A MODEL TO EXPLAIN HIGH VALUES OF pH IN AN ALKALI SODIC SOIL

For alkali sodic soils (pH>8.5), the “hydrolysis of exchangeable sodium” has been used as a possible explanation for the alkalinity production and rise in pH of these soils. As an alternative to this hypothesis, a model was developed to simulate and to explain that the alkalinity production and rise in pH is possible in a soil that accumulates alkaline sodium salts and CaCO 3 . Several simulations were performed by using different combinations of CO 2 partial pressures (P), presence or absence of MgCO 3 , along with experimental values of exchangeable sodium percentage (ESP) and ion concentrations in saturation extracts from an alkali sodic soil (named Pantanal). A hypothetical system with similar conditions to the Pantanal soil but with a Gapon selectivity coefficient (KG) of 0.01475 (mmol L) was also considered. Good agreement was obtained between experimental and predicted values for pH and ion concentrations in the soil solution when the model (without MgCO 3 ) was applied to the Pantanal soil. However, KG values calculated for the Pantanal soil were generally higher than 0.01475 (mmol L). Moreover, high pH values and elevated ionic strength were obtained when a KG of 0.01475 (mmol L) was used at high ESP (similar to those found in the Pantanal soil). KG values obtained for the Pantanal soil and the results obtained in the simulation of the hypothetical system are suggesting that a value higher than 0.01475 (mmol L) should be used to adequately simulate the behavior of the Pantanal soil at low ionic strength and high ESP values.


INTRODUCTION
For alkali sodic soils (pH > 8.5) the hydrolysis of exchangeable sodium has been used as a possible explanation for the alkalinity production and rise in pH.The reaction: NaX + H 2 O → HX + Na + + OH - (1) could be used to define the "hydrolysis of exchangeable sodium" (U.S. Salinity Laboratory Staff, 1954;Mashhady & Rowell, 1978).After an increase in the exchangeable Na, subsequent dilution of the soil solution by rainwater or irrigation would cause desorption and hydrolysis of the weakly adsorbed Na with a rise in pH (Brown & Miller, 1971;Shainberg, 1973;Mashhady & Rowell, 1978).Reaction (1) can, however be split in two parts: NaX + H + → HX + Na + (3) where ( 2) and (3) respectively define the water selfprotolysis and the sodium exchange by protons.
Scientia Agricola, v.59, n.4, p.763-770, out./dez.2002 In alkali sodic soils, the production of "H + ", as suggested by reaction 2, must be strongly suppressed and, consequently, monovalent hydrogen cannot compete with the sodium ion for exchange sites.Under these conditions, the presence of "protonated clays" (HX) would not be possible in these soils and, therefore, both NaOH and alkalinity production cannot be explained by reaction (1).
The purpose of this work was to find a model to simulate and to explain the alkalinity production and rise in pH in soils that accumulate alkaline sodium salts jointly with precipitated carbonates of divalent ions (CaCO 3 and MgCO 3 ) to relatively low ionic strength.Exchange of Ca-Mg-Na ions was considered.Other anions such as chlorides and sulfates were also included in the model to have conditions closer to real alkali sodic soils.The procedure of Nakayama (1970) was modified to establish a computational routine.

