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Thermochemistry of Gaseous Ammonium Nitrate, NH4NO3(g) D. L. Hildenbrand,*,† K. H. Lau,† and D. Chandra‡ SRI International, Menlo Park, California 94025 Metallurgical and Materials Engineering, UniVersity of NeVada, Reno, NeVada 89557 ReceiVed: August 20, 2009; ReVised Manuscript ReceiVed: October 20, 2009
From the measured molecular weight of vapor over NH4NO3(c) by the simultaneous torsion-effusion/mass loss method, the partial pressure of NH4NO3(g) was evaluated over the range 321-360 K; in addition, the presence of the gaseous nitrate was verified by effusion-beam mass spectrometry. Third-law calculations of the sublimation enthalpy of NH4NO3 were made with estimated molecular constants, yielding ∆Ho298(sub) ) 20.9 ( 2 kcal mol-1, as compared to a less-reliable second-law value of 23.2 ( 3 kcal mol-1. We prefer the third-law value, which leads to the enthalpy of formation ∆fHo298 (NH4NO3(g)) ) -66.5 ( 2.1 kcal mol-1 when combined with the known ∆fHo298 value of NH4NO3(c). Introduction The gas-generating properties of ammonium nitrate, NH4NO3, are of interest in connection with its use in automotive air bags, making its chemical and physical properties of special interest to engineers and scientists. It is known1,2 that condensed NH4NO3 vaporizes primarily by decomposition to NH3(g) and HNO3(g), rather than the equilibrium dissociation products N2(g), H2(g), and H2O(g). It is worth noting this tendency on the part of some thermodynamically unstable substances to dissociate only partially (likely due to kinetic barriers), since purely equilibrium calculations will sometimes be misleading as to the expected products. To our knowledge, however, the formation of a stable gaseous NH4NO3 molecule has not previously been established. In a current study of NH4NO3 vapor pressure and vapor composition in this laboratory,3 examination of the vapor by effusion-beam mass spectrometry clearly showed the presence of molecular NH4NO3, along with NH3 and HNO3; this work,3 however, did not include studies on the thermochemistry of NH4NO3(g). Furthermore, the analysis of vapor molecular weights derived from simultaneous torsion-effusion/ mass loss measurement yielded the partial pressures of these three species. Since nothing appears to be known about the thermochemistry of this gaseous nitrate, we estimated the molecular constants and did a third-law analysis of the sublimation process so as to evaluate the standard enthalpy of formation, o (NH4NO3(g)). ∆fH298 Because the torsion-effusion method of vapor pressure measurement and its application to determining vapor composition plays such a major role in the type of studies described here, it is worth a few words of comment. This remarkable method, elegant in its simplicity, was first reported by Volmer4 in 1931 when he and his students were primarily interested in determining the molecular weights of organic compounds in the room temperature region. The sample is contained in a chamber arranged with opposed, offset orifices and suspended from a small fiber or ribbon, all within an evacuated enclosure. Free molecular flow of sample vapor induces a recoil force and angular rotation of the cell. At sample pressures in the molecular flow region, total pressure can be evaluated from the angular * Corresponding author: E-mail:
[email protected]. † SRI International. ‡ University of Nevada.
