Evaluation6of Methods tDtmnC a E Isotherms c hang for May 1989 Agronomy and Soils Departmental Series No. 134 Alabama Agricultural Experiment Station Auburn University Lowell T.Frobish, Director Auburn University, Alabama EVALUATION OF METHODS TO DETERMINE CEC AND EXCHANGE ISOTHERMS FOR MODELING TRANSPORT Feike J. Leij and J.H. Dane Grauate .. Student and Professor of Agronomy and Soils Alabama Agricultural Experiment Station Auburn University Auburn University, Alabama Lowell T. Frobish, Director CONTENTS page LIST OF TABLES LIST OF FIGURES ABSTRACT INTRODUCTION . . . ... . . . . . . . . iv . . . . 1 MATERIALS AND METHODS Cation Exchange Capacity . Batch Method Vacuum Extraction Method AU Soil Testing Breakthrough Curves .... Exchange Isotherms RESULTS AND DISCUSSION. Cation Exchange Capacity Exchange Isotherms ERROR ANALYSIS .. . ... .. ... .. ... ... o : . . 5 6 6 .. . . .. . .. . . ... . . . l. . S . S. . . .. . . S. . . .. . . . . . .. . 10 11 17 17 26 39 50 52 54 56. 6 57 SUMMARY AND CONCLUSIONS LITERATURE CITED . APPENDIX A. Data for CEC Determination with the BM APPENDIX B. Data for CEC Determination with the VEM APPENDIX C. Data for Exchange Isotherms Data to Determine Exchange . ........ Isotherms . . . . APPENDIX D. SAS Program to Fit a Cubic Polynomial Through the 64 MAY 1989 Information contained herein is available to all without regard to. race, color, sex, or national origin. iii LIST OF TABLES page Table 1. Table 2. Classification of Soils .... .............. 5S 3 pH of 50 cm 0.01 M Br Solutions in Equilibrium with .. ..................... ... 30 g of Soil CEC Values Obtained by BM CEC Values Obtained by VEM Schematic of Treatments . ... ... ... ............. ............. .............. . 17 18 18 19 19 24 25 26 Table 3. Table 4. Table 5. Table 6. Table 7. Table 8. Table 9. Analysis of Variance for CEC Data of tables 3 and 4 Mean CEC for Soils .......... .. .......... ...... CEC Values from AU Soil Testing CEC Values Determined with BTC Experiments Table 10. Sum of Adsorbed Concentrations for Binary Systems . . at Various Ratios of Solution Concentrations Table 11. Estimated Values for &i . . 27 36 K and AG0 ex ex . . . . . . . Table 12. Calculation of the Relative Error, , Obtained Ca' from Data of the Na/Ca Exchange Curve for SAV I . . 5 dS , in S 42 on the Table 13. The Influence of the Extraction Volume, V eff' Error in the Determination of S K , (dS/S) K , for a Hypothetical K/Ca System Using one Extraction . . . 45 on the Table 14. The Influence of Extraction Volume V 1,eff Error in the Determination of SK for a Hypothetical K/Ca System Using Two Extractions ........ . . . 48 iv LIST OF FIGURES page FIG. 1A. FIG.1B. FIG.2. FIG.3. FIG.4. FIG.SA. FIG.SB. FIG.SC. FIG.6. CCof the effluent as a function of eluent volume Ca CK of the effluent as a function of eluent volume Exchange isotherms for Ca/K systems Exchange isotherms for K/Na systems Exchange isotherms for Na/Ca systems . . ......... .......... . . . . . . . . . . 13 13 29 31 33 37 37 ..... 38 e KN as a function of XK for Ca/K systems Prn as a function of X K N Na for K/Na systems en KN as a function of XCa for Na/Ca systems Theoretical error in the adsorbed concentration, (dS/S)C, based on data for SAV I . ........ Flux averaged and resident CK as a function of effluent volume for a one step extraction ...... 42 FIG.7. 44 FIG.8. Adsorbed concentration, SK , calculated with flux K' averaged and resident CK shown in figure 7 Theoretical error in SK , (dS/S)K , 44 FIG.9. using a flux from the averaged value for CK and deviations of S 'real' adsorbed concentration as a function of effluent volume for a one step extraction FIG.10. ........ f 48 Flux averaged CK of the effluent for the first (Cef ) as a function of the and second extraction (C 2,eff 3 volume of the first extraction (V2,ef f =20 cm ) FIG.11. Adsorbed concentration, SK , calculated according to Eq.(16) using flux-averaged CK shown in figure 10, as a function of the volume of the first a two step extraction FIG.12. 49 extraction for 49 .................... , Theoretical error in S K (dS/S)K , using a flux-averaged value for C K and deviations of S K from the 'real' adsorbed concentration as a function of the volume of the first extraction for a two-step extraction . . . 50 ABSTRACT Knowledge of cationic transport in soils is important from an agricultural and an environmental point of view. To reliably predict it is necessary transport of cations that react with the soil matrix, to know the cation exchange capacity (CEC) and the adsorption isotherms for the cations. This publication presents a two-step displacement aspects method to determine exchange isotherms and discusses CEC values several influencing the determination of CEC. were found to depend the saturating extractant. The on the method of determination (batch or displacement), cation (Ca, Na or K), and the concentration of the two-step method to determine exchange isotherms was relatively fast and yielded a complete curve using only one sample under conditions similar to those during transport. determinations method. All of exchange exchange An error analysis isotherms could indicated that out accurate be carried pronounced using this from isotherms showed deviations linearity. Based on these findings, it is concluded that more attention needs to be directed to the determination of exchange data in order to successfully model solute transport. vi INTRODUCT ION Solute transport solute exchange, reacts in and in soils is with the influenced soil. by the way in which the Precipitation, etc. are dissolution, all reactions exclusion, adsorption, complexation which can affect chemical transport. of cations by the soil will In this report, only the exchange effects of be considered. Two different exchange on transport can be distinguished. First, the mean velocity of a reactive solute differs from the mean velocity of the carrier. Cations, will which are adsorbed by the negatively charged soil particles, the average position of will the carrier front. Anions, lag behind which are generally excluded, Second, solute travel ahead of the carrier front. the amount of the nature of the exchange reaction determines spreading (1). These effects of ion exchange, retardation and are usually the transport spreading due -to non-linearity of the exchange isotherm, R, in accounted for by including the retardation factor, equation. This factor is defined as follows: R 1 p as -where p is the bulk density [ML -3 [L 3 L'1 S is 3 ], 0 is the volumetric water content in the adsorbed phase [MM - the solute concentration ], and C is the solute concentration in the liquid phase [ML_ ] . To solve the transport equation for a particular solute species, the total solute concentration in the adsorbed phase and the adsorbed isotherm and is liquid usually phase. For simplicity, in a binary however, system at the a e constant determined electrolyte level. This exchange investigation assumed instantaneous equilibrium The values foi the reactions and the absence of hysteresis. of the selectivity coefficient of these reactions determine the distribution of cations between the solution and adsorbed phase for a particular solute (8). In transport studies, this distribution is quantified with K dS .the slope of the exchange isotherm, for a binary is system not with constant over the of the distribution coefficient, which can be written as electrolyte whole range level. of the Usually the value exchange isotherm of K d constant trace (except for amounts solute or in case of partial exchange), and the exchange isotherm needs to be measured to predict transport. the more general case for OS/OC, Persaud and Wierenga (12) studied to be employed if the which needs restrictive conditions are not met. It is noted that various formal definitions exist to characterize exchange phase. capacity, According number to of the total solute (8), concentration ion exchange groups in the adsorbed is the of Helfferich capacity per (constant) potentially ionized amount exchanger. The value of the apparent exchange capacity, the number of exchangeable experimental amount amount of of counter ions per amount the of exchanger, depends is the on the conditions. taken up Finally, sorption rather the capacity ion total per solute by sorption value of than exchange, exchanger. The sorption capacity depends strongly on the experimental conditions. The overall is the combined exchange and sorption capacity. sorptive capacity In soil science, exchange capacity is referred to as anion and cation exchange capacity (AEC and CEC, respectively). To evaluate what type of exchange capacity is actually involved, one should consider the method of determination. Frequently, no distinction is made between exchange as a result of the charge of the exchanger and sorption. For the purpose of solute transport modeling, this is not necessary. From now on, it is therefore understood that experimental CEC values quantify both theoretical exchange, as defined before, and sorption. Values for the CEC vary substantially, depending on the method of determination soils, these (20). values Although, are not they always are widely used