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
