A TRANSITION STATE PHYSICOCHEMICAL MODEL PREDICTING NITRIFICATION RATES IN SOIL-WATER SYSTEMS by Marvin James Shaffer A Dissertation Submitted to the Faculty of the DEPARTMENT OF HYDROLOGY AND WATER RESOURCES In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY WITH A MAJOR IN HYDROLOGY In the Graduate College THE UNIVERSITY OF ARIZONA 1972 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE I hereby recommend that this dissertation prepared under my direction by entitled MARVIN JAMES SHAFFER A TRANSITION STATE PHYSICOCHEMICAL MODEL PREDICTING NITRIFICATION RATES IN SOIL—WATER SYSTEMS be accepted as fulfilling the dissertation requirement of the degree of DOCTOR OF PHILOSOPHY / Dissertation Director e-30- 7 Date After inspection of the final copy of the dissertation, the following members of the Final Examination Committee concur in its approval and recommend its acceptance:* This approval and acceptance is contingent on the candidate's adequate performance and defense of this dissertation at the final oral examination. The inclusion of this sheet bound into the library copy of the dissertation is evidence of satisfactory performance at the final examination. STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: ACKNOWLEDGMENTS Much appreciation and thanks are extended to Dr. Gordon R. Dutt for his assistance and direction in the pursuit of this program. Thanks are expressed to the members of my committee, Dr. Daniel D. Evans, Dr. Robert A. Phillips, Dr. Wallace H. Fuller, and Dr. Hinrich L. Bohn for their time and help. I wish to extend my thanks to the personnel of The University Computer Center for the use of their Multiple Linear Regression Program. The author is indebted to the United States Department of the Interior, Bureau of Reclamation, and the IBP Desert Biome for funds provided in support of this research under contracts 5010-4151-11 and 5010-4151-17, and 50204151-16, respectively. Finally, I would like to thank Miss Elvia Niebla for her assistance in many of the routine laboratory analyses. iii TABLE OF CONTENTS Page LIST OF TABLES vi LIST OF ILLUSTRATIONS viii ABSTRACT ix INTRODUCTION 1 LITERATURE REVIEW 4 Intermediates Oxygen Moisture and Salt Content pH Ammonium Nitrification Models Miyake Model Quastel and Scholefield Model Downing, Painter, and Knowles Model Sabey, Frederick, and Bartholomew Model . . McLaren Model Shaffer, Dutt, and Moore Model THEORY Transition State Derivation of Rate Expression Containing Partition Functions Partition Functions for Ideal Gases Reactions in Solution Dielectric Constant of Solvent Ionic Strength Soil pH Hydrostatic Pressure 6 7 7 8 9 10 10 11 12 14 15 17 20 20 21 26 28 29 29 30 31 33 33 34 34 36 38 39 EXPERIMENTAL MATERIALS AND METHODS Soils Nitrogen Source Soil Analyses Incubation Study Ammonium Exchange Study pH Study iv TABLE OF CONTENTS--Continued Page 41 RESULTS AND DISCUSSION Ammonium and Oxygen pH Partition Functions Partition Function for 02 Partition Function for 11 -1Partition Function for NH 4 4Partition Function for NH OH Partition Function for N2 Partition Function for NO2 Comparison of Equation Forms and Activated Complexes The Rate Model Basic Assumptions Computer Program Application of Nitrification Rate Model to Panoche and Desert Soils Additional Verification of Nitrification Rate Model SUMMARY AND CONCLUSIONS 41 45 50 50 52 53 55 56 58 60 68 69 70 71 76 89 92 APPENDIX A: COMPUTER LISTING OF RATE SUBROUTINE . . APPENDIX B: COMPUTER LISTING OF GENERAL COMPUTATIONAL PROGRAM 97 APPENDIX C: DATA COLLECTED IN INCUBATION STUDY . . 103 LITERATURE CITED 108 LIST OF TABLES Table 1. 2. 3. 4. 5. 6. 7. Page Some Chemical and Physical Properties of the Panoche and Desert Soils . . Some Chemical and Physical Properties of the Parshall and Gardena Soils 35 37 Correlations for Nitrification Reaction Rates versus NNH4 -1- Concentrations 42 Correlations for Nitrification Reaction Rates versus NNH 4 + Activities 42 Calculated and Observed Values for Percent of N NH4 on the Exchange Complex 44 Calculated and Observed pH Values for Panoche and Desert Soils 48 Calculated and Observed pH Values for Panoche and Desert Soils Treated with HC1 . . . . 51 8. Data for Rotational and Vibrational Partition 52 Functions for 0 2 9. Wave Lengths of Vibrational Modes for NH 4 + • • 54 10. Wave Lengths of Vibrational Modes for NH 2 OH . 57 11. Data for Rotational and Vibrational Partition Functions for NO 2 59 12. 13. 14. Partition Functions and Statistical Data for Equation (73) and Panoche Soil 64 Partition Functions and Statistical Data for Equation (74) and Panache Soil 65 Partition Functions and Statistical Data for Equation (73) and Desert Soil 66 15. Partition Functions and Statistical Data for Equation (74) and Desert Soil vi 67 vi i LIST OF TABLES--Continued Page Table 16. 17. 18. 19. 20. 21. Statistical Data from Pairing Calculated and Observed Rates for the Panache and Desert Soils 75 Calculated and Observed Nitrification Rates for the Parshall and Gardena Soils . . . . 77 Statistical Data from Pairing Calculated and Observed Nitrification Rates for the Parshall and Gardena Soils Estimated Soil Extract Analyses Used in Verification of Nitrification Model Statistical Data for N NH4 + Saturation Values in Parshall Soil Statistical Data for NNH4+ Saturation Values in Gardena Soil 78 86 87 88 LIST OF ILLUSTRATIONS Page Figure 1. 2. Potential Energy Versus Reaction Coordinate for a Typical Exothermic Chemical Reaction 22 Percent of NNH 4 1- on the Exchange Complex as a Function of Moisture Content 40 3. Block Diagram of Computerized Rate Subroutine • • 72 4. Relationship of Activation Energy to Ionic Strength for Panoche and Desert Soils . . • • 73 5. 6. 7. Calculated and Observed Rate Data for Parshall Soil at Various Moistures after 10 Days Incubation Calculated and Observed Rate Data for Parshall Soil at Various Moistures after 20 Days Incubation Calculated and Observed Rate Data for Parshall Soil at Various Moistures after 40 Days Incubation 80 81 82 Calculated and Observed Rate Data for Gardena Soil at Various Moistures after 10 Days Incubation 83 9. Calculated and Observed Rate Data for Gardena Soil at Various Moistures after 20 Days Incubation 84 8. viii ABSTRACT Transition state theory was applied to the nitrification process in soil-water systems, and a computerized, theoretical rate model was developed to include NH 4 + and 02 concentrations, pH, temperature, moisture content, and local differences in nitrifying capacities of Nitrosomonas bacteria. The model was restricted to enriched calcareous soils thus simplifying the application of basic physicochemical principles. Experimental rate data from an agricultural and a native desert soil provided verification of a zero order reaction for nitrification with respect to NH4+ concentrations above a certain saturation level, as previously reported. The saturation concentration in soils was found to be about 1.0 to 5.0 ppm. A theoretical linear relationship between activation energy and ionic strength was confirmed by application of the above data. However, each local population of nitrifiers tended to display different values for the slope and intercept of the linear relationship. The structure of the activated complex for NH 4 + oxidation to NO2 - was determined to be more like NH2OH or NH 4 + than NO 2 - • As a first approximation, the NH2OH ix activated complex was included in the rate model. The equation form for the equilibrium between the reactants and the activated complex was found to differ from the stoichiometric reaction between NH 4 + and 0 2 to form NH 2 OH. The equilibrium ' expression was found to be more closely approximated by the relationship, 2 NH4+ + 0 2 4— (ACTIVATED COMPLEX) .* + A method was developed to compute soil pH values as a function of moisture content. Verification was obtained by using data obtained from the agricultural and native desert soils, including cases where samples were acidified. The calculated pH values were used in the nitrification rate model. Further verification of the model was obtained using data from the literature for two soils from the Northern Great Plains. Data pairing of observed and predicted rates for these soils yielded R values of 0.944 and 0.940. The rate model was programmed in FORTRAN IV computer language and designed to operate in conjunction with existing computer models. Thus, this relatively sophisticated model may be applied to field simulation studies with a minimum of adaptive procedures. The model should aid in obtaining reliable predictions of NO 3 - formation and movement under a wide range of field conditions. INTRODUCTION Nitrogen pollution of streams, lakes, and groundwater has become a topic of considerable discussion in hydrology and related disciplines in recent years. N pollution sources may include municipal sewage effluents and various aspects of agriculture including cattle feed lots and overuse of commercial fertilizers in crop production. Also, native geologic deposits of NO3 - are a source of N contamination. Unborn children and infants are quite susceptible to methemoglobinemia, a disease related to NO 3 food supplies. NO 2 but NO 3 - - - in water and is actually responsible for the disease, can be reduced to NO 2 - by coliform microorganisms in the digestive tract. Methemoglobin is formed by the reaction of NO2 - with oxyhemoglobin in the blood. Unlike oxyhemoglobin, methemoglobin cannot transport oxygen resulting in "blue babies." Similarly, livestock, particularly ruminants, which consume water or feed containing appreciable quantities of NO 3 , are susceptible to methemoglobi- nemia. Algal blooms may occur in lakes and streams when sufficient NO 3 - and other nutrients are present. These or- ganisms may then die and the resulting decay processes may 1 2 remove the dissolved oxygen from the water and kill or exclude the fish population. Crop production may be adversely affected by NO 3 - and NH4+ concentrations in the root zone which are too high or too low depending on the stage of growth. Also, NO 2 toxicity to plant growth has been noted even at low NO2 - - concentrations. The process of converting NH4+ to NO 2 - and NO 3 - is known as nitrification. This is a microbial process accomplished almost exclusively by bacteria of the genera Nitrosomonas (NH 4 1-4-NO 2 ) and Nitrobacter (NO 2 -)-NO 3 ). Since - - - nitrification is such an important process with respect to N pollution and in other areas such as soil fertility and plant nutrition, the continued development of descriptive mathematical models seems highly desirable. These aid environmental impact studies, help to improve fertilizer efficiencies, and provide a better basic understanding of the nitrification process. Several attempts have already been made to model nitrification. However, since nitrogen chemistry is very complex, the models to date, in part, have been overly simplified and/or empirical. The need exists for a more detailed model capable of adequately describing the process as it occurs under field conditions. This paper reports on the develOpment of a transition state, rate process theory, model of nitrification in 3 soil-water systems. This represents the first known attempt to apply transition state concepts to the nitrification process. The model is designed to approximate the nitrification rate process under a range of temperatures, moisture contents, NH 4 +, 0 2 , and H+ concentrations, and salt levels common in soils under field situations. The model can be used in conjunction with existing models (e.g., Dutt, Shaffer, and Moore, 1972) to predict the NH 4 +, NO 3 , urea, - and organic N concentrations in soil-water systems and associated leachates. LITERATURE REVIEW Schloessing and Muntz (1877) were the first to show that nitrification in soil-water systems is a microbial process. Their experiment consisted of application of sewage effluent to a column of sand and chalk. Analyses of the applied sewage and leachate from the column indicated conversion of the input NH 4 + to NO 3 . The process was inhib- ited by chloroform, but restored by washings with sterile water followed by applications of washings from soil. The conclusion was made that the process was microbial. In