to to characterize studies. ion applicable transport Typically, the determination is performed via a two-stage process. The colloidal cation, displaced complex the of the or soil is first saturated which another cation in with is a selected saturating resident cation, subsequently at high by adding (3). an extractant The amount to of containing displaced the cation the in the concentration solution (meq/100 displaced is g). extracted cmol kg 1 C measured If the can obtain are exchange as capacity well, of the anions be displaced a amount of anions used as measure excess, i.e., non-adsorbed, resident cations. The difference between the total amount of resident cations and anions is the preferred way to obtain the CEC charge of the soil in the adsorbed complex. via However, sorption which characterizes the electric part of the cations accumulate phase instead of ion exchange or they might form complexes with anions, rendering this method unsuitable the overall were used in The exchange to obtain a CEC which characterizes Several methods to determine CEC amount of sorbed solute. this study. isotherm for ions is in exchange complex determined by resident and the selectivity incoming of the In solutions. general, the exchanger prefers (8): (1) the ion of higher valence, (2) (3) the ion with more strongly the ion with the smaller (solvated) equivalent volume, the greater polarizability, (4) the ion which interacts with the exchanger, and (5) the ion which participates least in complex formation with the co-ion. The consuming, non-linear 'therefore assumption amounts determination and no of exchange isotherms exist is for usually transport the exchange earlier, or for valid time of is analytical solutions In transport to be exchanging solutes. quite might often be assumed correct in studies, As linear. partial noted this trace (23). during exchange is of solute, the but general the assumption to be not Therefore, exchange that is isotherm needs determined, preferably with a method both relatively fast and for which the results are useful in transport studies. In this study, exchange isotherms were determined with a vacuum extraction method, VEM. In comparison with batch methods, BM, the VEM is simple, relatively quick, and inexpensive (15). of However, rather than saturating composition, the different samples to with solutions determine the by various ionic VIEM was modified whole exchange isotherm with only one sample. This was accomplished subsequently changing the ionic composition of the eluent and determining the solute concentrations for each change, thus yielding in the liquid and adsorbed phase of points for the exchange a number isotherm. MATERIALS AND METHODS In order to study the determination of CEC and exchange isotherms for a wide range was used. Five at of soil types, a variety of soils and fraction sizes used in this study. Subsoils were Alabama soils Alabama were collected units: the four Agricultural at Experiment (HEA); Station the research Wiregrass Substation Headland Prattville (PBU); and fifth soil Experiment Field (PRA); the Upper Coastal the Plant Breeding Unit at Tallassee Winfield (WIN). The Plain Substation at was a Troup sand from Union Springs (US), distribution These (250-500 pm). also used Soil which had a uniform pore size are given in Table 1. classifications soils were to study transport in soil columns during subsequent experiments. Table 1. Classification of Soils Symbol Location Soil series Family description DOT HEA Dothan Fine-loamy, siliceous, thermic Plinthic Paleudults Fine-loamy, mixed, thermic Typic Hapludults Fine-loamy, siliceous, thermic Typic Fragiudults Fine-loamy, siliceous, thermic Rhodic Pal eudul ts Loamy, siliceous, Pal eudul ts thermic Grossarenic WIC PBU Wickham SAV LUC WIN PRA Savannah Lucedale TRO US Troup 6 Cation Exchange Capacity In this section the CEC determination using (BM), (BTC), (2) a vacuum extraction method and (4) Auburn University (VEM), (3) (1) a batch method breakthrough procedures curves soil soil testing (AU testing) will be discussed. Batch Method To eliminate the effect of organic matter on the CEC, part of each soil sample was pretreated with bleach to oxidize organic matter. From both the unbleached and bleached soil, two fractions were obtained via sieving: a fraction < 250 jim and a fraction ranging from 500 to 840 Am. The grain size of the Troup sand varied between 250 and 500 Am. Four 3.00-g subsamples of each unbleached fraction 3 centrifuge and two of each bleached fraction were placed in 50-cm tubes. Half of the 2 bleached and unbleached samples were then saturated with CaBr other half with KBr. Three washings with approximately 35 cm KBr and 0.005 N CaBr a homoionic was shaken system. 3 and the of 0.01 M were used to saturate the soil complex and obtain Each time the solution for 2 hours on was added, the suspension shaker and then vigorously a mechanical centrifuged for 15 minutes at approximately 1500 rpm, upon which the supernatant solution density of (V liquid was decanted. obtained The volume of the remaining a soil liquid was )1,rem -3 ). gravimetrically of Ca, liquid (assuming K, and Na, 1 g cm The concentrations final supernatant yielding with (CCa+CK+CNa )dec, of the were determined (Na). the ICAP (Ca and K) of the amount and by atomic emission spectrometry eliminates Knowledge wash of the non-adsorbed cations the need to them out during subsequent steps. Washings with water-ethano.L mixtui-es for instance, might influence the CEC value (5). The next step in determining the CEC is to replace 3 the adsorbed of a neutral which was resident cations with an extractant. Approximately 30 cm 1 M NH4OAc solution was added to each 3-g soil suspension, followed by shaking, centrifuging, and decanting. The concentrations of Ca K Na ieldn ca+CK+C Na, Ca, K, and also andalsyielding (CCa KNa ) extr, were determined for each by atomic emission spectrometry were made decanted (AES). solution with the ICAP or Standard solutions, needed for these determinations, To verify that complete using 1 M NH4OAc. occurred, exchange of K and Ca had some samples. No the extraction procedure amounts was 2,rem of Ca, was repeated for found, of significant extraction solution (V K, and Na were Again, the indicating that one the remaining soil sufficient. weight ) was obtained after the extraction to determine the = decanted volume + V2,e net volume of the extracting solution (V net ,rem V 1, rem The CEC of each 3-g sample could then be calculated from: CEC 10 (Cca+CK+Ca) V -(C C +C V (2) CCCa K Na extr net Ca -3 K Na dec l,rem 3 where the units for C and V are mol C m and m , respectively. Because the CEC is pH dependent, the pH of soil samples saturated with the different KBr, 0.01 M NaBr, Br salts was determined. or 0.005 M CaBr 2 were Solutions of 50 cm added to 30-g 3 0.01 M of samples unsieved, 2 hours untreated soil. and upon The suspensions the were pH subsequently shaken for the supernatant was centrifugation of determined with a combination electrode. Vacuum Extraction Method The (Centurion adsorbed fractions CEC was also determined Inc.) with a vacuum the The extraction system in soil was a International, and were liquid used to displace NH40Ac. BM except air resident same the soils cation, and phase, as for with the 5 that dry bleaching was put omitted. From each soil plastic syringe. The type, of g of the soil into bottom syringe contained fiberglas and cotton to prevent loss of soil, while some fiberglas was placed on top of the sample to avoid splashing of the soil towards the sides of the The (air) dry soil was 3 of 0.005 M CaBr from a 2 syringe when the displacing solution was added. first saturated with CaBr 2 by twice leaching 50 cm through each sample. The CaBr 2 solution was supplied syringe was By situated on top of the one containing the soil while the effluent collected in a syringe below the the one containing the lower the soil. continuously withdrawing plunger of syringe, a slight vacuum was created which allowed extraction of the effluent. The speed of extraction was approximately 0.2 cm 3 .- l mmn . The amount of the while remaining soil solution (V ) was rem determined gravimetrically, the concentration of the resident cation in this solution was estimated from the concentration of the second effluent. Subsequently, two volumes of approximately 50 cm 1 M NH4OAc (pH=7) were leached through each sample. The volumes of effluent plus the volumes of the remaining soil solution were again determined gravimetrically to yield two net extraction volumes V1 in all and V2.extr eluent, i.e., The sum of the Ca, (CCa+CK+CNa K, and Na concentrations )el, and effluent, i.e.,(CCa +CK+CNa )e f f Ca K , Na ef f' solutions were obtained as indicated before. with CaBr 2 The was procedure of saturation and extraction with NH4OAc repeated with NaBr and KBr solutions. The CEC for a system saturated with cation species i, CECi2x( was calculated from: 1,extr+ (3) Ca+CK+CNa) 2,eff Ca+C K+CNa) 2,elI V2,extr i rem Ca+CK+CNa) 1,eff( CCa+CK+CNa) 1,el where the units for C and V are the same as for Eq.