Solving Simultaneous Equilibria
To the Editor:
To the Editor
The article by Cobranchi and Eyring [1991, 68, 401 is fine, I suppose, but illustrates a difficulty we a s chemical educators a r e having trouble shaking. We still fiddle around wlth a variety of mathematical w'hiz-bangery to get at solutions to multiple equilibria problems, when a simple, powerful, inexpe&ivetool is a t band. I refer to SEQS (Simultaneous Equation Solver, available from CET Research Group, Ltd., Norman, OK 73070). ARer scanning this article, I sat down in front of my computer, called up SEQS, entered the eight equations and a set of estimates for each unknown concentration, and, in less than 5 minutes total time. had all e i ~ hconcentrations. t Furthermore. I can now examine graphGally the effect of variation in any one concentration on anv other one with no difficultv whatever. I t is time for u s to stop being concerned about the mathematics involved, including techniques for finding approximate solutions, and concentrate on the chemistry of what are now trivially simply modelled-and-solved multiple equilibria problems.
The article by Cobranchi and Eyring [1991,68,401 is incomplete, misleading and pedagog~callypmr. Incomplete, because it omits mention of the inert negative ion (and 1s it really inert?^ thai is thc itwtinppartner oftotal TI'. 1 don't suppose they really mean to have, according to their eq 6, a net positive charge of 1.00 x lo3 M in their solution. Furthermore, the equilibrium constants they use have no more than two significant figures each and yet they report calculated species concentrations to three and four figures. The results of their complex computer program are no more significant than can be obtained by perusal of the relative values of the equilibrium constants with immediate solution of the quadratic equation for the dissociation of 1.00 x lo3 M HNOz followed by treating the other equilibria separately atter setting [TI+] = 1.00 x 103M, which proves to be consistent with the conservation equations. The results are
~.
Edwin F. Meyer
DePaul University Chicago. IL60614
To the Editor:
The paper is pedagogically poor because, overlooking the obvious, they use a complicated methodology to generate numbers to erroneous degrees of precision. Charles E. Hecht
Hunter College of CUNY 695 Park Avenue New York, NY 10021
E. F. Meyer is correct in asserting that SEQS rapidly solves the set of simultaneous equations considered in our pnper. A disadvantwe of this program in comparison to Morgan's continuution method is that SI.:QS rcouirct; an initial estimate of unknown variables. we-disagree with Meyer's opinion that less attention should be directed to the mathematics involved in solving chemical problems. Students may certainly use a program such as SEQS to a m v e a t a solution, but we believe students should also familiarize themselves with a s many alternative mathematical methods to solving chemical problems a s possible.
Volume 69 Number 12 December 1992
1039
Other readers have questioned our eq 6, a charge balance expression. We assumed the presence of a n inert counteranion such as CIOP a t lo3 M (the total thallium concentration). A question has also been raised a s to whether equilibrium 3 would exist in dilute solution. Finally, one reader properly objected to the excessive number of digits that we reported in the calculated concentrations. They were clearly not warranted by the significant figures in the equilibrium constants that we used. Daryl P. Cobranchi Edward M. Eyring David A. Sommerfeld University of Utah Salt Lake City, UT 84112 Comment on: "Empathy for the Exile: Chemistry and Classical Literature" To the Editor:
The measurement of the freezing temperature of wine [Tanner, A. C.; Johnson, J. F. "Empathy for the Exile: Chemistry and Classical Literature", J. Chem. Edm. 1990, 67,6901 indeed touches on a number of disciplines when it is linked to Ovid's Tristia. The concept of litero-historiothermometry is intriguing. However, in the process of adding "relevance" to a classic experiment in physical chemistry, Tanner and Johnson appear to have forgotten all that they never knew about the physical properties of solutions. First, thev attribute their failure to obtain a sham freezing point tekperature to the presence of "particul&e matter" (undissolved solids) in the wine. Such undissolved solids would, of themselves, have no effect on the properties of the solution since they are not a part of the solution. Removing the particles by filtration before determining the freezing temperature would not have changed the observed behavior on freezing (unless the solubility of the particulates in the wine increased with decreasing temperature). Second, the observation that the freezing orocess omduced a "&lushna t a temperature that slowly decreased as the mixture froze is precisely what should have been expected. Solutions, in general,-do not have a constant freezing point temperature but freeze over a temperature range. If it is assumed that the solid formed on freezing is the pure solvent (an assumption on which the approximate freezing point depression equation used by Tanner and Johnson is based) then the freezing process changes the com~ositionof the solution. As solvent is removed from the solution by the freezing process the concentration of solutes in the residual liouid increases and the orocess continues only at increasingly lower temperatures. At -7.5 C the concentration ofthe ~olutionremaining as liquid durmg the freezing of wine would correspond to removal of less than half of the water from the orieinal sam" pie. In principle, a liquid phase would continue to exist down to the eutectic temoerature. (The eutectic temoerature for water-ethanol mixtures has been notorious6 difficult to determine but is ~robablvbelow -120 'C). Frankly, the editors and the reGewers for the ~ o u r n aof l Chemical Education should be very embarrassed. C. Eugene Burchill University of Manitoba Winnipeg, ME, Canada R3T 2NZ
1040
Journal of Chemical Education
To the Editor:
Burchill is of course correct in pointing out my glaring error (1).His sarcastic remark about my forgettim all I never knew about the physical properti& ofsolut&s is closer to the truth than he realizes. My undergraduate education was far stronger in modern logic andfoundations of mathematics than in physical chemistry I have never had a n elementary course in chemical thermodynamics and, to the best of my recollection, as a student I never saw a t e m ~ e r a t u r ~ o m ~ o s i tdiaeram ion in anv course. That's an explanation but no excuse, since our eq 1is simple; a little thought would have prevented the error. I compartmentalized facts that I do know; in haste I was thoughtless about an unapt term, and I made a false analow with the h~ilin~-~oin