the early 1890's, Frankland and Frankland (1890), Warington (1891), and Winogradsky (1890) independently isolated the NHe oxidizing microorganisms. In addition, Winogradsky (1890) isolated the NO 2 - microorganisms. These results established the two stage nature of the nitrification process. Stevens and Withers (1909) compared the nitrification rate of NHe in soil with that obtained in solution culture. A more rapid rate was observed in soil suggesting possible influences of solid phase materials. Miyake (1916) and Pulley and Greayes (1932) found that NO 3 - concentration as a function of time follows a sigmoid type curve for the nitrification process. Caster, Martin, and Buehrer (1942), 4 5 Fraps and Sturges (1939), and Pikovkaya (1940) showed that nitrifying microorganisms isolated from different soils have different nitrifying capacities. Intermediate products in the nitrification process were studied at early dates. The presence of hyponitrous acid in solution culture during nitrification was demonstrated by Beesley (1914) and Corbet (1935). Hydroxylamine was suggested as a possible intermediate by Kluyver and Donker (1925). Lees and Quastel (1946) introduced the method and apparatus for soil perfusion studies. Soil perfusion techniques treat the soil as a biological whole, much as if it were a living plant or animal tissue. Changes within the soil during the experiment are observed under a specified set of conditions. Lees and Quastel (1946) first applied the soil perfusion techniques to the study of nitrification. These same authors determined that nitrifying bacteria grow on the surfaces of clay particles and utilize adsorbed NH 4 4- • Quastel and Scholefield (1951) noted that nitrifying bacteria eventually reach a state in which all the available sites for growth are saturated with nitrifying microorganisms. In this saturated state, the soil is said to be "enriched." Also, the same authors noted that an enriched soil shows no initial lag period during the nitrification process. 6 Intermediates Various intermediate compounds have been suggested in the nitrification pathway between NH 4 + and NO 2 . The - most frequently studied are hydroxylamine, hyponitrite, and nitrohydroxylamine. Yoshida and Alexander (1964) demonstrated that hydroxylamine is formed by Nitrosomonas europaea. Nicholus and Jones (1960) found that the cells of Nitrosomonas contain the enzyme for conversion of hydroxylamine probably serves as a precursor to NO2 . The same - authors found that when high concentrations of hydroxylamine are being oxidized to NO2 , N20 and some NO and NO2 are - evolved. However, the N20 was not oxidized to NO2 , and - the conclusion was made that N20 is an unlikely intermediate in the nitrification process. Hofman and Lees (1953), and Yoshida and Alexander (1964) found that hydrazine is an inhibitor of the conversion of hydroxylamine to NO2 . Alexander (1961) suggested - that hyponitrite might be an intermediate between hydroxylamine and NO2 . Campbell and Lees (1967) pointed out that - hyponitrite is not oxidized by Nitrosomonas and therefore is not a likely intermediate. These same authors suggested nitrohydroxylamine (NO2.N H.OH) as a likely intermediate. . Also, they mentioned nitroxyl (NON) and nitramide (NO2.NH2) as possible but unlikely intermediates. 7 Oxygen Aerobic conditions are required for the oxidation of NH4+ to NO2 - and NO3 . Longmuir (1954), Griffin (1963), - Greenwood (1968), and Macauley and Griffin (1969) all noted that aerobic respiration is unimpeded by lowering oxygen partial pressures until exceptionally low values occur at the microbial surfaces. Greenwood (1962) found that nitrification in solution is not inhibited by oxygen concentrations until they drop to below 0.16 mg/L. Boon and Laudelout (1962) found the Michaelis saturation constant Km for oxygen is about 0.25 mg/L at 18° C and 0.5 mg/L at 32°C. The apparent up- per limit for the effect of oxygen concentrations on the nitrification process can be explained by the enzymatic nature of the process as noted by McLaren (1970). Moisture and Salt Content The effect of moisture and salt on nitrification has received considerable attention. Parker and Larson (1962) found inhibition of nitrification at soil moisture contents less than 0.05 bar suction. Justice and Smith (1962) observed no nitrification at moisture contents below 115 bars suction, with increased rates at higher moisture contents. Miller and Johnson (1964) observed a peak in nitrification rates at 0.50 to 0.15 bar suction. Robinson (1957) found that nitrification did not occur at moisture contents less than one-half the permanent wilting percentage. Shaffer 8 (1970) found that nitrification rates in soils are independent of moisture content at moistures greater than about 10 bars suction. Although it is difficult or impossible to separate moisture effects from purely osmotic effects, several authors have determined nitrification rates as a function of osmotic pressure. Johnson and Guenzi (1963) found that increased osmotic tension reduced nitrification rates in a linear manner in soil-water systems. Also, these same authors found that nitrifiers in different soils show different tolerances to salt content. Reichman, Grunes, and Viets (1966) showed that nitrification rates in soils decrease as the moisture contents decrease and the osmotic tensions increase. pH The effects of pH on nitrification are well known. Since H+ is formed during the oxidation of NH4+, the pH tends to fall as nitrification progresses This in turn may inhibit the reaction unless pH buffering takes place. Meyerhof (1916) found that the optimum pH for Nitrosomonas is 8.5 to 8.8, while for Nitrobacter, 8.3 to 9.3. Quastel and Scholefield (1951) noted that the optimum pH for nitrification in pure culture is 8.5, while the lower limit was placed at 4.0. These same author found that a soil with pH 4.5 did not oxidize NH4+. Broadbent, Tyler, and Hill (1957) found that NH4+ is oxidized more rapidly in soils which are amended with OH-. 9 These authors also noted inhibition of Nitrobacter at 800 ppm NNH4 + in alkaline soils. This may have been due to the deleterious effects of free ammonia on these microorganisms. The accumulation of NO2 - following field application of NH4+ to alkaline calcareous soils has been reported by Fuller, Martin, and McGeorge (1950). Caster et al. (1942) found a threshold pH of 7.6 to 7.8 above which there is no NO 2 - oxidation to NO 3 . Broad- bent et al. (1957) found that oxidation of NH4+ becomes very slow near pH 5.0. Ammonium The effect of NH4+ concentrations on nitrification rates has been the subject of many articles. Stojanovic and Alexander (1958) pointed out that high NH4+ concentrations have little effect on the rate of NH4+ oxidation to NO2 , - but that high NH 4 + tends to suppress the conversion of NO2 - to NO 3 -. Broadbent et al. (1957) found that under low NH4+ concentrations and other conducive conditions, conversion of NH 4 + to NO 3 - proceeds rapidly to completion. McIntosh and Frederick (1958) concluded that NO 3 - formation from NH4+ takes place more rapidly where the NH 4 + concentration is less than 400 ppm. McLaren (1970) noted that nitrification rates in enriched soils are first order with respect to substrate at low substrate concentrations. In the case of NH4+ oxidation 10 to NO 2 - , Knowles, Downing, and Barrett (1965) placed the boundary between high and low NH4 + concentrations at about 1 ppm N NH4 +. Boon and Laudelout (1962), and Laudelout and Tichelen (1960) gave values of 23 and 9 ppm NNO2 -, respectively for a similar boundary in the case of NO2 - oxidation to NO 3 - . The zero order nature of the nitrification process in enriched soils with high N NH e concentrations has been given a theoretical basis by McLaren (1970). Also, the same author noted that growing populations of nitrifiers may exhibit maximum growth rates at high substrate concentrations. It is not known whether the boundaries between high and low substrate concentrations previously mentioned apply equally to enriched and unenriched soils. Nitrification Models Several mathematical relationships have been proposed to describe nitrification in soil-water systems. All of these to date have either been simplified models for nitrification under specific, limited conditions or semiempirical models for nitrification under a wider range of conditions. A review is presented here to demonstrate some attributes and deficiencies inherent in these models. Miyake Model Miyake (1916) proposed the following equation describing nitrification in soils 11 Y = (A"-Y)exp(K(t-t1)) where Y is the NNo3 - (1) produced A" is the asymptotic value approached by Y t is time t1 is time to Y=A"/2 K is a constant. This equation fits the classic sigmoid curve observed when soils with less than maximal populations of nitrifying microorganisms are incubated under conditions conducive to microbial activity. The equation does not apply to initially enriched soils, which lack the lag portion of the sigmoid curve. In addition, the equation does not allow for changes in pH, NH 4 + and 0 2 concentrations, temperature, and moisture content. Quastel and Scholefield Model Quastel and Scholefield (1951) derived the following relationship for nitrification in soils Y = K' exp(Ct) (2) where Y is the NNO 3 - produced t is time K'and C are constants. The equation has the boundary condition that Y=0 when t=0. It models the lag and the essentially constant rate portion of the experimentally observed sigmoid nitrification curve. The model does not account for limiting NH 4 + concentrations 12 nor does it allow changes in pH, 0 2 concentration, temperature, and moisture and salt content. Downing, Painter, and Knowles Model Downing, Painter, and Knowles (1964) published an integrated form of the Michaelis (e.g., McLaren, 1970) type equation for nitrification in river water. These authors related mass of NNH44. produced to dry mass of Nitrosomonas organisms by using the expression Cm - CA = Em(NN41-- NNH4+) (3) where Cm is the concentration of Nitrosomonas 0 NNH4+ is the initial N NH e concentration is the N NH concentration 4 the initial concentration of CA is Nitrosomonas NNH 4 E m is the dry mass of Nitrosomonas produced per oxidation of unit mass of N NH e Combination of this equation with the Michaelis equation in the form d N mu + - - 4= dt K Cm NNH 4 + Km NNH4 4- where K is the growth rate constant Km is the Michaelis constant t is time. yields the following expression upon integration (4) 13 Kut - 1/A'= EmKmln (NN4+/NNH4+) (A' - EmKm ) ln [(A' - E mKm )/CM where A' = CA + E m N NH ° 4. 4 (5) (6) Knowles et al. (1965) determined values for K", C m , and Km . They used a trial procedure and a digital computer program together with experimental values for NNH 4 + and NNH+. The value for Em was taken as 0.05. To account for changes in K" as a function of temperature, a regression equation was derived and may be written logK" = 0.0413T - 0.944 (7) where T is temperature K" has units of days -1 . Also, an expression relating the Michaelis constant Km to temperature was derived in a similar manner and may be written logKm = 0.051T - 1.158 (8) where Km has units of mg/L NNH 4 +. No equations were presented for the variation in K" and Km with changes in 02 and H -1- concentrations. The authors noted that K" is independent of 0 2 concentration above about 2 mg/L 02. This model incorporates empirical regression equations to account for the effects of temperature variation on a Michaelis type rate equation. The data used to derive the regression eqations were taken from samples of river water 14 containing soil particles. Different expressions might be expected for lower moisture contents encountered in soils under field conditions. In addition, pH, limiting NH4+ and 02 concentrations, and salt effects were not considered. Sabey, Frederick, and Bartholomew Model The amount of nitrate nitrogen accumulating in time may be described by the following equation proposed by Sabey, Frederick, and Bartholomew (1969) NNO3 - = K f Rk (t - t f r t ) (9) where t is time Kf is the characteristic nitrifying capacity Rk is a composite factor or rate index based on the relative maximum N No ,- accumulation rates under less favorable donditions of moisture, temperature, pH, texture, aeration, etc. tf is the characteristic delay period under optimum conditions r t is a composite factor or delay index based on the relative delay periods under less favorable conditions where Rk = Rt RERpH R tex Ra R x(10) r t = r t rEr pHr tex r a r pr x(11) etc. are relative rate indexes, rt , etc. where R t' are relative delay indexes, and where the subscript t is temperature M is moisture pH is pH 15 tex is texture a is aeration p is population of nitrifiers x is a composite of all other influencial factors. This model incorporates many of the variables known to influence nitrification rates in soil-water systems. However, the manner in which the variables are interrelated appears to be rather empirical. The model could yield useful predictions provided values for the respective indexes can be determined. The authors did not present values for more than three of the indexes. McLaren Model McLaren (1970) proposed the following equation for NH4+ oxidation rates in soils (similar expressions were given for NO2 - oxidation, etc.) d(NH4+) _ AdM dt dt ^ 7m K'"13A(NH4-1-) Km + (NH4+) (12) where NH4+ is the substrate (NH4 4- ) concentration M is biomass A,y, and fi are proportionality constants Km is the saturation (Michaelis) constant K"' is the specific rate constant. 