(2) and C.V 1 rem denotes the amount of non-adsorbed species i prior to the displacement with NH4 0Ac. AU Soil Testing Routine determinations of the CEC are well documented (3, 13) and will only be mentioned briefly. Two of these routine methods were also used to determine the CEC (9). First, the sum of cations displaced from the soil sample was determined as a measure of the CEC. Obviously, this is not a reliable method if a significant amount of soluble salts is present. NH OAc 4 The second method consisted of saturating at pH=7. Excess salt was removed by 4 the soil with 1 M washing with an ethanol-water mixture and was halted if no more NH in the effluent solution. Next, applied as a 10% KCl the NH at 4 could be detected was displaced by K, which was pH=2.5. The amount of NH4 , solution representing the CEC, was measured by distillation and titration. 10 Breakthrough Curves The determination of breakthrough curves (BTC's), commonly employed to determine dispersion coefficients and retardation factors (11), facilitates the determination of an effective value advantage is that the conditions under viz. of the CEC. CEC is An obvious which the obtained and for which it is going to be used, the description of reactive solute transport, are similar. These experiments involved Ca/K exchange at a total concentration in ranging from 0.005 to 0.01 3 . M. The bulk volume of soil much larger amount previously each column was approximately 600 cm was used in BTC experiments BTC Since a of soil CEC than for the are more BTC discussed determinations, experiments likely to yield CEC values representative for natural soil systems. experiments (16). These resident determinations with considered binary systems C0 , 0 was in which can also be used to approximate the adsorption isotherm the by cation, initial : concentration 0 . displaced another cation also at concentration C curve for a step change in By observing the breakthrough at the inlet boundary, the concentration holdup H for that soil column follows from: H = (I 00 - C/C0 ) dT (4) where T is the number of pore volumes C/C is leached through the column and the dimensionless exit concentration of the displacing solute. Van Genuchten and Wierenga (24) described how R can be determined from H. Alternatively, one can consider the initial amount of the resident 11 solute in the column, described with: H = V(OC + pS) [L3] and all exchange O (S) other symbols have 0 where V is the volume of the column been defined before. In case of linear (OSCEC and OC C ), Eqs.(1) and (5) indicate that R = H/(VOC ). Once R is determined, an effective value for the CEC (22) can be computed using Eq.(1), where the slope O of the exchange curve is approximated according to 8S/OC CEC/C . For a pulse type of displacement, an effective value for R can be found by comparing the movement of the solute relative to the movement of the solvent. Exchange Isotherms Exchange isotherms for the binary systems, with a constant total electrolyte level, were also obtained with the previously described the CEC VEM. Measurements were made on the determination. The samples were first same samples as used for saturated with 0.005 M CaBr and level, KBr subsequently leached with solutions of equal but with decreasing CaBr total and electrolyte increasing concentrations in eluent and concentrations. Each yielded "final" a point on increment the effluent For each concentrations increment, the exchange isotherm. concentration of the adsorbed cation was calculated from the "initially" adsorbed concentration and application of the general mass balance principle for a particular' cation A: (V AC + mAS ) = (VC ) - (VC )(6 A eff Ael Asoil rem A (6) 12 is where V rem is the remaining volume of the liquid phase of the soil, m the air dry weight of the soil, and C A and S A are the concentration of A in liquid and adsorbed phase, respectively. The left hand side of Eq. (6) denotes the change of the amount of A present in the soil and the right hand side is the net amount of A supplied to the soil. The important. small change choice of the volume of the eluent, in the extractant, is is too the be If the absolute amount of solute large compared to the in amount and the extractant in the or too in present liquid of soil, cannot concentration determined. behaves To as adsorbed an phase how of the adequately get impression of the effluent five concentration a function 3 volume eluent, volumes of approximately 10 cm of a 0.0045 M Ca/0.001 M K solution plug. was were added to the feed reservoir and leached through the soil After each extraction, the solution in the collection syringe weighed and used to determine the Ca and K concentrations. The Ca and K concentrations are shown as a function of volume of effluent for four soil types in figures and 1A and 1B, respectively. During the last equal, extraction, eluent effluent concentrations were roughly although equality is not a necessary condition to obtain a point on the exchange isotherm. Based on this result, an eluent volume of 50 cm 3 was chosen for the first extraction of every increment in K concentration, followed by a second extraction concentration concentration Analysis). as in the the first soil with 20 cm to (see 3 of eluent with the same eluent solution it determine also the the equilibrium Error section all Referring to Eq.(6), should be noted that terms of 13 E 10.250 N 10.O~ , Ca in SOLUTION x x LUC I + 0 * * WIC I DOT SAV I 0 9.7.5. oz 9.50 1t t-Li 0 0 + * 4. x 9.25-t 9.00 I 10 x 0 i z ) 0 CFIG. 10 20 30 40 50 VOLUME [cm3] A. CCa of the effluent as a function of eluent volume. K in SOLUTION E I 08-1.0 x LUC 0.8 E - 0.6-- + WIC o DOT *SAV + o6 z 0 -> CaBr 2 KBr (9-b) (9-c) + + +Br 0 0- - Na +Br -> NaBr (9-d) Unfortunately, very few thermodynamical data are available for these reactions, but more data are available for Cl. Ca were considered as: K +-+ Cl 2+ + -- Complexation with K and - KCl CaCl + log K0 =-0.7 log K= (10-a) (10-b) Ca Cl o 0.42 constant, (19), where from the values Smith the K, and for the Martell Ca thermodynamic (18) and equilibrium et al. more K° , are Sposito respectively. than and the Because divalent it forms considerably to ignore complexes (9-c) monovalent seems reasonable reactions (9-d). 23 To evaluate (9-a), consider Cu(Il), for which Smith and Martell (18) provided the following: C 2+ +__ Cu Cu 2+ + Cl Br - - CuC CuBr + log K° =0.40 (11-a) (11-b) + -> log K ° = -0.03 o Equation (10-b) to the same degree. + and (11-a) suggest that Ca and Cu form complexes this leads + Based on Eq. (1l-b), to the conclusion that CaBr observed is less likely to be formed than CaCl increase in CEC for Ca soils cannot , suggesting that the attributed to the be formation of Ca complexes. It and should be noted that the soils used are all highly weathered, low base saturation ECEC, is (6). Frequently, an effective have a fairly cation exchange capacity in capacity, used to characterize the exchange these soils (25). The value of the ECEC, H and Al, determined as the lower than the sum of exchangeable bases, is considerably value of the CEC determined after saturation with 1 M NH OAc (17, 25). 4 Obviously, soils. this has its ramifications (21) for the classification of these of the In Uehara and Gillman pointed out that of ions a large part onto the surface charge is created by sorption surface. other words, the charge of the surface is determined by the type of ion which is sorbed with in Na, excess. K, and Differences Ca might in CEC values be for soils to saturated therefore attributed differences in sorptive capacity. Because the CEC values in these weathered soils depend so much on the experimental conditions, the use of "effective" CEC values is stressed. These values are to be obtained under similar conditions as 24 for which transport needs to be modeled. soil characterization will in these soils. Finally, table 7 contains the mean CEC values for the different With the exception of the Wickham It is hoped that an improved benefit the simulation of solute transport soils obtained with the BM and VEM. series, the CEC is larger for the finer fraction. Table 7. Mean CEC for Soils Soil No. of samples Mean CEC cmol /kg C SD DOT DOT WIC WIC SAV SAV LUC LUC TRO I II I II I II I II 9 9 9 9 9 8 9 9 9 3.95 1.75 4.40 4.48 6.67 5.38 5.59 3.14 0.22 0.946 0.801 0.768 0.811 1.002 0.821 0.852 0.885 0.446 I : fraction < 250 jm. II : fraction 500-840 pm. Table 8 contains two sets of CEC values obtained with the AU soil testing procedures. The CEC values obtained from the sum of the displaced cations seem rather high, which were attributed to soluble or excess salts. The values obtained by means of NH4OAc saturation correspond roughly to those determined with the BM, but are generally somewhat smaller than those obtained by the VEM if K was the saturating cation cation. and generally considerably smaller if Ca was the saturating 25 Table 8. CEC Values from AU Soil Testing Method DOTI DOTII S'o i WICI WICII Type SAVI SAVII LUCI LUCII TRO -------------------- CEC [cmol /kg]------------------C Z cations NH4OAc I II 8.13 4.08 4.54 3.50 6.27 6.27 7.92 3.92 9.64 6.34 7.12 10.37 6.22 4.58 3.82 5.18 1.35 0.90 : fraction < 250 urm. : fraction 500-840 urm. Values of the CEC derived from some selected breakthrough curves involving Ca and K are given in table 9. These CEC values, calculated under the assumption of linear exchange, are generally lower than those obtained with the methods previously described with the Troup soil. the exception of The results for TRO obtained with BTC's are probably more reliable than values from the other methods discussed previously because of the small amounts of soil used for the other determinations. A reasonable agreement exists with values obtained with the BM for other soils except for SAV I. from breakthrough Compared to the VEM, lower. Except all values derived II, the soil lower experiments are for LUC testing procedures yielded considerably higher CEC values. The CEC values derived from BTC experiments are presumably due to the fact that the extractant had a 100-fold smaller concentration. The use of CEC values, measured according to any the batch method, vacuum extraction to transport studies, R of the procedures outlined for method and AU soil because under the the testing and R value is applied is debatable obtained overestimated (Eq.