deflection, the torsion constant of the filament, and the geometrical constants of the cell. If the mass loss of the sample is measured simultaneously, the molecular weight of the sample vapor can be evaluated. Since then, many others have applied the torsion method to study high-temperature vaporization processes. Over nearly a half century, our experience has been that the method is exceptionally reliable, particularly if one takes special care in determination of the angular deflection for each data point. Experimental Aspects For the NH4NO3 torsion pressure and vapor molecular weight measurements, two different Pt-Rh effusion cells were used with orifice diameters of 0.06 (P2) and 0.11 (P1) cm, each pair having essentially equal orifice dimensions. The cell is suspended from a Pt-10% Ni ribbon attached to the arm of a Cahn 1000 electrobalance. Checks with laboratory standards indicate that absolute pressures and vapor molecular weights are accurate to within 5%. The experimental procedure is described in the literature.5,6 For complex vaporization processes, the individual partial pressures can be evaluated from the measured vapor molecular weights, as described previously.7 Mass spectrometric analysis of the vapor over NH4NO3(c) was done with the magnetic sector instrument used in many previous studies.8,9 This instrument has an effusion cell source with a movable slit that differentiates between ion signals from the sample and from possible background gases. For the vapor analysis, the NH4NO3(c) sample was contained in a Pt effusion cell. The NH4NO3 sample used in these measurements was an ACS grade of 98% purity. Determination of Species Partial Pressures As noted above, mass spectrometric analysis of the vapor over NH4NO3(c) indicated the presence of a moderately strong beam signal at m/e 80 from NH4NO3(g), in addition to those from NH3(g) and HNO3(g). These individual species partial pressures were sorted out by analysis of the measured vapor molecular weights, M*. The torsion total pressures were obtained with the smaller orifice cell, P2, over the range 332.8-360.4 K and are summarized in Table 1; pressures obtained with P1 were
10.1021/jp908062d 2010 American Chemical Society Published on Web 11/20/2009
Thermochemistry of NH4NO3(g)
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TABLE 1: Mass Loss Rates, Total Pressure, and Molecular Weights of Vapor Over NH4NO3(c) in Pt/Rh Cell P2
TABLE 2: Third Law Analysis of the Sublimation Process NH4NO3(c) ) NH4NO3(g)
T, K
mass loss, mg/h
PT, bar
M*, g/mol
T, K
P, (NH4NO3), bar
∆gef298, cal mol-1
∆Ho298, kcal mol-1
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
0.304 0.309 0.359 0.478 0.520 0.620 0.630 0.716 0.952 1.056 1.112 1.284 1.812 2.180 2.300 2.345 2.980 3.064 3.000 3.524 3.536
8.51 × 10-7 8.85 × 10-7 1.02 × 10-6 1.37 × 10-6 1.45 × 10-6 1.78 × 10-6 1.77 × 10-6 2.10 × 10-6 2.76 × 10-6 3.08 × 10-6 3.24 × 10-6 3.74 × 10-6 5.20 × 10-6 6.33 × 10-6 6.69 × 10-6 6.99 × 10-6 8.23 × 10-6 9.17 × 10-6 8.95 × 10-6 1.04 × 10-5 1.06 × 10-5 av M* )
52.9 50.0 51.4 50.2 53.5 50.6 52.9 48.7 50.4 50.1 50.0 50.4 52.5 51.6 51.5 49.1 50.3 49.2 49.5 50.7 49.6 50.7 ( 1.1 g/mol
321.0 323.8 325.0 328.1 328.9 332.8 333.4 334.6 337.6 338.5 340.5 342.1 344.8 345.9 346.5 348.1 351.7 353.8 354.6 355.0 358.2 358.4 358.9 360.0 360.4
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 2.80 × 10-7 3.05 × 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
32.18 32.17 32.16 32.16 32.15 32.14 32.14 32.14 32.13 32.12 32.12 32.11 32.11 32.10 32.10 32.10 32.08 32.08 32.08 32.08 32.07 32.06 32.06 32.06 32.06 third law second law
21.06 21.05 21.03 21.02 21.00 20.97 20.98 20.97 20.95 20.97 20.95 20.93 20.91 20.90 20.90 20.90 20.88 20.86 20.88 20.85 20.88 20.86 20.91 20.86 20.88 av 20.93 ∆Ho298 ) 23.2 ( 3
only marginally lower, showing a small orifice size effect. As can be seen, these weight-average M* values are reasonably consistent at 50.7 ( 1.1 g/mol and are essentially temperatureindependent over the range studied. The contributions from the individual species can be expressed in the composite expression
(∑ n
M* )
miMi-1/2
[(
i)1
)
-2
)
1/2 1/2 1/2 (1 - b)MNH + bMNH + bMHNO 4NO3 3 3
(1 - b)MNH4NO3 + bMNH3 + bMHNO3
)]
-2
(1)
where m and M are the species mass fractions and molecular weights, respectively. The full eq 1 follows from the expression for the average molecular weight of a multicomponent effusing vapor, as described previously.7 M* now refers to the molecular weight of the composite system of NH3, HNO3, and NH4NO3. Equation 1 can be reduced to the expression
M* ) [(8.9467 + 3.1182b)/80.0432]-2
(2)
when the individual molecular weights are substituted. From the experimental value M* ) 50.7, eq 2 yields the value b ) 0.736. The partial pressure of NH4NO3(g) can then be evaluated from the expression PNH4NO3/PT ) 8.9467(1 - b)/(8.9467 + 3.1182b) ) 0.210
Similarly, the partial pressures of NH3 and HNO3 are 0.270 and 0.520, respectively. Note that these two values are not equal under effusion conditions, since the gas kinetic velocities of the two differ significantly, and the system adapts the effusion rates to keep the stoichiometry of NH4NO3(c) in the cell unchanged.
