--..-- -, RALPHK. BIRDWHISTELL
textbook forum
Univenity of West Florida Pensamla, FL32504
Phase Diagrams of One-Component Systems What Most Textbooks Don't Say, but Should! Gavin D. Peckham
University of Zululand, Private Bag X I 001,Kwa Dlangezwa, 3886,South Africa Ian J. McNaught
University of Natal, P. 0.Box 375,Pietermaritzburg, 3200,South Africa The pressure-temperature phase diagrams of simple one- component systems form a part of most chemistry courses ( I )both at high school and at undergraduate level. Thus, the topic is covered by a large number of reputable textbooks. It is surprising to find that many of them contain errors and omissions that have drawn little comment in educational journals (2,3). Figure 1shows the way in which the P-Tphase diagram for a one-component system is typically presented. The fact that the liquidhapor equilibrium line terminates at a critical point is strongly emphasized in virtually every textbook. Despite this emphasis, both the diagrams and the accompanying explanations fail to give equal treatment to the other equilibrium lines that usually are drawn ending in the middle of nowhere (see Fig. 1).In fact, the solidhapor line goes to the origin in all known cases except that of helium (4) (see Fig. 2) and the solicllliquid line has no known upper limit (5).It may be a good idea to emphasize this fact by ending the solicllliquid line with an arrow head or with a series of dots (see Fig. 2). The vast majority of textbooks take care to indicate that the liquidlvapor equilibrium line cannot extend to regions above the critical temperature but fail to indicate that the solidniquid equilibrium line is not restricted in this way and also extends above the critical temperature at very
A
) CRITICAL
SOLID
Y
e
g B
3
3'
LIOUIO
TEMPERANRE
w
Figure 1. A simple phase diagram typical of those used in many textbooks.
560
Journal of Chemical Education
a Y
m 3 "w 7
e e -CRITICAL
TEMPERATURE
POINT
TC
Figure2, A better representationof a simplephase diagram,
high pressure (6).As a direct result of this omission, it is common for students to believe that only the gas phase can exist at temperatures above the critical temperature while in fact solid phases also will exist there at high pressures (See Figs. 2 and 3). Attention oRen is drawn to the fact that several different solid phases may exist, each characterized by a different crystal structure (allotropy or polymorphism). The phase forms is commonly diagram of sulfur used showing as anits example. rhombicHaving and monoclinic drawn attention to the possible existence of several solid phases, it might be expected that the liquid and vapor phases would receive similar attention. However, this is not the case, and it is rarely mentioned that for all known one-component systems there is only ever one vapor phase and one liquid phase except in the case of helium that is unique in having two liquid phases (7). Specificreference should be made to the fact that the diagrams are not drawn to scale and that this is done deliberately in order to emphasize certain features that may not be apparent on a scale diagram. It may not be necessary to discuss these features, but for example, the important pos-
4,000 ORDINARY ICE
0
the two systems. It is a useful exercise to ask students to draw sketch diagrams of the two systems on the same set of scaled axes after providinr them with the relevant data. Many texts fail tdemphasize that these phase diagrams a ~ p l vonlv to Dure substances (one-wm~onentsvstems) a;;d that the p;esence of any other subs&nce, even something like air, may make a difference to the way the system behaves. Many of these differences may be small, such as the small difference between the normal meltiw mint of pure water (0.002 T) and t h a t of air-saturaGd water (0.000 'C). However, failure to appreciate this point may lead the student into more serious miswnceptions. For example the P-T phase diagram for water suggests correctly that ice will sublime only a t pressures below about 0.006 bar, but students are likely to be puzzled by the fact that ice does, in fact, sublime in winter and in deep freezers a t normal atmospheric pressures of around 1bar, well above the upper limit suggested by the phase diagram. It is then necessary to explain that sublimation will occur only when the ~ a r t i aoressure l of the water vanor in the two-comuo- - *~ ~ n e 2 wateriair system is below abo;t 0.006 bar, although the total Dressure is far above that of the t r i ~ l ooint. e The t&ical general chemistry textbook for freshmen devotes an average of about three pages to a discussion of one-component Dhase diagrams. Their resenta at ion and complet&ess w i l d be enh-anced signific&tly by the addition of just a few carefully worded sentences, and slight modifications to the accompanying diagrams, along the lines suggested in this article. ~
-60
-30
0
30
MI
90
120
A
Figure 3. The phase diagram of water at high pressures itive or negative slope of the solifliquid equilibrium line essentially would vanish and appear as a vertical line unless the scales were distorted. Also, for many systems, the solid vapor, and much of the liquidlvapor equilibrium lines would merge with the temperature axis on a linear scale drawins (see Fie. . ~.3). The problem ol'scales becomes especially apparent when the phase diagrams of carbon dioxide and watcr are drawn alongside each other, as they often are, with almost every detail the snmr and only the slope of the solidAiquid equilibrium line distinzuiiihine between the two diamams. This creates the false imGession that the slopeof the solifliquid line is the only distinguishing feature between ~7
~
A
Literature Cited 1. Jones,D.E.;Roswell,D. F.J. C h m Edue. 1815,50,35w60. 2. Swint0to.F. L. J Chem. Educ. lW1.44,641. 3. Knsml,~. S.J. cham E ~ W 1914.51, . masm. 4. Lesk,A. M. Intmduecion Lo Pkyslml Chemistry, Rentice-Hall:Englewood Cliffs, NJ. 1982, p 412. 5. Bowden, S. T. ThPhnaoRulp andPhoseReoefloru:MacmilIm:Landon,19.54, p 20. 6. Scholsky,K M. J. Chem Educ. 1989,66,989490. I. Atkhs, P.W Physical Chemistry, 2nd ed.; Oxford University Preas: M m d , 1982, p 195.
Volume 70 Number 7 July 1993
561