(l)). values experimental 26 conditions preferred. for which solute transport needs to be modeled are to be Table 9. CEC Values Determined with BTC Experiments DOT I DOT II SAV I C LUC II TRO TRO ------------------ cmol /kg-----------------2.92 I II 1.55 2.31 3.27 0.38 0.37 : fraction < 250 ,im : fraction 500-840 urm ExchangeIsotherms The described eluent and measurement earlier. effluent of the exchange C isotherms measured volumes was carried out as of and Appendix as well contains as the concentrations through leached remaining in the soil plugs. during the Table 10 gives of the sum of the adsorbed the exchange curves of 9 concentrations determination soil types for all 7 cation ratios. These values carry a larger degree of uncertainty than the CEC determinations discussed before, because of the errors in the determination of the exchange curves. Considering the sand as a blank, the Ca/K system seemed to yield the most reliable results. Summation of the adsorbed concentrations resulted in smaller values for the CEC than for the determinations described under Cation Exchange exception effective levels of Capacity, of the in the materials and methods procedure. studies with N) are section, with the the Breakthrough, Curve Apparently, CEC values the during displacement (e.g. , 0.01 low electrolyte than those extractant smaller determined with the Batch Method, Vacuum Extraction Method, and AU Soil Testing procedures in of the "regular" breakthrough (viz. 1P1). These low electrolyte levels also occur studies displacing during the determination solution served as an solute displacement curves, where the ext ractant. Table 10. Sum of Adsorbed Concentrations for Binary Systems at Various Ratios of' Solution Concentrations VI V1 VU 1~VIII VUkII VUI ~L rJIILIL IIL U1~3h/l~ SAVII Ratio I I 1 DOTI DOTII WICI WICII SAVI LUCI LUCII TRO -----------------------cNa/Ca erno 1 /kg------------------------- 0/10 1/9 3/7 5/5 7/3 9/1 10/0 cC a/C K 0/10 1/9 3/7 5/5 7/3 9/1 10/0 cK /CNa 0/10 1/9 3/7 5/5 7/3 9/1 10//0 I 2.10 3.14 3.41 3.34 2.76 1.12 -0.90 0.43 1.62 1.76 2.32 1.98 2. 15 3.76 4.52 4.52 4.58 3.47 4. 17 2.79 3.01 3.90 3. 91 4.00 2. 57 3.33 3.341 4.33 4.89 4.83 5. 192 3.92 2.39 4. 13 6.91 6.01 6.81 5.06 5.47 0.12 5.39 6. 15 6.23 5.42 5.25 2.51 1.74 2.29 3.25 3.43 3.60 4.29 2.13 1.07 -0. 46 0.36 0.38 0.52 1.29 1.56 1.50. 3.42 3.16 3.10 3. 13 3.06 2.98 3.04 0.70 0.45 1.68 1.75 164 1.63 2. 16 2.82 2.33 3.04 3.25 3. 27 3.30 3.30 1.83 1. 56 3.58 3. 68 3.613.62 5.041 3.33 303 4.21 3.00 2.66 3.45 3.61 4I. 295 3.61 3.60 /1.43 3.59 3.98 3.60 4.70 4.63 4.59 4.59 4.41 1.47 1.26 2.76 2.69 2.67 2.60 2.49 0.24 0.18 0.14 0.07 -0.02 -0. 07 -0. 05 3.04 3.26 3.44 4.60 4.04 3.01 3.42 2. 16 1.99 2.27' 2.64 3.93 2.42 2.78 2.54 2.82 2.89 3.64 2.76 2.7 9 3.43 2.55 2.69 2.91 2.81 3.31 3.79 S9Q 3.93 3.95 4.27 4.88 3. 54 3. 98 4 .'3 7 2.69 2.64 2.70 3. 19 3.81 3.85 4.91 3.31 3.66 4.28 4.'82 4.57 4.52 5.09 1.04 1.39 2.31 2.99 1.44 3.36 3.43 0.34 0.49 0.61 1.18 0.73 2.15 2.35 fraction < 250 tim. II fraction 500-840 /tm. A SAS program, Appendix 0, wa-s used to correlate YA and XA with a cubic polynomial. The resulting curvves, showing the dimensionless 28 amfiount of A in the of adsorbed A in phase the (YA) as phase a function are of given the in dimensionless amount liquid (X A ) A' figures 2 to 4 for Ca/K, K/Na, and Na/Ca, respectively. The adsorption complex clearly favors Ca and K over Na. For the Ca/K system, the cation for which XA< 0.5 was favored, A (10) and derived theoretically by which was also found by Jensen For the K/Na exchange, -larmsen (7). adsorption of K was favored in all instances. Based on the results of the CEC determinations by the VEM, table 4, a pronounced increase in CEC can be expected the if a Na soil becomes saturated with Ca. This influenced determination of the exchange intermediate curves for Na/Ca exchange as can be seen in figure 4. At values for XCa' values of X YCa does not increase at the same rate as for very low For many Ca/Na in X Ca isotherms, Similar even a decrease were in YCa occurred with an Sposito et al. using Cl increase findings reported by (19) for Na/Ca and Na/Mg exchange on Wyoming bentonite + + salts. which These authors concluded on that the are CaCl and MgCl surfaces were of formed, are adsorbed favorably and Mg2 + internal adsorbed on montmorillonite, surfaces. whereas Ca2 + the outer In case ClO4 salts were used, with negligible complexation, It is noted be for no change in total adsorbed concentration, ST) was found. that, in analogy by to CEC the determinations, anion as in well CEC, exchange in order curves to might obtained displacing account complexation. that Ignoring the change similar curve the Ca/Na as for the isotherms Ca/K suggest a somewhat is found isotherms, except that Ca is adsorbed much more favorably for the Ca/Na system. 29 Ca & K exchange for Dothan I 1.( Ca & K exchange for WickhamI 0. LUJ Vr) VF) LUj 0 LU 0 c0.1 V)0., (A 0.', 2 3 0 .4 0m Y=-0.03+2.44X-5. 13X ±3.81X r 0.2 2 =0.99 adj 0.14 0.6 0.8 1.0 0.2 0.4 0.6 0.6 1.0 K in SOLUTION K in SOLUTION Ca & K exchange for Dothon 11 Ca & K exchange for Wickham 11 LU VI) a_ LUJ c0. U 0 C/) 1.0 K in SOLUTION K in SOLUTION FIG.2. Exchange isother'ms for Ca/K systems. 30 Ca & K exchange for Savannah I Ca & K exchange for Lucedale I V!) 00. LUJ CK 0. 0, U!) a0.1 0 ~0., 0. 0.2 0.4- 0.6 0.8 0.4 0.6 0.8 1.0 K in SOLUTION Ca & K exchange for Savannah 11 K in SOLUTION Ca & K exchange for Lucedale 11 Li V~) 0.1 C/) 0.( LUJ mo 0 0) cf) LUJ 0 S0.( U)0., 0. 0 C :0., 0.( .0 0.2 0.4 0.6 1.0 0.4 0.6 0.8 1.0 K in SOLUTION Ca & K exchange f or Troup sand I. OT K in SOLUTION ClLUJ C \<. 0 .82X 2 - . 53X 3 0.2 0.4 0.6 K in SOLUTION FIG.2. Exchange isotherms for Ca/K systems. 31 Na & K exchange f or Dothan I 3 2 Y=0.31X-0.42X +1.25X Na & K exchange for Wickham I LUJ 0. w 0.8 32X3 Y=-0.04±1 .08X2.25X2 +2. r2 =0.96 adj r2=0.98 adj LUJ 0 V) < r m~0.6m 0 0 . - C) 0.1 o0.42- -H 0.2 0.4 0.6 0.8 1.0 0.0oo0.0 0.2 0.4 0.6 0.8 1.0 Na in SOLUTION Nc in SOLUTION Na & K exchange f or Dothan 11 3 2 Y=0.01+1.22X-1 .41X +1.19x NA & K exchange for Wickham 11 1.0- LUJ 0. CL r 0.98 aj= a_ LUL cci 2 LUJ 0.8V) Y=-0 .02+0 .53X-0 .26X2+0. 81X r 2=0.99 adj C 0.( LUJ 0 U) z~0 n 0.6- C 0.4 0.2- 0.8 1.0 0.0 0.0 0.2 0.4 0.6 0.6 1.0 Na in SOLUTION FIG.3. No in SOLUTION Exchange isotherms for K/Na systems. 32 Na & K exchange f or Savannah I 1.0Y=0.54X-0.48X +1.06X r20.9 .9 adjO LUJ 0-1 2 3 Na & K exchange for LucedaleI 1.0- Lu 0 .8E- (n U 0.8< Y=-0.01+0.08X+0.24X 2+0.83X3 r 2=0.99 adj a0.6- 30.6- 0 a0.4C a- Z0. 2- 0.41 0.04 0. 0.0 0.2 0.4 0.6 0 1.0 Na in SOLUTION Na & K exchange for Savannah 11 1.0Y=-0.01+i1A5X-2.15X +2.09X r2=0.99 adj 2 3 LU Na in SOLUTION Na & K exchange for Lucedale 1 1.0 2 3 U 0. 6- .6--0.01±0.37X-1.57X +2.33X r 2-0.99 adj < n- a 0.60 00.- a0. 603 CfL 0 . - C) 0 z 0. 2- 7' 0.2- 0.Q0 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.6 1.0 Na in SOLUTION Na & K exchanae f or Troup sand 2 3 Na in SOLUTION Y-0.0I-0.2IX+3.19X -1.94X r 2=0.99* adj L cr0 U) 0. 0. Na in SOLUTION FIG.3. Exchange isotherms for K/Na systems. 33 Na & Ca exchange f or Dothan 1 I Na & Ca exchange for Wickham I * -OT -UT A ni VI) it * * Lu VI) 0.1 al0.60 / / / aLUJ m 0 C/) aQ 0 C F / 0) 0.24- Y=2.32X-2.2lX +0.94X r =0.92 adj 1 2 3 0 ~j Y=O. 26+4.01X-7.65X 2+4.43X3 2 r .=0.55 ad) 0 .0-1 0.0 0.2 -+ 0.4 Ii- 0.6 - - - 0.8 1.0 0.2 0.4 0.6 0.8 1.0 Ca in SOLUTION Ca in SOLUTION 11 ,krinrin Na & Ca exclHUHllryjJCfrr nntknn UlLJtUIUHII 1 Na & Co exchonge for Wickhoam 11 IlOT* I . OT^ LUJ U.8ift el I LU~ 0.f CL) c)0.6m ci) / C) 0.( LUJ cr3 0 C) 0.4- / Y=0.02+3.90X-7.05X +4.2iX r 2=0.74 adj 2 3 V) 0. 2 3 0 0.2-/ 00.; Y=0.31+4.06X-8.12X +4.82X 2 r p0.34 ad) 0.00.0 0.2 0.4 0.6 0.8 1.0 .0 0.2 0.4 0.6 0.8 1.0 Ca in SOLUTION Co in SOLUTION FIG.4. Exchange isotherrms for Na/Ca systems. 34 Na & Ca exchange f or Savannah I I-O Na & Ca IlOT LUJ0.1 V) a3-)0.1 LUJ a- 00 0 0 (f) C)0. Y=0. 16+4.67X-8.79X2+5.02X r 2=0.82 adj C) 0.1 C) 0.; Y=0.02±6.14X-11.48X 2+6.37X3 r2=0.91 adj 1.0 Ca in SOLUTION Na & Ca exchange for Savannah 11 1. 