It is certainly true that the ultimate arbiter of how far a reaction goes-and i t is perfectly legitimate to regard the formation of a solution as a reaction-is the equilihrium constant defined by AGO = - RT 1°K orequivalently
letters Retrograde Solubility To the Editor: The paper hy K. C. Lilje and R. S. Macomher entitled "Recrystallization: Unexpected Behavior" [J. CHEM. EDUC., 50, 567 (1973)l contains many inaccuracies and misleading statements. I refer particularly to (1) the thermodynamic discussion of retrograde soluhility and (2) the "partial phase diagrams" presented. The authors' eqn. (I), as representing a condition of equilihrium, can hardly be called an equation. I t is not susceptible to thermodynamic treatment as i t stands, and i t is misleading to try to do so. Do the authors imply that "solvent" on both sides of the "equation" can he cancelled? In writing AG = -RT In K do they mean AGO? If so, to what change does this refer? Certainly not to eqn. (1). In the situation under discussion the equilihrium is, in fact, simply between undissolved and dissolved pyridine hydrobromide, and solvent does not appear explicitly in the equation a t all. Consequently their eqns. (2) and (31, as applied to ( l ) , are veryfuzzy indeed. The equilibrium, then, should be represented as Solute(s)s Salute (dissolved) whence it is clear that whether the isobaric solubility increases or decreases with temperature increase depends on whether the sign of A H for this change, i.e., the differential enthalpy of solution in the saturated solution, is positive or negative. (The exact relationship was referred to recently by R. M. Mazo and R. Barnhard [J. CHEM. EDUC., 49,639 (1972)1. Figures 1 and 2 both show a field for "solid solution." The article makes no reference to such a phase, so the diagrams are not pertinent. If they were, they are erroneous, even as "partial phase diagrams." In Figure 1 "liquid solution" and "solid solution" are separated by what is presumably a two-phase region labelled "solution solid solute," which is contradictory. Further, if the solid phase is solid solute, why the lower curved line? Moreover, if the left edge of the figure represents n.,l,t. = 0, and if solid solute and solid solvent are the only saturating phases, the liquidus line must fall in moving to the right before rising. Figure 2 is, similarly, faulty.
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If K is increased the reaction "goes further," and viceversa. If we restrict our attention to a single temperature, then it is true that a decrease in AG" favors products, etc. However, if-as in the analysis under consideration-we are concerned with the influence of temperature changes on the position of the equilihrium, it is not the change in AG" alone hut rather the change in A G 0 / T which determines the shift in equilihrium position. Thus the temperature coefficient desired is not
hut
The sign of the temperature coefficient of soluhility is therefore determined entirely by the sign of the heat of solution (they are the same), whereas the actual magnitude of soluhility is determined by the competition hetween AH" and AS". Walter Miller W. R. Salzman University of Arizona Tucson. Arizona 85721
To the Editor: Several readers have brought to my attention that the thermodynamic arguments in our recent paper [J. CHEM. EDUC., 50, 567 (1973)l are in error. While the experimental data is correct, our conclusions with regard to solvations effects and the significance of AS (solution) have been questioned. Below is a corrected interpretation of the thermodynamics of retrograde soluhility. Consider the dissolving process a t constant pressure and temperature, which can be viewed as a composite of solute fusion and solvent-solute mixing Solutei.,
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solution
Sol~ent,,~
Solute (dissolved)
Norman 0.Smith Fordham University New York, N.Y. 10458
To the Editor: The analysis of Lilje and Macomher [J. CHEM. EDUC., 50, 567 (1973)l of their system showing a clear case of decreasing soluhility with increasing temperature points up a misconception which many of us who teach chemical thermodynamics may he unwittingly propagating. We are fond of neat generalizations as to how this or that among AGO, AHD, or AS" affects a reaction's ability to "go" and we occasionally do not properly stress the conditions under which the individual statements are valid.
