THERMODYNAMIC PROPERTIES OF OXIDESOF KITROGEN
Dec., 1961
Results and Discussion The values of In K 2 obtained in this work were compared with those of previous investigators. The value of K2 a t 25’ as calculated from equation 10 is 0.01032, which compares very well with reported values.* The only previous work as a function of temperature was that of Young, Klotz and Singleterry6 in which K 2 was determined over the range of 5 to 55’ and an equation 11 was obtained for K 2 us. temperature to 155’ by utilization of the conductivity data of Noyes.6 l n K 2 = - T 1785‘390
+ 15.99658 - 0.0489236T
each temperature, as calculated from equation 10, and as obtained from equation 11. In Table I1 are summarized the thermodynamic constants for the reaction HSOd-
TABLE I1 THERMODYNAMIC CONSTANTS FOR TRE REACTION HSO,‘ H + SO&-
TABLE I A FUNCTION OF TEMPERATURE
VALUESOF Loa K z AS
-log Kz (eq. 10)
-log K, (es. 11)
I . 891 2.374 2.699 3.010 3,334 3.688 4.087 4.489 4.941
1.987 2.301 2.636 2.987 3.352 3.728 4.113 4.506 4.905
1.988 2.318 2.677 3.059 3.460 3.876
-1OK
25 50
75 100 125 150 175 200 225
+ SO*-
+
(11)
(from solubilities)
H+
from 25 to 225’ as computed by using equation 10. All calculations in this paper were carried out on an IBM-7090 computer.
In Table I are summarized values of log Kz us. temperature as computed from the solubilities at
t
2249
(4) R. A. Robinson and R . H. Stokes, “Electrolyte Solutions,” Academic Press. Inc., New York, N. Y., 1955, p. 374. (5) I. M. Klotz and C. R. Singleterry, Theses, University of Chicago, 1940; R. A. Robineon and R. H. Stokes, “Electrolyte Solutions,” Academic Press. Inc., New York, N. Y., 1955 p. 376; T. F. Young, L. F. hlaranville and H. M. Smitb, “The Structure of Electrolytia Solutions,” edited by W. J. Hamer, John Wiley and Sons, Inc., New York. N. Y., 1949, Chap. 4; T. F. Young, unpublished a-ork. (6) A. A. Noyes, “The Electrical Conductivity of Aqueous Sohtions,” The Carnegie Institution of Washington, Washington, D. C., 1907.
t
AFQ8cal.
25 50 75 100 125 150 175 200 225
2.712 3.403 4.200 5.102 6.108 7.219 8.436 9 * 757 11.183
AHO, cal.
ASQ, 8.u.
-18.280
-25.6 -29.8 -34.0 -38.2 -42.4 -46.5 -50.7 -54.9 -59.1
- 4.911 - 6.214 - 7.623 - 9.136 -10.750 - 12.480 -14.310 - 16.240
=
It is interesting to note that the entropy of dissociation of HSOI- is negative and attains a higher negative value the higher the temperature. A similar effect was found2 for the dissociation of Uoz804 into U02++and SO4--, and for the dissolution of Ag2S04. Thus it appears that the formation of SO4-- in water increased the amount of “order” or “structure” shown by the solvent at any temperature and that this effect is much greater the higher the temperature. Acknowledgments.-The authors wish to thank Dr. H. A. Levy and Mrs. M. P. Lietzke for helpful advice on the mathematical procedures and the computer programming.
THERMODYNAMIC PROPERTIES OF SOME OXIDES OF NITROGEN1 BY I. C. HISATSUNE Department of Chemistry, Pennsylvania State University, University Park, Pa. Received Auguat 4, 1961
Available spectroscopic and structural data have been used to calculate the thermodynamic functions for NzOa, NzOd and NzOs, and dissociation equilibria of these oxides. For the N z O dissociation, ~ the necessary functions for NOs radical were estimated from vibrational frequencies calculated with Urey-Bradley force constants. These data together with those obtained from other sources lead to the following estimated properties for ideal gases a t one atmosphere and 25”. CpO(cal./ deg. mole)
SQ(cal./ deg. mole)
AHfQ (kcal./mole)
AFrQ (kcal./mole)
11.22 15.68 18.47 20.22
60.36 73.92 72.73 85.00
16.95 20 00 2.54 3.35
27.36 33.49 23.66 28.18
I
Introduction are of considerable interest in air pollution, geoThe oxides of nitrogen, which form a “happy physics3 and recently in astrophysics4 as well. hunting ground’12afor chemical kineticists and have There are approximately twenty of these oxides been subjected to extensive kinetic investigations,2b (3) L. E. Miller, “The Chemistry and Vertical Distribution of the (1) Supported by the PHS Grant RG-8192 and the Air Force Geophysics Research Directorate. (2) (a) F. Daniela, Chem. Enp. Nema, 33, 2370 (1955); (b) see for recent reviews S. W. Benson, “The Foundation of Chemical Kinetics,” McGraw-Hill Book Co., Inc.. New York, N. Y., 1960.
Oxides of Nitrogen in the Atmoaphere,” U. 5. Air Force Geophysical Research Paper No. 38, AFCRCTR-56-207, 1954. (4) C. C. Kiess, C. H. Corlisa and H. K. Kieae, Science, 131, 1319 (1960); F. J. Heyden, C. C. Kiess and H. K. Kieaa, ibid., 130, 1195 (1959).
2250
I. C. HISATSIJNE
Vol. 65
including ions which have been characterized ture QzNONOz were estimated to be: nitro bo5d chemically. However, with only few exceptions, 1.18 A., nit,ro angle 137", central KO bond 1.47 A., the physical properties such as the important and central N-0-N angle 127". These estimations thermodynamic functions for these compounds were made from N204 and HK02 structures.8*10 have not been established satisfactorily. These We also tried 150" for the central N-0-N angle, oxides, especially the higher oxides, are reactive but this produced only insignificant differences in and often exist in equilibrium mixtures so that they the calculated results. Frequencies of 2 X 1728, are difficult t o handle experimentally. Direct 1338, 1247, 860, 3 X 743, 614, 577, and 2 X 353 calorimetric measurements on them do not appear cm.-l were employed in the calculations. The possible and one must resort to estimation of two torsional modes were assumed to be free rotathermodynamic functions from statistical calcula- tions. One additional frequency corresponding to tions using spectroscopic data. the central N-0-N angle bending mode could not Vibrational frequencies of the higher oxides can be determined experimentally. This frequency was be obtained directly by using low temperature taken to be 170 cm.-', which forced the calculated methods of infrared spectroscopy. At sufficiently entropy to agree with the experimental vaIue.'l low temperatures, the compounds can be stabilized The vibrational spectrum of this molecule and the so that satisfactory spectra can be obtained. structure will be discussed elsewhere. Furthermore, the interpretation of these low temNO3.-Structural and spectroscopic data for perature data is usually simplified because the this free radical are lacking. Such information equilibria are shifted t o one extreme. Even therefore was deduced in the following manner. when frequencies cannot be determined experi- The molecular symmetry of NO3 was taken to be mentally, we now have sufficient normal coordinate Dah because, according to Walsh's LCAO-MO analysis data to allow us to make reasonable esti- correlation diagrarn,'z this radical is formed by the mates of the force constants and calculate these removal of one electron from a bonding MO in frequencies. These calculated frequencies are KO3- with no change in molecular symmetry. reliable enough to be used in the computations of From the changes in bond distance in XZand K\T~+, thermodynamic functions. I n this paper we report we estimate that there will be about 2% elongation the thermodynamic functions for Nz03, Nz04 of the NO bond in NOy- when one bonding electron and N206, and their dissociation equilibria esti- is removed. Thus, the estimated bond distance mated from spectroscopic and limited kinetic and angle in the radical are 1.27 A. and 120". and thermochemical data. Vibrational frequencies for the planar modes Calculations were calculated from the equations given by Janz Statistical equations and physical constants and Mikawa for the Urey-Bradley force field treatnecessary to calculate the standard thermodynamic ment of D3h tetra-atomic system^.'