0 w0.8aa- Ca in SOLUTION Na & Ca exchange f or Lucedale 11 LUJ 0.1 U) 00. co Dt0' U) C) 0. Y=0. 15+5.29X-9.83X +5.44X 2 r.=0. 88 ad) w--0.%J 0.0 2 3 0 (-) 0.;r Y=0,01+3.31X-4.53X 2+2.35X r2. 0.96 ad) 0.2 0.4 0.6 0.8 1.0 0.2' 0.4 0.6 0.8 1.0 Ca in SOLUTION Na &Ca exchange f or Troup sand IJ0 Ca in SOLUTION LJ 00 U 0, ()0 66X C) 3 .0 0.2 0.4 0.6 0.8 1.0 Ca in SOLUTION FIG.4. Exchange isotherms for Na/Ca systems. 35 A more general description of the exchange process can be given from a thermodynamic point of view. Consider the following exchange reaction for cations A and B (2): zA A s + zB B -- zA A + zB B s (12) where the subscript s denotes the adsorbed phase and z is the valence of the cation. As mentioned before, no distinction is made between the free metal and metal-ligand complexes. The formation of these complexes is usually not considered for most exchange data reported to date. The reaction given by Eq. (12) selectivity coefficient, KN: is commonly characterized by the rational Y K =B N 1/z 1 B a 1/z A A(13) /z 1/z B A a Y B A where a is the cation activity (the product of molar concentration and the activity coefficient). were calculated with the Mean values for the activity coefficients extended Debye-H~ckel equation. Gaines and Thomas (4) derived the following relationship between the thermodynamic and K· exchange constant for one equivalent of exchanger, K, N ex' LK =[ 0 Z. + }aKN 0 dYB (14) It is noted that K0 The value of K ex ex is constant over the whole concentration range. in Eq. (14) depends only on temperature. The integral can be approximated as (2): Fa KN d B . The standard free were determined as an average of tn KN over the range in solution concentration ratio of 1/9 to 9/1. ra K0 and AG0 ex ex Ca/K K/Na Na/Ca Table 11. Estimated Values for Soil Ca/Kt K/Na t K0 ex Na/Ca [kJ/mol ] AG0 c ex -0.67 -1.49 -1.62 -1.05 -1.06 0.15 0.10 -1.13 c~ /~ hl~ /hlc~ I/ 'k DOT DOT WIC WIC SAV SAV LUC LUC I II I II I II I II I II 2.05 2.04 2.69 2.40 2.11 2.08 2.16 2.11 -1.35 -0.28 -1.09 -1.07 -0.75 -0.73 -1.29 -1.68 -5.08 -5.06 -6.66 -5.95 -5.23 -5.14 -5.36 -5.23 3.35 0.69 2.71 2.65 1.85 1.81 3.20 4.17 1.63 3.68 4.01 2.59 2.54 -0.37 -0.26 2.81 : fraction < 250 Wm. : fraction 500-840 tim. t Resident ion A/displacing ion B. The behavior of individual ta K SA to SC as a function of XB . when K displaces Ca. It is values is illustrated in figure n. KN the Figure SA shows the behavior of Therefore, clear that K>1 for all XK . tends to the right reaction given by Eq.(12) and the complex favors K over Ca. When Na displaces K, figure SB, the reaction tends to the left and the complex favors K over Na. The Na/Ca system, figure SC, does not show a consistent The values dependency in table of lat 11 KN on the adsorbed concentration. also indicate that K is adsorbed for K0 ex preferentially over Ca and Na, whereas the complex favors Na somewhat 37 Ca/K system 3.0T xLUC I + WIC I oDOT I * SAV I 2.O0 X * 0 1.0" 0 0 0.0 0.0 I I I 0.2 0.4 0.6 0.8 1.0 Xk FIG. SA. en K N as a function of X K for Ca/K systems. K/Na system OT x -1+ X 0 0 -2+ x LUC + WIC o DOT * SAV 1 I I I I - I\/IYU 0.0 0.2 0.4 0.6 0.8 1.0 Xna FIG. SB. n K as a function of XN for K/Na systems. N Na 38 Na/Ca system 0.5r 0 + -0.5 * -1.5x LUC II + WIC I o DOT II *SAV I -2.5 0.0 FIG. SC. 0.2 0.4 4 -I- -1 0.6 0.8 1.0 1.0 Xca tn K as a function of XCa for Na/Ca systems. Ca N over Ca. agree It should be noted that the graphical these findings might not necessarily of figure 2, because different with results expressions for liquid and adsorbed concentration were used and because of the way the equilibrium constant was defined (viz., (14)). with Eq. (13) and ERROR ANALYSIS The determination of the exchange isotherm using the solution concentration of section on exchange isotherms, increments is the feed solution as described results in a larger error in the than for procedures which use one sample for each point on the isotherm. Two reasons can be pointed out in this respect: - The absolute amounts of cations displaced/exchanged will for the "increment" method than for regular methods, be smaller where every point of the isotherm is obtained with a different sample, in a larger relative error for the first method. - The error of the adsorbed concentration in the cumulative, used to increment resulting method is since the value of a previous adsorbed concentration is the present in value. an Furthermore, way, the adsorbed calculate is concentration determined indirect based on various resident with solution concentrations and volumes of solutions, them. all of which have input, output, and some degree of error associated Obviously, these errors are a drawback of the increment method. However, an advantage of the stepwise adsorption of A/desorption of B is a reduction in time. Extraction of the "old" resident ions and saturation with the "new" resident ions takes place simultaneously. In addition, more efficient use is being made of equipment and chemical.s, only one sample is needed to determine an isotherm, and the method is convenient for replicate studies. The volumes errors can be minimized by choosing appropriate These choices are extraction to and concentration increments. subjected 39 40 s;everal constraints. to ensure exchange First, the volume of eluent has been should be at sufficient the new equilibrium reached concentration. For simplicity, this can be assumed to be true if eluent and effluent concentrations are equal. Second, the concentration of the eluent exhibit and a the time averaged change concentration to detect of of the effluent in the be should adsorbed large. significant changes concentrations. Therefore, the volume eluent cannot too The soils which we investigated possessed fairly low CEC values, which increases the relative error in the adsorbed concentration. The low electrolyte this total effect. error levels of the systems might have partially To in study the the contribution of individual S, compensated for errors to the was adsorbed concentration, an error analysis carried out. The adsorbed concentration for a soil with mass m [kg], extractions according to: at each increment as described before, is using two determined S = S or + m [(V C ) + C -v rem,or rem,or rem,fin rem,fin +V2,eff (C2 ,el C2,eff)] V1,eff (C1,el -C1,eff where the for S or is the solute concentration in the adsorbed -1 phase before increment change in eluent concentration [cmol kg C ] and the units it was C and V are mol m C -3 and 3 m , respectively. Furthermore, assumed that effluent and eluent volumes were equal for each increment. Using the first degree Taylor expansion for S=f(a,b,c,..), the error in S, dS, can be approximated by: 41 dS - af da +- af db + af dc + da Ob e where da, db, and dc are errors in the factors a, b, and (17) c, respectively. Application to Eq.(16) yields the following: dS = dS + 0.01 m 0.01 [ or + dC + C dV V rem,or rem,or rem,or rem,or -V rem,finremfin dC -C remin dV rem,fin + V l,eff (dC 1,el + + + dC +dC + ) + (C - C )dV +V 2,eff (dC2,el 1,eff l,eff 1,eff ) + (C,el 2 ,eff) + (C2,el C2,eff)dV2,eff] dm V -2 C -V C + m L rem,or rem,or rem,fin rem,fin Vl,eff(C1,el - Cl,eff ) + (18) V2,eff(C 2 ,el C2 ,eff Note that the maximum error in VC, viz. ±dVC, follows from (V+dV)(C+dC) VC+CdV+VdC+dVdC, where we assume dVdC=O. As an example, the Na/Ca exchange curve for SAV I was used. other pair of cations or soil could have been used as well. arbi trari'ly, the following errors were assigned: -6 3 m Any Somewhat dV = ±0.03 x 10 -3 dC = + (0.05 + 0.02C) mol m3 dS 0.25 cmol kg _3C or kg dm = + 0.03x 10 Table 12 contains the data used for the error calculation in SCa, Eq.(16) to calculate V, C, Sa S or and , = + -1 using the Eq.(18) to determine dS a using maximum error in for XCa>0.5, and m. The error increases quite rapidly with a relative minimum at about XCa=0.3, as can be seen figure 6, which shows the in the bottom line of table 12 as well as in relative error as a function of XCa. 42 dS. Table 12. Calculation of the Relative Error,, in S Obtained from Data of the Na/Ca Exchange Curve for SAV I 0 0.1 7.73 7.75 53.40 23.96 1.00 0. 99 0.01 0.00 0.00 0.25 [% 1.54 0.15 9.72 0.3 7.77 7.73 50. 14 25.75 2.90 2.89 0.45 1.93 4.19 0.40 9.51 -3 0.5 7.80 7.77 54.95 25. 78 5.00 5.08 4.17 4.47 5.05 0.84 16.64 0.7 7.80 7.80 56. 22 29. 55 7.23 7.20 6.43 6.96 5.66 1.48 26. 15 0.9 7.81 7.80 57.85 27. 93 9.40 9.00 8.81 9.14 6.11 2.28 37.40 1.0 7.81 7.81 56.68 28.53 10. 59 10.55 10. 