A TRANSITION STATE PHYSICOCHEMICAL MODEL PREDICTING NITRIFICATION RATES IN SOIL-WATER SYSTEMS by

A TRANSITION STATE PHYSICOCHEMICAL MODEL PREDICTING NITRIFICATION RATES IN SOIL-WATER SYSTEMS by
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).
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64
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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
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