Theoretical evaluations reported in the literature disagree with respect to which is the valid exchange expression for determining ideal solid solution behavior and for calculating adsorbed-ion activity coefficients. One group of scientists argues that the Argersinger approach, which uses the Vanselow exchange equation and employs the mole fraction, is the correct approach. Another group argues that the Gaines and Thomas approach, which employs charge fractions, is equally valid and whichever of the two is used in soils is a matter of preference. Because the two approaches lead to different numerical answers, a need exists for an algebraic evaluation of the interrelationships between the two equations (Vanselow versus Gaines and Thomas). Additionally, a need exists to establish differences between the two approaches for estimating and evaluating thermodynamic parameters statistically, employing experimental data. In this study, algebraic analysis of the interrelationship between the Vanselow (Kv) and Gaines and Thomas (Kc) exchange selectivity coefficients for monovalent-bivalent exchange (Na+– M2+;M= Ca2+or Mg2+) showed thatKc= 0.5K→vwhenENa→ 0 and whenENa→ 1,Kc= 0.71Kv(ENa= charge fraction of Na+on the exchanger). The overall relationship betweenKvandKc,Kc= (Kv)[1 +ENa]1/2, is slightly curvilinear. Furthermore, it is shown that the correspondingKvandKcadsorbed-ion activity coefficients γiandfi, respectively, are interrelated byfNa/γNa= 2/(1 +ENa) andfM/γM= 1/(1 +ENa). We tested the above relationships by employing previously reported experimental data for Na-Ca and Na-Mg exchange of clay minerals and soil, carried out in perchlorate background media. The results of the experimental data confirm that these interrelationships are met.