16 The first term in equation (12) is the Monad growth rate expression for microorganisms, the second is the Pirt maintenance term, and the third represents oxidation of the NH 4 + due to the enzyme system. At small NH 4 + concentrations and in a fully enriched soil (e.g.,a soil in which the Nitrosomonas population is maximal and constant), equatic:n (12) can be written d(NH4+) Ykax + K(NH 4 +) (13) dt where K = KmBM__max -m - (14) For large NH 4 + concentrations equation (12) becomes d(NH 4 +) dt Ykax+ K"'13- %ax = v (15) where v is a constant. McLaren (1971) developed an equation for NH 4 + oxidation rates in soils with populations << Mmax and large NH 4 + concentrations. Here (NH4 +) (16) Kg + (N 11 4 +) where y cc, and Kg are characteristic growth constants for Nitrosomonas, which reduces to Y = Yco (17) at large NH4+ concentrations. Also A M 0 exp(y o6t) (18) 17 where Mo is the initial biomass t is time. dA dT Y m(1 - If A/Amax ) (19) (Lees and Quastel, 1946), then at large NH 4 + concentrations and M « — max -d (NH +) 4 - dt CM exp(yi,t) — 0 (20) where C is a constant. McLaren's model incorporates microbial growth and maintenance relationships as well as the Michaelis relationship describing enzyme catalized processes such as nitrification. His model should apply to soil-water systems with submaximal as well as maximal populations of nitrifiers. However, McLaren did not include temperature as a variable (a drawback in the Michaelis approach) nor did he consider the effects of pH/oxygen concentration or moisture content. These variables would have to be held constant whenever the constants in McLaren's model are determined. Since the variables mentioned tend to vary in soil-water systems under field conditions, McLaren's model is not yet applicable to the field. Shaffer, Dutt, and Moore Model Shaffer, Dutt, and Moore (1969) used a semi-empirical approach involving a multiple linear regression analysis 18 of published data for several alkaline soils to derive the following equation for nitrification rates in soil-water systems dNH4-1dt = 4.64 + 1.62.10 -3 T (NNH4 + (21) 4.50 log(N NH4 4-) - 2.51 log(N NO3 _) where T is temperature N NH4+ is the NNH4+ concentration N N0 - is the N N0 _ concentration. 3 3 Adjustments were made to rates computed by this equation to account for effects due to moisture contents below 10 bars suction. The following assumptions were made to allow application of this model to the field situation. 1. The soil moisture content remains in the range approximately bounded by field capacity and permanent wilting point. 2. The soil pH remains in the range 7.0 to 8.5. 3. Denitrification is insignificant. 4. Gaseous losses of NH 3 are insignificant. 5. Fixation of N 2 gas is insignificant. 6. Nitrification rate is unaffected by ionic strength. 7. Different microbial populations respond about equally to the input variables. 19 8. The response of microorganisms to pH is about the same from pH 7.0 to 8.51 9. 10. Fixation of NH 4 + in clay lattices is insignificant. The effects of varying 0 2 partial pressures are insignificant. 11. NO 2 - accumulation is insignificant. THEORY Transition State Consider the reaction for NH + oxidation to 4 NH 4 + + 3/2 0 2NO2- + 2 H + + H 2 0. NO - 2 (22) A plot of the potential energy curve for a typical exothermic reaction such as NH 4 + oxidation, equation (22), appears in Figure 1. The energy of activation, AE c , (or AE 0 if zero point energies are included) represents the highest energy barrier which must be overcome between the reactants (e.g., NH 4 + and 0 2 ) and products (e.g., NO 2 -- , H -F, and H 2 0). If the assumption is made that a transition state or activated complex at the top of the energy barrier is in equilibrium with the reactants, then equation (22) becomes NH NO 2 ACT* 4 + 3/2 0 2 -7 2 H H 2 O. (23) Another basic assumption of transition state theory states that the rate of reaction is first order with respect to the activated complex. Thus for equation (23)(Stevens, 1970) dNH 4 + = vACT* (24) dt where y is the frequency per unit time with which the activated complexes cross the barrier to form products ACT* is the concentration of the activated complex (number/unit volume). 20 21 AG in Figure 1 represents the free energy change associated with the overall reaction. For NH 4 + oxidation to NO 2 -, AG is about -66.5 Kcal/mole. Derivation of Rate Expression Containing Partition Functions The values of y and ACT* can be obtained as follows. For clarity consider a general reaction of the form aA + bB — 7 cACT* + dD (25) Then from statistical thermodynamics (Hill, 1960) pcp d ACT* D a b P A B rACT [ c1 B1 d V _ (41 [ V d p K V .., b = (26) eq V where p is the number density (number of molecules or ions/unit volume) for the specie indi•cated by the subscript q is the partition function for the specie indicated by the subscript ✓ is volume K eq is the equilibrium constant for the reaction represented by equation (25). In general, the q's appearing in equation (26) are products of their component partition functions. Thus, q (total)• - qtran qrot qvib qele (27) where q(total) is the total partition function for the particular specie is the partition function for translational motion 22 AOH3N3 1V11.113.10d 23 groti rotational motion qvi b, vibrational motion ciele , electronic motion. Other partition functions may be included here (such as qatomic) but usually make insignificant contributions to the total function at ordinary temperatures. Motion along the reaction coordinate (or pathway between the reactants and products in potential energy space) at the activated complex is treated as translational motion in one dimension. The assumption is made that one normal mode of vibrational freedom is directed along the reaction coordinate. This vibrational mode is usually the mode associated with the weakest bond. Thus clACT* = qtran g rot qvib* qz qele where q (28) is the partition function for the ACT* activated complex q z is the partition function for the reaction coordinate the vibrational partition function qvib* is less one made of vibrational freedom. The expression of q z may be written q z = Az 27M*kT h2 (29) where Az is the length along the reaction coordi nate M* is the mass of the activated complex - 24 k is Boltzmann's constant T is temperature h is Planck's constant. This expression is the classical representation for translational motion in one dimension. Let If N't be the velocity along the reaction coordinate. the reaction is assumed to proceed. If N.0. 0, the reaction does not take place. The fraction of all activated complexes with is in the range (Hill, .\./. to + d . 7- may be expressed 1960) 7 exp( — pes:Oc“7 = 2 • M* v )dv (30) +Œ :_l oo exp(_ f. M*Ni 2 )d .‘r 2 where P( . 7. )d1.7 6 is is the probability of finding an activated complex with velocity to dt 1/kT. The denominator of equation (30) may be integrated in closed form to give p(N:7)di- = exp( 2TrkT A2 M* 2 (31) )d An activated complex with velocity must be within a distance to cross the barrier in unit time. Let p l be the number of activated complexes per unit length and per unit volume along the reaction coordinate. Then, p • 'v is the number of activated complexes crossing the barrier per unit time with velocity The expression for the total number 25 of activated complexes crossing the barrier per unit time at any velocity > 0 is (Hill, 1960) Rate = (32) where Rate is the rate of reaction. Combining this equation with equation (31) and integrating gives Rate = p .*kT 2TrkT = p M* kT (33) 27M* Also, Azpl is the number of activated complexes per unit volume of the system (not per unit volume along the reaction coordinate at the activated state.) Combining this result with equations (26) and (33) yields 27 m * kT Az)/v] [ci l (Azpy) c p D _ ACT*j h2 a b qA ab PA PB (77) c q d ( D) V(34) the total partition function for the where qACT* lis activated complex with q z removed. By removing the electronic portions of each partition function in equation (34) and combining them into a single expression, the exponential is now included in the rate expression which may be written 26 Rate - kT h ' qACT* cip d/c (-7) V a/c b/c qB ciA (-V) V a/c b/c PA PB d/c PD (35) exp[-AE c /(kT)] where AE is is the energy of activation with the zero point energies excluded ' denotes the partition function less the electronic contribution kT FE is and the remaining right side of the equation isAJACT* (see equation, 24). Partition Functions for Ideal Gases Use of activity coefficients allows the application of existing partition functions for ideal gases to nonideal soil-water systems. The following is a detailed discussion of the translational, rotational, and vibrational parts of total partition functions for ideal gases. A total partition function may be defined as the probability of the occurrence of a specie in a particular volume. The parts of the total function may be thought of as contributions due to the particular motion being modeled, e.g., translational, vibrational, etc. The classical partition function for translation in 3-dimensional space is written (Amis, 1949) qtran = V( 27MkT 3/2 2 ) h where M is the mass of the specie being considered. 