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.
+
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.,
+
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)
+
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
