047
Spectroscopic Study of the N02-N204 System
A Spectroscopic Study of the N02-N204System by the Infrared Absorption Technique Robert J. Nordstrom* and Walter H. Chan Department of Physics, and the Department of Chemistry, The Ohio State University, Columbus, Ohio 432 10 (Received October 24, 1975) Publication costs assisted by the US.Environmental Protection Agency
We report the results of a new technique for the determination of the equilibrium constant for the reactions N204 + 2N02. Fourier transform spectroscopy was used to record infrared spectra of the u2 band of NO2 near 13.3 I*. Spectra were recorded alternately through two absorption cells of different lengths. Working within the validity of the Beer-Lambert law of absorption of radiation, an equation is derived which relates the equilibrium constant to pairs of gas pressures which give the same spectral absorbance of NO2 in the two unequal cells. No knowledge of the absorption coefficient is needed using this technique. All samples were pressurized to 740 Torr with high-purity nitrogen and measurements were taken a t room temperature (296 f 1 K). Using this two cell technique, we have found K,, = 0.14 f 0.02 atm at room temperature.
I. Introduction During the past few years, nitrogen dioxide has become the subject of an increasing number of research studies. This interest stems largely from attempts to monitor NO2 effluents in the troposphere and from attempts to follow photochemical processes involving NO2 both in the troposphere and in the strat0sphere.l Laboratory studies involving NO2, however, are often compromised by the presence of dinitrogen tetroxide in the sample. This N2O4 interference can be eliminated either by heating the sample chamber2f3to dissociate the N204, or by using extremely low partial pressures of NO2 to reduce the quantity of N2O4 to a negligible amount. Both of these techniques suffer from possible shortcomings. They force the experimenter to investigate properties of NO2 in a temperature or pressure region which might not be feasible or relevant. For studies of NO2 a t temperatures and pressures at which NzO4 is present, then, it is necessary to know the equilibrium constant for the dissociation-association reactions N2Q4 e 2N02. This paper reports our results on the determination of this equilibrium constant. This work constitutes the preliminary steps of an investigation of gas kinetics involving NO2 and other gases at room temperature, using Fourier transform spectroscopy. Our value for the equilibrium constant K is in good agreement with values previously reported. The emphasis of this paper is on the technique used to investigate the equilibrium of the system. We have developed a method using infrared spectroscopy and two absorption cells of different lengths to study the equilibrium. This method is significantly different from the method of Vosper4 who reported the use of two absorption cells to study the equilibrium constant. Furthermore, our method differs from the infrared study of Dunn, Wark, and Agnew3 which relied on data taken at higher temperatures for the evaluation of the equilibrium constant at room temperature. Harris and Churney5 evaluated the equilibrium constant by observing the transmittances of the 5461-A mercuNzO4 a t several ry line through a cell containing' NO2
+
* Address correspondence to this author at the Department of Physics, Ohio State University.
pressures. The equations which they developed are similar to those developed in this paper.
11. Experimental Section The apparatus used to measure the equilibrium constant of the NO2-N2O4 system is shown in Figure 1. Radiation from the Nernst glower is collimated and passes through the interferometer. The beam exists the interferometer and passes through one of the two absorption cells. The radiation is then focused on the Cu-Ge detector. The output from the detector is called the interferogram and is the autocorrelation function of the electric field. This interferogram signal is digitized by the analog-to-digital converter and is stored by the computer. Our computer is a Nova 1200 minicomputer with 4K (4096) of core and 128K additional data storage od a fixed head disk. The entire apparatus including the interferometer was purchased from Digilab Inc. Once the interferogram has been stored in the computer, it is transformed to produce the spectrum. The usable spectral region is defined by the response of the Cu-Ge detector which is from about 500 to 3500 cmT1. Both absorption cells which were used were constructed of stainless steel and were fitted with sodium chloride windows. The lengths of the cells were L1 = 39.5 cm and L2 = 7.5 cm, which gives a ratio L1IL2 = 5.27. The NO2 (+ N2O4) was obtained from Matheson Gas Co. Nominal purity was 99.5%. The gas was expanded into a gas handling system which was connected to the absorption cells and pressure gauges. The gas handling system was built entirely of glass and stainless steel and is fitted with Teflon stopcocks. A line sketch of this apparatus is shown in Figure 2. The gas was first collected in a liquid nitrogen cooled trap and degassed to remove any volatile impurities (NO, N20, etc.). When the cold trap was warmed to room temperature, the sample gas was expanded into an evacuated storage bulb. From this storage bulb, the gas was injected into the two sample cells simultaneously. The pressure of NO2 + N204 was measured on a calibrated WallaceTiernan gauge and a mercury manometer both of which were isolated from the reactive gas by a glass spiral gauge, which was used as a null instrument. Pressures could be The Journal of Physical Chemistry, Vol. 80, No. 8, 1976
-
S A M P L E CELL
1
-. . .. -. .-, .