^ The Ureyfunctions were taken from Pitzer's t e ~ t b o o k . ~Bradley force constants for the radical were estiEquations for internal rotations and tables of mated as fgllows. The K N O was found to be 3.50 harmonic oscillator contributions from this source millidyne /A. from an approximate linear rclationalso were used. Each nitrogen oxide was assumed ship betmeen K N o and ?-NO for the nitrogen oxides to behave as an ideal gas with all internal vibrations N204, KO*, KOZ-, S O 3 - , and the nitryl halides being harmonic and with only rigid rotations al- XN02. The Urey-Bradley force constants for lowed. Vibrational frequencies and molecular these species, except for the nitrate ion, had been geometries used in our calculations were as follows. reported earlier.I4 The nitrate KNO was taken N20s.-The geometry of this oxide was estimated from the work of Jana and hfikawn. previously from the interpretation of its vibrational The bending constant H was taken to be the spectrum in terms of Urey-Bradley force field same as in NOa- but was corrected for th? scaling calculations.'j The best estimates were nitroso bond bond distance to give 0.53 millidyne/A. This 1.12 8., nitro bond 1.18 8., nitro angle 134,", bending constant was found in our earlier calcunitroso ON-N angle 110' and E N bond 2.08 A. l a t i o n ~to~be ~ related to the quadratic non-bonded Vibrational frequencies were taken t o be 1863, atom interaction constant F through the sum F -I1589, 1297, 783, 627, 407, 313 and 253 cm.-'. 2H. Among structurally related molecules this We assumed free rotation about the NN bond as sum for the nitro group appeared to be relatively suggested from the entropy c~nsideration.~ invariant: ClN02, 2.65; 02KS02, 2.66; 0x02-, Nz04.-Accurate geometric parameters reported 2.67. Thus F for the radical x7as evaluated from by Smith and Hedbergs were used for this moolecule, F 2H =, 2.67 with H = 0.53 to get F = 1.61 ie., NN bond 1.750 8.,nitro bond 1.180 A., nitro millidyne/A. The remaining linear repulsive conangle 133.7") and V h molecular symmetry. Fre- stant F' was taken to be -0.1 F as is usually done. quencies used were 1748, 1710, 1373, 1261, 812, The calculated planar mode frequencies were 750,675,480,385,260 and 50 ~ m . - l . ~ 2 X 1158, 940 and 2 X 704 cm.-l. The out-ofN205.-The geometric parameters for the struc-
+
( 5 ) K. S. Pitzer, "Quantum Chemistry," Prentice-Hall, Inc., New York, N. Y., 1953. (6) J. P. Devlin and I. C. Hisatsune, Spectrochim. Acto, 17, 218 (1981). (7) I. 6. Hieatsune and J. P. Devlin, ibid., 16, 401 (1960). (8) D W. Smith and K. Hedberg. J . Chem. Phy8., as. 1282 (1956). (9) I. C. Hisstaune. J. P. Devlin and Yasuo Wada, ibid., 33, 714 (1960).
(10) L. H. Jones, R. If. Badger and G. E. Moore. ibid., 19, 1599 (1951). (11) J. D. Ray and R. A. Ogg, Jr., ibid., 26, 984 (1957). (12) A. D. Walsh, J . Chem. Soc., 2301 (1953). (13) G.J. Janz and Y. Mikawa, J . Mol. Spectroscopy, 6 92 (1960). (14) I. C. Hisataiine, J. P. Devlin and 9. Califano, Speetruchim. Acta. 16. 450 (1960): J. P. Devlin and I. C. Hisatsune, ibid., 1'7, 206 11961).
Dec., 1961
THERMODYNAMIC PROPERTIES OF OXIDESOF NITROGEN
plane wagging frequency was taken to be 765 the same as in gaseous nitric acid."
2251
TABLEI11 THERMODYNAMIC FUNCTIONS FOR NzOs (CAL./DEO. hhE)
-
