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J. Phys. Chem. A 2010, 114, 11654–11655
Revised Thermochemistry of Gaseous Ammonium Nitrate, NH4NO3(g) D. L. Hildenbrand,*,† K. H. Lau,† and D. Chandra‡ SRI International, Menlo Park, California 94025, United States, and Metallurgical and Materials Engineering, UniVersity of NeVada, Reno, NeVada 89557, United States ReceiVed: June 22, 2010; ReVised Manuscript ReceiVed: July 20, 2010
In an earlier paper (Hildenbrand, D. L.; Lau, K. H.; Chandra, D. J. Phys. Chem. B 2010, 114, 330.), we detected the presence of NH4NO3(g) in the vapor over the solid nitrate and evaluated its partial pressure along with those of HNO3 and NH3. The molecular constants of the gaseous nitrate were estimated in the absence of experimental values in an attempt to derive its enthalpies of sublimation and formation. After publication, we became aware of the sought molecular data, evaluated primarily from high-level theoretical calculations, and revised the analysis to yield ∆fH°298(NH4NO3(g)) ) -61.8 ( 5 kcal mol-1. TABLE 1: Revised Molecular Constants of NH4NO3(g)
Introduction 1
As described in a recent paper, we studied the vaporization of crystalline ammonium nitrate, NH4NO3(c), in the range of 320-360 K, by the torsion-effusion method, with vapor analysis by mass spectrometry. In addition to the expected HNO3 and NH3, the MS identified the stable parent ion, NH4NO3+, with a threshold ionization energy of 11.0 ( 0.3 eV, clearly indicating the presence of NH4NO3(g); no N-H-O fragment ions were observed. From simultaneous measurement of total pressure and mass loss using the torsion-effusion method, the partial pressures of the three species were determined,1,2 and an attempt was made to evaluate the enthalpies of vaporization and formation of NH4NO3(g). The thermodynamic analysis required information about the rotational and vibrational energy levels of NH4NO3(g), but in the absence of experimental data, we estimated these molecular parameters from data on similar molecules and submitted the resulting information. After publication,1 we became aware of an experimental determination of the structure and rotational constants of NH4NO3(g), along with several theoretical papers reporting both the calculated structural and vibrational parameters of NH4NO3(g), all done with high-level ab initio calculations. It seemed worthwhile to use this information in revising the third law calculations of the enthalpies of sublimation and formation of NH4NO3(g), and this was done, as described in the next sections. In particular, the ab initio vibrational frequencies made a large difference in the final results. Selected Molecular Constants of NH4NO3(g) In order to do the preferred third law analysis of NH4NO3 sublimation, we adopted the rotational constants of Ott and Leopold3 obtained from microwave spectroscopy and also the ab initio results of Tao,4 which yielded rotational constants agreeing within a few percent. When the average values were converted to units of g cm2, they yielded the moment of inertia product IXIYIZ ) 8.50 × 10-114 g3 cm6. This value was then used to calculate the rotational contribution to the thermodynamic functions of NH4NO3(g). * To whom correspondence
[email protected]. † SRI International. ‡ University of Nevada.
should
be
addressed.
