Thermodynamics of Potassium Exchange in Soil Using a Kinetics Approach

Thermodynamics of potassium (K) exchange using a kinetics approach was investigated in Ca-saturated samples from the Ap and B21t horizons of a Matapeake soil from Delaware. Kinetics of adsorption and desorption were determined at temperatures of 0, 25, and 40°C on each soil horizon using a miscible displacement technique. Energies of activation for adsorption and for desorption (£„ and Ed, respectively) ranged from 3.83 to 5.52 kcal mol'. The Ed values were higher than the £„ values, indicating that more energy was needed to desorb K than to adsorb K. Thermodynamic and pseudothermodynamic parameters were determined using Gibbs' and Eyring's reaction rate theories. The free energy for K exchange (AG°) values were negative (ranging from 1,155 to 1,294 cal mol*) and increased with increasing temperature. The free energy of activation values were higher for K desorption (AC**) than for K adsorption (AG_i), suggesting a greater free energy requirement to desorb K. The excellent agreement between AG° calculated from Gibbs' theory and from Eyring's reaction rate theory indicated that pure thermodynamic parameters could be calculated using a chemical kinetics approach. The enthalpy (A//°) values were exothermic and indicated stronger binding of K' ions in the B21t horizon than in the Ap horizon of the 1 Contribution from the Dep. of Plant Science, Univ. of Delaware, Newark, DE 19711. Published with the approval of the Director of the Delaware Agric. Exp. Stn. as Misc. Paper no. 940. Contribution no. 127 of the Dep. of Plant Science. Received 27 Mar. 1981. Approved 20 July 1981. 2 Assistant Professor of Soil Chemistry and Undergraduate Student, respectively. Matapeake soil. The latter was related to the difference in external surface-to-interlayer surface-charge ratio in the two horizons. The enthalpy of activation (A//t) values in both horizons were higher for desorption (A/ftj), than for adsorption (AW,,*), suggesting the heat energy required to overcome the K desorption barrier was greater than for that of K adsorption. Additional Index Words: enthalpy, entropy, ionic diffusion. Sparks, D. L., and P. M. Jardine. 1981. Thermodynamics of potassium exchange in soil using a kinetics approach. Soil Sci. Soc. Am. J. 45:1094-1099. T PRINCIPLES have been used for many years to characterize exchange equilibria on clay and on soil surfaces (Argersinger et al., 1950; Gaines and Thomas, 1953; Babcock, 1963; Sposito, 1980). These principles have been used to obtain exchange coefficients and thermodynamic parameters for various cation exchange systems (Hutcheon, 1966; Deist and Talibudeen, 1967; Jensen, 1972; Udo, 1978). However, the use of a chemical kinetic approach to determine thermodynamic parameters has received little attention. This is particularly true for potassium (K) exchange in clays and in soils. Most thermodynamic studies on clays and soils have involved the calculation of the free energy of exchange SPARKS & JARDINE: THERMODYNAMICS OF POTASSIUM EXCHANGE USING A KINETICS APPROACH 1095 (AG) from equilibrium constants (K) determined through the Gibbs-Duhem equation (Argersinger et al., 1950). Using the latter, negative AG values were reported by Hutcheon (1966) for the formation of K-from Ca-montmorillonite. Udo (1978) investigated the thermodynamics of K-Ca and of Mg-Ca exchange on a kaolinitic soil clay. For K-Ca exchange, AG values were -2,360 and -1,650 cal mol' at 10 and 30°C, respectively. Deist and Talibudeen (1967) found AG values ranged from -1,770 to 3,420 cal mol' at 25°C and from 1,240 to 3,010 cal mol' at 50°C in some British soils. Little can be deduced about the binding strength of cations on negatively charged surfaces from AG values alone since these strengths are defined primarily in terms of enthalpy (Moore, 1972; Filep and Khargitan, 1977). For reactions involving electrostatic or coulombic interactions, such as those for ion exchange, bonding is predominately exothermic (Moreale and Van Bladel, 1979). Deist and Talibudeen (1967) found enthalpy (AH°) values of 910 to 8,490 cal mol" for K-Ca exchange in selected British soils. The negative A//° values indicated the exchange reactions were not energy consuming (Deist and Talibudeen, 1967; Evans and Jurinak, 1976). The entropy of a system (AS°) is related to probability in that, as the number of ways a system can arrange itself increases, AS increases or becomes more positive. Calculated AS values include entropies in both the solid and solution phases. Hutcheon (1966) gave the absolute entropies of K* and Ca* ions in pure water, each corrected to an ionic strength of O.OIN, as +33.4 and -2.9 e.u., respectively. Thus, K* ions caused an increase in the entropy of the dissolving water, possibly by altering water's pseudotetrahedral structure. Conversely, Ca ions increased the structural order of water. The objective of this study was to determine thermodynamic parameters for K exchange in a Matapeake soil from Delaware using a kinetics approach. Pseudothermodynamic parameters were also obtained from absolute reaction rate theory. MATERIALS AND METHODS Theoretical Considerations In previous studies (Sparks et al., 1980a and b), it was found that K adsorption and desorption in soils conformed to firstorder kinetics. Using a miscible displacement technique, the apparent adsorption and desorption rate coefficients (k,' and kd', respectively) can be determined from first-order kinetic equations as derived below. APPARENT ADSORPTION RATE COEFFICIENT (k,') d (K/KJ = k (K,» K,) At, [1] where K, = amount of K on the soil at time /, and K«, = amount of K on the soil at equilibrium. Separating variables: