A Simple Derivation of the Existence of a Critical Temperature FRIEDRICH L. HAHN Institute Qtcimico-Agricola National, Guatemala, Gautemala, Central America (Translated by Ralph E. Oesper, University of Cincinnati)
ANY students come from high school improperly is to establish the type of the graph. With perhaps a prepared to continue their chemical training a t little aid, the L-curve of the diagram (Figure 1) is the college level. The principal defect arises from the easily developed. Should some of the class attempt to common practice of requiring them to memorize far draw this curve convex t o the temperature-axis, a few too many facts and definitions, which they must accept leading questions will soon convince them of the fala t face value, without any opportunity to check them lacious consequence. As the temperature continues by logical development or experiment. Ordinarily to rise, the expansion would eventually cease or i t might little attempt is made to correlate these definitions even be reversed, an obvious impossibility. How will the density of the saturated vapor change properly. The inevitable result is a lamentable confusion of these ideas, that have been learned by rote as the temperature rises? Again a few judicious quesand recited parrot-fashion. Heat and temperature, tions are sure t o bring out the correct response. Since boiling and evaporation, transition point and critical many more molecules enter the vapor space with each temperature are often regarded as synonymous. A rise in temperature, the density of the vapor must little quizzing will demonstrate all too soon that few, inaease considerably. The class is now asked to plot if any, of the group can correctly define and dierenti- the V-curve. It will become apparent almost immediate such fundamental concepts. Consequently, the instructor finds that an important part of his task Density is to develop a clear understanding of such ideas. He will be amply rewarded when he observes how thormg / ml oughly his students learn to appreciate his efforts along these lines. is particularly difficult when the conThe cept cannot be derived mathematically, either because the requisite mathematical skill is beyond the student's range, or when the idea cannot be made understandable by recourse to ordinary logical reasoning, inasmuch as the facts themselves do not seem logical. A typical example is the existence of a critical temperature. There is nothing logical about the fact that hundreds of millions of atmospheres of pressure are not enough to liquefy water vapor a t 375'C., while 218 atmospheres suffice a t 374°C. None the less, this seeming anomaly can be explained and made intelligible by a perfectly logical study of the situation. Every student will know that a liquid expands when its temperature is raised, that is, its density becomes less. A short discussion will also teach the class that when a liquid is confined in a partly filled vessel, an equilibrium is soon reached between the liquid and its vapor, and the higher the temperature the more molecules in the vapor space. The class should now be told Temperature to plot the density of the liquid, that is, its weight per unit volume, as a function of the temperature. It be impressed On the that the curve FIGURE 1.-DENSITYOF A LIQUIDAND OF I Y S SATURATED VAPOR not represent the actual data, but the important point AS A FUNCTION OF ITS TEMPERATURE (SCHEXATIC) 233
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ately that the two curves must intersect a t some point, no matter what the actual position of the curves referring to a particular liquid. The students, quite independently, will now draw the conclusion that a t the temperature corresponding to this point, and all the more so a t any higher temperature, there can no longer be any dBerence between the liquid and its vapor. In other words, a t temperatures higher than this (the critical temperature), the liquid cannot exist, no matter how much pressure is imposed. Practically always a t this point in the discussion, some one asks: "May i t not alternatively be assumed that the vapor disappears and only liquid remains?" This question serves as a lead to correct the only inaccuracy that has been carried along through all the derivation. As a matter of fact, the curves do not intersect; rather, they merge into each other (broken
line). The instructor should now discuss highly compressed gases. He should point out that they are so much like liquids that the transformation is not sudden but occurs almost continuously. He can profitably introduce the terms "liquiform" and "gasiform," that is, a fluid that forms drops, and a fluid that is gaseous. The question that was raised can moreover be answered by pointing' out that every vapor (gas) possesses the general characteristic that it homogeneously occupies any space in which it is confined. This occurs 7,t the critical point; the boundary between the phases disappears. Accordingly, it is quite correct to state that liquid is no longer present, and the vessel contains only vapor. This is a typical instance of the manner in which many of the basic concepts of general chemistry can be derived, and made comprehensible, in a quite simple way.
