Alan F. Berndt University of Missouri-St. Louis St. Louis 63121
I n most physical chemistry texts and in some introductory texts binary phase diagrams are presented in detail.' I n the discussion of the phase diagram for a binary system having a congruently melting compound i t is often stated that this diagram can be thought of as consisting of two juxtaposed simple eutectic diagrams. This concept is a useful pedagogic tool for understanding equilibrium relationships among phases hut leads to erroneous results when applied to a quantitative description of the slope of the liquidus. I n a binary eutectic diagram the liquidus has nonzero slope a t the melting points of the pure components. Juxtaposition of two diagrams of this type would imply that the liquidus would similarly have nonzero slope a t the melting point of the compound. That this is not true is a well known experimental fact and has been the subject of a theoretical proof for the general casez in which no assumptions about the detailed nature of the liquid phase are made. The liquidus actually has a horizontal tangent, i.e., zero slope, a t the melting point of a congruently melting compound. The phase diaSuggestions of material suitable for this column and guest columna suitable for puMicstion directly should be sent with as many details as possible, and particularly with reference to modern textbooks, to W. H. Eberhardt, School of Chemistry, Georgja Institute of Technology, Atlant,a, Georgia 30332. Since the purpose of this column is to prevent the spread and continuation of errors and not the evaluation of individual t,exts, the sources of errors discussed will not be cited. In order to be presented, an error must occur in s t l a s t two independent recent standard books. %BERNDT, A. F., AND DII,:STLER, D. J., J. Phys. Chem., 72, 2263 (1968).
An additional aspect of phase equilibrium diagrams which has been the subject of extensive correspondence to the Editor of This Column concerns partial solidstate solubility and the very basic question of whether or not a "pure" solid substance can be present in an equilibrium system with a liquid solution containing a second component. I n particular, Dr. Stig Holmquist of Ferro Corporation, Cleveland, Ohio has been most insistent that treatments are inadequate if they present phase diagrams which do not show such partial solubility or if they do not make clear in thc text that such solubility exists. The problem becomes particularly interesting and acute in systems where very small mole fractions of minor components alter dramatically thc electrical or 594
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Journal of Chemical
Education
Textbook Errors,
93
Binary Phase Diagrams
Schematic phase d i a g r a m for b i n m y system having a congruently melting compound, ( o j , correct; (bj, incorrect.
gram for the compound system is therefore not quantitatively equivalent to two juxtaposed eutectic diagrams. This results from the inclusion of the entropy of mixing term into the expression for the Gibbs free energy. The entropy of mixing expressed as a function of the mole fraction of one component has infinite derivative at the composition of the pure components but has a finite derivative a t the compound composition. Although this point may be rather subtle the texts should clarify the difference in order to make the student aware of this feature. I n addition many texts add to the misunderstanding by presenting incorrect illustrative phase diagrams in which the liquidus is shown to have a cusp (point) a t the melting point of a congruently melting compound (Part (b) of the figure) rather than correctly illustrating the slope of the liquidus (Part (a) of the figure).
mechanical properties of the major component. Some presentations accentuate the small solubility of the minor component by plotting the concentration on a logarithmic scale so that the range of concentration between .001 and .O1 mole % is thc same length as that between .Ol and .1 mole % or between 1and 10 mole %. Whether or not limited solubility is a consequence of general thermodynamic theory or a specific statistical model is a moot point, but there is little doubt that, experimentally, limited solubility is the rule rather than the exception. The implications concerning the word "pure" are especially interesting and deserve detailed consideration.
