Research: Science and Education
Equations of State and Phase Diagrams of Ammonia Leslie Glasser Nanochemistry Research Institute, Department of Applied Chemistry, Curtin University of Technology, Perth WA, 6845, Australia;
[email protected];
[email protected] • Solid and vapor densities (or molar volumes) for the sublimation–condensation curves (A and B)
• Solid and liquid densities for the melting–freezing curves (E)
• Liquid and vapor densities for the saturation curve (“coexistence dome”) (C and D)
4
II
critical point
solids I
liquid
E
pT projection
C
Tb
B. Vapor condensation, in equilibrium with solid (estimated)
C. Liquid saturation, in equilibrium with vapor
D. Vapor saturation, in equilibrium with liquid
E. Solid–liquid melt equilibria, for solid phases I to III. The two separate curves, for solid and liquid in equilibrium, nearly overlay one another on the scale of the diagram.
Data for ammonia are incomplete in that little information exists below the triple-point temperature (‒77.75 °C = 195.4 K). Thus, the curves A and B are estimated and, correspondingly, indicated with dots. The pT properties of the solid phases, I–V, and their relation to the liquid phase are represented in Figure 2. The II– III-fluid triple point has not yet been determined because no corresponding discontinuity has been observed on the melting
0
vapor
D
∙2
triple “point” line 1
A
2
log
3
B
∙4
VT projection
400
300 4
10(V m
200
5
/ [cm3 m6
7
100
ol∙1]
T/K
)
Figure 1. Perspective 3-D pVT diagram for ammonia, with projections onto the pT, pV, and VT planes. To accommodate the full range of data, logarithms of pressure and molar volume are used. Horizontal lines (constant pT ) are tielines connecting phases (of differing volume) in mechanical and thermal equilibrium across the phase gaps; the label Tb is attached to the boiling point (100 kPa) tieline. The end dot of the liquid–vapor line in the pT projection represents its termination at the critical point. Volumes in the diagram (actually “space curves”, corresponding to areas in the projections) are labeled solid, liquid, vapor, and (above the critical point) gas. I, II, and III refer to the respective solid phases that can equilibrate with liquid ammonia.
V orthorhombic
14
12
Pressure / GPa
A. Solid sublimation, in equilibrium with vapor (estimated)
2
pV projection
The space curves depicted in Figure 1 are
gas
liquid
log10(p / MPa)
III
solids
Ammonia is a material of considerable importance industrially, commercially, and theoretically (1). It is produced in exceedingly large quantities internationally (with annual production approaching or even exceeding 150 million tonnes), is widely used for agriculture and refrigeration, and has many applications in synthesis, such as for explosives, plastics, pharmaceuticals, and so forth. It is used in liquid form as a nonaqueous ionizing solvent, permitting the exploration of solute properties under novel conditions. Ammonia is abundant cosmically, being proposed to exist as “hot ices” in the interiors of Uranus and Neptune, as stoichiometric hydrates in many icy moons of the outer planets, and present in the cloud layers on Jupiter and Saturn (2). Together with hydrogen and water, it is believed on theoretical grounds to exhibit a “superionic” phase under extremes of pressure and temperature (3), returning to a hydrogenbonded form under still more extreme conditions (3b), but such phases have not yet been observed experimentally. Consequently, there is interest in the thermodynamic and other properties of ammonia in each of its gaseous or vapor, liquid, and solid phases. We present thermodynamic data (in the form of equations of state, EoS) on ammonia in these phases, together with a three-dimensional (3D) pVT phase diagram that is not available elsewhere. The current presentation follows earlier presentations of the phase diagrams of carbon dioxide (4) and of “ordinary water substance” (5), in which details of the nature and interpretation of EoS and of phase diagrams are laid out. The data required for the phase diagram (Figure 1) are equilibrium temperatures and pressures and
IV orthorhombic
10
8
6
4
2
III fcc I cubic
II hcp
fluid
0 200
250
300
350
Temperature / K Figure 2. Phase diagram projected onto the pT plane for the condensed phases of ammonia (NH3), including a depiction of the structure of solid IV. Modified from Figure 1 of S. Ninet and F. Datchi, J. Chem. Phys. 2008, 128, 154508.