E-mail:
moments of inertia product vibration frequencies, ω, in cm-1 ground state symmetry number ) 1
IXIYIZ ) 8.50 × 10-114 g3 cm6 3586, 3472, 2732,1733, 1656,1511, 1326, 1151, 953, 691, 660, 430, 248, 106, 3592, 1668, 1097, 791, 339, 73, 61 1 Σ, no significant excited states
Likewise, the 21 harmonic frequencies of NH4NO3(g) were evaluated from the derived molecular structure and the theoretical calculations. The calculated frequencies of Alavi and Thompson,5 and Kumarasiri, Swalina, and Hammes-Schiffer6 differ only slightly and were accepted; also in accord are those of Nguyen, Jamka, Cazar, and Tao.7 The selected molecular constants are listed in Table 1; these functions are based on the ideal gas state at 1 bar of pressure. They were used in calculating the revised Gibbs energy functions of NH4NO3(g), which were needed, in turn, in evaluating the third law enthalpy of sublimation of NH4NO3. Sublimation Enthalpy and ∆fH°298 of NH4NO3(g) Table 2 lists the sublimation pressure, P, of NH4NO3(g) over the range of 321-360 K, as derived from the total pressures measured by the torsion-effusion method and the NH4NO3 partial pressure of (0.21PT), evaluated as described in the earlier paper.1 Also shown are the changes in the Gibbs energy function, ∆gef, and the corresponding third law enthalpies of sublimation for each data point, calculated from the relation ∆H°298 ) T(∆gef - R ln K), where R is the gas constant and K is the reaction equilibrium constant. For the sublimation data reported here, K is the pressure P. These new molecular constants, derived primarily from the ab initio calculations,3-7 lead to an average third law value of ∆H°298 ) 25.6 kcal mol-1 for the reaction NH4NO3(c) ) NH4NO3(g) at 298 K. The earlier reported value1 of ∆H°298 was 20.9 kcal mol-1, based on estimated molecular constants. Presumably, the new molecular constants are more reliable than the earlier values,1 but it is nevertheless difficult to gauge the level of uncertainty in the new enthalpy of sublimation, which is strongly dependent on the accuracy of the ab initio calculations. Perhaps it is best to be cautious at this point and adopt a value of 25.6 ( 5 kcal mol-1 for the NH4NO3 enthalpy
10.1021/jp105773q 2010 American Chemical Society Published on Web 10/08/2010
Revised Thermochemistry of NH4NO3(g)
J. Phys. Chem. A, Vol. 114, No. 43, 2010 11655
TABLE 2: Third Law Analysis of the Sublimation Process NH4NO3(c) ) NH4NO3(g) T, K
P, NH4NO3, bar
∆gef298,cal mol-1
∆H°298, kcal mol-1
321.0 323.8 325.0 328.1 328.9 332.8 333.4 334.6 337.6 338.5 340.1 340.5 342.1 344.8 345.9 346.5 348.1 351.7 353.8 354.8 355.0 358.2 358.4 358.9 360.0 360.4
4.95 × 10-8 6.68 × 10-8 7.75 × 10-8 1.06 × 10-7 1.18 × 10-7 1.79 × 10-7 1.86 × 10-7 2.13 × 10-7 2.89 × 10-7 3.05 × 10-7 3.75 × 10-7 3.72 × 10-7 4.42 × 10-7 5.80 × 10-7 6.46 × 10-7 6.82 × 10-7 7.86 × 10-7 1.09 × 10-6 1.33 × 10-6 1.41 × 10-6 1.50 × 10-6 1.85 × 10-6 1.93 × 10-6 1.88 × 10-6 2.19 × 10-6 2.22 × 10-6
45.69 45.68 45.67 45.66 45.66 45.65 45.65 45.64 45.64 45.63 45.63 45.63 45.62 45.62 45.62 45.61 45.61 45.60 45.60 45.60 45.60 45.50 45.59 45.59 45.59 45.59 third law avg second law 298
25.40 25.42 25.42 25.45 25.44 25.47 25.49 25.49 25.51 25.54 25.52 25.55 25.56 25.57 25.58 25.58 25.60 25.63 25.65 25.68 25.65 25.73 25.71 25.77 25.73 25.75 25.6 23.2 ( 3
TABLE 3: Revised Ideal Gas Thermodynamic Functions of NH4NO3(g) ∆fH°298 ) -61.8 kcal mol-1 T, K
-(G° - H°298)/T, cal deg-1 mol-1
S°, T cal deg-1 mol-1
H°T - H°298, kcal mol-1
Cp, cal deg-1 mol-1
298 300 400 500 600 700 800 900 1000
81.82 81.82 82.74 84.58 86.78 89.10 91.43 93.74 96.00
81.82 81.95 88.87 94.97 100.46 105.46 110.06 114.32 118.28
0.00 0.04 2.45 5.19 8.21 11.46 14.90 18.52 22.28
22.30 22.37 25.83 28.84 31.39 33.54 35.36 36.92 38.27
of sublimation. Combining this sublimation enthalpy of NH4NO3 with the enthalpy of formation of the solid8 gives for the gas ∆fH°298(NH4NO3(g)) ) (25.6 ( 5) + (-87.4 ( 0.7) ) -61.8 ( 5 kcal mol-1 or -258.6 ( 21 kJ mol-1 (see Table 3). Discussion The adjoining paper in this journal10 contains a purely theoretical treatment of the thermochemistry of NH4NO3(g), by K. K. Irikura, yielding ∆fH°298(NH4NO3(g)) ) -55.1 ( 0.7 kcal mol-1 or -230.6 ( 3 kJ mol-1. This is 6.7 kcal mol-1 less negative than our experimental value, which has an approximate uncertainty of 5 kcal mol-1; it is difficult to account for this difference. At present, there is no clear clue to specific sources of error in the experimental work or in the auxiliary thermodynamic data. The measured total pressure over NH4NO3(c) is known to be accurate within 5% from checks with vapor
pressure standards.9 To then account for the 6.7 kcal mol-1 difference, the derived partial pressure of NH4NO3(g) would have to be too large by a factor of more than 104, which seems incredible from the ion intensities observed. Therefore, the disparity between experimental and theoretical values for the enthalpy of formation of NH4NO3(g) remains unresolved. Incidentally, in the earlier paper,1 we encouraged interested theoreticians to evaluate some of the structural and thermochemical properties of NH4NO3, and the adjoining paper by Irikura10 is a response to that call. It is ironic that most of what we now know about the physical properties of gaseous NH4NO3 is related to the significant number of theoretical calculations initiated to learn more about the role of this interesting molecule in atmospheric chemistry. Even this thermochemical analysis is highly dependent on the calculated molecular structure and vibrational frequencies. However, it surely simplifies the calculations to be dealing with atoms number 1, 7, and 8 in the periodic table. Reference 4 contains the following statement in the Conclusions section: “Our previous study of HNO3-NH3 has concluded that it is unlikely for nitric acid and ammonia to form gaseous ammonium nitrate and that the formation of particulate ammonium nitrate most likely involves a heterogeneous mechanism. This conclusion is primarily based on the ab initio results that pure ammonium nitrate does not exist in the gas phase.” Taken at face value, this conclusion contradicts the experimental structural data obtained by microwave spectroscopy3 and the mass spectrometric data reported here. However, the statement is perhaps largely a matter of semantics and depends on whether one is referring to an ionic structure of gaseous NH4NO3, as it apparently is here, or the hydrogen-bonded structure. There is no doubt that the gaseous NH4NO3 molecule is indeed stable and that this must be the hydrogen-bonded structure. In any event, it is scientifically interesting to know that research on the properties of atmospheric trace gases such as ammonia and nitric acid, along with others, is being actively carried on by means of chemical modeling, using high-level theoretical calculations. In truth, however, there will always be a need for both theoretical and experimental studies as the two methods are dependent on each other in dealing with disparities which need resolution. Acknowledgment. D.L.H. is grateful for many helpful exchanges with Dr. K. K. Irikura during the preparation of this paper. References and Notes (1) Hildenbrand, D. L.; Lau, K. H.; Chandra, D. J. Phys. Chem. B 2010, 114, 330. (2) Lau, K. H.; Cubicciotti, D.; Hildenbrand, D. L. J. Electrochem. Soc. 1979, 126, 490. (3) Ott, M. E.; Leopold, K. R. J. Phys. Chem. A 1999, 103, 1322. (4) Tao, F.-M. J. Chem. Phys. 1998, 108, 193. (5) Alavi, S.; Thompson, D. T. J. Chem. Phys. 2002, 117, 2599. (6) Kumarasiri, M.; Swalina, C.; Hammes-Schiffer, S. J. Phys. Chem. B 2007, 111, 4653. (7) Nguyen, M.-T.; Jamka, A. J.; Cazar, R. A.; Tao, F.-M. J. Chem. Phys. 1997, 106, 8710. (8) IVTANTHERMO Database on Thermodynamic Properties of IndiVidual Substances; CRC Press: Boca Raton, FL, 2005. (9) Naphthalene, C10H8, is used as a standard in the room-temperature region, with Ag and Au used at elevated temperatures. (10) Irikura, K. K. J. Phys. Chem. A 2010, 114, DOI: 10.1021/jp105770d.
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