Results Table 2 lists the sublimation pressures of NH4NO3(g) over the range 321-360 K, as derived from the total pressures measured by the torsion-effusion method and the NH4NO3 partial pressure of (0.210PT), evaluated as described above from the measured vapor molecular weight data. Also shown are the changes in Gibbs energy function, ∆gef, and the corresponding third-law enthalpies of sublimation for each data point. gef298 is the thermodynamic quantity -(GoT - Ho298)/T which can be evaluated for each gaseous species from spectroscopic and molecular constant data, and with which the third-law enthalpies of reaction can be derived from the o ) T(∆gef298 - R ln K), where R is the gas relation ∆H298 constant and K is the reaction equilibrium constant. For the sublimation pressure data treated here, K is the pressure, P, and as seen in Table 2, the third law analysis yields an average o (sub) ) 20.9 ( 2 kcal mol-1. The estimated uncertainty ∆H298 o (sub) is essentially wholly due to uncertainties in the in ∆H298 gef values for NH4NO3(g). The second law enthalpy, derived in this instance from the slope of the total pressure, log PT vs 1/T, and corrected to 298 K is in reasonably good agreement at 23.2 ( 3 kcal mol-1. Note that only PT was measured (from the cell angular deflection), not the individual ion signals from gaseous NH4NO3, NH3, and HNO3. We prefer the more direct third-law enthalpy of sublimation. Combining this with the tabulated value10 ∆fHo298(NH4NO3(c)) ) -87.4 ( 0.7 kcal mol-1, one derives for o (NH4NO3(g)) ) -87.4 + 20.9 ) the gaseous molecule ∆fH298 -1 -66.5 ( 2.1 kcal mol . These thermodynamic data for the gaseous nitrate should serve well enough in modeling calculations until an improved value appears. A table of the standard thermodynamic functions of NH4NO3(g), calculated from the constants described below is given in Table 3; these functions are based on the ideal gas state at 1 bar pressure. As long as the thermal functions tabulated here are used, equilibrium
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TABLE 3: Ideal Gas Thermodynamic Functions of o NH4NO3(g) ∆fH298 ) -66.5 kcal mol-1 T, K
-(Go - Ho298)/T, cal deg-1 mol-1
STo , cal deg-1 mol-1
HTo - Ho298, kcal mol-1
Cp, cal deg-1 mol-1
298 300 400 500 600 700 800 900 1000
68.28 68.28 69.09 70.77 72.82 75.00 77.23 79.44 81.62
68.28 68.40 74.59 80.34 85.64 90.53 95.04 99.22 103.12
0.00 0.04 2.20 4.78 7.70 10.87 14.25 17.80 21.50
19.14 19.24 23.91 27.61 30.51 32.82 34.72 36.33 37.70
TABLE 4: Summary of Estimated Molecular Constants of NH4NO3(g) moments of inertia product vibrational frequencies, ωi in cm-1 ground state symmetry number ) 2
IxIyIz ) 4.0 × 10-114 g3 cm6 350, 400, 450, 500, 600, 700(2), 800, 830, 890, 1020, 1050, 1300, 1320, 1700(3), 3500, 3600(3) 1 Σ; no significant excited states
