Geophysical Research Letters
Supporting Information for
Nitrogen isotope exchange between NO and NO2 and its implications for δ15N variations in
tropospheric NOx and atmospheric nitrate
Wendell W. Walters*†, Damian S. Simonini‡, and Greg Michalski†‡
†Department
of Earth, Atmospheric, and Planetary Sciences Purdue University, 550 Stadium Mall Drive, West
Lafayette, IN 47907, United States
‡Department
of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, IN 47907, United States
Contents of this file
I.
N2O4 and N2O3 Equilibrium Calculations .......................................................... 2-3
a. Text .........................................................................................................2
b. NO + NO2 ↔ N2O3 Kp Fit (Figure S1) ....................................................3
II. Summary of Experimental Data 3
a. Appendix Table (Table S1) .......................................................................3
III. Theoretical Calculation of αNO2/NO ...................................................................... 4-6
a. Text ................................................................................................... 4-5
b. NO and NO2 N Isotopologue Experimental Data (Table S2) ....................5
c. NO and NO2 β Fits (Table S3) ..................................................................5
d. αNO2/NO Fits (Table S4) ...............................................................................6
IV. References
.......................................................................................................6
Introduction
Section I includes a description of calculated N2O4 and N2O3 pressures under our experimental
conditions based on fitted Kp values for these equilibrium processes. Section II includes an
appendix table (Table S1) that contains experimental conditions (i.e. pressures of NO and NO2
and reaction temperatures), measured δ15N-NO2, and experimental determined αNO2/NO values for
each NO and NO2 exchange trial conducted in this study. Section III includes the details for our
theoretical calculation of αNO2/NO using a modified version of the Bigeleisen-Mayer equation
corrected for accurate zero-point energies. Experimental values needed for this calculation are
provided in Table S2. Additionally, regression parameters for the reduced partition function
ratios of NO and NO2 (Table S3) as well as for αNO2/NO as a function of temperature are
summarized (Table S4). References used within the Supporting Information are included in
section IV.
1
I. N2O4 and N2O3 Equilibrium Calculations.
NO2 exists in equilibrium with N2O4, and this equilibrium can be written as the
following:
N 2 O 4 
 2NO 2
(Eq. S1)
The pressure dependent equilibrium constant, Kp, is written as:
p 
K =
2
NO2
p
(Eq. S2)
p N 2 O4
Previously, from measured experimental values of Kp at various temperatures, a temperature
dependent polynomial expansion of log10[Kp] has been derived over the temperature range of 233
– 404 K [Hurtmans et al., 1993]. At our experimental temperatures of 278 K, 297 K, and 310 K,
these fitted Kp values are: 2.68 kPa, 13.3 kPa, and 35.6 kPa, respectively. From these fitted Kp
values and an NO2 pressure of 6.67 Pa (average NO2 pressure in exchange trials), the pressure of
N2O4 in our system was calculated to be 16.6 mPa, 3.35 mPa, and 1.25 mPa at 278 K, 297 K, and
310 K, respectively. At the highest N2O4 pressure of 16.6 mPa, which occurred at 278 K, N2O4
represents ~ 0.25% of the total NO2 and N2O4 pressures.
Similarly, NO and NO2 exists in equilibrium with N2O3:
N 2 O3 
 NO + NO 2
Kp for this equilibrium is written as:
Kp =
 p NO   p NO
p 
2

(Eq. S3)
(Eq. S4)
N 2 O3
Previously, Kp for the N2O3 equilibrium has been measured at 298 K, 308 K, and 318 K [Verhoek
and Daniels, 1931]. We derived a polynomial expansion of log10[Kp] for these experimental Kp
values (Figure S1). Our method is similar to the fitted Kp values for the N2O4 ↔ 2NO2
equilibrium [Hurtmans et al., 1993]. Our fitted Kp values at our experimental temperatures of
278 K, 297 K, and 310 K are: 86.8 kPa, 202.9 kPa, and 420.4 kPa, respectively. Using these
fitted Kp values, an NO pressure of 26.6 Pa, and an NO2 pressure of 6.67 Pa, the N2O3 pressure in
our system was calculated to be 2.05 mPa, 0.876 mPa, and 0.423 mPa at 278 K, 297 K, and 310
K, respectively. While the fitted Kp values at 297 K and 310 K are within the temperature range
of experimentally measured Kp values, the value at 278 K was extrapolated. However, the fit we
used was previously successful in predicting Kp of the N2O4 ↔ 2NO2 equilibrium over a wide
temperature range (233 K – 404 K) [Hurtmans et al., 1993], and therefore should give an
approximate Kp value. At 278 K, N2O3 pressure is extremely small relative to the NO2 and NO
pressures in the system, representing approximately 0.006% of total NO, NO2, and N2O3 pressure
in our system. Therefore, even if the Kp value at 278 K slightly differs from our extrapolated
value, it should have a negligible effect on the impact of N2O3 pressure in our system compared
to NO and NO2 pressures. Overall, we believe that the formation of N2O4 and N2O3 should be
negligible in our experiment set-up, and should have no impact on the measured N isotope
exchange between NO and NO2.