Development of the model
The balance of charges in solution for a system composed by sodium carbonates and bicarbonates; an exchanger limited to Ca-Mg-Na ions; CaCO 3 ; MgCO 3 ; an external CO 2 source; and chlorides and sulfates; can be given by: where the brackets for chemical species [ ] denote molar concentration in aqueous solution.
Concentrations of H + , Ca 2+ , Mg 2+ , HCO 3 -, CO 3 2and OH -are regulated by the constants of dissociation, ionization or precipitation, which have been adapted from Nakayama (1970) where K 1A and K 2A respectively define the first and second constants of H 2 CO 3 ionization; Kw= water self-protolysis constant; K S = solubility product constant of CaCO 3 ; K S2 = solubility product constant of MgCO 3 ; k= Henry's law constant for the solubility of CO 2 ; P= partial pressure of CO 2 ; and I= ionic strength of the resulting solution.r 1 , r 2 , r 3 , r 4 , r 5 and r 9 are respectively the activity coefficients for H + , OH -, HCO 3 -, CO 3 2-, Ca 2+ and Mg 2+ .The activity coefficients for Na + , Cl -and SO 4 2-ions, not explicitly included in equations from (4) to (11) but necessary in the calculations, are respectively r 6 , r 7 and r 8 .Brackets for chemical species ( ) define the activities in solution.
The Ca-Na exchange reaction, as initially proposed by Gapon (Bohn et al., 1979), has the form: Considering for the magnesium ion an analogue behavior to the calcium ion (Porta et al., 1999), the Gapon selectivity coefficient (KG) can be calculated as follows: where the concentrations of exchangeable cations, [NaX] or [Ca 1/2 X+Mg 1/2 X], are expressed on cmol(+) kg -1 , and the soluble cation concentrations are expressed as mol L -1 .From equation ( 13), it follows that sodium concentration in the solution can be estimated from the equivalent fractions of sodium on the exchanger (E Na ), [Ca 2+ + Mg 2+ ] and KG as follows: Combining equations ( 5), ( 6), ( 7), ( 8) and ( 9) with equations ( 10), ( 11), ( 14) and (4) results: [ ] The same experimental values of ESP and ion concentrations used in the second simulation were also employed in a third simulation.However, the partial pressures of CO 2 were additionally varied to generate the pH values in the saturation pastes of the Pantanal soil (Table 1).Results of third simulation are shown in Table 4.
A system composed by alkaline sodium salts, CaCO 3 (without MgCO 3 ) and an exchanger of ions (Ca-Mg-Na) with an hypothetical KG of 0.01475 (mmol L -1 ) -1/2 [U.S. Salinity Laboratory Staff, 1954], was also simulated by using equations ( 20) to ( 24).The pH and concentrations of all chemical species in solution were generated at 10% ESP (exchangeable sodium percentage) intervals, from 10 up to 90%.Chloride, sulfate and magnesium concentrations of respectively 4, 1 and 1 mmol c+ L -1 (similar to those found in the Pantanal soil) were considered (Table 5).To study the effect of the ionic strength and to maintain the validity of the approximation [Mg 2+ ]>>>[Ca 2+ ] (necessary to operate the model), the sulfate concentration was increased in 2 mmol c+ L -1 for each 10% ESP intervals from a initial value of 2 mmol c+ L -1 (Table 6).
In all simulations, the models use an autoconsistent iterative method, similar to the one of Nakayama (1970), which compare consecutive values of the ionic strength and hydrogen ion activity (H + ); the latter comparison is "nested" into the ionic strength iterations.At the first stage of the computational process, a reasonable initial "guess" of the ionic strength was necessary for estimating the ionic activity coefficients, which were calculated according to the extended Debye-Hückel equation (Peters et al., 1974).This step was necessary because the ionic concentrations were unknown at this stage (Nakayama, 1970).
The initial activity coefficients, in combination with the equilibrium constants, KG, ESP, P, and chloride, along with sulfate and magnesium (when necessary) concentrations, were used to compute the coefficients (equations from 17 to 21 or from 20 to 24) of the 4 th grade polynomial (equation 16).To solve the 4 th grade polynomial equation for (H + ), the Newton-Raphson iterative procedure was used, which also needs a reasonable initial "guess" of pH.This iterative procedure was continued until two similar consecutive values of (H + ) [differences <10 -30 ] were obtained.The first (H + ) value (first iteration for ionic strength) and the necessary set of equations (equations from 5 to 11 and 14) were then used to compute the cation and anion concentrations and, consequently, a new ionic strength value was obtained.This new ionic strength was used in the second iteration to improve the activity coefficients.The iterative procedure for the ionic strength was continued until obtaining two close successive values (differences <10 -21 ).
In the first, second and third simulations, in order to find a KG value compatible to both, the concentrations of exchangeable ions as well as soluble ions, the ionic strength iterations were nested in a computational [ ] The preceding procedure used to obtain polynomial coefficients of equation ( 16) can be also employed to obtain an equivalent expression to equation 15 but considering that precipitated MgCO 3 does not control the presence of magnesium in solution.To facilitate the resolution of this equivalent expression it is necessary to assume that [Mg 2+ ] is much higher as compared to [Ca 2+ ] ([Mg 2+ ]>>>[Ca 2+ ]).In consequence, it can be shown that F1, F2 and F3, new coefficients of equation ( 16), correspond to the following expressions: (24) In this case, F4 and F5 do not change and they are respectively equal to equations ( 20) and ( 21).

MATERIAL AND METHODS
In order to calculate pH, concentrations of all chemical species in aqueous solution and KG (when necessary), the models (equations from 17 to 21 or from 20 to 24) were translated into the BASIC language and operated using a digital computer system.The programs (when necessary) used different partial pressures of CO 2 (P).
In the first and the second simulations, a natural system with accumulation of alkaline sodic salts, CaCO 3 , MgCO 3 (only CaCO 3 in the second simulation) and the partial atmospheric pressure of CO 2 (P) [0.35x10 -4 MPa] was assumed.Both programs used experimental values of ESP and, [Cl -], [SO 4 2-], [Mg 2+ ] (assumed as [Ca+Mg] in the second simulation and predicted in the first simulation) and [Na + ] in the saturation extracts, from an alkali sodic soil named Pantanal (Table 1).These values were employed to predict pH, KG, and [CO 3  2 and 3.
Samples were collected from a pedon belonging to the Chaguaramas Series (Chaguaramas, Guárico State-Venezuela), 9° 20' 36'' NL and 66° 14' 40'' WL.The pedon, named here as Pantanal soil, was classified as a Typic Natrustalf (Soil Survey Staff, 1998) and was sampled at 0.1 m depth intervals up to the 2.5 m depth.The twenty-five soil samples obtained were air dried and passed through a 2 mm sieve.The material >2 mm was individually crushed to sizes <2 mm and incorporated to the previously sieved soil less than 2 mm, and then homogenized.
In every individually homogenized soil samples, the pH was measured in the saturation paste, and the extract was used for determination of Ca 2+ +Mg 2+ , Na to process them with the clarifying technique of Robbins (1989).
On the other hand, 100 g of the same twenty five processed soil samples were additionally crushed to sizes <0.425 mm and homogenized.These samples were used for the determination of the cation exchange capacity (CEC) and ESP (U.S. Salinity Laboratory Staff, 1954).Calcium and magnesium carbonates were analyzed as described by Pla-Sentís (1969).
All determinations were carried out in triplicate and the experimental values shown in the Table 1 are the averages of these determinations.

