Nonpreference Homovalent Isotherms

For a homovalent ion-exchange reaction (e.g., Ca2+-Mg2+), when Ca Mg = 1 it follows from Equation 4.35 that 

Substituting the right-hand side of Equation H for/in Equation G gives 

Dividing the numerator and the denominator of Equation I by (Mg2+)2 Ca2+ produces Equation F. Therefore, a plot of [ExCa/CEC] versus [Ca2+]/[Ca2+ + Mg2+] (see Eq. E) produces a straight line with slope 1 (nonpreference isotherm). Furthermore, upon considering Equation F and introducing cation-solution activities, it appears that since yCa approximately equals VMg (where y. equals the single-ion activity coefficient for species i in solution), the relationship of ExCa/CEC versus [Ca2+]/[Ca2+ + Mg2+] is shown to be independent of ionic strength. 

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FIGURE 5.7 Homovalent K+-Na+ exchange on a Brucedale subsoil (Bond 1995) at I = 0.05 M. (a) Measured exchange isotherms open symbols—K+ mole fraction, closed symbols—Na+ mole fraction. Dashed line nonpreference isotherm, (b) In Ky plot to determine the equilibrium constant The dotted lines are extrapolations and the stars represent extrapolated points. 

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