2
Figure S1. 2nd order polynomial fit of log10(Kp) of experimental measured Kp values of the NO +
NO2 ↔ N2O3 equilibrium.
II. Summary of Experimental Data.
Table S1. Summary of NO pressure (pNO), NO2 pressure (pNO2), measured δ15N-NO2, and
experimentally determined αNO2/NO for each trial conducted at 278 K, 297 K, and 310 K.
Temperature (K)
pNO (Pa)
pNO2 (Pa)
δ15N-NO2(‰)
278
278
278
278
278
25.33
29.33
28.00
25.33
25.33
13.33
12.00
9.33
9.33
6.67
-10.2
-10.5
-10.2
-10.5
-14.3
297
297
297
297
297
310
310
310
310
310
a
29.33
29.33
30.66
22.66
29.33
25.33
20.00
26.66
25.33
25.33
9.33
9.33
9.33
6.67
9.33
6.67
5.33
10.67
5.33
8.00
αNO2/NO
x̄a
σb
1.0398
1.0393
1.0417
1.0420
1.0403
1.0403
0.0015
x̄a
σb
1.0359
1.0366
1.0373
1.0349
1.0334
1.0356
0.0015
x̄a
σb
1.0355
1.0317
1.0344
1.0331
1.0332
1.0336
0.0014
-14.1
-13.6
-12.9
-17.6
-15.9
-16.5
-21.3
-15.0
-18.8
-17.3
x̄ = mean. bσ = standard deviation.
3
III. Theoretical calculation of αNO2/NO:
Urey reported equilibrium isotope exchange fractionation factors in 1947 in terms of
isotopic partition function ratios [Urey, 1947]. Also in 1947, Bigeleisen and Mayer introduced
the isotopic reduced partition function ratio (RPFR) [Bigeleisen and Mayer, 1947]. In the BornOppenheimer and harmonic oscillator approximations, the RPFR (commonly denoted as β) for an
isotopic pair is written as:
N
β =
i
μ2
 N μ -μ
× exp   1i 2i
μ1
2
 i
 N 1-exp(-μ1i )
 ×  1-exp(-μ )
 i
2i
(Eq. S5)
= (CF) (ZPE) (EXC)
where subscripts 1 and 2 refer to the light (14N) and heavy (15N) isotopologue respectively, μi =
hcωi/kT, h is Planck’s constant, c is speed of light, ωi is harmonic frequency, k is Boltzmann
constant, T is temperature, i refers to a single vibrational mode, and N refers to the total normal
mode frequencies. Eq. S5 points out that β is the product of the classical factor (CF), which
accounts for the translational and rotational energy, the zero point energy contribution (ZPE), and
an excitation factor (EXC).
A general representation for an equilibrium isotope exchange reaction involving two
different chemical species A and B is:
A1 + B2  A 2 + B1
(Eq. S6)
where subscripts 1 and 2 again refer to the light and heavy isotopologue respectively. The
reduced equilibrium constant, KA/B, which is also defined as the equilibrium isotope fractionation
factor (αA/B), can be obtained from the β of A and B:
(Eq. S7)
K A/B = αA/B = βA /βB
Using this notation, the equilibrium isotope exchange between NO and NO2 involving the 14N and
15
N isotopologue pair is written as:
15
NO + 14 NO 2  14 NO + 15 NO 2
(Eq. S8)
Subsequently, the reduced equilibrium constant for this exchange is written as:
K NO2 /NO = α NO2 /NO
 15 N 
=  14  NO 2
 N
 15 N 
 14  NO
 N
(Eq. S9)
= β NO2 β NO
Equation S5 points out that equilibrium exchange αA/B only depends on the isotopic
dependent vibrational frequencies. If the N isotopologue vibrational frequencies are known,
theoretical αA/B can be calculated in the rigid-rotor and harmonic oscillator approximations. From
a theoretical perspective, pure harmonic frequencies with no corrections for anharmonicity must
be used to satisfy the Teller-Redlich product rule for proper use of the Bigeleisen-Mayer equation
(Eq. S5) [Liu et al., 2010]. Corrections for anharmonicity can be applied to αA/B by using a
modified version of the Bigeleisen-Mayer equation (Liu et al., 2010):
β anhar =
exp   ZPEanhar ,2 kT  N  μ 2   1-exp(-μ1i ) 
  

exp   ZPEanhar ,1 kT  i  μ1  1-exp(-μ 2i ) 
(Eq. S10)
where ZPEanhar is the anharmonic corrected ground ZPE, subscripts 1 and 2 refer to the light and
heavy isotopologue respectively. This is a modified version of the Bigeleisen-Mayer equation
(Eq. S5) with anharmonic corrections via direct inclusion of zero-point energy, which results in
more accurate calculations for β [Liu et al., 2010].
