-phase mixture approach to NH -Ba2+-La3+ exchange on clays.

A soil is equilibrated with a solution of SAR = 20. Based on the Gapon equation, what would be its equilibrium exchangeable sodium percentage (ESP) If the soil had instead been equilibrated with the same solution diluted fivefold with salt-free water, what would have been the corresponding SAR and ESP values ... 

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