27 The rotational partition function for diatomic molecules is (Hill, 1960) =v grot ( aer (37) ) where a is the symmetry number O r is the rotational temperature. The symmetry number corresponds to the number of different ways a molecule or ion can achieve, by rotation, the same orientation in space. The rotational temperature has components associated with the moment of inertia about the center of mass. Monatomic gases do not display rotational degrees of freedom and therefore do not have rotational partition functions. Polyatomic molecules possess a more complex rotational partition function as follows (Hill, 1960) 47 grot = a - 1/2 T3 k)21 O B O c (38) ) where OA, GB, Oc are the rotational temperatures for the three principal moments of inertia. ' The vibrational partition function for diatomic molecules is (Hill, 1960) gvib = exp[-Ov/2T)]/[1-exp(-0y/T)] where Ov is the vibrational temperature. (39) 28 The vibrational temperature is related to a vibrational frequency which can be calculated from quantum mechanics or deduced from vibrational spectra. The vibrational partition function for polyatomic molecules qvib = yexp[-O vi /(2T)]/[1-exp(-0.94 /T)] where 0 (40) is the vibrational temperature for the . ith normal mode of vibration. The vibrational temperatures can be determined from vibrational frequencies using O v . = v.h/k (41) where v i is the frequency of the ith mode. The number of vibrational modes for nonlinear polyatomic molecules or ions is (Hill, 1960) Number of Modes = 3n - 6 (42) where n is the number of nuclei. For linear molecules or ions, the number of vibrational modes is Number of Modes = 3n - 5 . (43) Reactions in Solution The general rate expression derived up to this point, equation (35), may be applied to chemical reactions in general. However, derivation of partition functions for the motions of molecules and ions in a nonideal condensed medium such as liquid water is a difficult task. 29 Another approach involves application of partition functions for motions of the reacting species in an ideal gas, together with activity coefficients for the solution phase. Dielectric Constant of Solvent The effect on the reaction rate due to changes in the dielectric constant can be calculated using existing relationships (e.g.,Harris, 1966). However, changes in the dielectric constant in aqueous solutions usually contribute much less to rate changes than alterations in the total concentration of ionic species. For this reason, changes in the dielectric constant were ignored in the development of the rate model. Ionic Strength In aqueous solutions, one of the main environmental factors influencing the reaction rate is the ionic strength of the solution. Activity coefficients for charged species in solution may be approximated by the Debye-Huckel expression (Garrels and Christ, 1965) - logy, = 4 (0.509)p 1/ 2 1 + p1/2 (44) where y i is the activity coefficient of the ith specie z i is the charge on the ith specie p is the ionic strength of the solution Here 1 2 P = TEZi C i (45) 30 where C i is the concentration of the ith specie. Activity coefficients for neutral molecules in solution may be computed by the expression (Harris, 1966) logY i = Rinu (46) where Kra is a semi-empirical constant. In practice activity coefficients will often cancel out of the rate expression leaving a somewhat simplified relationship for the variation of the rate constant and observed activation energy with ionic strength. Soil pH In calcareous soil-water systems, the following set of equations may be combined to form an expression for the hydrogen ion activity at equilibrium (Garrels and Christ, 1965) [H2CO3]K CO2 (47) - 1 [H t ] [HCO -3 ] [H2CO 3 ] K2 [H + ] [C0 --3 ] [HCO3- ] (48) (49) and [Ca l-1- 1[CO 3 = ] = K sp (50) where P CO is the partial pressure of CO2 2 [1 refers to the activity of the indicated specie 31 K K2, 2/ and K sp are constants. These equations may be combined to yield cif+] = [Cal-11 ,iKKKP 1 2 3 CO 2 (51) sp which reduces to [H t ] = JKP 4 CO 2 [Ca] (52) where K 4 is a combination of previous constants. pH may then be determined by using the familiar equation pH = -log[H+ ] . (53) Hydrostatic Pressure Variation of reaction rates in solution with changes in hydrostatic pressure can be calculated by using the approach developed by van't Hoff. The variation of an equilibrium constant such as K eg with pressure may be expressed by the van't Hoff equation 31n K eq_ 3 p AV* (54) RT where P is pressure AV* is the volume of activation R is the gas constant and (Laidler, 1963) k R = (kT/h) K eq (55) 32 where k R is the rate constant. If the assumption is made that AV* is independent of pressure, equation (54) can be integrated after combination with equation (55) to yield ln k R = ln k° - AV*p (56) RT where k 0 is the rate constant at zero pressure (close R to the value at atmospheric pressure). Since pressures on the order of several thousand lbs/in 2 are needed to produce significant changes in rate constants, the pressure effect can be neglected in applications to most soilwater systems. Application of nitrification rate data for soils together with the theoretical rate expression, equation (35), and the activity coefficients just discussed should allow the development of a transition state model for nitrification in soil-water systems. EXPERIMENTAL MATERIALS AND METHODS Three studies were conducted on two soils to obtain data to develop the nitrification model. An incubation study provided nitrification rate data at various moisture contents, temperatures, NH 4 + concentrations, and pH values. An NH4+ exchange study yielded data which were used to test an existing NH 4 + exchange model. pH data from the third study allowed the development of a method to compute soil pH as a function of moisture content. Nitrification rate data from the literature provided further verification of the completed rate model. Soils Five soils were included in this study. The first two, a Panoche fine sandy loam (Typic Torriorthent) from California and an unnamed gravelly loamy sand (Typic Torrifluvent) from a desert area of Pima County, Arizona, were used in the incubation, NH 4 + exchange, and pH studies. Data from the third and fourth soils, Parshall fine sandy loam and Gardena loam, both from the Northern Great Plains, were used to further verify the final, theoretical rate model. The fifth soil, an unnamed clay loam from the Page Ranch, Pima County, Arizona, was initially included in the incubation study. However, the soil did not develop a significant 33 34 population of nitrifiers until it had been incubated with an application of 400 pg/g N NH4 +, and at 25°C and 1/3 bar suction for about five months. As a result, time did not allow collection of rate data for this soil which could be used to develop or verify the nitrification model. Nitrogen Source Analytical reagent grade NH 4 C1 (Mallinckrodt Chemical Works) was used as a source of nitrogen in the incubation, NH 4 + exchange, and pH studies. Soil Analyses The Panoche and desert soils were analyzed by the author for the various parameters listed in Table 1. NH 4 + and NO 3 - were determined using steam distillation techniques with MgO followed by Devarda's alloy. The Ca ++ and Mg++ were run by application of the 1,2-diaminocyclohexane-N,N, N I 1 N 1 -tetraacetic acid (DCyTA) method (Meites, 1963). Na + was determined using flame emission techniques. C O 3 = and concentrations were found by titration with H 2 SO 4 to 3 the phenolphthalein and methyl orange endpoints, respec- HCO tively. Cl - was determined using the Mohr method. SO= was run by application of the Thorin method (Brown, Skougstad, and Fishman, 1970). Cation exchange capacity was determined using the NH 4 0Ac - NH 4 NO 3 method described by Keeney and Bremner (1969). pH was determined with the soil particles in 35 Table 1. Some Chemical and Physical Properties of the Panoche and Desert Soils Parameter Composition of 1:5 Soil Water Extract Units Panoche Desert Pg/g NH 4 1- -N 3.2 2.3 NO 3 - -N 28.0 8.5 Ca ++ 277. mg++ 50.8 Na + 164. HCO 3 - 147. 79.2 32.8 17.3 249. CO3= 0.0 0.0 Cl - 61.6 30.0 1931. S O 4= Cation Exchange Capacity meq/100 g pH Value (1:5 extract) 84.3 12.1 6.4 8.4 7.9 0.056 0.15 Total N % Sand % 71.8 86.9 Silt % 15.7 7.6 Clay % 12.4 5.6 Soil Moisture Content bars % by weight 0.3 13.3 0.3 10.5 bars % by weight 5.0 7.7 5.0 5.0 bars % by weight 15.0 6.5 15.0 2.4 bars % by weight air dry 1.6 air dry 1.0 36 contact with the soil extract and the electrodes in the extract alone. The Kjeldahl digestion method was used to determine organic N. The soil particle size analyses were run using the hydrometer method. Soil moisture content measurements were made with pressure membrane apparatus. Data for the Parshall and Gardena soils were taken from the literature (Reichman et al., 1966) and appear in Table 2. Incubation Study Data for nitrification rates as a function of temperature, moisture content, NNH concentration, and pH were 4 obtained from an incubation experiment involving the Panache and desert soils. Initially, 25 g samples of each soil were treated with 400 pg/g N NH and incubated at a temperature of 4 25°C and a moisture content of about 1/3 bar suction. The incubation chamber was humidified to control evaporation. This run was continued until a maximal population of nitrifiers was established in each soil as evidenced by the shape of the NO 2 - plus NO 3 - versus time curve. Incubation times used to insure establishment of the maximal populations ranged from two weeks with the Panoche soil to four weeks with the desert soil. Remaining samples were then incubated in duplicate at temperatures of 15, 25, and 35°C, and at moisture contents 37 Table 2. Some Chemical and Physical Properties of the Parshall and Gardena Soils* Parameter Units Parshall NH4 + -N Pg/g 15.0 NO3 - -N Pg/g 2.0 Total N o o Gardena 26.4 - 5.1 0.090 0.20 6.6 7.2 17.9 24.2 pH value (saturated paste) Cation Exchange Capacity meq/100g Conductivity (saturation extract) mmhos/cm Soil Moisture Content bars % by weight saturation 28.7 saturation 41.6 bars % by weight 0.2 15.0 0.2 20.0 bars % by weight 1. 0 9.0 1. 0 13.4 bars % by weight 5.0 6.8 5.0 9.8 bars % by weight 15.0 5.8 15.0 8.2 bars % by weight 50.0 4.5 50.0 6.4 0.42 *Data taken from Reichman et al. (1966) 0.80 38 ranging from about 1/3 to 15 bars suction in humidified incubation chambers. Duplicate samples were removed from the incubation chambers at time intervals ranging from 10 to 20 days for a period of up to 60 days. Following centrifuging, the supernatant solutions from 1:6 water extracts of these samples were analyzed for NNH4+, NNO2- plus NNO 3 - , and pH. pH values were determined while the supernatant solutions were in contact with the soil particles. The N analyses were conducted by semi-micro steam distillation techniques with MgO followed by Devarda's alloy. Total NNH 4 + in each sample was calculated from soluble N NH4 + using experimental curves for exchangeable versus soluble NNH 4 -1- measured at the 1:6 dilution. A listing of the experimental data collected in the incubation study appears in Appendix C. Ammonium Exchange Study This study was done to help assess the ability of a computer model previously developed (Dutt et al., 1972) to calculate the distribution between soluble and exchangeable NNH 4 -I- at equilibrium. Experimental values were determined for soluble and exchangeable N NH4 + concentrations in equilibrated samples over a range of moisture contents. Data were collected for the Panoche and desert soils. N NH4 4- (400 pg/g) in the form of NH4C1 dissolved in distilled water was applied to triplicate samples of the two soils. Sample size 39 ranged from 25 to 500 g soil. Extracts at each moisture content were obtained either by centrifuging or by extracting in pressure membrane apparatus. The extracts were then analyzed for N NH using steam distillation techniques and MgO. KC1 4 extracts (1N) of similar samples contained 93 to 95% of the NNH4 + applied to the two soils. The experimental results of the NHe exchange study are presented in Figure 2. pH Study pH data were collected in duplicate for the Panoche and desert soils treated with 400 pg/g NNH 4 -1- in the form of NH4C1. The moisture contents of these determinations were 20, 30, 40, 60, 100, 200, and 400% by weight. The soil- water extracts were separated from the soil particles by centrifuging, and pH measurements were made on the supernatant solutions. The liquid remained in contact with the - soil particles during the measurements. A second set of similar pH determinations was made except that HC1 was added to each sample to lower the pH. The same amount of HC1 was applied to each sample, but the quantity added lowered the pH of the 400% extract by about 1 pH unit. In addition, Ca were deter- mined in each of the supernatant solutions by the DCyTA method. The results of this two-part study appear later in the paper. 40 .4. H N % RESULTS AND DISCUSSION Ammonium and Oxygen Previous researchers (e.g., Stojanovic and Alexander, 1957) have found that for enriched soils, the rate of NH 4 4oxidation is independent of NH4 + and 0 2 concentrated above respective saturation levels. This is probably caused by saturation of a limited number of active sites where the enzyme catalyzed reaction occurs. To test this hypothesis for NH4+, correlation analyses were run on rates of reaction versus N NH4 + concentrations and activities. Rates were included for the Panoche and desert soils, temperatures of 15, 25, and 35°C, and moisture contents ranging from about 1/3 to 15 bars. The results of these correlations appear in Tables 3 and 4. Activities were included because they were more likely to represent a true driving force in the reaction. Note that in no case was there a significant correlation at the 0.05 level of significance even though various ways of expressing the NNH4+ concentrations were used. The conclusions were made that this work confirmed the findings of previous researchers, and that the NH 4 -1- concentrations and activities tested were in general above the critical saturation level for NH 4 + oxidation to NO2-. A significant correlation might be expected for N NH4 4" concentrations and/or activities below the saturation level. 