The harmonic frequencies and experimental zero-point energies have been previously
measured for the N isotopologues of NO and NO2 [Olman et al., 1964; Blank and Hause, 1970;
4
Henry et al., 1978; Teffo et al., 1980; Michalski et al., 2004] (Table S2). Using these
experimental values, β for NO and NO2 was calculated from Eq. S10, and the results are
displayed in Table S3. From these β values, the isotope exchange αNO2/NO was calculated using
Eq. S9, and the results are displayed in Table S4.
Table S2. Summary of harmonic frequencies (ωi) and zero-point energies (ZPE) experimentally
measured (a-e) for the N isotopologues of NO and NO2.
.
Molecule
ωia,b (cm-1)
ZPEc-e (cm-1)
14
N16O
1904.09
948.53
15
N16O
1869.99
931.64
14
N16O2
1355.90
756.80
1663.50
1871.05
15
N16O2
1338.50
747.10
1628.30
1841.06
a [Olman et al., 1964]
b [Blank and Hause, 1970]
c [Teffo et al., 1980]
d [Henry et al., 1978]
e [Michalski et al., 2004]
Table S3. Calculated regression coefficients for β of NO and NO2 N isotopologues over the
temperature range of 150 to 450 K.
1000(α NO2 /NO -1)=
NO
NO2
A
B
C
D
×1010 + 3 ×108 + 2 ×106 + ×104
4
T
T
T
T
A
5.4514
9.1576
B
-9.7830
-17.1535
C
6.6749
12.9932
D
0.6073
0.2935
Typical misfit in the regression is < 0.2‰
5
Table S4. Calculated regression coefficients for the N isotope exchange between NO2 and NO
with corrections for anharmonic zero-point energies over the temperature range of 150 to 450 K.
1000(α NO2 /NO -1)=
A
3.9768
A
B
C
D
×1010 + 3 ×108 + 2 ×106 + ×104
4
T
T
T
T
B
-7.9646
C
6.2144
D
-0.2911
Typical misfit in the regression is < 0.3‰
IV. References.
Bigeleisen, J., and M. G. Mayer (1947), Calculation of Equilibrium Constants for Isotopic
Exchange Reactions, J. Chem. Phys., 15(5), 261–267.
Blank, R. E., and C. D. Hause (1970), Molecular constants for the (3, 0, 1) band of NO2, J. Mol.
Spectrosc., 34(3), 478–486.
Henry, A., M. F. Le Moal, P. Cardinet, and A. Valentin (1978), Overtone bands of 14N16O and
determination of molecular constants, J. Mol. Spectrosc., 70(1), 18–26.
Hurtmans, D., M. Herman, and J. Vander Auwera (1993), Integrated band intensities in N2O4 in
the infrared range, J. Quant. Spectrosc. Radiat. Transf., 50(6), 595–602.
Liu, Q., J. A. Tossell, and Y. Liu (2010), On the proper use of the Bigeleisen–Mayer equation and
corrections to it in the calculation of isotopic fractionation equilibrium constants,
Geochim. Cosmochim. Acta, 74(24), 6965–6983.
Michalski, G., R. Jost, D. Sugny, M. Joyeux, and M. Thiemens (2004), Dissociation energies of
six NO2 isotopologues by laser induced fluorescence spectroscopy and zero point energy
of some triatomic molecules, J. Chem. Phys., 121(15), 7153–7161.
Olman, M. D., M. D. McNelis, and C. D. Hause (1964), Molecular constants of nitric oxide from
the near infrared spectrum, J. Mol. Spectrosc., 14(1–4), 62–78.
Teffo, J. L., A. Henry, P. Cardinet, and A. Valentin (1980), Determination of molecular constants
of nitric oxide from (1-0), (2-0), (3-0) bands of the 15N16O and 15N18O isotopic species, J.
Mol. Spectrosc., 82(2), 348–363.
Urey, H. C. (1947), The thermodynamic properties of isotopic substances, J Chem Soc, 7, 562–
581.
Verhoek, F. H., and F. Daniels (1931), The dissociation constant of nitrogen tetroxide and of
nitrogen trioxide, J. Am. Chem. Soc., 53(4), 1250–1263.
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