- .. _. ..
T
t!I
I
1NTERFEROMETER
PLOTTER
CONTROLLER
Figure 1. The experimental apparatus. Either the 7.5-cm sample cell or the 39.5-cm sample cell can be positioned in the infrared beam.
750
700
'
BOO
850 ,
i
FREOUENCY AIR
4
Hp MANOMETER
_
I
('cM-')
Figure 3. Transmission spectrum of NO2 700 to 900 cm-'.
+ Nz04 in the region from
when needed. This ratioing procedure gave transmission spectra of NO2 N204 from which absorbance data could be obtained.
+
SPIRAL M U G E
L A S E R TARQET
111. Theory When radiation passes through a cell of length L which contains an absorbing gas at partial pressure p , the spectral absorbance can be written
NOz+N204
A(u) = -In (T(u))= a(u)pL
L$ COLO TRAP
Figure 2. The gas handling system. The sample gas is injected into the storage bulb and the pressure is read on the Wallace-Tiernan gauge and mercury manometer which are isolated from the NOn N204 by a glass spiral gauge.
+
measured with reasonable accuracy in a range from a few Torr to 760 Torr. After the absorption cells were filled to the desired pressure of sample gas, the valves on the cells were closed. The NO2 Nz04in the glass tubing of the gas handling system was pumped out, and the system was flushed with highpurity nitrogen gas. The valves on the absorption cells were again opened and nitrogen was injected into the cells until the total pressure in both cells was 740 Torr. The valves on the cells were finally closed and the two absorption cells were removed from the gas handling system, and each cell in turn was positioned in the optical path. Single beam spectra were recorded through each cell. All spectra taken through the 39.5-cm cell were ratioed against a background spectrum through the same cell. Similarly, all spectra taken through the 7.5-cm cell were ratioed against a background spectrum recorded through that cell. These two background spectra were prepared by filling each absorption cell to 740 Torr with high-purity nitrogen and recording a spectrum through each cell. These background spectra were stored in the computer and could be recalled
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The Journal of Physical Chemistry, Voi. 80,No. 8, 1976
(1)
This equation is a form of the Beer-Lambert law of absorption of radiation which includes the added assumption of the validity of the ideal gas law. Here T(v)is the spectral transmittance at frequency u and a(u) is the absorption coefficient. When the product of pressure times length becomes too large the approximations of the Beer-Lambert law no longer apply and the absorbance deviates from this simple l'inear behavior. For cells of fixed length, then, there is an upper limit to the pressure which can be used with eq 1. The equilibrium constant for the reactions NzO4 ~t 2N02 can be calculated from Keq
= PN0z2/PNp0a
(2)
where P N O ~and p ~ are~ the0partial ~ pressures of the two gasses. Expressing the equilibrium constant in terms of the total sample gas pressure P = PNOZf
PN204
(3)
the equilibrium constant can be written Keq
= PN0z2/(P
- PN02)
(4)
The only directly measurable quantity in this expression is the total gas pressure p. The partial pressure of NO2 can be monitored indirectly by infrared absorption measurements if the absorption coefficient for NO2 is known. If the ab-
849
Spectroscopic Study of the NO2-NzO4 System i
'
7
TABLE I: Data for the Determination of the Equilibrium Constant of the N02-N20~ Svstem
Approximate Q branch location
Spectral
(in crn-l)
absorbance
791 791 791 807 807 807 823 823 823
0.05 0.10 0.15 0.05 0.10 0.15 0.05 0.10 0.15
~~
Pi, Torr
Pz,
Keq,
Torr
Torr
1.00 2.10 3.15 1.22 2.50 3.72 1.44 2.70 3.94
5.47 12.00 18.65 6.75 14.40 22.40 8.00 15.70 23.90
~~
&.-A 0
25
50
100
75
125
TOTAL PRESSURE N%*N,O,
TABLE 11: Comparison of Results with Previously Reported Data ~ _ _ _ _ ~ ~ ~
(TORR)
Flgure 4. Plots of absorbance of the 791-cm-' NO2 Q branch as a function of total sample gas pressure.