At saturation (equilihrium), with unit activity assigned to the reactants, the following relationships apply AG,.,.. = 0 = AG",,. RT ln[Solute(disaolved)1 (1)
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AH^,.^, = + A@ , (3) Assuming that AH",,,., and AS",,I,,, are independent of temperature, the Gihhs-Helmholtz relation gives d In [~olute(dissolkd)]
AH".,,, dT Thus, compounds with positive (endothermic) heats of solution will become more soluble with increasing temper-
Volume 5 1 , Numbera, August 1974 / 555
ature, and inversely (conclusions which can be reached from considerations of Le Chatelier's Principle). As can be seen from eqn. (3), the heat of solution can be dissected into a heat of solute fusion (necessarily positive) and a heat of mixing. With most solute-solvent pairs AH0,,~,, > 0 (solubility increases with temperature), requiring that either AH",,,,,,, is positive, or if negative, smaller in magnitude than 4H"r,,ion. In the case of the pyridine hydrobromide-chlomform system, its retrograde solubility requires that A H " m , , < 0, and hence AH",,,,., must he negatiue and larger in magnitude than AWrUsr,,. It is appealing to rationalize this exothermic AH",,.,,, in terms of a strong solvating interaction between solute and solvent. In microscopic terms, it can be inferred that the AH" requirements for separating solute particles from the crystal and separating solvent molecules in the liquid state is more than compensated by the favorable AH" of specifically solvating solute particles with solvent. The solubility phase diagrams in the original paper are also misleading, and cannot he constructed in their entirety without additional information. I t is correct to say, however, that in phase diagrams of mole fraction solute (abscissa) versus temperature (ordinate), the solubility tie-line separating unsaturated solution from saturated solution solid solute will have a positiue slope for "normal" hehavior (with unsaturated solution above the tieline), and a negatiue slope for retrograde behavior (with unstaturated solution below the tie-line). Notice that the s l o ~ e sof these lines have the same sign as ~ H " . , I , , ,as required by eqn. (4). I a~ologizeto anyone who was misled by the original arguments. Roger S . Macomber Universitv of Cincinnati cineinn&, Ohio 45221
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Method for Slides To the Editor: Professor Richard E. Powell described a simple and inexpensive method for the production of 3% X 4 in. Polaroid mount slides in his letter [J. CHEM. EDUC., 50, 798, (1973)l. Undoubtedly the method is suitable for the usual horizontally arranged 3% X 4Ya-in. projector. However, for those who use, as we do, a vertically arranged 3Y4 X 4Y4-in. overhead projector, the heat transfer in the upward direction is enough to deform Polaroid mounts within a period of a few minutes. We use a 3'14 X 4Y4-in. glass carrier. The slides are made on Transparent Contact, a matte finished material of 4-mil thickness, widely available at $0.50 per yard and supplied adhering to a paper backing. Slides are drawn on acetatemounted matte finished plastic using Higgins $892 black engrossing ink and with any color hall point or felt pen. The acetate mount is sandwiched into a glass carrier. Legends as in graphs are typed on strips of Transparent Contact. The typed legends are then peeled off and transferred to a 20-mil clear acetate mount. The overhead projector in use, an old Delineascope Model B, gives accurate focus over the whole slide and allows the use of overlays as well. Excellent visihility is possible in a fully lighted lecture hall.
Another Method for Obtaining Electron Dot Structures To the Editor: A recent letter by L. H. Berka (J. Chem. Educ., 51, 215 (1974)), pointed out that the methods for obtaining electron dot structures given by A. B. P. Lever [J. CHEM. EDUC., 49, 819 (197311 are quite complicated, and suggested a s i m ~ l e rmethod. This has the disadvantaee that the student Ean only check whether his hypothetical molecule is a plausible one after he has written it down in detail. The equation Number of bonds
556 1 Journal 01 Chemical Education
EN
- ( E - 2n) 2
where N is the number of atoms other than hydrogen in the molecule, E the total numher of valence electrons, and n the number of hydrogen atoms, can he used to calculate the number of bonds that have to be present in the molecule if the octet rule is obeyed. We have found that with this information the freshman student has no trouble in writing plausible structures, including ones containing multiple bonds or which are cyclic. If the calculated number of bonds is one less than the number of atoms in the molecule then one atom in the molecule has ten valence electrons, if two less then one atom has twelve valence electrons. Like most such schemes this method tends to break down if the molecule contains more than one "unusual" feature, and the student must use the trial and error technique. Brian D. Kybett University of Saskatchewan Regina. Saskatchewan S4S OAZ, Canada
Slope Determination To the Editor: The recent article on determining the slope of a curve (Patel, C. K., and Patel, R. D., J. CHEM. EDUC., 51,230 (1974)) recalled an article I had done some years ago in Industrial and Engineering Chemistry. It seems to offer two still more facile ways of determining the slope of a curve. Actually, what one does in both cases is to determine the reciprocal of the slope. In one case one lays a glass rod perpendicular to the curve and turns it until the curve appears to continue smoothly through the glass rod. When this happens, the rod is normal to the curve. The other technique involves use of a mirror which is again laid normal to the curve but perpendicular to the plane of the paper and turned so that the reflection of the curve appears to he a smooth continuation of the curve. Aeain. the mirror is then normal to the curve. Both these techniques can he readily used for graphical differentiation. a useful technique, . . in kinetics and other kinds of scientific measurements.
B. J. Luberoff, Editor
Sidney P. Harris BueenaCollcpr, (:.I'.N.Y. Flu~hing.New York I I R l i i
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Chemical Technology Bassett Building Summit, New Jersey 07901