RESULTS AND DISCUSSION
Results obtained by our model, assuming a soil that accumulates alkaline sodium salts, CaCO 3 and MgCO 3 (using equations from 17 to 21), show that the values of pH measured in the Pantanal soil were similar to the predicted ones (the differences were lower than 3% of measured data) to 0.5-2.5 m depth (Figure 1; Tables 1 and 2).However, predicted [Mg 2+ ] (  carbonates in the Pantanal soil seem to be mainly composed by CaCO 3 , which was additionally corroborated by the analysis of precipitated salts (not reported here) in this soil (Guerrero-Alves, 1998).
Taking into account these previous results, a new model was used for the Pantanal soil, which excludes the presence of MgCO 3 (using equations from 20 to 24) and employs [Ca+Mg] as magnesium concentrations.The values of pH measured in the Pantanal soil were also similar to the predicted ones, except for the 0.0-0.2m depth (Figure 2) where the differences were over 4%.This can be due to the very low concentrations of precipitated calcium carbonates found at that depth (Table 1), or the assumption that the CO 2 partial pressure is atmospheric (0.35x10 -4 MPa) is not very realistic for a saturation paste.On the other hand, this model seems to predict adequately [HCO 3 -]+[CO 3 2-] in the saturation extracts, as is shown in Figure 3.In 90% of the cases below 0.2 m depth, differences between experimental and predicted data (Tables 1 and 3, respectively) oscillated between 2 and 21% of experimental [HCO 3 -]+[CO 3 2-]; which are respectively representing differences between 0.3 and 2.6 In relation to divalent ions below 0.2 m depth (Table 3), predicted values of [Ca 2+ ] (between 0.01 and 0.08 mmol c+ L -1 ) correspond around to 1-10% of the experimental [Ca+Mg] (assumed totally as [Mg 2+ ]) in 90% of these values; which indicates that the approximation [Mg 2+ ]>>>[Ca 2+ ] (necessary to operate the model) was reasonable in these systems that accumulate alkaline sodium salts and CaCO 3 .Excluding the 0.0-0.2m depth, where the model had a bad performance, the main differences between experimental and predicted concentrations can be due to the fact that the pH was measured in saturation pastes, whereas experimental concentrations were measured in saturation extracts.On the other hand, for predicting the pH and concentration values shown in Figures 2 and 3, the model with the best performance (using equations from 20 to 24) generates KG values (Table 3) between 2 and 17 times greater than 0.01475 (mmol L -1 ) -1/2 ; except for 0.0-0.1 m depth where is comparable to this value.These KG values are identical, until the fourth decimal figure, to the KG values (not reported here) calculated by using the experimental values of ESP, [Na + ] and [Ca+Mg] (Table 1) in equation 14.Bohn et al. (1979) indicated that the Gapon equation, with a KG value of 0.01475 (mmol L -1 ) -1/2 , cannot be satisfactorily applied for soils when ESP values are above 40%.All ESPs for the Pantanal soil, except at a 0.0-0.1 m depth, are higher than 40% (Table 1).1).Under these conditions, a poor competition of divalent ions for the exchange sites can be expected and also a progressive sodification of the exchanger phase.The KG values obtained in conditions where alkaline sodium salts in    ---------------------mmol c+ L -1 ---------------------

F1=
] and[Mg 2+ ] (only in the first simulation) in the soil solution.Equations from (17) to (21) and from (20) to (24) were respectively used in the first and the second simulations.Results are shown in Tables

Figure 2 -
Figure 2 -Experimental pH values measured in saturation paste (SP) and pH values predicted by using the proposed model (MOD) [equations from 20 to 24], at 0.1 m depth intervals, in the Pantanal soil.

Table 1 -
Experimental values* of pH, exchangeable sodium percentage (ESP), soluble ions and precipitated carbonates (Carbp) of the Pantanal soil, determined at 0.1 m depth intervals.
-(U.S. Salinity Laboratory Staff,  1954).As all extracts were dark colored, it was necessary *Results are the average of three determinations.

Table 2 )
were 16 to 92 times higher than[Ca+Mg]measured in saturation extracts at the same depth (Table1).These results indicate that MgCO 3 phase is not controlling the [Mg 2+ ] in the soil solution of the Pantanal soil.Precipitated