sorption coefficient is not known, the following method can be used. Using two cells of different lengths, the NO2 absorbances at a given frequency uo are equal through the two cells when (ANo~(vo))I = ( Y N O ~ ( U O ) ( P N=O ~ ) ~ L ~ ~NO~(VO)(PNO =~(ANO~(UO))Z )ZLZ (5) where the subscript 1 refers to the first cell and subscript 2 refers to the second cell. From eq 5 ( p ~ 0 ~ ) i= L (i P N O J Z L Z
112 102 103 102 110 105 111 106 104 Av 105.7 (0.140 & 0.020 atm)
Ref
Temp, K
Equilibrium constant, atm
296 273.2 299.7 298 296
3 4 5 6
This
0.13a 0.016 0.1624 0.1426b 0.14
work a This number was read from graph. Ignoring their correction factor for pressure variation.
I
(6)
When this condition applies, the absorbances in the two cells are equal. If the slight correction due to pressure is ignored: the equilibrium constant for the two cells can be written
Keq =
(PN0z)l2
=
(PN0z)Z2
(7)
p1 - (PN02)l PZ - (PN02)Z where p1 and p z are the total pressures of sample gas in cell 1and cell 2, respectively. Now, combining eq 6 and 7
0
where u = L1/L2. By substituting this equation into the expression for K,, in eq 7
5
15
IO
pNo:L
20
25
30
35
( T O R R METER )
Figure 5. Plot of absorbance of the 791-cm-I NOn Q branch as a function of partial pressure of NO2 times the path length. Data from the 39.5-cm cell (circles)and the 7.5-cm cell (squares)are plotted.
Thus, the value of the equilibrium constant K,, for the NOp-NzO4 system can be determined at a single temperature by measuring the total sample gas pressures p1 and pz in cells of length L1 and Lz which give equal absorbances. IV. Results
The infrared absorption band of NO2 which was chosen to study the equilibrium constant expressed in eq 9 was the u p band near 13.3 w . Only the abundant isotope 14N1602was investigated.2 This band is partially overlapped by the u12 band of NzO4. Figure 3 shows a spectrum of this region recorded through the 7.5-cm cell a t a nominal resolution of 0.5 cm-l. The pressure of NO2 + Nz04 was 12 Torr and the
cell was filled with nitrogen to 740 Torr. The regularly spaced absorption spikes are due to NO2 Q-branch transitions, while the broad central feature is mostly due to Nz04 and partially due to NOz. All spectra were recorded at 0.5-cm-l resolution. The absorbance at several NO2 Q-branch center frequencies were chosen as monitors of the NO2 concentration. Although peak absorbance in a spectrum is dependent on the resolution used to record the spectrum, nevertheless the peak absorbance provides an unambiguous measure of concentration of all spectra which are recorded a t the same resolution. The Journal of Physical Chemistry, Val. 80, No. 8, 1976
Howard L. Yeager and Henry Reid
850
From the recorded spectra, the absorbances of the NO2 Q-branches near 791, 807, and 823 cm-l were measured. Plots of the abscrbances as a function of sample gas pressure in both cells were made. Figure 4 shows absorbance plots for the 791-cm-l Q-branch through the 7.5-cm cell and the 39.5-cm cell. Using these plots and similar plots for the other Q-branch absorbances, a pair of pressures p1 and p2 can be determined for any chosen absorbance of a particular Q branch. From these pressures, values of the equilibrium constant were calculated using eq 9. A region of linear dependence of absorbance on pressure is not apparent in these plots because the independent variable is the total sample gas pressure, not the NO2 partial pressure. The absorbance values used to calculate the equilibrium constant were chosen to be sufficiently small to assure that we were well within the pressure limits defined by the validity of the Beer-Lambert law of both cells. Table I shows the results of these calculations for the three NO2 Q branches whith were studied. The average of the calculated equilibrium constants is 0.140 atm a t 296 f 1 K and is in good agreement with values reported previously.
