Chemical Education Today
Letters Inflection at the Triple Point
The author replies:
I have two reactions to the article about the inflection at the triple point (J. Chem. Educ. 1999, 76, 226). “Methinks thou dost protest too much” and “Much Ado About Nothing”. Most phase diagrams for water go up to the critical point, at 22,064 kPa and 647.14 K. The triple point is at 0.61173 kPa and 273.16 K. The normal freezing point is at 101.325 kPa and 273.15 K. One cannot actually show the difference between these latter temperatures on a usual phase diagram, but we frequently do. At 233.15 K the vapor pressure of liquid water is 0.0213 kPa, that for ice is 0.013. The slope of the vapor pressure curve for ice, near the melting point, is 0.0480 kPa/K, that for liquid is 0.0459. Yes, this difference is difficult to detect, but not impossible. However, the only way I know to actually graph these huge variations in pressure is to use a logarithmic scale for pressure. When one does this, the vapor pressure curve for liquid is concave downward, instead of concave upward. The latter is the usual way the phase diagram is drawn. There is an even more crucial problem in depicting the freezing point of ice as a function of pressure. In the range of pressures in a typical phase diagram, the slope is ᎑11,956 kPa/K. It is utterly impossible to distinguish this from a truly vertical line, yet we always show a perceptible negative slope for this line. The fact is that one should always sketch out a “phase diagram” and state clearly that it is not to scale.
My note on the triple point was the only part of a much longer paper that the reviewers found interesting. Since Dr. Myers finds even this to be much ado about nothing, readers can imagine how boring the rest of the paper must have been. The points he makes are correct, and readers must decide whether they are important. An error that he did not find has been pointed out by other correspondents, namely, that the left side of the equation is inverted, so that the equation as printed gives the reciprocal of the correct ratio. The correct equation is:
R. Thomas Myers Kent State University Department of Chemistry Kent, OH 44242-0001
∆H solid/liquid slope dP/dT below T t =1+ slope dP/dT above T t ∆H liquid/gas Stephen J. Hawkes Department of Chemistry Oregon State University Corvallis, OR 97331-4003
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Correction Figure 1 of the article Using Overhead Projector to Simulate X-ray Diffraction Experiments by Veljko Dragojlovic (J. Chem. Educ. 1999, 76, 1240–1241) had the images for the red filter and the blue filter reversed. The correctly labeled a
images are shown below. These images are shown in color in the JCE Online version of this article (http://jchemed.chem. wisc.edu/Journal/issues/1999/Sep/abs1240.html).
b
c
Figure 2. Diffraction patterns obtained with (a) red filter, (b) blue filter, and (c) without a filter.
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Journal of Chemical Education • Vol. 77 No. 2 February 2000 • JChemEd.chem.wisc.edu