22 10.36 5.47 3.19 58.28 XCa vrem, f in v rem, or vi1eff v,eff ci1,el C2 ,el1 cl1eff C2 ,ef f s Ca dSCa (dS/S) Ca 3 Units: V in cm, Cin moim and Sin cmol-kg el-cl,40a ) -o/S 60-60 CO4 20-20 0.0 0.2 0.4 0.6 0.8 1.0 xCo FIG.6. Theoretical error in the adsorbed concentration, (dS/S)Ca on data for SAV I. based 43 Also to consider is that the measured concentrations values (11). are flux-averaged best values rather than volume-averaged example, This is illustrated by a hypothetical involving Ca/K exchange. For this idealized situation, we assume piston displacement and linear euilibrium exchange. Assume a dry dry soil weight of 5 g with a CEC of -1 values: experimental 5 cmol kg and the following hypothetical C rem finremor S Ca,or 2 31V =5 mol =6 cm3Cc c Caor m Ca) kg , (C)-3 (Ca) 3 cmol m c (K) C Ko= 5 tol (K) kg -3 m; C2K,or 1 -3 and with C a=3 mol (C Ca) m concentration accompanying cmol cmol = A feed solution CK -3 is applied. When the 7 molC(K) m reaches are, these values, SCa,fin the 1 of the soil solution adsorbed concentrations = 4 cmol presumably, c2 (1 Ca) kg and S kK,fin process in is C (K) kgonly one a extraction step change per in The increment effluent begun by considering eluent concentration. occurs at Theoretically, the in C K moment the concentration the invading in solute and -3 m. establishes prescribed change i.e., concentrations liquid adsorbed phase of the soil, However, changes from 5 to 7 mol (K) c is determined as the effluent concentration V Veff a flux averaged concentration observed. similar (i.e., { 0K CK dV) and the step change will not types. be A Figure 7 shows the behavior comparison can be made of both concentration the adsorbed between concentration calculated with Eq.(16) using one extraction, based on the theoretical resident concentration, and the one calculated in with the hypothetical flux averaged concentration as observed in experimental experiments. The differences figure 8. and correct values for S K are shown in 44 Kin SOLUTION 0 flux -averaged 0 L 0 (94 0 25 50 75 100 125 150 VOLUME [cm3] FIG.7. Flux-averaged and resident CKas a function of effluent volume for a one step extraction. 4.504.25m flux-averageded 4.00-3.75- resident L~J Enc -3.503.253.00-/ 0 25 50 75 100 125 150 VOLUME [cm3] FIG.8. Adsorbed concentration, SK calculated with resident CK shown in f igure 7. flux- averaged and 45 The flux-averaged concentration of the effluent does not in give a correct estimate of the concentration the liquid phase of the soil. will be made, the especia.l) If this is not recognized, errors in S K and C for smaller effluent volumes. For larger volumes, flux-averagec but concentration will approach the theoretical resident concentration, this will this lead to increased computational errors in the error in SK , (dS/S) K, S. To investigate according contains to the further using was calculated Table 13 Eq.(18) flux-averaged concentrations. flux-averaged values for Ceff (figure 7) and the values for SK based on this concentration volume (figure 8), as a function of the chosen extraction S The -1 (Ve), as well as the absolute and relative errors in relative error with respect to the 'real' value of S K , 4 cmol(K) kg is also included. Table 13. The Influence of the Extraction Volume, V on the S/ eff Error in the Determination of S, (dS/S), for a Hypothetical K/Ca System Using One Extraction K/Ca V eff cm 5/5 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 0 10 20 25 31 40 60 80 100 120 140 3 C el ---- C eff flux -3 mol m --C eff res. C dS K -cmol C S K -1 kg -3.00 3.40 3.80 4.00 4.24 4.19 4.12 4.09 4.07 4.06 4.05 dS/S (S-S )/S real K K real --------- Pct.--------16.66 17.72 17.50 17.41 17.30 18.99 22.69 26.21 29.71 33.14 36.60 -25.00 -15.00 -5.00 0.00 6.00 4.75 3.00 2.25 1.75 1.50 1.26 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 7.0 7.0 7.0 5.0 5.0 5.0 5.0 5.0 5.5 6.0 6.2 6.4 6.5 6.6 0.50 0.60 0.67 0.70 0.73 0.80 0.93 1.07 1.21 1.35 1.48 46 0dS/S15 - 20 (I) 10 -Srea /Sreal[ -5 0 0 25 50 75 100 125 0 150 VOLUME [cm3] FIG.9. Theoretical error in SK , (dS/S) K , using a flux-averaged value the 'real' adsorbed of S from for C and deviations K K concentration as a function of effluent volume for a one step extract ion. The results of table 13 are illustrated in figure 9, which contains both types of relative errors as a function of the volume of effluent. An increase in the extraction volume minimizes the difference between real and theoretically determined concentrations, but at the expense of an increased experimental error. For this hypothetical case the optimum 3 displacement volume is approximately 31 cm , table 13. The results can be improved by using a second extraction after the soil solution and adsorbed concentrations have reached their final values at the particular input concentration. In this way, the total extraction volume for can the be kept relatively small and to the the effluent resident concentration second extraction converges concentration, yielding a reliable estimate for the final concentration 47 in the soil. The constant 3 arbitrarily chosen as 20 cm Table 14 contains some of the relevant data to determine the volume of the second extraction was errors associated with the two-step extraction using the volume of the first extraction as the determine extraction. after the what the error 10 independent variable. in SK the From table 14, one can is for a chosen volume theoretical extraction for a small effluent (C 1,eff volume resident eluent. of the first concentrations and of the C 2,eff' first Figure first It shows and appears second that the respectively). extraction, afte'r the C ,f soil SK is approaches saturated theoretical the new concentration The adsorbed with concentration, based on the two-step extraction is given in figure K'K approached associated considerably with this faster. Finally, the theoretical of the volume errors of the it extraction, as a function 12. first extraction, are given in figure was decided to use a volume of 50 cm 3 Based on these results, fur the first extraction; dS/S is is assumed to be sufficient relatively small and the amount of' solute to achieve complete displacement. 48 Table 14. The Influence of Extraction Volume V on the Error in the Determination of S K for a Hypothetical K/Ca System Two Extractions K/Ca V C C C 1,eff C1,eff 2,eff res ---- flux-----3 ----- mol m------C l,eff dS dSK S SK dS/S (S-S )/S dSK/SK real real cm 5/5 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 7/3 C 3 -cmol C kg - - ----- Pct.-16.66 14.36 14.42 14.43 15.19 16.17 17.18 18.23 18.44 19.14 20.01 21.74 23.50 26.96 30.32 33.68 -25.00 0.00 5.00 6.00 4.80 3.30 1.80 0.30 0.00 -0.03 0.00 0.00 -0.10 -0.20 0.00 0.20 0 5 10 11 15 20 25 30 31 35 40 50 60 80 100 120 =C 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7 mol 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.2 5.5 5.8 6.0 6.2 6.4 6.5 (K) m 5.0 5.0 5.0 5.0 5.4 5.9 6.4 6.9 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 -3 , V 0.50 0.57 0.61 0.61 0.64 0.67 0.70 0.73 0.74 0.77 0.80 0.87 0.94 1.08 1.21 1.35 = 20 3.00 4.00 4.20 4.24 4.19 4.13 4.07 4.01 4.00 4.00 4.00 4.00 4.00 3.99 4.00 4.01 cm 3 1,el 2,el 2, eff . 49 Kin SOLUTION Clef f 0 25 50 75 100 125 150 VOLUME of FIRST EXTRACTION [cm3] FIG. 10.. Flux-averaged CK of the effluent for the first (C )f and of the as a function of the volume second extraction (C) 2,eff =20 cm first extraction (V 2,eff 4.5( 07 3. , 25 50 75 100 125 150 VOLUME of FIRST EXTRACTION [cm3] FIG. 11.' Adsorbed concentration, S calculated according to Eq.(16) K' using flux-averaged CK shown in figure 10, as a function of the volume of the first extraction for a two-step extraction. 50 1O 20--)0 10 -Sreac/Sreal 5 /0 on 0 25 50 75 100 125 150 VOLUME [cm3] FIG.12. Theoretical error in SK , (dS/S)K for CK and deviations as a of SK of , using a from the the flux-averaged 'real' of value adsorbed the first concentration function volume extraction for a two-step extraction. SUMMARY AND CONCLUSIONS A considerable amount of variation was found in the CEC values obtained by different methods, and different saturating cations. The VEM gave a more complete recovery of the cationic species than the BM. Values of the CEC determined under conditions similar to those during solute CEC transport are generally lower than those obtained with common (e.g., BM, VEM, and AU soil testing) using determinations extractants of high concentration (e.g., 1 M). This overestimation of the CEC could have serious ramifications when the movement of hazardous solutes needs to be predicted in time and space. Effective values of 51 the CEC should be used, determined is under similar experimental conditions as the solute transport studied. The effective CEC value characterizes the total amount of sorbed cation. No distinction between the various sorption mechanisms determination of the exchange is required. The same CEC for is a true for the Na soil is isotherms.The significantly less than for a K or a Ca soil, presumably because of different sorptive behavior. Using exchange errors increments via the to this in the solution to concentration be a feasible to determine The curves VEM appeared method. inherent method could be reduced by using a two-step extraction volumes. The Ca/K, Na/Ca, extraction method and appropriate and K/Na isotherms showed pronounced differences for all soil types and seemed to be reactive useful for further systems research involving the with similar chemical transport and of solutes in soil physical characteristics. The under similar independent determination of exchange properties, as the transport their processes being studied, i.e., conditions deserves careful attention because of variability (CEC), depending on the method of determination, isotherm). and non-linearity (exchange LITERATURE CITED (1) BOLT, G.H. 1982. Thermodynamics of Cation Exchange. In (Ed.). Soil Chemistry. B. Physico-chemical Models, Amsterdam. G.H. Bolt Elsevier, (2) BRUGGENWERT, M.G.M. and A. KAMPHORST. 