V. Conclusions The results in Table I show that the two cell technique provides a reasonable method for the determination of the equilibrium constant for the N02-Nz04 system. Using the average value of the equilibrium constant determined by this technique, the partial pressure of NO2 can be evaluated. Plotting the absorbance of each Q branch vs. the product p ~ o &for both cells shows a linear dependence. The linear region extends well beyond the largest values of
absorbance used in Table I1 to evaluate Keq.This indicates that the data were recorded within the limits of the validity of the Beer-Lambert law. Figure 5 shows the dependence of the 791 Q-branch absorbance on the product PNO&. Error treatment suggests that a theoretical error of about 15%is expected with this technique. This error is based on an estimate of a 1% error in measuring the pressure. Thus, by this technique, we estimate the value of the equilibrium constant for the reactions N204 2N02 at room temperature to be 0.14 f 0.02 atm. Table I1 shows a comparison of this result with previously reported values. The value of Harris and Churney5 is their data taken closest to 296 K. This two cell technique provides a reasonably accurate method for determining the equilibrium constant of a two component system. A variation of this method would be to use a single multiple-traversal cell and record spectra of various concentrations of sample at several different path lengths. These data could be used with eq 9 to make the equilibrium determination.
Acknowledgment. The authors wish to thank W. M. Uselman for his discussion on this project. This work was supported by EPA Grant No. 803075. References and Notes (1) J-C. Fontanella, A. Girard, L. Gramont, and N . Louisnard, Appl. Opt., 14, 825 (1975). (2) S. Hurlock, K. Narahari Rao, L. A. Weller, and P. K. L. Yin, J. Mol. Spectrosc., 48, 372 (1973). (3) M. G. Dunn, K. Wark, Jr., and J. T. Agnew, J. Chem. Phys., 3, 2445 (1962). (4) A. J. Vosper, J. Chem. SOC.A, 625 (1970). (5) L. Harris and K. L. Churney, J. Chem. Phys., 47, 1703 (1967). (6)F . H. Verhoek and F . Daniels, J. Am. Chem. Soc., 55, 1250 (1931).
Spectroscopic Studies of Ionic Association in Propylene Carbonate Howard L. Yeager* and Henry Reid Department of Chemistry, The University of Calgary, C a g r y , Alberta, Canada T2N IN4 (Received July 13, 1975; Revised Manuscript Received January 13, 1976) Publication costs assisted by the National Research Council of Canada
Far-infrared and 19FNMR spectroscopic techniques have been used to study lithium, sodium, potassium, and rubidium trifluoroacetates in propylene carbonate solutions. NMR results indicate that simple ion pairing predominates for the potassium and rubidium salts but that ion aggregation occurs for the lithium and sodium salts. The far-infrared cation solvation bands for the alkali metal trifluoroacetates are shifted from the corresponding nitrate and perchlorate salt band positions, the lithium ion band to lower frequency, and the other bands to higher frequencies. Plots of integrated absorbance vs. concentration for the lithium and sodium salts are linear. Results of the two techniques are compared, and the utility of the far-infrared method as a tool for studying ion association is discussed.
Introduction A number of investigators have used far-infrared spectroscopy to study alkali metal ion solvation in a variety of s ~ l v e n t s . l -The ~ main features of this approach have been discussed by Edgell.6 Alkali metal ions in solution exhibit The Journal of Physical Chemistry, Vol. 80, No. 8, 1976
broad absorption bands in the far-infrared region corresponding to their vibration with adjacent solution species. Band positions depend upon the alkali metal ion and solvent used, but generally do not depend on the anion of the salt. However, for solvents which have poor donor properties or low dielectric constants, the band positions may also