41 42 Table 3. Correlations for Nitrification Reaction Rates versus NNH 4 + Concentrations Specie **R-NH4 + -N R-NH4 + -N ***S-NH4 1- -N S-NH4 1- -N ****T-NH4 + -N T-NH4 4- -N Concentration Units r* pg/g soil -0.110 pg/ml water -0.199 pg/g soil 0.241 pg/ml water 0.0771 pg/g soil -0.0988 pg/ml water -0.231 ** R = exchangeable *** S = soluble * r must be at least 0.273 to be significant at the 0.05 level **** T = total Table 4. Correlations for Nitrification Reaction Rates versus NNH4 -4- Activities Specie Concentration Units r* R-NH 4 + -N pg/g soil -0.0947 R-NH4 1- -N pg/g ml water -0.204 S-NH4+-N Pg/g soil 0.255 S-NH4+-N Pg/ml water 0.0997 T-NH4 1- -N pg/g soil -0.0821 T-NH4 4- -N pg/ml water -0.201 43 An NNH4+ concentration of 1.1 ppm has been men- tioned (e.g., Knowles, Downing, and Barrett, 1965) as a saturation level for NHe oxidation. However, since all exchangeable N 1- concentrations encountered in the incuNH4 bation study were above about 5.0 ppm, the only inference which could be made was that the saturation level probably was about 5.0 ppm or less. Experimental curves for percent of N NH4 1- on the exchange complex at various moisture contents and 23°C appear previously in Figure 2. The concentration of total N NH4 -1present in each case was equal to the concentration initially established in the samples used in the incubation experiment. These data were used to verify a computer model developed by Dutt et al. (1972) with respect to the distribution of N NH4 + between the soluble and exchangeable forms. The model appeared to yield results which agreed well with experiment below about 20 to 40 percent moisture content by weight, but deviated at higher mostures. Table 5 lists some experimental and calculated values for the Panoche and desert soils in the moisture range where reasonable agreement was obtained with experiment. The experimental NH 4 + - Na+ exchange constants used to obtain the calculated values in Table 5 were 0.025 and 0.005 for the Panoche and desert soils, respec- tively. Since the moisture contents in this study and in most soils under field conditions generally fall within the 44 Table 5. Calculated and Observed Values for Percent of N NH 4+ on the Exchange Complex Moisture Content (% by weight) (% Exchangeable NNH 4 + ) Panoche Desert (exp) (calc) (exp) (calc) 40 72.0 71.1 65.3 30.5 20 91.5 90.0 86.8 84.1 9 96.9 95.4 7 98.3 89.3 93.4 92.3 45 range where reasonable agreement was obtained with experiment and because of the relatively high percentage of exchangeable NNH 4 -1- in this range, the computer model was utilized to calculate the distribution between soluble and exchangeable N NH4 +. Applications to problems such as sediment laden streams and lakes where the moiSture contents are considerably higher would require modification of the NHe exchange portion of the model. Replacement of the NHe - Na + exchange reaction with NHe - Ca ++ exchange may improve the model in these moisture regions. With respect to 0 2 , the assumption was made that the oxygen concentrations remained above the saturation level for oxygen in the NH4+ oxidation process. No attempt was made to gather experimental data for oxygen concentrations. A saturation value of 0.25 ppm was selected for 02 • This agrees with a number suggested by Boon and Laudelout (1962). pH Because hydrogen ion activity has been shown to be an important variable in the nitrification process, some method was needed to include pH in the rate model. pH values for soil-water extracts could have been applied directly. However, since pH varies with moisture content, a procedure was developed to approximate pH values at field moisture contents from soil-water extract pH. The assumption was made that the pH values calculated in this manner 46 were proportional to the microscopic pH values important at the active enzyme sites. Dutt et al. (1972) made the assumption of constant CO partial pressure at constant moisture content and applied 2 the relationship K K sp2 K3 fCa ++ 1[HCO 3 - ] 2 (57) [H 2 CO 3 ] where [ ] denotes the activity of the particular specie K sp , K 2 , and 1‹ are equilibrium solubility and dissociation contants. Combining equation (57) with the assumption of constant CO 2 partial pressure at constant moisture content yields K2 [H2003] K' = [c a ++][Hc0 3 - ] = K sp K3 (58) where K' is a constant at constant moisture content. Dutt et al. (1972) determined the relationship between K' and moisture content for several soils and combined these results to obtain the expression log K' = - 1.68 log M - 4.46 (59) where M is moisture content (% by weight). Rearrangement of equation (51) yields the expression [H+] 2 = K l K l K 3 P CO2 [Ca] ++ (60) 47 With the assumption of constant P constant moisture content, equation (60) may be written [H4]2 = K" [Ca++] (61) and K" - K1 K2 K3 PCO2 (62) SP where K" is a constant at constant moisture. Combining equations (58) and (62) leads to K" = K' K2 3 K 2 SP (63) Finally, combining equations (61) and (63) (64) Experimental differences in K' are probably caused by changes in P m and hydrogen ion exchange. 2 To test the above theory, experimental values for pH were determined in soil-water extracts from the Panoche and desert soils. Extracts were included for a range of moisture contents from 400 to 20 percent by weight. The 1:5 extract analyses and other soil data (see Table 1) were used to calculate values for the slope and Y-intercept in equation (59) together with values for Ca++ activities and finally pH at the various moistures. Calculated versus measured pH vales appear in Table 6. 48 Table 6. Calculated and Observed pH Values for Panoche and Desert Soils Soil % Moisture pH Calculated Observed Panoche 400 200 100 60 40 30* 20* 8.1 7.9 7.6 7.4 7.3 7.2 7.0 8.1 7.9 7.7 7.6 7.4 7.3 7.2 Desert 400 200 100 60 40 30* 20* 8.0 7.7 7.5 7.3 7.1 7.0 6.9 8.0 7.7 7.6 7.5 7.2 7.1 7.0 *pH determined on supernatant solution out of contact with the soil. 49 Data pairing of these calculated and measured pH values yielded R values of 0.987 and 0.980 for the Panoche and desert soils, respectively. The assumption was made that the agreement between experiment and theory shown by the data in Table 6 exists at moisture contents below 20%. It was not possible to obtain sufficient extract volumes below about 40% to allow pH readings where the extracts were in contact with the soil particles while the measuring electrodes were in the extracts alone. Since the nitrification reaction generates H+, soil pH tends to become lower as the reaction progresses depending on the buffer capacity of the particular soil. A method was needed to allow calculation of soil pH without the necessity for new values for the slope and Y-intercept in equation (59) as the soil pH changed. As a first approximation, the assumption was made that for small changes in pH (e.g., one pH unit or less) the slope in equation (59) remained about constant. With this assumption, the Y-intercept could be calculated from experimental soil-water extract pH and the Ca ++ activity in the same sample. Thus INT = -SLOPE log M - log K' where INT is the Y-intercept SLOPE is the slope M is the moisture content of the extract K' is determined from extract pH and Ca ++ activity. (65) 50 To test this approach, experimental values for pH and Cã were determined in soil-water ex- tracts from the Panoche and desert soils treated with HC1 and at various moisture contents. Using these data, the extract and soil data previously mentioned, and the above procedure, the values appearing in Table 7 were obtained. Partition Functions Before the data could be applied to calculate experimental values for AE c partition functions had to be derived describing the motions of the various molecules and ions. Basically, partition functions were derived for NH2OH, N 2 0, 02, H+, and NO. Several combinations of these were used in addition to the ones for NH 2 OH and N 2 0 to learn something of the structure of the activated complex. In addition, the 0 2 , NH 4 4- , and H -F partition functions were used directly in each of the models tested. Partition Function for 0 2 Recall from equation (27) that q(total) = q qe le tran g rot q vib g ele was not needed because it was removed and included in AE c (or AP qtran for 02 was obtained by application of equation (36) for translational motion in three dimensions together with the mass of the 0 2 molecule. Since 0 2 is a diatomic molecule, equations (37) and (39) for rotational 51 Table 7. Calculated and Observed pH Values for Panoche and Desert Soils Treated with HC1 Soil % Moisture pH Calculated Measured Panoche 400 200 100 60 40 30* 20* 7.1 6.9 6.6 6.4 6.3 6.2 6.0 7.1 6.9 6.7 6.5 6.5 6.3 6.2 Desert 400 200 100 60 40 30* 20* 7.0 6.7 6.5 6.3 6.1 6.0 5.9 7.0 6.8 6.6 6.4 6.2 6.1 6.0 *pH determined on supernatant solution out of contact with the soil. 52 and vibrational motion respectively, were applied to obtain the remaining q's. The necessary temperatures and symmetry number (Hill, 1960) are given in Table 8. q 02 the total partition function of 0 2 is 2w Mo, kT 4 C1 0 2 = V( )3/2 TRaer) exp[-Ov/(2T)]/ h2 (66) [1-exp(-0 v /T)] where MO 2 is the mass of the 02 molecule. Table 8. Data for Rotational and Vibrational Partition Functions and for 0 2 Parameter Units Value 2 Or.07 °K 2230. Ov °K 2. Symmetry Number Partition Function for H IThis function is relatively simple since monatomic species do not have rotational and vibrational degrees of freedom. Derivation consisted of applying equation (36) together with the mass of the hydrogen ion. Thus 2ff M H + kT = V( ) 3/2 (67) 53 where M H + is the mass of the hydrogen ion. Partition Function for NE14 4Derivation of the total partition function for the polyatomic NH 4 + ion consisted of applying equations (36), (38), and (40), together with other information. There are few experimental data available on the specific rotational and vibrational temperatures for the NH 4 + ion. However, experimental work has been done on a molecule with a very similar configuration, CH 4 (methane). Both CH 4 and NH 4 + have a tetrahedral (spherical top) shape. Of course some differences do exist due to different bond lengths and the presence of the positive charge. The partition function, however, is determined primarily by the special configuration. Therefore, the assumption was made that methane data have application here. The rotational temperature for methane is the same for all three moments of inertia and equal to 7.47°K. The symmetry number is 12. The vibrational temperatures for the 9 vibrational modes (3.5 - 6) were deduced from spectral data (e.g., Sadtler Research Laboratories, 1967). The modes occurring at about 3.35 microns are known to possess 4-fold degeneracy due to stretching of each hydrogen bond. In addition, the mode at about 7.65 microns was assumed to possess 2-fold degeneracy due to the nature of the peaks in this region. The wave lengths selected appear in Table 9. 54 Table 9. Wave Lengths of Vibrational Modes for NH 4 + Wave Length (microns) Assumed Degeneracy Totals 2.38 None 1 3.35 4-fold 4 7.40 None 1 7.65 2-fold 2 15.00 None 1 Total 9 55 The wave length was converted to frequency by v = C/X (68) where v is frequency X is wave length C is the spread of light. The final form of q NH4 + can be written 27 M NH2 1- kT qNH +4 = v( h 9 3/2 17— 1. ' a 2• T3 exp[-G. /(2T)]/[1-exp(-O vi/T)] 7 1/2 0A0 C0 C (69) v.=1 where MNH4 + is the mass of NH4+ i varies from 1 to 9. Partition Function for NH2OH The translational and rotational partition functions for NH 2 OH have the same basic form as for any polyatomic molecule or ion. The mass of NH 2 OH was included in the translational part while a symmetry number of 3 was used in the rotational function. Since the rotational moments for NH 2 OH are difficult to determine, two rotational temperatures were assumed to be approximated by the rotational temperatures used for NH 4 + , and the third was assumed equal to the rotational temperature for 02. Here the basic assumptions were that the molecule has a configuration similar to a symmetrical top and the same symmetry number as NH3. 