(HO H o 9 / T,OK. T SO CPQ Thermodynamic functions calculated on the 100 11.89 10.53 57.75 68.28 basis of molecular geometries and frequencies 200 16.13 12.24 65.54 77,77 described above for x203, 1\'204, h'zO6 and KO3 are 250 13.23 81.61 18.30 68.37 listed, respectively, in Tables I to 1V. These 275 69.66 83.40 19.32 13.74 results together with those available for nitric 298.16 20.22 14.21 70.79 85.00 oxide16 and KO2'' then were used to calculate the 14.25 300 20.28 70.87 85.12 enthalpy and free energy changes and equilibrium 21.19 325 14.75 72.04 86.78 constants for the dissociation equilibria of Nz03, 350 22.04 73.15 15.24 88.39 Sz04 and N205. 400 23.58 16.19 75.24 91.43 500 26.11 96.98 17.93 79.05 TABLEI 19.46 82.46 101.9 600 28.03 THERMODYNAMIC FUNCTIONS FOR NzOl (CAL./DEG. MOLE) 700 20.79 85.56 106.4 29.49 ( H a - Hoe))/ - ( F a - Hoe)/ 21.95 88.41 110.4 30.61 800 T CPO T SO T , OK. 900 31.48 22.97 01.06 114.0 100 10.35 9.27 50.63 59.90 32.15 117.4 1000 23.84 93.51 200 13.50 10.64 57.45 68.09 120.5 24.63 95.83 32.69 250 14.71 11.34 59.90 71.24 1100 123.4 25.32 97.95 1200 33.12 275 15.23 11.67 61.00 72.67 1300 33.47 126.0 25.94 100.1 298.16 15.68 11.96 61.96 73.92 26.49 102.0 33. i 6 128.5 11.98 300 15.72 62.03 74.01 1400 130.8 26.98 103.9 34.00 16.17 12.29 63.00 325 75.29 1500 12.58 63.92 76.50 350 16.60 400 17 39 13.13 TABLEIV 65.64 78.77 18.73 14,12 68.68 500 82.80 THERMODYNAMIC FUNCTIONS FOR NO3 (CAL./DEG. MOLE 600 19.82 14.99 71.33 86.32 (Ho - Roo)/ -(FO - Hoo) T SO CPO T T.OK. io0 20.69 15.74 73. 70 89.44 100 7.97 7.95 42.66 50.61 800 21.39 16.41 75.84 92.25 200 9.02 48.21 56.35 8.15 16.99 900 21.94 77.81 94.80 250 10.10 8.42 50.06 58.48 1000 22.38 17.51 79.63 97.14 275 10.68 8.60 50.87 59.47 1100 22. 73 17.97 81 .32 99.29 298.16 11 22 8.79 51.57 60.36 1200 23.02 18.38 82. 90 101.3 8.80 51.63 60.42 300 11.26 1300 23.25 18.74 84.38 103.1 9.01 52.34 61.35 325 11.83 1400 23.44 19.07 85.79 104.9 53.01 62.25 12.37 9.23 350 1500 23.61 19.37 87.11 106.5 400 13.21 9.62 54.25 63 87 TABLE I1 500 14.96 10.59 56.54 67.13 THERMODYNABIIC FUNCTIONS FOR NsO, (CAL./DEG. MOLE) 6oo 16.11 11.42 58.54 69.06 $00 16.92 12.15 60.36 72.51 (Ho - HnO)/ -. ( F o - Hoe)/ T T SO T,OK. CPO 800 17.51 12.79 62.02 74.81 9.57 100 11.06 47.57 57.14 900 17.95 13.34 63.56 76.90 11.32 200 15.11 54.71 66.04 1000 18.28 13.82 64.119 78.81 12.27 250 16.93 57.34 69.61 14.23 1100 18.53 66.33 80.56 12.73 2i8 17.76 58.53 71.26 1200 14.60 67.58 82.18 18.73 13.15 298.16 15.47 59.58 72.73 1300 18.89 14.92 68.76 83.69 13.18 59.66 300 18.63 72.84 1400 15.21 19.02 69.88 85.09 60.73 325 19.25 13.62 74.35 1500 i o . 94 19.12 15.47 86.41 14.04 61.76 350 19.92 75.80 400 21.16 63 69 14.86 78.55 The enthalpy change a t 0°K. for the NzOa 500 23.24 67.17 16.34 83.50 dissociation equilibrium was calculated from the 600 22.86 70. 26 17.63 87.89 experimental data reported by Beattie and Bell. I* 700 26.13 73.07 18.76 91.86 Verhoek and Daniels'g also reported some data for 800 27.12 $5 64 19.74 95.38 this equilibrium, but entropy calculations reported 20.61 000 27.89 78.01 08.62 earlier' showed that their data were not as reason1000 25.49 101.6 80.27 21.37 able as those reported by Beattie and Bell. How22.04 1100 28.98 104.5 82.44 ever, AH0 for the n'02-SzO4 equilibrium was evalu1200 29.37 22.63 lOG.9 84.24 ated from the experimental data reported by Ver1300 20 , (in 23.16 109.4 56.24 hoek and Daniels.19 In the case of NzOs dissocia1400 29.95 111.5 23.64 87.85 6.3 kcal.! tion equilibrium, AF0(460°K.) of 1500 30.16 24.07 113.5 89.45 mole reported by Schott and DavidsonZ0was used
Results
+
(15) H. Cohn, C. K. Ingold and H. G . Poole, J . Chem. Soc., 4272 (1952). (16) "Selected T'a1iir.n of Pronertier of Hydrocarbons." Katl. Bur. of Standards Circ. No. 461 (1947). (17) A. P. Altshuller. J . I'hye. Chem., 61, 251 (1957).
to estimate
N o .
The thermodynamic functions
(18) I. R. Beattie and 8. W. Bell, J . Chem. Soc., 1681 (1957) (19) F. H. Verhoek and F. Daniels, J . A m . Cheni. Sac.. 63, 1250 (1931). (20) G . Sohott and N. Davidson, rhid., 80, 1841 (19%).