calculations will reproduce the NH4NO3 measured partial pressures listed in Table 2. Estimation of Molecular Constants In the absence of any established molecular constants, a planar structure was assumed for NH4NO3, similar to that of HNO3(g),11,12 with an NH3 group joined at the H position of HNO3, making a symmetrical NH4 arrangement. The N-H, O-H, and N-O internuclear distances plus the O-N-O angles were taken from the JANAF Table11 values for NH3 and HNO3. This arrangement yielded the calculated moments of inertia product IxIyIz ) 4.0 × 10-114 g3 cm6. A provisional set of vibrational frequencies was assembled by taking the nine known values of HNO3 (1320, 890, 700, 1700, 600, 800, 3600, 1300, and 500 cm-1) and the six of NH3 (3500, 1020, 3600(2), and 1700(2) cm-1) plus estimated values of 350, 400, and 450 cm-1 for the expected bending modes in the joined molecule. Three additional values of 700, 830, and 1050 cm-1 were adopted on the basis of those observed in the infrared and Raman spectra of thin films of solid NH4NO3 at low temperatures;13,14 these are internal modes, not lattice modes. These estimated molecular constants are summarized in Table o 4. A plot of the calculated functions -(GTo - H298 )/T and Cp over the range 300-1000 K is shown in Figure 1. Discussion It would be highly desirable to have theoretical calculations for both the structure and the vibrational frequencies of NH4NO3, something that should be reasonably accurate, even for a for a nine-atom molecule made up of these first- and second-row elements. Because of the demise of experimental thermochemistry, theoretical calculations would be especially welcome, and comparison of the calculated thermochemical results for
Figure 1. Plot of Gibbs energy function and heat capacity of NH4NO3(g) from 300 to 1000 K, calculated from estimated molecular constants. NH4NO3(c) f 0.21 NH4NO3(g) + 0.27 NH3(g) + 0.52 HNO3(g).
NH4NO3 (g) from several of the popular theoretical methods such as the G2 and DFT would also be very instructive and useful in firming up the properties of this industrially important nitrate. References and Notes (1) Feick, G. J. Am. Chem. Soc. 1954, 76, 5858. (2) Brandner, J. D.; Junk, N. M.; Lawrence, J. W.; Robins, J. J. Chem. Eng. Data 1962, 7, 227. (3) Chien, W. M.; Chandra, D.; Lau, K. H.; Helmy, A. K. Vapor Pressure Measurement of NH4NO3 by the Torsion Effusion Method. J. Chem. Eng. Data., to be submitted for publication. (4) Volmer, M. Z. Phys. Chem., Bodenstein Festband, 1931 , 863. (5) Lau, K. H.; Cubicciotti, D.; Hildenbrand, D. L. J. Chem. Phys. 1977, 66, 4532. (6) Colominas, C.; Lau, K. H.; Hildenbrand, D. L.; Crouch-Baker, S.; Sanjurjo, A. J. Chem. Eng. Data 2001, 46, 446. (7) Lau, K. H.; Cubicciotti, D.; Hildenbrand, D. L. J. Electrochem. Soc. 1979, 126, 490. (8) Hildenbrand, D. L. J. Chem. Phys. 1968, 48, 3647; 1970, 52, 5751. (9) Lau, K. H.; Hildenbrand, D. L. J. Chem. Phys. 1987, 86, 2949. (10) IVTANTHERMO Database on Thermodynamic Properties of IndiVidual Substances; CRC Press: Boca Raton, FL, 2005. (11) Chase, M. W.; Davies, C. A.; Downey, J. R.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables. J. Phys. Chem. Ref. Data 1985, 14, Suppl. No. 1. (12) Forsythe, W. R.; Giauque, W. F. J. Am. Chem. Soc. 1942, 64, 48. (13) Theoret, A.; Sandorfy, C. Can. J. Chem. 1964, 42, 57. (14) Akiyama, K.; Moriyoka, Y.; Nakagawa, I. Bull. Chem. Soc. Jpn. 1981, 54, 1667.
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