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 86 No. 12 December 2009 • Journal of Chemical Education
1457
Research: Science and Education
curve. Both phases II and III are plastic with large orientational disorder, hence very similar in properties; thus, the transition is represented in Figure 2 (3a) as a broad range. The extension of the IV–V coexistence line to high temperature and low pressure is uncertain. The volume difference between phases IV and V is very small, and any discontinuity at a supposed III–IV–V triple point would be difficult to detect. Alternatively, the IV–V coexistence curve may simply terminate in a Landau critical point (3a). The principal resource for data on the liquid and vapor phase properties of NH3 is the comprehensive early review by Haar and Gallagher (6), supplemented by the update of Xiang (7). The situation is more complex for the solid phases because many of these have only been discovered in more recent years. Equations of state for the various phase equilibria of NH3 (and used in the preparation of Figure 1) are listed in the online material; a chronological bibliography (with titles) provides access to much of the important recent and relevant literature. Thermodynamics Although it has not been emphasized in these presentations (4, 5), there is much thermodynamic information associated with the EoS and the accompanying phase diagrams, such as the transition entropies, enthalpies, and volumes through the Clapeyron equation:
dp Δ S Δ trans Hm = trans m = dT Δ trans Vm Ttrans Δ trans Vm
(1)
and the counterpart Clausius–Clapeyron equation, applicable when one of the phases involved is gaseous and treated as ideal:
d ln p Δ H = vap 2m dT R Tvap
(2)
These equations describe the slopes of the curves in the pT projection. The Clausius–Clapeyron slope is always positive because the transition enthalpy from condensed to gaseous phase is always positive. The Clapeyron slope may be positive (as in the I–II transition of Figure 2) or negative (as in the I–IV and IV–V transitions), depending on the sign of the volume change on the phase transition because the enthalpy change on temperature increase is positive. Extensive collations of such data for liquid and vapor NH3 (as well as for many other materials, such as carbon dioxide and water) are available from the NIST Chemistry WebBook (8) and in a series of articles by Yaws and colleagues in the journal Chemical Engineering (9). Thermodynamic data for the solid phases can often be found in the literature listed in the accompanying chronological bibliography (see the online material).
1458
Virtual Interactive Three-Dimensional Phase Diagrams Virtual, interactive, 3D versions of the phase diagrams of carbon dioxide (4) and water (5), programmed in Jmol by Angel Herráez, have been described in a recent letter to this Journal (10) and are available as supporting online material (11). With ammonia added, the set of three Jmol phase diagrams is available from the biomodel Web site (12). Literature Cited 1. Wikipedia Entry for Ammonia. http://en.wikipedia.org/wiki/ Ammonia (accessed Oct 2009). 2. Fortes, A. D.; Brodholt, J. P.; Wood, I. G.; Vočadlo, L. J. Chem. Phys. 2003, 118, 5987–5994. 3. (a) Ninet, S.; Datchi, F. J. Chem. Phys. 2008, 128, 154508. (b) Pickard, C. J.; Needs, R. J. Nature Matls. 2008, 7, 775–779. 4. Glasser, L. J. Chem. Educ. 2002, 79, 874–876; (The factor 106 was incorrectly omitted from the value for the van der Waals a of CO2). 5. Glasser, L. J. Chem. Educ. 2004, 81, 414–418, 645; (In the final equation, for the sublimation–pressure curve of ice, the last exponent should be ‒1.25 rather than 1.25). 6. Haar, L.; Gallagher, J. S. J. Phys. Chem. Ref. Data 1978, 7, 635–792. 7. Xiang, H. W. J. Phys. Chem. Ref. Data 2004, 33, 1005–1011. 8. NIST Chemistry WebBook. http://webbook.nist.gov/chemistry/ (accessed Oct 2009). 9. Ammonia and hydrazine: Yaws, C. L.; Hopper, J. R.; Rojas, M. G. Chem. Eng. 1974, 81(25), 91–100. Carbon monoxide and dioxide: Yaws, C. L.; Li, K. Y.; Kuo, C. H. Chem. Eng. 1974, 81 (20), 115–122. Water and hydrogen peroxide: Yaws, C. L.; Setty, H. S. N. Chem. Eng. 1974, 81 (27), 67–74. 10. Herráez, A.; Hanson, R. M.; Glasser, L. J. Chem. Educ. 2009, 86, 566. 11. 3D Phase Diagrams. http://www.jce.divched.org/Journal/ Issues/2009/May/jcesubscriber/JCESupp/JCE2009p0566W/ phase-diagrams.htm (accessed Oct 2009). 12. Biomodel Web site. http://biomodel.uah.es/Jmol/plots/ phase-diagrams/ (accessed Sep 2009).
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2009/Dec/abs1457.html Abstract and keywords Full text (PDF) Links to cited URLs and JCE articles Figures 1 and 2 in color Supplement Notes on subscripts, suffixes and constants Equations and data for ammonia Chronological bibliography of the phases of ammonia
Journal of Chemical Education • Vol. 86 No. 12 December 2009 • www.JCE.DivCHED.org • © Division of Chemical Education