I. C. HXSATSUNE
2252 TABLE V THERMODYNAMIC FUNCTIONS FOR Nz03 i=? NO ( A H o o = 8.63 KCALJMOLE) T,OK. 100 200 250 275 298.16 300 325 350 400 500 600 700 800 900 1000
AH0 (kcal./mole)
AFQ (kcal./mole)
+ NOz
Vol. 65
for equilibria of Nz03, N204 and N206dissociations are given in Tables V to VII.
Discussion
Kw. (atm.) 3.46 x 10-14 6.58 x 10-4 8.15 x 4.61 x 10-l 1.91 2.11 7.20 2.13 X 10 1.22 x 102 1.38 x 103 6.87 x 103 2.12 x 104 4.88 x 104 9.20 x 104 1.52 X lo6
Among the higher oxides of nitrogen considered 6.16 9.24 here, only X204 has a known molecular structure. 9.59 2.92 Yo experimental geometric parameters are avail9.66 1.25 able for the remaining oxides. Even the vibrational 0.42 9.68 frequencies are not known unequivocally. It was -0.38 9.69 necessary to assume free internal rotations in both 9.69 -0.45 N203 and K205 and the torsional frequency in -1.28 9.69 N204 also was estimated theoretically. All vi-2.13 9.69 brational frequencies of NO3 and one bending -3.82 9.67 frequency in K205 were estimated values. I n 9.59 -7.19 view of these uncertainties, we must consider 9.48 -10.53 the reliability of the calculated thermodynamic -13.86 9.33 functions reported here. 9.18 -17.16 It was found earlier7 that the uncertainty in 9.01 -20.44 the geometry of N2O3 did not affect the calculated -23.71 8.84 entropy value very much. When the geometric parameters were varied over a wide but reasonable range of values, only about 0.5 cal./deg. mole TABLE VI change was produced in the calculated total THERMODYNAMIC FUNCTIONS FOR NzO, i=? 2N02 (AH8 = entropy a t 25". There are two other evidences 12.69 KCAL./MOLE) which show that the estimated thermodynamic AH0 AFO (kcal./mole) (kcal./mole) K e g (atm.) T,OK. functions, a t least in the room temperature region, 13.32 9.35 3.61 X 100 are reliable. The change in entropy for the re13.62 5.24 1.86 X 200 NO2 a t 25" is 33.78 e.& from action K203F? NO 1.78 X lo-* 13.66 3.15 250 our calculations, and this compares well with the 13.65 2.09 2.16 X 275 experimental value of 33.25 f 0.35 e.u. reported 13.64 1.12 1.51 X lo-' 298.16 by Beattie and Bell.18 If we take the standard 13.64 1.04 1.74 X lo-' 300 heat of formation of NO2 as 8.09 kcal./mole,zl 13.62 -0.01 1.01 325 then the AH, (25") of 20.0 is obtained for KzO3 13.59 -1.05 4.52 350 from our results. This value is in agreement 13.50 -3.14 5.18 X 10 400 with that reported by -4bel and Proisl.2z 1.51 x 103 13.29 -7.27 500 Extensive thermodynamic data on the NO213.03 -11.36 1.38 x 104 600 N204system had been reported earlier by Giauque 6.44 x 104 12.74 -15.40 700 and Kemp.Z3 Our free energy functions in the 2.00 x 105 12.43 -19.40 800 temperature range 2 i 5 to 400°K. are larger by ap4.71 x 105 12.10 -23.36 900 proximately 0.5 to 0.3 e.u. than those reported 8.95 X los 11.76 -27.24 1000 by Giauque and Kemp. Our AH&' of 12.69 kcal./ mole may be compared to 12.88 kcal./mole estiTABLE VI1 mated by these investigators. These differences THERMODYNAMIC FUNCTIONS FOR Nz06 f NO3 are due to the use of more recent vibrational frequencies in our work. I n order to check (AH#= 20.51 KCAL./MOLE) whether the torsional frequency deduced from the AFQ AH0 (kcal./mole) (kcal. /mole) T,OK. Keq (atm.) difference between the experimental and spectro21.05 17.97 5.25 X 100 scopic entropy was reasonable or not, we had 21.29 7.01 x 10-17 14.78 200 calculated earlierz4the Cp values in the tempera13.15 21.33 3.19 X 250 ture range of 20 to 260°K. for solid XZO4using the 21.33 1.58 X 12.33 275 method of Lord.25 We also calculated the entropy 3.28 x 10-9 11.57 21.33 298.16 of the solid a t 262"1