1982. Survey of Experimental In G.H. Bolt. Information on Cation Exchange in Soil Systems. (Ed.). Soil Chemistry. B. Physico-chemical Models, Elsevier, Amsterdam. (3) DEWIS, J. and F. FREITAS. 1976. Physical and Chemical Methods Soil and Water Analysis. Soils Bulletin 10, FAO, Rome. (4) GAINES, G.L. and H.C. THOMAS. 1953. Adsorption Studies Minerals. II. A Formulation of the Thermodynamics of Adsorption. J. Chem. Phys. 21:714-718. of on Clay Exchange (5) GUPTA, R.K., C.P. SINGH, and I.P. ABROL. 1985. Determining Cation Exchange Capacity and Exchangeable Sodium in Alkali Soils. Soil Sci. 139:326-332. (6) HAJEK, B.F., F. ADAMS, and J.T. COPE. 1972. Rapid Determination of for Soil Saturation Acidity, and Base Exchangeable Bases, Characterization. Soil Sci. Soc. Amer. Proc. 36:436-438. Adsorption by (7) HARMSEN, K. 1982. Theories of Cation Constituents: Discrete-site Models. In G.H. Bolt (Ed.). Chemistry. B. Physico-Chemical Models. Elsevier, Amsterdam. (8) HELFFERICH, F. 1962. Ion Exchange. McGraw-Hill. New York. Procedures Used by Auburn (9) HUE, N.V. and C.E. EVANS. 1979. University Soil Testing Laboratory. Ala. Agr. Exp. Sta. Dept. of Agronomy and Soils Ser. No. 16:13. (10) JENSEN, J.R. 1984. Potassium Dynamics in Soil During Steady Soil Sci. 138:285-293. (11) Flow. Soil Soil PARKER, J.C. and M.Th. VAN GENUCHTEN. 1984. Determining Transport Parameters from Laboratory and Field Tracer Experiments. Va. Agr. Exp. Stat. Bull. 84-3. 1982. A Differential Model for (12) PERSAUD, N. and P.J. WIERENGA. in Discrete Homo-ionic Transport Cation One-dimensional Ion-exchange Media. Soil Sci. Soc. Amer. J. 46:482-490. (13) In Page et al. RHOADES, J.D. 1982. Cation Exchange Capacity. Chemical and Part 2. Soil Analysis. Methods of (Eds.) 9. Amer. Soc. Agron. Properties. Agron Monogr. Microbiological Madison, Wis. 52 53 (14) RHUE, R.D. and R.S. MANSELL. 1988. The Effect of pH on Na-Ca and K-Ca Exchange Selectivity for Cecil Soil. Soil Sci. Soc. Amer. J. 52:641-647. (15) ROBIN, M.J.L. and D.E. ELRICK. 1985. Effect of Cation Exchange on Calculated Hydrodynamic Dispersion Coefficients. Soil Sci. Soc. Amer. J. 49:39-45. (16) SCHWEICH, D., M. SARDIN, and J.P. GAUDET. 1983. Measurement of a Cation Exchange Isotherm from Elution Curves Obtained in a Soil Column: Preliminary results. Soil Sci. Soc. Amer. J. 47:32-37. (17) SHONGWE, Musa M. 1985. Characterization of Subgroup of Ultisols. M.Sc. Thesis. Tuskegee Ala. a Proposed "Kandi" Institute, Tuskegee, (18) SMITH, R.M. and A.E. MARTELL. 1976. Critical Stability Vol.4: Inorganic Complexes. Plenum Press, New York. Constants. (19) SPOSITO, G., K.M. HOLTZCLAW, L. CHARLET, C. JOUANY, and A.L. PAGE. 1983. Sodium-calcium and Sodium-magnesium Exchange on Wyoming Bentonite in Perchlorate and Chloride Background Ionic Media. Soil Sci. Soc. Amer. J. 47:51-56. (20) THOMAS, G.W. 1977. Historical Developments in Soil Chemistry: Exchange. Soil Sci. Soc. Amer. Proc. 41:230-238. Ion (21) UEHARA, G. and G. GILLMAN. 1981. The Mineralogy, Chemistry and Physics of Tropical Soils with Variable Charge Clays. Westview Tropical Agr. Ser. No.4, pp. 31-32. (22) VALOCCHI, A.J. 1984. Describing the Transport of Ion-exchanging Contaminants Using an Effective Kd Approach. Water Resour. Res. 20:499-503. (23) VAN GENUCHTEN, M.Th. and W.A. JURY. 1987. Progress in Unsaturated Flow and Transport Modeling. Rev. of Geophys. 25:135-140. (24) and P.J. WIERENGA. 1986. Solute Dispersion Coefficients and Retardation Coefficients. In Methods of Soil Analysis. Part 1. Physical and Mineralogical Methods. Agron. Monogr. 9. Amer. Soc. Agron. Madison, Wis. (25) WYSOCKI, D.A., D.A. LIETZKE, and L.W. ZELAZNY. 1988. Effects of Parent Material Weathering on Chemical and Mineralogical Properties of Selected Haplidults Sci. Soc. Amer. J. 52:196-203. in the Virginia Piedmont. Soil APPENDIX A. Data for CEC Determination with the BM Soil V rem C Ca C K C Na V net C Ca C K CEC Resident sol. DOT DOT DOT DOT DOT DOT DOT DOT DOT DOT DOT DOT WIC WIC WIC WIC WIC WIC WIC WIC WIC WIC WIC WIC SAV SAV SAV SAV SAV SAV SAV SAV SAV SAV SAV SAV I-Ca-u I-Ca-u I-Ca-b I-K-u I-K-u I-K-b II-Ca-u II-Ca-u II-Ca-b II-K-u II-K-u II-K-b I-Ca-u I-Ca-u I-Ca-b I-K-u I-K-u I-K-b II-Ca-u II-Ca-u II-Ca-b II-K-u II-K-u II-K-b I-Ca-u I-Ca-u I-Ca-b I-K-u I-K-u I-K-b II-Ca-u II-Ca-u II-Ca-b II-K-u II-K-u II-K-b 1.54 1.78 3.17 1.63 1.68 2.07 1.54 1.55 3.33 1.49 1.52 1.45 1.75 1.72 1.89 1.98 2.00 1.94 1.95 1.85 1.90 2.14 2.07 2.03 1.73 1.91 1.91 1.75 1.78 1.91 1.44 1.52 1.80 1.57 1.77 1.51 9.92 0.01 9.80 0.03 10.22 0.00 0.26 9.67 0.26 9.84 0.26 9.95 10.02 0.00 10.24 0.00 10.44 0.00 0.06 10.18 0.06 10.13 0.08 10.08 10.12 0.30 9.92 0.00 10.62 0.00 0.32 9.78 0.30 9.79 0.30 9.87 10.04 0.00 9.54 0.00 10.44 0.00 0.30 9.80 0.32 9.53 0.32 9.90 9.88 0.00 10.00 0.00 10.40 0.00 0.30 9.65 0.28 9.61 0.60 9.77 10.10 0.00 10.36 0.00 10.22 0.00 0.24 9.80 0.22 9.72 0.32 9.53 0.07 0.07 0.01 0.06 0.06 0.07 0.06 0.06 0.07 0.06 0.06 0.06 0.01 0.01 0.06 0.12 0.12 0.01 0. 12 0.12 0.01 0. 12 0.12 0.12 0.23 0.23 0.12 0.22 0.22 0.23 0.22 0.22 0.23 0.22 0.22 0.22 35.48 35.33 35.64 35.53 35.13 35.39 35.68 35.18 35.52 35.67 35.79 39.21 36.10 35.63 35.37 35.33 35.71 37.04 35.57 35.89 35.45 35.70 35.26 35.37 35.49 36.03 36.37 35.42 35.65 36.29 35.50 35.62 35.35 35.70 35.41 35.65 Decanted sol. 3.34 3.65 3.60 0.33 0.34 0.35 1.42 1.59 1.14 0.04 0.04 0.06 3.93 3.99 4.03 0.60 0.59 0.55 4.34 4.26 4.21 0.62 0.64 0.62 6.16 6.27 5.08 0.79 0.77 0.80 4.55 4.48 4.32 0.56 0.53 1.11 0.04 0.05 0.05 2.93 3.26 3.01 0.01 0.02 0.03 1.31 1.37 1.34 0.05 0.05 0.06 3.37 3.28 3.28 0.06 0.06 0.07 3.46 3.52 3.55 0.18 0.21 0.15 5.11 5.07 4.07 0.07 0.06 0.09 4.25 4.46 0.38 3.54 3.83 3.31 3.38 3.71 3.31 1.25 1.41 1.47 1.15 1.22 1.40 4.25 4.29 4.21 4.06 3.98 4.13 4.61 4.64 4.46 4.19 4.27 4.27 6.98 7.19 5.73 6.44 6.39 5.28 5.03 4.91 4.63 5.25 5.36 1.33 (Continued) 54 APPENDIX A. Data for CEC Determination with the BM Soilt V C C C V CCa Ca C CEC rem Ca K Nan net K resident sol. LUC LUC LUC LUC LUC LUC LUC LUC LUC LUC LUC LUC TRO TRO TRO TRO TRO TRO I-Ca-u I-Ca-u I-Ca-b I-K-u I-K-u I-K-b II-Ca-u II-Ca-u II-K-u II-Ca-b II-K-u II-K-b Ca-u Ca-u Ca-b K-u K-u K-b 1.85 1.58 1.80 1.73 1.83 1.99 1.46 1.41 1.43 1.28 1.64 1.34 1.48 1.50 1.24 1.18 1.36 1.15 10.02 0.00 10.68 0.01 9.66 0.00 0.36 9.56 0.34 9.81 0.38 9.72 10.12 0.01 10.00 0.00 0.18 9.91 10.44 0.00 0.18 9.93 0.16 9.72 10.40 0.00 10.26 0.00 10.36 0.00 0.02 10.14 0.02 10.18 0.02 10.01 0.01 0.01 0.22 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 35.50 35.98 36.62 35.53 35.81 35.34 35.37 36.19 35.72 35.72 35.74 35.61 35.24 35.63 35.41 35.46 35.79 35.28 decanted sol. 4.64 4.62 4.82 0.86 0.79 0.46 2.64 2.70 0.30 2.84 0.31 0.35 0.48 0.45 0.41 0.02 0.01 0.00 0.13 0.11 0.13 3.93 3.83 3.86 0.06 0.05 2.34 0.07 2.39 2.33 0.02 0.01 0.03 0.36 0.41 0.37 * 5.14 5.18 S. S1 5.51 5.16 4.96 5.01 2.76 2.91 2.72 3.07 2.72 2.79 0.14 0.09 0.14 0.10 0.09 0.11 t Soil type-saturating cation-blieached or unbleached. : Na-concentration in extractant was estimated to be 0.05 -3 based on several measurements. mol m C -1 -3 3 and CEC in cmol kg Units: V in cm , C in mol m C C 55 APPENDIX B. Data for CEC Determination with the VEM DOT I DOT II Ca soil V rem C 6.46 t 10 0 53.75 6.38 0.15 53.33 0.14 6.91 10 0 52.38 4.76 0.03 53.87 0.05 7.02 10 0 55.85 6.62 0.19 52.10 0.12 7.25 10 0 50.28 6.64 0.34 52.13 0.39 7.78 10 0 52.93 9.01 0.61 51.46 0.08 7.11 10 0 54.03 7.34 0.15 52.30 0.09 6.82 10 0 55.46 7.43 0.19 53.78 0.08 7.25 10 0 53.18 6.17 0.08 53.15 0.08 5.52 10 0 54.92 2.26 0.00 51.37 WIC I WIC II SAV I SAV II LUC I LUC IT TRO Ca, rem CKremt K,rem V1,eff l,eff C Ca, 1, eff C K, 1,eff V2,eff CCa,2,eff 0.13 C K,2,eff CECCa Ga K soil V rem C Ca, rem CKre K, rem V 1,eff ,eff 0.00 5.76 0.00 3.58 0.00 6.22 0.04 5.92 0.03 8.64 0.02 6.68 0.01 7.08 0.01 5.24 0.00 1.40 6.47 0.01 9.79 58.34 7.03 0.00 9.61 58.54 0.01 3.42 48.51 0.01 0.00 2.51 7.02 0.00 9.96 55.58 0.02 5.75 50.62 0.02 0.00 4.91 7.35 0.00 9.49 57.96 0.00 5.47 50.55 0.04 0.32 5.12 7.81 0.00 9.58 55.09 0.03 8.14 47.98 0.00 0.00 7.33 7.18 0.01 9.59 54.90 0.05 7.33 49.88 0.01 0.00 6.57 6.86 0.00 9.83 55.65 0.07 7.58 47.99 0.01 0.00 7.05 7.32 0.00 9.83 57.36 0.07 4.57 49.34 0.01 0.00 3.76 5.36 0.00 9.75 58.36 0.00 1.00 51.07 0.00 0.00 -0.01 0.05 C Ca, 1,eff .65 CK, 1, eff 5K,,eff V2,eff 50.50 CC a,2,eff 0.03 Ga,2,eff 0.13 C K,2,eff 5.41 CEC K K Na soil V rem C, re m Na, 6.46 10.62 6.91 10.55 50.02 3.18 54.95 0.03 1.76 -3 7.02 10.55 47.48 5.24 53.04 0.06 3.56 3 7.25 9.95 50.59 3.80 54.56 0.44 2.88 7.78 10.09 49.05 7.75 53.64 0.00 6.03 7.11 9.67 49.49 5.90 52.30 0.07 4.54 -1 6.82 9.59 48.70 6.64 52.38 0.03 5.19 7.25 9.83 50.97 3.57 55.33 0.03 2.25 5.52 10.64 48.87 1.15 55.41 0.00 -0.05 V Na, 1,eoff 48.37 C Na, 1, eff 4.87 V Na, 2,eff , 52 36 C Na, 2, eff 0 00 3.34 CEC Na t Estimate. Units: C in mol m C , V in cm and CEC in cmol kg C 56 APPENDIX C. Data for Exchange Isotherms DOT I'DOT II Ga/K= 10/0 v T 6.78 6.98 10. 03 0.15 =9.04, C 7.10 9.98 0.08 7.71 9.98 0.13 =0.99 9.88 10.23 0.02 9.08 10.28 0.16 9.92 9.16 0.53 10.82 9.26 0.65 9.76 8.87 0.73 7.35 10.17 10.02 0.11 9.57 9.75 0.40 9.37 9.42 0.49 10.59 9.42 0.57 10.07 8.99 0.70 7.78 9.96 10.07 0.19 11.57 9.95 0.54 11.34 9.15 0.48 9.48 9.17 0.68 11.34 9.16 0.83 7.17 9.68 10.14 0.05 10.69 9.99 0.18 9.80 9.04 0. 