Comparison Between the Gapon and Vanselow Exchange Selectivity Coefficients

Abstract

The Gapon exchange equation is commonly employed in the literature to study binary heterovalent exchange reactions. However, the Gapon equation is not consistent with thermodynamics of exchange reactions. The Vanselow exchange equation, on the other hand, is consistent with thermodynamics of exchange reactions. Algebraic analysis on the interrelationship between the Vanselow (KV) and the Gapon (KG) exchange selectivity coefficients for monovalent-bivalent exchange (Na+-M2+; M = Ca2+ or Mg2+), KG = KV (1 + ENa)1/2/[2(1 − ENa)1/2], has shown that KG = 0.5 KV when ENa → 0, and KG = ∞ when ENa → 1 (ENa = charge fraction of Na on the exchanger). Also, KV and KG are equal at a sodium equivalent fraction of the exchanger (ENa) = 0.60. These KV-KG interrelationships as a function of ENa are independent of the magnitude of the cation exchange capacity (CEC). This study was conducted to test whether experimental data of monovalent-bivalent binary exchange on soil clay minerals conform to the algebraic interrelationships between KV and KG. This was tested by estimating values of KV and KG with previously reported experimental data for Na-Ca and Na-Mg exchange of clay minerals and a soil, carried out in perchlorate background media. The results of the experimental data confirm that these interrelationships are met.