56 Since NH2OH contains five nuclei, the total number of vibrational energy modes would be 8 (not 9) because one mode (degree of freedom) is taken up by the reaction coordinate. The 8 vibrational wave lengths were deduced from the IR spectra for NH 2 OH.HC1 and HC1. The HC1 spectrum was used to eliminate the HC1 contribution from the NH OH.HC1 2 spectrum at about 3.5 microns. Remaining peaks were assumed to be due to NH 2 OH. A summary of the wave lengths for the 8 vibrational modes appears in Table 10. OH is The total partition function(a - -NH 2 OH ) for NH 2 ff 2M = V( cINH2OH NH OH 2 kT 3 3/2.57- h 2A ( T / ) 12 c 0 0-0 L. (70) 8 7 rexPNe/( 211 ) 1 v. v i ., where MNH2OH is /[ 1- exP (-0 vi1 T ) ] the mass of NH OH 2 i varies from 1 to 8. Partition Function for N 2 0 N20 is a linear molecule with the structure NNO. This means the symmetry number is equal to 1. The rotational temperature is about 2.42°K, and the 4 vibrational temperatures are 850, 850, 1840, and 3200°K. The usual translational partition function was applied (with N 2 0 mass) 57 Table 10. Wave Lengths of Vibrational Modes for NH 2 OH Wave Lengths (microns) Assumed Degeneracy Totals 3.4 None 1 4.4 None 1 5.5 None 1 6.4 None 1 6.8 None 1 7.2 None 1 8.4 None 1 8.7 None 1 Total 8 58 together with the rotational function for diatomic molecules (always used for linear molecules). Finally, the vibrational partition function for nonlinear molecules was used with one degree of vibrational freedom removed for the reaction coordinate. The total partition function (qN20 ) is 27 M N20 k T „ n )--)/ G , ciN 2QT = V( kfrvn uu r , (71) 3 H exp[ - O vi /(2T)]/[1-exp(-O vi /T)] V .=1 Partition Function for NO 2 The nitrite ion (NO 2 - ) has a v-shaped structure 0 similar to H20. The N-0 bond length is 1.24 A and the bond angle is 115°, Jolly (1964). This may be compared with a H-0 bond length of 0.96X and an angle of 104° for H 2 0. Because of these similarities and the availability of the partition function for water (e.g.,Hill, 1960), the assumption was made that (IN° - can be approximated by application 2 Since qN0 - was used as a partition function for of qH 20 ° 2 an activated complex, one vibrational degree of freedom was omitted to allow for the reaction coordinate. Values used for the various parameters contained in qrot and qvib for this polyatomic ion are presented in Table 11. 59 Table 11. Data for Rotational and Vibrational Partition Functions for NO2 Parameter 0 A Value e B rotational Units 3.941O 2.10.10 -39°K 1.37'10 1°K 0v 5.2810 3°K 1 . vibrational ev 5.43°10 3°K 2 a 60 The total partition function (c1NO2-) may be written 27 MNO2- kT - V( -NO 2- - 3/2 h2 47a ) 1/2 ( T3 0 A B 0C (72) 2 exp[-Ovi/(2T)]/[1-exp(-Ovi/T)] H v.=1 where MNO 2 - is the mass of NO 2 - i varies from 1 to 2. Comparison of Equation Forms and Activated Complexes To obtain some insight into the mechanisms governing the NHe oxidation process, various equation forms and activated complexes were applied to the experimental rate data from the Panoche and desert soils. Two promising equation forms for the equilibrium between the reactants and the activated complex are NH + + 1/2 02 4 (73) ACT* + 2NH 4 + + Q 2-17=7- ACT* + + H + (74) If ACT* in equation (73) is replaced with NH2OH, we have interthe familiar equation for the formation of the NH 2 OH mediate. Equation (74) was selected because it initially showed promising agreement with the experimental results. 61 Other equations were tried such as 2NH + + OH ACT* + H +(75) 4 + 02 —7 and equations that were even higher order with respect to NH 4 + and 0 2 but lacked the OH . These equations, however, - did not fit experiment as well as equations (73) and (74). Using equations (73) and (74), various activated complexes were applied to the experimental data. Both equations should have, in theory, yielded a linear relationship for the observed activation enrgy versus ionic strength. For example, equation (74) yields the following expression when concentrations in equation (35) are replaced with activities 2 1NH 4 (NH 4 +)2Y RATE = kT/h[q's] 02 (0 ) 2 (76) YACT* + YH + (H + ) exp (-Ac c /kT) where q's denotes the partition functions in equation (35) ( ) stands for concentration is the activity coefficient. Equation (76) reduces to (NH 4 71 ) 2 (0 2 )exp(K ra p) RATE = kT/h [q's] (H+) exp(- AE /kT) (77) c 62 when combined with equation (46). Also (NH 4 +) (0 2 ) 2 RATE = kT/h [q's] exp(-Acm/kT) (78) (H+) where Ac m is the measured activation energy per molecule at the ionic strength of the solution. At this point, equations (77) and (78) may be equated to give exp(Rm p) exp(-Ac c /kT) = exp (-Ac m /kT) (79) which reduces to Acm = Ac c - kT (80) The temperature effect can be ignored over a narrow temperature range (e.g.,the range encountered in this study) to yield As = As c - K s p (81) where K s is a constant Ac c is the activation energy per molecule at infinite dilution. Equation (81) may be rewritten as AE = AE c - sp (82) where AE andAE are activation energies expressed m c in Kcal/mole R s is a constant. 63 Any deviation from the linearity predicted by equation (82) indicated failure of the theory to fit experiment or experimental errors in the data. Since the same data set (Parshall and Gardena soils) was used for all combinations of equations and activated complexes, any changes in the goodness of fit of a regression of AE m on p indicated changes in agreement between theory and experiment. A summary of the activated complexes tried for each equation form and the corresponding statistics appears in Tables 12 through 15. In some cases partition functions for different activated complexes were multiplied together to simulate interactions between these functions. These cases are denoted by a dot between q subscript parts; each basic partition function being on either side. In general the R values and F ratios are higher for the application of equation (74) than for equation (73). Also, equation (74) yielded lower s y and Sb values. Equa- tion (74) appears to more nearly model the experimental data used here for the Panoche and desert soils. This means that a reaction between NH + and 0 to stoichiometrically form 4 2 NH 2 OH probably does not represent the equation form for the equilibrium between the reactants and the activated complex for NH 4 + oxidation to NO 2 -. The actual form of the equilibrium equation probably is closer to that represented by equation (74). ▪ • • + • N▪ • 64 Cd Ln N'e •:1) co 1/4.OHN,-IcoNN • • • • 1/4.0 h h 00010H •• COM NNCONNOlh a) o co rci Cd CU cn CO 44 -Q M LC) k..0N OCTIMN NO h h 0 h h d,NN • • • • OC\INNNNN'4ILI)L0 Cd -H Cd rd • 0 Q-4 0) H •0 Ln c, 1/4.0 C D CU (z)C CU c) H cs.) Cg pl r--1 0 H H CU H Ln Ln 4-) 4-1 O 0 N N 4-) O ▪ -P nzi niH u) -H -P -H W Q) rd 0 cd rd 0- t 0 -H 1- O 0 NZ 0+ NO Nd' • 0 N Z N Z Z • Z Z + Z O • • l' 1 I N d'•zt'• 0 00 NNN NNNNO 0 0 • Z Z OZ Z Z Z Z Z Z 01 01 01 01 01 01 01 01 01 01 • -P -H cd -H N M H h CO Ln 0 CO 01 Q N N 01 H N CO en M C51 hCO h h h h h Ln Ln Ln 0.) 04 H O) rd 1 0 Q) niP cd rd4-J Ul cd cdP • W 0 G) -P -P • U) -H -H WP >1 A 0 Z 4< r=4 • 0▪• 0▪ ▪• • • 0 65 Ln in CO 0 0 H N . . . . . . N 01 CO CO si, in H Ln H H H H •r, 1/1 H Cr% H ts::, H H tr) -Q lOr •;zr H in t.․) H H H H ts) H H H H c H 0 H H 0 0 H H O l0 Q O • •q• Cr) Q Ln h cs, co co c) Ln no Q N co LnH Ln Ln h co in in CO lO 01 01 0• 0 0 • 0 0 rn H cs) NH I-- •‘1,N •7r, ksD 01 CO 01 CO 00 01 01 0• 0 0 0 0 N 0 0 N ± ZN • + Z CD 0 0 0 + N d H H H co l9 l0 0 0 CD , Z z I "q' •7t' • 0 0 0 N NN NNO Z Z Z 0 Z Z Z Z 01 01 01 01 01 01 01 011 0 66 r0 0 H h h -P CO h C51 -H ni cl ni tr) 0 H cr Q 0 R4, • • OCOOONNN 124 H H (1) Ul H H H H H -P r=4 0 rd cl .-Q N N cr)C)cr)H N c V H N Ce) N Cr) h P 0 0 0 0 0 0 d, h cr) 111 1/4-0 MC) Cr) CO h h 0 0 0 cr) 0 0 ni 1/4.0 Crl U) h h in In C5) CO 0 01 CO Ln 0 0 0 0 '4' 1/49 Cl H CO CO •q, 0 0 H En 0 In Cl Cl Q H h 0 • • N 4-) -P >1 ni H (1) (f) 0 -H 4-) In N 1/49 1/49 N N N N N m H N N N 0 0 0 0 0 0 -4, c) H (1w tr)Ln Li) 0 0 U) (24 0 0 W O -H 0 -H 4-) ni tri 0 N Z • o 0 N Z 0-, + -,:t. Z 01 + :i , , Z 01 0 N 0 N Z • N 0 01 Z 0 N Z 01 • 0 N Z 01 E-1 0 NO + cP Z Z • 0 Z I N NO Z 01 N Z Z 01 I I N 0 Z tD1 N 0 Z 01 08 (1) -P 0 • Q• Q• Q• QQ• Q• ▪• 0 • 0 • QQ • + QQ• 67 Ln (n L.0 .41m •zr •71 0.) , H 0 .1., ks)• m H 0 H• N H N N N H N H N iflC51 H H H H H H 0 0 cs.) cr) d", 01 d^ 01 Ln ts) H H m vz, co H H H H H H re) .e Ln Ln 0 Ln 0 % - 0 0 1/4.0C cs1 • N k.c) co cr, • 0 Ln co 01 ln N N CO H In N dr, co 0 m L.oin Ln N ▪ 0 01 cp H H H N H N N co ce) tzr kOLn En Ln N r--- Ln O M 0 N0+ NO N d, • 0 N Z N Z Z Z Z • Z• I I I O + • N N N 0 0 0 N 't' 't' • NNNNO0 0 Z • Z Z 0 Z Z Z Z Z Z . 01 0101 01 01 01 01 01 01 01 68 The determination of the exact structure of the activated complex or the significant part(s) of the complex is an extremely difficult task. However, some insight may be gained by examining the values for the statistical parameters calculated for each hypothetical activated complex tried. Relatively poor agreement with experiment was obtained in the cases of the NO - and NO - related complexes. 2 2 Relative agreement with experiment occurred when application was made of theoretical models containing NH 4 -1- , NH 2 OH, and related activated complexes. The activated complex involved in NH 4 + oxidation to NO - probably is closer in structure to NH 2 4 and/or NH 2 OH than to NO 2 - . The true activated complex probably has a structure somewhere intermediate between NH + and 4 NH 2 OH. Future investigations centered around this type intermediate could reveal more structural details. The Rate Model Although certain other activated complexes showed promise ' a-NH OH and equation (74) were selected for the 2 rate model. qNH 011 was selected because NH OH is a known 2 2 intermediate in the nitrification pathway and because it yielded promising values for the statistical parameters evaluated in the regression analyses. Equation (74) was selected because of its consistently closer agreement with experiment for the various activated complexes. These 69 parameters were combined into the previously discussed rate theory to form the final rate model. Basic Assumptions To insure best use of the rate model, the basic assumptions inherent in it are listed below. 1. 2. (1 NH 2 OH is a satisfactory approximation of the true activated complex or active part of that complex. Equation (74) represents a satisfactory approximation of the equilibrium reaction between the reactants and the activated complex. 3. The population of Nitrosomonas is maximal and constant. 4. Nitrobacter is uninhibited, or if inhibited, NH 4 + oxidation to NO 2 modeled. In the first case, the model applies to the entire nitrification process. 5. Nitrosomonas is not inhibited by factors not consi- dered in the model (e.g., sufficient phosphorus and carbon are present.) 6. Any missing part(s) of the activated complex either contribute insignificantly to the rate process or contribute in a constant manner. 7. The enzyme system and activated complex are unaffected by environmental factors such as temperature, moisture content, and pH. 70 8. A linear relationship (as predicted by theory) exists between AE 9. 10. m and p. The soil is calcareous. The NH 4 +, 0 2 1 and H+ activities used in the model are proportional to the localized activities at the active sites. 11. HI remains below the saturation level (if one ex- ists at measurable reaction rates). 12. Activities of saturation values vary with ionic strength while concentrations are independent of the same. 13. The saturation concentration for N soil. 14. The saturation concentration for 0 , is 1.0 pg/g NH 4 -r 2 is 0.25 3Jg/m1 water. 15. Saturation values are independent of temperature. 16. The assumptions used to derive the partition functions used in the model are valid. 17. The reaction rate is unaffected by changes in hydrostatic pressure. 