42 10.58 9.32 0.62 9.94 9.11 0.74 6.84 10.42 10.19 0.11 8.23 9.87 0.27 9.74 9.18 0.62 10.86 9.18 0.84 9.61 8.95 0.90 7.27 9.95 9.64 0.46 9.85 9.29 0.97 9.25 8.85 0.98 10.20 8.87 1.00 9.59 9.04 1.02 5.59 7.66 9.98 0. 16 7.49 9.87 0.01 6.64 9.98 0.05 8.42 9.05 0.01 5.57 9.51 0.00 WIG I WIG II I 1~1 ~1 I\II I SAV I SAV II I ~ LUC I LUG II TRO ~\1 I I.IYIII I\ I cCa, remfI 10.03 0. 15 CK, rem Ca/K=9/ 1 C00 v C 1024 9.310.39 10.12 0.11 9.88 9.66 0.62 9.78 9.35 0.87 10.81 9.01 0.90 9.73 8.95 0.96 7.03 19' 09 =7. 55. 01 6.65 51.58 7.86 2.11 34.96 6.41 2.54 7.02 10.10 0.03 9.14 10.02 0.24 9.20 9.45 0.63 10.00 9.53 0.62 10.16 9.15 0.71 7.1.5 CGa, ,eff 994 K,2,eff C95 10.81 v2ef 2, C04 eff Ca, , eff K, 2,eff 897 V 3,eff C06 9.0 C Ga, ,eff K, 3,eff 4,eff C06 VGa, 4,eff9 92 K, C90 4,eff , C06eff , Ga, eff K, 5,eff 53.30 6. 46 1.64 34.75 7.12 2.62 7.25 54. 41 6.90 1.89 33. 64 6.85 2.67 7.78. 57. 96 7.21 1.97 34. 36 7. 18 2.77 7.11 51.76 7.29 1.72 33.00 6.97 2.68 6.82 53. 00 6.58 1.95 33. 90 6.96 2.75 7.25 53.29 7.32 2.62 36. 19 7.06 2.81 5.52 v rem 6.45 2.14 33. 27 7. 11 2.80 6.91 (Continued) 57 APPENDIX C. Data for Exchange Isotherms DOT I DOT II Ca/K=5/5 V C C 1,eff eff Ca, 1, WAIIWIC SAV I SAV II -U LUC I LUC II TRO C =501 C Ca, el =5.09, K,el=. 58.36 57.16 57.45 58.08 562 5.45 4.68 20.97 5.10 5.57 4.48 22.12 5.14 4.97 6.60 C 54.95 372 6.90 =3.07 55.53 3.50 7.02 5.58 4.51 22.48 5.28 4.89 7.40 58. 31 5.81 4.33 21.23 5.15 4.96 7.77 58.06 5.67 4.42 19.53 5.10 5.02 7.12 58.31 5 .90 4.33 22. 96 5.23 4.97 6.52 58.01 5.66 4.60 22.72 5.12 5.05 7.28 57. 93 5.30 4.93 24. 32 5.10 5.11 5.36 452 K, 1,eff 24.63 v2,eff 2~,eff C 5.24 C, 2,eff K,2,eff V rem Ca/K=3/7 V C Leff Ca, l,eff cK,el=73 51.20 50.00 3.76 6.62 20.10 3.09 7.22 6.98 3.77 6.67 20.80 3.18 7. 15 7.31 49.78 3.98 6.37 20. 12 3.21 7. 14 7.71 54. 00 3.80 6.60 18.48 3. 12 7.20 7.06 53.91 3.88 6.51 24. 89 3.20 7. 15 6.58 49.95 3.72 6.71 20.59 3.08 7.21 7.23 52.15 3.29 7.18 21.73 3.04 7.34 5.30 cK, l,eff 6. 25.20 21.23 V 2, eff 3.09. 3.03 C Ca, 2,eff .3 cK,2,eff7.0 v rem Ca/K=1/9 C V ,f cCa~~f C ,ef 2,eff cCa,,f C V K,2,eff rem V 6.61 6.91 =0.51, Ca, el 49.13 50.81 1.66 8.34 21.55 0.94 8.94 6.58 1.33 8.65 22.57 0.53 9.22 6.95 cK, el=.4 50.04 49.56 1.78 8.17 23.92 0.69 9..00 7.16 1.53 8.47 23.15 0.89 8.67 7.34 55.11 2. 19 7.82 21.71 0.85 8.95 7.72 48.39 1.88 8. 10 20. 14 0.88 8.90 7.08 52. 75 2 .13 7.81 19. 27 0.81 9.00 6.63 49.04 1.69 8. 36 20.32 0.60 9.21 7.10 49.50 0.83 9.16 24. 64 0.52 9.26 5.34 (Continued) 58 APPENDIX C. Data for Exchange Isotheerns DOT I DOT II Ga/K=0/10 V 1,eff Ga, 1,eff G 9.64 GK, 1,eff 0580 V 2090 I,eff Ga,2,eff G K,2,eff V rem 20 3. 10.24 6.95 = WIG I WIG II V~ u--- SAV I SAV II LUG I LUG II TRO G,=0.00, GK~l=10. 04 CaK, el 50.37 54.70 53. 66 0.53 99 0.34 21.28 9.74 0.60 9.58 21.62 0.36 9.96 7.10 9.98 7.39 54.18 0.61 9.60 18.58 0.41 10.02 7.77 50. 38 0.59 9.53 21.08 0.33 10.09 7.07 50. 16 0.60 9.66 20.44 0.41 10. 07 6.65 52.60 0.44 9.77 22. 00 0.22 10.22 7.19 52. 29 0.10 10.04 19.68 0.02 10.38 5.32 6.61 a Na/K=0/l Na/K= 1/9 V 1,eff =9. 15 'K, el 547'53.90 53.91 54.75 G 1 0.85 0.85 9.10 28.86 1. 15 9. 15 7.38 52.95 0.60 9. 15 25.76 1. 15 9.35 7.72 54.28 0.85 9.20 27. 02 1.15 9.30 7.08 56. 19 0.85 9.05 23.68 1.05 9.05 6.71 52.41 0.80 8.95 26. 83 1.10 9.20 7.37 55.71 0.95 9.10 27. 06 1.15 9.05 5.34 Na, l,eff G 9.15 K, 1,eff V 25 4 2,eff 9.40 81 8.95 24.68 1.10 9.25 7.07 S7. 15 GK, el cNa, 2,eff 31 K,2,eff v rem 6.51 6.93 .5 54.-293 53.77 2.60 2.60 54.48 2.55 6.95 25.72 3.00 6.95 7.71 51. 59 2.65 7. 10 29. 16 3. 15 7. 10 7.07 51.52 2.10 7. 15 23.97 3.25 7. 15 6.77 51.76 2.50 7.05 25. 35 3.10 7.05 7.35 52. 12 2.85 7.15. 25. 13 3.20 7.15 5.31 6.55 36.95 26.87 S29.28 3.1 i 3.05 .6.55 36.95 7.07 17.37 (Cont nued) 59 APPENDIX C. Data for' Exchange Isothermns DOT 1 DOT I I Na/K=/5 V ,eff C 54.02 =5.20 53.73 48 5.45 23.58 4.75 5.00 6.91 =7.10 57.62 7.05 3.95 32.26 4.60 2.50 6.89 WIC 1 IWI I I I \ LJ r I 1 I~ 51.37 4.35 5.65 23.96 4.75 4.95 7.75 53. 70 4.50 5.35 24. 13 5.35 4.95 6.91 SAV I SAV II LUC I LUC II TRO =515 C K,el 53.19 55. 13 4.60 5.35 25.34 4.70 4.85 7.07 4.80 5.50 26.97 5.40 4.95 7.35 50. 09 4.40 5.45 23. 94 5.30 4.85 6.77 52.27 4 75 5.30 22. 86 4.65 4.90 7.35 51.45 4.90 5.35 23.74 4.55 4.80 5.42 440 C Na, l,eff C 515 K, 1, eff V 20.11 2,eff C 4.80 Na, 2, eff 480 C K, 2, eff 6.50 V rem Na/K=7/3 V ,eff C 55.83 cK, el =.3 55.42 56.84 5.~ 54.50 6.95 -4.05 33. 07 7.3' 54. 29 6.15 3.70 30.01 6.80 2.85 7.02 53.29 6.35 3.95 .29.34 6.80 3.35 6.87 55. 68 6.85 3.65 31.04 8.45 3.00 7.36 54. 37 6.95 3.60 30.77 7.05 2.90 5.43 C 645 Na, 1, eff C 395 K, 1, eff V 32.87 2, eff "f 6.95 C 2 c K2e' V rem Na/K=9/1 v ,eff c N~~f 3.35 6.51 6.85 3.80 32.07 7.6(1 OC 6.55 3.80 33.95 2.70 7.08 2.95 7. 37 3.20 7.6 7 CKe =0.98 53.40 8.35 50.20 8.65 2.05 31.29 9.40 .2 6.85 53.97 7.85 2.25 29.78 8.55 1.-20 7.03 52. 99 7.65 2.05F 33.39 8.3,9 53.8.6 7.70 2.55 33.47 7. 85 1.25 7.69 56. 16 7.85 2.20 29.78 8.35 1.30 7.08 52. 72 7.90 2.35 30.32 8.25 1.35 6.92 54. 20 7.70 2.00 30. 75 7.00 1.10 7.16 53.28 7.60 1.45 32. 85 8.10 1.25 5.42 2.40 C K,1, eff 30.17 v 2, e ff 9.05 c N,,f cK,2,eff1.0 v rem 1.20 7.37 6.50 C'~ ~I (Continued) 60 APPENDIX C. Data for Exchange Isotherms DOT I DOT II Na/K=10/0 v ,f Cna, el= 10 97 52.29 54.34 WIG I WIC If SAV 1 SAV II LUC I LUC II TRO 56.50 55.18 51.42 54.46 56.24 56.44 57.64 C~K 100 91 cNa,1, effeff 2, C v2ef Na, 2,eff cK, 2,eff v rem 05 6.47 94 23.47 9.35 0.70 27.03 10.02 0.20 6.91 8.85 0.90 25.9 9.76 0.40 7.07 7.40 0.90 28.00 9.81 0. 40 7.49 8.90 1. 10 24.74 9.47 0.4/5 7(.759 8.40 0.90 27.63 9.93 0.35 7.09 8.85 0.95 28. 09 9.60 0.60 6.95 9.10 0. 75 26.27 10. 19 0.30 7.24 9.55 0.15 27. 36 10. 91 0.00 5.42 Ca/Na0/ 10§ Ca,, eff Ca/Na=1/9 V C CNl v ,f C 1,eff e . CaKel CCae= 1. 00 56.43 0.05 8.90 25.42 0.09 56.76 0.16 9.45 24.88 0.58 9.30 6.91 Nafe CNeI=9.03 56.24 0.11 0.30 24.68 0.03 9.10 7.04 52.18 0.08 9.F3() 25.63 0.18 10.60 7.40 ~53.40 0.01 0.70 23.96 0.00 10.55 7.73 57.61 0.00 9.35 23.96 0.09 9.80 7.12 54.36 0.00 9.55 25.06 0.00 9.80 6.92 53. 18 0.00 9.35 26.62 0.07 9.60 7.30 53. 89 0.83 9.10 24.82 0.99 9.30 5.35 C8.80 Na,2,eff Ca, 1.,eff 6.52 V rem , V =6.41 C =2.90 2475249 C Ca/Na=3/7 26.712 2.2 Nael Ca,el 55.97 56.28 51.08 52.61 V 1,efF 1.0 1.48 2.47 1 69 C 6.50 C Na, 2, eff 7.00 8.85 8.00 50. 14 0.45 0.75 25.75 1.93 8.60 54. 29 1.43 8.95 25.27 2.05 8. 15 8. 13 54. 44 0.52 7.60 24.86 1.58 5.55 6.93 52. 24 1.58 5.90 25.73 2.75 6.25 7.32 50.51 2.77 6.80 23.28 2.77 6.70 5.44 v rem 6.48 6.93 7.00 7.43 7.77 - -- -- -(Continued) 01 APPENDIX C. Data for Exchange Isotherms DOT I DOT II Ca/Na=5/5 V 1,eff C WIC I WIC II SAV I SAV II LUC I LUC II TRO =4.73 =5.08, C Na,el Ca,el 55.15 56.60 56.63 56.22 4.69 4.80 26.68 4.86 4.42 6.97 4.51 4.80 27.07 4.18 4.14 7.01 4.40 4.55 27.86 4.06 4.63 7.40 54.95 4.17 5.45 25.78 4.47 4.47 7.80 54.74 4.15 5.80 26.04 4.98 4.86 7.15 57.21 3.92 4.85 28.12 5.30 4.97 6.96 55.08 4.52 5.10 27.64 5.03 5.46 7.30 54.72 4.91 4.50 28.17 4.68 6.44 5.39 C 4 66 Ca, , eff C 4.35 Na, l,eff V 26.02 2,eff C 5.09 Ca,2,eff CNaeff 4.46 Na,2,eff V 6.54 rem Ca/Na=7/3 Veff C C =7 23, C =2.69 Ca,el Na,el 54, 39 56.66 57.10 54.73 6.86 3.60 28.71 7.14 3.15 6.94 =9 26Y ' 56.22 6.43 3.00 29.55 6.96 3.85 7.80 57.68 6.37 2.80 28.32 7.01 3.40 7.19 55.85 6.40 2.85 32.12 7.19 3.35 6.84 55.57 6.74 3.25 27.92 7.19 3.55 7.35 57.42 6.93 3.35 30.18 7.02 3.25 5.65 6.87 Ca, 1,eff CNa,l,eff 3.20 V2, 31.43 2,eff CCa,2,eff 7.21 C 2.95 Na,2,eff V 6.51 rem C Ca,el 6.42 3.30 31.54 7.15 3.45 7.03 C Na,el 6.57 3.50 28.26 6.86 3.25 7.44 =1.14 55.19 8.96 1.65 27.13 9.16 1.20 7.42 Ca/Na=9/1 Veff 50.50 53.23 9.03 1.65 26.26 9.22 1.25 6.98 53.31 8.89 1.70 27.23 9.34 1.10 7.13 57.85 8.81 1.85 27.93 9.14 1.30 7.81 53.72 8.97 1.65 29.24 9.25 1.05 7.16 57.43 8.98 1.70 28.51 9.32 1.10 6.87 54.83 8.97 1.75 29.33 9.25 1.30 7.34 57.77 9.19 1.45 29.74 9.29 1.15 5.37 8.88 C Ca,.1,eff 1.55 C Na,1,eff 29.34 V 2,eff C a,2,eff 9.17 CNa, 2,eff V rem .80 6.52 (Cont inued) 62 APPENDIX C. Data for Exchange Isotherms IIf LUC I LUC II TRO DOT' Ca/Na=l0/0 v ,f c. IDOT T1IW IC1IW I(I'I11 C C =10.55,C 57.80 10. 56 0.12 30.30 10.63 0.00 6.99 55.66 10. 18 0.20 29.77 10. 58 0.00 6.97 977 = OC 55.10 10.27 0.22 %AV I SE 55.47 56.68 10. 22 0.19 56.31 10. 16 0.17 25.64 10.37 0.00 7. 15 53.01 10.25 0.22 28. 72 10.49 0.00 6.76 55.34 10. 41 0.16 30. 10 10. 59 0.00 7.30 56.10 10.34 0.06 28.27 10. 55 0.00 5.51 Ca, 1,eff 2,eff cNa,1, eff 01 29.52 V2ef cCa, 2,eff105 cNa, 2,eff 00 6.-51 V rem Na rem 10.55 28. 9/1 28.53 10. 55 0.00 7.43 2894 10.36 0.00 7.81 285 I-concentr'ation is expressed in mol C m Ca u3 -3 vlme in cm and C K and V §Ca follow from the-values at Ca/K=0/10, CNa=0. rem and Vram follow from the valuecs at Na/Kl10/0, C =aO 63 APPENDIX D. SAS Program to Fit a Cubic Polynomial Through the Data to Determine Exchange Isotherms data feike; input x y; xsq=x*x; cards; 0 0 .1 .01 .3 .08 .5 .17 .7 .34 .9 1.0 .59 1.0 proc reg data=feike; model y=x xsq( xcu; p=pred 195=195 u95=u95; output out=yz proc plot data=yz; plot y*x='o' pred*x='p' /overlay vpos=40 hpos=80; r un; 64