18. The reaction rate is unaffected by changes in di- electric constant. Computer Program Since many of the computations involved in the rate model are tedious and time consuming, the rate function was 71 programmed in FORTRAN IV computer language for C.D.C. 6000 series machines. The calculations involved in the development of the rate model were similarly programmed. A block diagram of the final nitrification rate subroutine appears in Figure 3. A complete FORTRAN listing of this subroutine and the program used to develop the rate model appears in Appendices A and B, respectively. Application of Nitrification Rate Model to Panoche and Desert Soils Plots of measured activation energy (AE) versus ionic strength for the Panoche and desert soils appear in Figure 4. These data were obtained using the rate model just described. Neither the Y-intercepts nor the slopes of the best-fit regression lines through these data sets agree closely. Still different Y-intercepts and slopes were obtained for the Northern Plains soils used in the verification procedure described later. Intercept differences may reflect differences in maximal population sizes. Soils with different size populations of Nitrosomonas would be expected to exhibit different values for the activation energy at infinite dilution (AB). Differences in slope are more difficult to resolve, but may reflect variations in local populations of nitrifiers. For example, Nitrosomonas subspecies from desert regions might be expected to be more tolerant of lower moisture contents and resulting higher ionic strengths. This appears to 72 I N PUT EXCHANGEABLE NH TEMPERATURE ION IC STRENGTH MOISTURE CONTENT Ca ++ COMPUTE COMBINE PARTITION 0 2 CONCENTRATION FUNCTIONS PARTITION FUNCTIONS AN D CONCENTRATIONS —> COMPUTE PH AE m RATE RETURN TO CALLING PROGRAM Figure 3. Block Diagram of Computerized Rate Subroutine. 73 00 o o o 0 o (alow /lop >i) u-I 2 74 be the case with the native desert soil, since it has a lower slope than the Panoche soil from California. Also, various other researches (e.g.,Quastel and Scholefield, 1951) have noted that populations of nitrifiers do not all display the same nitrifying capacities. Since Nitrosomonas must depend on NHe oxidation for its sole energy source and therefore its survival, it is easy to imagine the strong adaptive influences of environmental conditions on the process. Even with local variations, however, Nitrosomonas appears to display characteristics which can be described by the theory previously discussed. A linear relationship between AE and p appears to hold regardless of local population variations. To gain some appreciation for the predictive capabilities of the rate model as applied to the Panoche and desert soils, rates were computed based on the input data used to develop the model. Although the model would be expected to fit this data with a reasonable degree of accuracy, a comparison of observed and calculated rates could indicate the potential of the model. The resulting statistics from a data pairing of 51 pairs of nitrification rate data from the Panoche and desert soils appears in Table 16. 75 Table 16. Statistical Data from Pairing Calculated and Observed Rates for the Panoche and Desert Soils Parameter Value* 0.956 Y 1.04 Y-intercept -0.438 1.19 F ratio *Rates expressed in ppm/day 540. 76 Additional Verification of Nitrification Rate Model To further verify the theoretical rate model, data for two Northern Plains soils were taken from the litera- ture (Reichman et al., 1966). Nitrification rate data were available for a temperature of 28°C and moisture contents ranging from about 0.2 to 50 bars suction. Assuming the previously determined linear relationship between AE m and p, the following regression equations were derived for the Parshall and Gardena soils (Parshall) AE m = 50.8 + 48.7p (Gardena) AE m = 49.8 + 8.57p (83) (84) where the Y-intercept (AE c ) is the activation energy at infinite dilution. Ionic strength was determined using the Dutt Model (e.g, Dutt et al., 1972). Equations (83) and (84) were used in the theoretical rate model together with the other necessary data to calcu- late predicted nitrification rates and NNo 3 - concentrations with time. A summary of calculated and observed nitrification rates appears in Table 17. Data pairing of the rates presented in Table 18. " 77 Table 17. Calculated and Observed Nitrification Rates for the Parshall and Gardena Soils Soil Rate (ppm/10 days) Observed Calculated Parshall 3.45 3.39 3.26 3.00 10.1 8.71 5.92 0.324 15.7 13.7 9.63 1.51 5.43 4.82 3.52 3.02 9.42 7.25 3.31 0.392 20.9 14.6 7.76 1.03 Gardena 16.3 13.4 7.57 14.4 12.3 8.09 20.9 17.2 9.69 30.5 25.1 14.3 13.4 11.4 6.79 15.7 13.0 10.2 22.5 19.5 12.9 27.6 21.0 12.8 78 Table 18. Statistical Data from Pairing Calculated and Observed Nitrification Rates for Parshall and Gardena Soils Soil Parameter Parshall Value 0.944 Y 2.066 1.13 Y-intercept F ratio Gardena -0.629 81.5 0.940 Y 2.14 0.812 Y-intercept F ratio 2.72 74.4 79 Plots of calculated and observed NNO 3 - concentrations as a function of moisture content appear in Figures 5 through 9. These data were based on the rates in Table 17. The following assumptions and approximations were used in making the verification runs on the Parshall and Gardena soils. 1. The assumptions already mentioned with respect to the model were assumed to hold in this case. 2. The assumption was made that NO 2 - oxidation is faster than NH 3. oxidation. 4 In calculating the distribution of NH 4 + between soluble and exchangeable forms, the NH 4- - Na l- exchange 4 constant was set equal to 0.22; a mean value for several soils and used in the current version of the model developed by Dutt, Shaffer, and Moore (1972). 4. The slope of equation (59) was set equal to the best-fit value of 1.68 determined by Dutt et al. (1972). The Y-intercept values in the same equa- tion were determined from experimental and calculated data using the method previously discussed. 5. Additional data for the soil extract analyses needed to approximate ionic strengths and partition the total N into exchangeable and soluble fractions NH4 were obtained from the data of Reichman et al. 80 OD 0 (b/6 n) 2_0 fl N 44° 81 0 II co N K) 0.) 0 1 1N 0 CD ('J CV 1- - (6/6n )0N N co sr 82 00 al -I-) Ci MI N 0) tp -r-i ri-, o co ef C\1 C\J (6/6n) 2 0 N - N o cv (.0 C\I ^ - 83 OD 0 cf'4' (0 1,0 o.) ro (6/6n) ON N OD N cf 0 Cg 84 0.) Z:7) -H F1-4 0 to to co .çr 0 (6/f5n) 2 0 N N re) CO tf) 85 (1966), see Table 2, and from data on soils with similar chemical properties. A summary of these estimates appears in Table 19. 6. The saturation constant for NN H4 was set equal to 5.0 ppm for the Parshall soil and 1.2 ppm (McLaren, 1970) for the Gardena soil. The 5.0 value was based on a regression study of measured activation energy (AEm ) versus at various as- sumed saturation levels for NNH4+. The results of this study appear in Tables 20 and 21. 7. Reichman et al. (1966) listed initial pH and pH values for the two soils after 20 days incubation at 0.2 bar suction. Other needed pH values were estimated from these values plus the assumption that pH changes were proportional to the reaction rate. 86 Table 19. Estimated Soil Extract Analyses Used in Verification of Nitrification Model Parameter Composition of Saturation Extract Parshall Gardena meq/L meq/L CA 3.61 mg++ 1.58 3.01 Na + 0.84 1.60 HCO 3 - 1.82 3.47 CO3= 0.00 0.00 Cl - 0.61 1.16 SO 4 = 1.46 2.79 87 Table 20. Statistical Data for N NH4 1- Saturation Values in Parshall Soil Saturation Value (Pg NNH 4 1- /g soil) sY Sb F ratio 15.0 0.00361 0.542 23.3 0.001 10.0 0.178 0.346 14.9 0.329 8.0 0.358 0.240 10.3 1.21 5.0 0.756 0.155 6.67 4.0 0.684 0.468 8.97 3.0 0.626 0.268 11.5 6.45 2.0 0.626 0.268 11.5 6.45 1.0 0.626 0.268 11.5 6.45 13.3 8.78 88 Table 21. Statistical Data for N NH4 Saturation Values in Gardena Soil Saturation Value N 4 4- /g soil) Sy sb F ratio 15.0 0.00730 0.454 81.9 0.001 10.0 0.221 0.253 45.7 0.512 8.0 0.321 0.174 31.5 1.15 5.0 0.465 0.113 20.5 2.76 4.0 0.465 0.113 20.5 2.76 3.0 0.465 0.113 20.5 2.76 2.0 0.465 0.113 20.5 2.76 1.0 0.465 0.113 20.5 2.76 SUMMARY AND CONCLUSIONS The objective of this study was the development of a transition state model to predict nitrification (nitrate formation) or (NH4 + -4- NO 3 - ) in soil-water systems. An incubation study involving two soils provided rate data as a function of temperature, moisture content, pH, and N NH4 concentration. The assumption was made that the 0 2 concentration remained above the saturation level and could be treated as a constant in the equations. Application of this data confirmed observations of other researchers that NNH4 + oxidation is zero order with respect to NNH 4 + concentrations above a saturation level of about 1.0 to 5.0 ppm. A computer model was tested to determine its ability to describe NH4 4- exchange in these same soils. This model gave satisfactory predictions below about 20 to 40 percent moisture but needs improvement at higher moistures. The model was used to compute exchangeable NH 4 + concentrations in this study since the moisture contents were relatively low. A method was developed to compute soil pH values as a function of moisture content. An existing semi-empirical relationship was modified to include H I- . The assumption was made that the slope in the relationship remains relatively 89 90 constant, but the intercept value shifts when H I- is added to the soil-water system. Data pairing of calculated and observed pH values yielded correlation coefficients of 0.987 and 0.980 for the Panoche and desert soils, respec- tively. The incubation data were used to attempt to learn something about the structure of the activated complex in NH 4 oxidation to NO 2 -The conclusion was made that the complex or active part of the complex has a structure closer to NH 2 OH or NH 4 + than NO 2 - . Also, the equation form for the equilibrium between NH 4 -1- and 02 and the activated complex was investigated. The form was found to differ from the stoichiometric reaction between NH 4 + and 02 to form NH OH. 2 The model developed included NH 2 OH as the activated complex and equation (74) as being representative of the equilibrium between the reactants and activated complex. A theoretical linear relationship between the measured activation energy and ionic strength was included in the model. The slope and intercept in this expression were calculated from experimental data for each soil. The linearity was found to be independent of soil, but microbial population sizes and other variations probably account for the different intercepts and slopes, respectively, encountered experimentally. 91 The model was applied to the Panoche and desert soils and yielded an R value of 0.956 for data pairing of 51 observed and calculated rates. Additional verification of the model was obtained by application to two soils from the Northern Great Plains. Data pairing of observed and calculated rate data showed R values of 0.944 and 0.940 for the Parshall and Gardena soils, respectively. The model was programmed in FORTRAN IV computer language. This allowed the computations to be done easily and provided a simple means of connecting this model to existing or future simulation models. The nitrification rate predictions from the model should have application in optimization research, environmental impact studies, and soil fertility and plant nutrition. APPENDIX A COMPUTER LISTING OF RATE SUBROUTINE 92 93 SUBROUTINE NITR(ANH4,TEMP,AMOIS,UU,CA,RATE) THIS SUBROUTINE COMPUTES NITRIFICATION RATES BASED ON A TRANSITION STATE PHYSICOCHEMICAL MODEL SLOPE,AINT, AND DELTAE1(U) MUST BE SPECIFIED FOR EACH 0 0 SOIL DIMENSION VTHA(8) PEAL K ,K0 COMMON/A/ HIK,RI,SORTPI DATA (K0=3.0E..<3),(V=1.E18) DATA (H=66625&-27),(K=1.380E16),(P1=3.142),(SORTPI=1. 1777) DATA (RTA=7.47),(RT0=2.07) 9 (D00=8.138E...12),(00A=8.138E 1°12) DATA (VT0=2023E3)0VT1A=6.11151E7),(VT2A4.299E3),(VT3A= 11.933E7) DATA (VT4A=/,883E3),(VT5A=9.601E2),(0M=5.312E23),(AM= 12.93PE-..23) DATA (VTHA(1)=.7.4L."i),(VTHAt2)=4.4E...-4),(VTHA(3)=5e5E4 1),(VTHA(4)= 16 6 4E..-4),(VTHA(5)=6.8E),(VTHA(6)=7.2E4),(VTHA(7)8.4 1E...4),(VTHA(8)=8.7E.'..4) THESE CONSTANTS MUST PE SPECIFIED FOR EACH SOIL DATA(SLOPE=1.6i),(AINT=4.460) .C.FUNCTION FOR 0 VIBRATIONAL OVIBP(T,VT) =EXP(....VT/(2. 4. T))/T1e-..EXP(....VT/T)) FUNCTION FOR 0 ROTATIONAL DIATOMIC MOLECULE OPOTO(T,SYM,RT) = T/(SYM*RT) FUNCTION FOR DERYE—HUCKEL ACTIVITY COEF ACT(U) = 1./(10.**(+0.509*U/(1.3 + 1.em») C-----FUNCTION FOR ACTIVATION ENERGY AS A FUNCTION OF IONIC STRENGTH THIS FUNCTION MUST BE SPECIFIED FOR EACH DELTAEl(U) = (40.7P + 0.6495*U)/1.439E13 SOIL BEGIN CALCULATIONS CALL SUBROUTINE TO COMPUTE PH AT FIELD MOISTURE CALL PHCALC(CA I AMOIS,SLOPE,AINT9PH ) 94 COMPUTE VIBRATIONAL TEMPERATURES FOR NH2OH 00 3 1=1,8 3 VTHA(I) = 3.0E10/VTHA(I)*H/K SET UPPER LIMIT FOR EXCHANGEABLE NH4 CONCENTRATION IF(CNH4 .GT.1.) CNH4 = 1.0 CONVERT = 0.4976E12/AMOIS CTEMP = TEMP T = TEMP 4- 273. 020 = PPH02(0TEMP) SET UPPER LIMIT FOR OXYGEN CONCENTRATION 020 = 0.25 COMPUTE 0 VIBRATIONAL FOR HYDROXYLAMINE OVIE1HA = 1.0 00 2 1=1,8 OVIBHA = OVIBHA * OVIBP(T,VTHA(I)) 2 CONVERT UNITS TO NUMBER OF MOLECULES/ UNIT VOLUME CH = 10.**(-PH)*6.02E21/ACT(SORT(UU)) CNH4 = CNH4*4.30E16/AMOIS 02 0 = 02C*1.881E16 COMPUTE 0 TOTAL FOR OXYGEN 002 = OTRAN(T 7 V 1 0M) * OPOTO(T,20,RTO) * OVI3P(T,VTO) COMPUTE 0 VIBRATIONAL FOR NH4 OVIBA = 0VIBP(T,VT1A)*OVIBP(T,VT2A)**4 * OVIPP(T.VT3A) i*OVIBP(TOT4A)**2 * OVIBP(T,VT5A) COMPUTE TOTAL 0 FOR NH4 ONH4 = OTRAN(T9V ,AM) * OPOTP(T 1A 7 12.1RTA,RTA,RTA) *OVIB COMPUTE TOTAL 0 FOR HYDROGEN OH = QTRAN(T,V,1.66E-24) COMPUTE TOTAL 0 FOR ACTIVATED COMPLEX(NH2OH) OHA=OTRAN(T,V 9 0M*1.03)*OROTP(T,7.,RTA,FTA,RTO )* OVIBM lA COMPUTE DELTA E DELE = DELTAF1(UU) COMPUTE PART OF RATE FUNCTION X = EXP(DELE/(KT))*DHA 95 Ç CALL SUBROUTINE TO COMBINE PARTITION FUNCTIONS AND CONCENTRATIONS CALL COMP(V9OH,CNH4,020,0NH4,002,0H,T,SUB) COMPUTE PATE PATE = X*SUB CONVERT UNITS ON RATE TO UG/G SOIL/DAY RATE = RATE/CONVERT RETURN TO SUBROUTINE TRNSFH OR CALLING ROUTINE RETURN ENO FUNCTION OROTP ( T,SYM,THA,THR,THC) THIS FUNCTION COMPUTES 0 ROTATIONAL FOR A POLYATOMIC MOLECULE COMMON/A/ H,K,PI,SORTRI OROTP = SOPTPI / SYM*SORT(T**3/(THA*THB*THC)) RETUPN END FUNCTION 1TRAN(T 9 V,M) THIS FUNCTION COMPUTES 0 TRANSLATIONAL REAL K9M COMMON/A/ H,K,PI,SORTPI OTRAN = V*<SOPT(6.28*M*K*T/(H"2)))**3 TUPN END SUBROUTINE COMP(V 9 OH,CNH4,020,QNH4,002pCH,79SUB) THIS SUBROUTINE COMBINES PARTITION FUNCTIONS AND CON- OENTP,ATIONS COMMON/A/ H I K,PI,SORTPI' PEAL K BEGIN CALCULATIONS PART' = K*T/(V*H1 * CNH4**2 * 02C PART? = (QH/V) PART = (ONH4/V)**2*(002/V) * CH SUB = PARTi*PART2/PAPT3 o RETURN TO SUBROUTINE NITR PETUPN END SUBROUTINE PHCALC(CA,AmOIS,SLOPE,AINT9PH) HIS SUBROUTINL COMPUTES PH AS A FUNCTION OF MOISTURE T 96 CONTENT REAL KDP,KP,KSP,K3 DATAfKSP=5.012E-9),(K3=5.012E-11) BEGIN CALCULATIONS AMOIS = AMOIS*110. KP = 10.**(SLOPL:*ALOG10(AMOIS) - AINT) KOP = KP*K3**2/KSP**2 H = SORT(KDP*CA) PH = -ALOG10(H) RETURN TO SUBROUTINE NITR RETURN FND APPENDIX B COMPUTER LISTING OF GENERAL COMPUTATIONAL PROGRAM 97 98 PROGRAM RATF(INPUT.OUTPUT.TAFE1=INPUT,PUNCH) DIMENSION TEMP(99),02C(99).CNH4(99).RATE(99).PH199),CH 1(99).VTHA(9) 1.UU(99).AMOIS(99).RNH4(99).CONVERT(99),OHC(99).ORS(99) 1,CA(99) REAL K .KD COMMON/A/ H.K.PIISORTPI DATA (KD=3.0E°.3).(V=1.E-18) DATA (H=6.625E°27).(K=1.380F...16),(PI=3.142),(SORTPI=1. 1773) DATA (RTA=7.47),(RT0=2.07),(D00=8.138E12),(00A=8.13E 1.12) DATA (VT0=2.23E3),(VT1A=6.051E3),IVT2A=4.299E3),(VT3A= 11.933E3) DATA (VT4A=1.3E3),(VT5A=9.631E2),(0M=5.312E23),(AM= 12.988E-23) DATA (VTHA(1)=3.4F4),(VTHA(2)=4.4E4),(VTHA(3)=5.5E ....4 1),(VTHA(4)=6.4E-4).(VTHA15)=6.8E4).(VTHA( 6 )= 7 . 2 E"+ ) . ( 1VTHA(7)=8.4E..-4),(VTHA(5)=807E4),(VTHA(9)=10.0E ."+) DATA(OC = 0.132) FUNCTION FOR 0 VIRRATIONAL OVIRP(T.VT) =EXP(—VT/(2. 4( T))/(1....EXP(VT/T)) 0 FUNCTION FOR 0 ROTATIONAL DIATOMIC MOLECULE OPOTD(T,SYX.RT) = T/(SYM*RT) FUNCTION FOP DERYE—HUCKEL ACTIVITY COEF ACT(U) = 1e/(10.**(1-0.509*U/(1.0 4 1.00*U))) FUNCTION FOR 02 CONCENTFATION IN WATER AS A FUNCTION OF TEMPERATURE PPMO2(T) = 14.619 15E•.. 5 *T 4. *3 0.403964IT 8.7996E*3*T**2 8.991 FUNCTIONS FOR DELTA E AS A FUNCTION OF IONIC STRENGTH DELTAEl(U) = (49.390 4 29.262*U)/1.439E13 DELTAE2(U) = 3 (50.554 4.4562*U)/1.439E13 REGIN CALCULATIONS III = DO 3 I=1.8 VTHA(I) = 3.0F10/VTHA(I)*H/K IPUNM = READ SLOPE AND MOISTURE AT WHICH PH WAS DETERMINED 99 600 READ 110, SLOPE, AAMOIS DELE = 0.0 SAVE = 1.0 ITEST = 1 J1=ICON=0 PRINT 116 DO 54 J=1,100 READ RATE, NH4, R- NHL, PH, IONIC STRENGTH, AND TEMP., MOISTURE CONTENT, CA ACTIVITY READ 100, RATE(J),ONH4(J),RNH4(J1,PH(J),UU(J),TEMP(J), iAMOIS(J),AOA(J) 66 IF(E0F,1)99,66 III = III + 1 IF(RATE(J).E000,)) GO 70 53 J1=J1+1 CALL SUBROUTINE TO COMPUTE PH CALL PHCALC(CA(J),PH(J),AMOIS(J),1,SLOPE,AOA,AAMOIS) OBSfJ) = RATE(J) RNH4(J) CNH4(J) = IF(CNH4(J),GT01.) ONH6(J) = 1.0 SET CONVERSION FACTOR CONVERT(J) = 0.4976E12/AMOIS(J) CTEMP = TEMP(J) - 273. 02C(J) = 0,25 CONTINUE 54 53 6 PRINT INPUT AND OTHER DATA PRINT 105,(RATE(J),CNH4(J)102C(J),TEMP(J),PH(J),J= 1 ,J 1 1) DO 1 J=1,J1 T = TEMP(J) COMPUTE 0 VIRRATIONAL FOR HYDROXYLAMINE OVIBHA = 1.0 DO 2 I=10 OVIBHA = OVIRHA * OVIRP(T,VTHA(I)) 2 CONVERT UNITS TO NO. OF MOLECULES/UNIT VOLDAE /AOT(SQRT(UU(J) CH(J) = 10/11.**(PH(J)) * 6.02E20 CNH4(J) = ONH4(J)*.3CE16/AMOIS(J) 02 0 (J) = 02C(J)*1.8B1E16 RATE(J) = RATE(J) * CONV 7LPT(J) OHO(J) = 10E-14/(10/10.**(PH(J))) COMPUTE 0 TOTAL FOR OXYr,EN 100 002 = OTPAN(T,V ,OM) * OR0TDtT,2.,RTO) * OVIRP(T,VTO) PARTITION FUNCTION FOR OH 00H=0TRAN(T,VIOM*.531)*OROTD(T,1.,RTO)*OVIBP(TOTO) COMPUTE 0 VIBRATIONAL FOR NH4 OVIBA = OVIBP(T,VT1A) 4 QVI6P(T,VT2A)**4 * OVIEP(T,VT3A) 1*OVIBP(TOT4A)**2*OVIPP(TOT5A) COMPUTE TOTAL Q FOR NH4 0 ONH4 = OTRAN(T,V ,AM) * OROTP(T,12.,RTA,RTA,RTA) *OVIB 1A COMPUTE TOTAL 0 FOR HYDROGEN OH = OTRAN(T,V,1.66E24) COMPUTE TOTAL 0 FOR HYDROXYLAMINE 0HA=OTRAN(T,V,OM*1.07)*OPOTP(Tp7.,R7A,RTA,PTO)*OVIBH lA O ROTATIONAL FOR N20 ORN20 = OROTO(T,1.,202) 0 VIBRATIONAL FOR N20 OVN20 = CIVI3P(T,85.0.)**2 10.) * OVIBP(7,184rj.)*QVIBP(T,323 0 TRANSLATIONAL FOR N20 OTRN20 = OTRAN(T,V,0M*1$38) TOTAL.0 FOR N20 0 N20 = ORN20*OVN20*OTRN20 XXX = ()HA 700 701 0 IF(ITEST.EQ.1)700,701 IF(III.E0.1) DFLE = DELTAE1(UU(J)) IF(III.E0.2) DELL = OELTAE2(UUTJ)) CONTINUE ICON = 1 X = EXP(•..DELE/(K*T))*XXX CALL SUBROUTINE 70 COMBINE PARTITION FUNCTIONS CALL HYAMINFAV,QH 2 ONH4(J),02C(J),0NH 4 ,002,OH ( J ) ,RATE 1),X,T,ICON,00H2OHC(J)) IF(ICON.E0.1) GO TO 7 0 COMPUTE DELTA E DELE = •“ALOG(X) ...ALO( .(XXX ))*(K*T) SAVE = SAVE -4- DELE 7 PATE(J) = RATE(J) / CONVERT(J) IF(ICON.E0.1) DELE = PELE*1.439E13 *1.439E13 (,) 101 SOION = UU(J) PRINT RESULTS PRINT 131,0BS(J)IPATF(J),TEMP(J),PH(J),SOION,DELE,OHA, 10NH4,002 IF(IPUNM,E0.1) GO TO 600 STOP IF(ICON.E0.1) GO TO 603 COMPUTE MEAN ACTIVATION ENEPGY DFLE = SAVF/(J1*1.439E13) ICON = 1 99 ACTIV = SAVE/J1 GO TO 6 STOP 100 101 FORMAT(BF10,0) FORMAT(5Y,6F10,4,3E15.3) 105 106 109 800 FOkMAT(5F10,2) FOPMAT(1H1,*PAPPM/04)*2X*NH4(PPM)*3X*02(PPM)*3X 1*TEHP(K) 4 8X*PH 4 ) FOPMAT(5F10,4) .FORmAT(///1X*AOTIVATION ENERGY = * ,, F10,3) END FUNCTION OROTP(T,SYM,THA,THR,THO) THIS FUNCTION COMPUTES 0 ROTATIONAL FOP POLYATOMIC MOLECULES COMMON/A/ H,K,PT,SORTPI OROTR = SQPTPI / Srl*SORT(T**3/(THA*THB*THC)) RETURN END FUNCTION OTRAN(T,V,M) THIS FUNCTION COMPUTES 0 TRANSLATIONAL REAL K,M COMMON/A/ H,K,RI,SORTPT OTPAN = V*(SORT(6423 RETURN END SUBROUTINE HYAMINE(V 11,001-1,0HO) **3 4- M*KT/(H**2))) I OH,CNH4,02CONH4,002,0HIRATE,Y,T, THIS SUBROUTINE COMBINES THE PARTITION FUNCTIONS 102 COMMON/A/ HO< PI,SORTPI REAL K BEGIN CALCULATIONS 1 PAPT1 = K*T/(V*H) PART2 = (OH/V) * CNH4**2 4 02C PART3 = (QNH4/V)**2*(002/V) * CH IF(I.E0.1) GO TO 1 X = RATE/(PART1 * PART2/PART3) RETUPN CONTINUE RATE = X * (PART/ * PART2/PART3) PETUPN ENO SUBROUTINE PHCALC(CA,PH,AMOIStICOUNT,SLOPE.AOA,AAMOIS) 0 THIS SUBROUTINE COMPUTES PH AS A FUNCTION OF MOISTURE CONTENT PEAL KOP,KP,KSP,K3 OATA(KSP=5.0125*°90,(K3=5.012E11) BEGIN CALCULATIONS 1 BBMOIS = AAMOIS*100. RMOIS = AMOIS*1000 KOP = (104**(..4)H))**2/ACA KP = KOP*KSP**2/K3**2 AINT = SLOPP*ALOG1(2(BBHOIS).... ALOG10(KP) AINT) KP = 100**(SLOPE*ALOG10(RMOIS) KOP = KP*K3**2/KSP**2 H = SQRT(KOP*CA) PH = ALOG10(H) RETURN END APPENDIX C DATA COLLECTED IN INCUBATION STUDY 103 104 IDENT COL. COL. 3•..4 COL. 5.•.6 02 PANOCHE SOIL 11 = DESERT SOIL TIME IN DAYS TEMPERATURE IN DEGPEES C NH4 AMMONIUM N (UG/G SOIL) NO3 NITRATE N MOIS MOISTURE CONTENT (G WATER/G AIR DRY SOIL 'DENT 020015 92 015 021415 021415 022815 022815 024615 024615 026015 026015 120015 020015 021415 322815 022815 026015 021415 021415 322815 022815 026015 026015 02025 02 0025 021125 022525 022525 023925 027925 025325 u25325 021125 J21125 022525 023925 PH 8.32 8.31 8.20 8.32 8.20 8.20 8.26 8.30 8.75 8.30 8.40 8.36 8.25 8.25 8,25 8.50 8.26 8.28 8.70 8.73 8.50 8.49 8.28 8.33 8.10 8.09 8.08 8.29 8.27 8,48 8.41 8.25 8.25 8.30 8.41 NITRITE N (UG/G SOIL) NH4 132.7 127.4 126.9 81.6 92.4 76.4 22.9 49.6 53.4 23.1 127.3 129.9 148.6 143.0 150.1 136.8 122.2 155.2 146.2 154.7 147.7 146.2 175.6 177.6 92.9 10.7 4.0 4.6 4.5 2.3 4.5 133.4 172.4 120.8 141.5 NO3 19.9 19.6 74.2 92.1 154.7 176.7 301.1 235.3 226.1 285.7 16.6 13.2 24.3 29,1 34.3 33.2 13.4 9,2 11.6 14.8 15.6 15.6 11.4 13.7 85.3 266.1 282.9 381.1 376.3 769.7 370.9 9.4 8.4 10.4 12.3 MOIS .096 .098 .095 .094 .074 .088 .082 .066 6057 .064 .076 .069 .068 .064 .053 .045 .058 .053 .048 .055 .057 .044 .126 .128 .120 .104 .118 .108 .099 .109 .093 .063 .061 .054 .058 105 023925 025325 020025 021125 021125 027925 023925 025325 020075 020375 021135 021175 022535 927935 025335 021135 021135 022535 022575 023935 023935 025335 025335 326035 020035 021135 021135 022535 922535 027935 023935 025335 025335 011415 011415 012815 012815 014615 014615 016015 016 015 010015 010015 0 11415 011415 010015 910015 611415 311415 012815 8.48 8,65 8.24 8.73 8.25 8,40 8.41 8.60 8.32 8.25 8,25 8.28 8.30 8.40 8.50 8.30 8.30 8.28 8.35 8.45 8.43 8.58 8.55 8.36 8.38 8.26 8,71 8,35 8.30 8,75 8.43 8.58 8.60 6.63 6.70 6.45 6.60 6.33 6.38 6.41 6.43 6.65 6.85 6.84 6.90 6.80 6,65 6.84 6.72 6,75 157,2 11609 172.,, 134,5 129.1 150.0 145,6 123.4 174.1 161.8 149.4 148.1 108.6 146.4 129.6 151.0 155. 8 118.0 117.5 157.3 154.1 139.5 152.9 172.1 175.2 158.3 162.7 119.5 115.0 157.9 157.3 151.5 143.7 159.3 163.2 165.9 151.9 157.5 1 65.4 142.3 144.3 92.7 174.8 159.2 159.1 156.7 155.4 146.2 153.5 141.4 13.9 12.3 12.0 11.7 11.4 13.1 12.3 12.4 13.0 13.1 23.6 21.6 16.2 15.9 16.2 17.1 17.8 3.8 13.3 11.3 11.5 1. 0 .6 7.2 11.7 13.1 17.9 15.2 11.9 7.6 10.4 9.2 13.4 10.1 117.1 114.8 112.1 131.7 130.1 122.5 142.1 141.0 101.4 112.7 126.8 125.9 112.6 116.7 121.2 114.1 176.5 .045 .048 .056 .041 .057 .050 .046 .058 .122 . 1 21 .049 .043 .017 .015 .014 .031 .033 .017 .016 .016 .013 .015 .013 .060 .053 .034 .031 .016 .017 .014 .016 .013 .014 . 1 36 .100 .121 .102 .111 .123 .084 .078 .035 .049 .039 .036 .034 .038 .028 .027 .034 106 . 012815 016615 311125 011125 012525 012525 0179 2 5 013925 015325 015325 011125 011125 012525 012525 013325 013925 015325 015325 010925 013025 011125 012525 012525 013925 015325 015325 010035 010035 011135 011135 .012535 012535 013935 017935 315375 015335 1 13035 010335 U11135 011135 012535 012535 017975 013975 015335 010935 010035 0 11/35 012535 012535 6.65 6.65 6.40 6.60 6.68 6.48 6.55 6.45 6,55 6,43 6.58 6.82 6,80 6.70 6,80 6.39 6.72 6,8e - 6.95 6.95 6.62 6.95 6.95 7.00 7.12 7.08 6.69 6.75 6.42 6,37 6.78 6.69 6.69 6.76 6.55 6.62 6.70 6.95 6.69 6.80 6 0 80 6.73 6.82 6.80 6.75 6,65 6,49 6.39 6.52 6.53 151.4 148,7 112.3 111.1 147.2 143.6 142.6 134.2 132.3 135.9 114.9 120.8 117.8 147.0 148.5 145.1 1 43.5 164.4 123,4 145.5 155.9 89.6 162.5 171.2 167.0 163.0 114.5 112.0 153.2 143.4 142.4 139.8 133.6 137.8 177.5 140.5 95.0 116.0 152.9 151.1 1 41.6 150.8 143.0 152.5 140.5 106.9 109.3 141.1 133.4 146.7 124.3 137.5 111.6 117.7 117.0 146.9 14700 165.3 165.4 169.9 83.6 92.0 106.7 135.0 161.4 132.9 134,6 137.3 87.9 69.1 95.7 1.06.1 93.5 103.2 111.0 107.3 103.5 110,3 133.2 138.6 131.5 147.9 153.6 139.1 146.9 141.0 87.2 92.6 106.1 113.6 103.6 123.6 19.5 116.7 114.2 123.5 103.6 155.2 155.8 153.4 .331 .016 .087 .067 .063 .063 .064 .050 .034 .065 .026 .040 .043 .026 .050 .022 .022 .052 .030 .031 .018 .022 .030 .033 .033 .025 .018 .017 .090 .086 .010 .009 .011 *010 .025 .009 .U14 .014 .331 .027 .008 .043 .008 .007 .007 .019 .016 .023 .010 .310 107 O 13935 D13935 015335 015335 6.80' 6.60 6.60 6.45 144.4 145.0 129.7 148.1 146.5 135.1 158.8 143.5 .011 .010 .01U .009 LITERATURE CITED Alexander, M. 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