Metal-Ligand Complexes-A Calculation Challenge R. W. Ramette Carleton College, Northfield, MN 55057 Data for a Metal-Ligand System
Ever since the revelation by N. Bjerrum that metal ions in solution can have their water molecules displaced by other ligands in a series of overlapped steps, many experimental studies have attempted to find the values of stepwise equilibrium constants. Numerous results are tabulated in well known reference works and in most general and analytical textbooks. The purpose of this paper is to illustrate one of the most imuortant experimental methods for studying complex rquililnria .tnd to pre>rnt y ~ l h r r i data c an A ,.li:~llwgv118 rile I I I ~ I I Ys o ~ h i s t i ~ - ac~: e ~~l ld n i oprwedurt,~ t~ t h:11 vnjc~?various degrees bf loyalty around the world. The model is a simple one, without complications of polynuclear complexes or other types of side effects. Let us consider a four-step complexation of metal ion M with ligand
ymv)
L,
which can be described completely by six equations:
CM = [MI + [MLI + [MLi + [MLd + IM41
(21
(material balance for metal) CL = [L] + [ML] + 2[MLz]+ 3[ML7] + 4[MLa] (materialbalance for llgandi
(3)
M ~ L )
Run 1
Run 2
0 1.000 1.274 1.624 2.069 2.637 3.360 4.281 5.456 6.952 8.859 11.288 14.385 18.330 23.357 29.764 37.927 48.329 61.585 78.476 100000
0.0 -10.3 -12.3 -14.4 -16.9 -20.0 -23.4 -27.3 -31.8 -37.1 -42.7 -49.5 -56.6 -64.1 -71.8 -79.7 -87.2 -94.6 -101.3 -108.0 -113.8
00 -10.1 -12.1 -14.4 -17.0 -20.0 -23.4 -27.3 -31.8 -37.0 -42.9 -49.5 -56.6 -64.1 -71.8 -79.6 -67.2 -94.6 -101.6 -108.1 -114.0
The Experiment
the system. One data set was generated without any electrode error. exceot that it was assumed that the voltmeter outuut was rbundld to the nearest 0.1 mV. The other set of poten& has random error superimposed by a subroutine that generated errors in accord with the gaussian model and with a standard deviation of 0.1 mV. In both cases the Nernstian slope was error-free and equal to 29.5785 mvldecade. Thus, even with the added error the data are much more accurate than the great majority of published studies.
Exactly 100 mL of 1.000 m M metal ion solution are placed in each compartment of the following cell:
The Challenge
Pa = [MLnll[Ml[L14 (the four beta expressions)
M(si1leftcompartmentlrightcompartmentlM(s)
(8)
Chemists from near and far are cordially invited to submit their entries in answer to the following questions:
We assume that the metal electrodes respond to the activity of the metal ion in perfect accord with the Nernst equation and the reduction half-reaction: M2++ 2e = M(s)
(9)
At the start of the experiment both electrodes are identical and the cell potential is zero. Now let precise volumes of a 2.000 M ligand solution, which also contains 1.000 m M metal ion, be added to the right compartment. We will assume that the ionic strength of the solution does not change with these additions, and that there is no liquid junction potential. The concentration of metal in the solution, CM,will be constant, and the total ligand concentration in the right compartment will be CL = 2.000 X Vl(100 + V ) . With 20 additions in each of two independent runs, the data shown in the table result. The two runs are in excellent agreement by the usual standards for this type of experiment. The average absolute deviation in corresponding potential values is only 0.08 mV. The Truth
Both sets of data were generated by a BASIC computer program called GENPOTDAT, using a set of beta-values for 946
Journal of Chemical Education
(1) Do the data support the model of four complexes, or is it more consistent with three or with five complexes? (21 What are the numerical beta values for the M-L svstem'? (3; What are the confidence limits on the beta values, considering
each set separately?
(4) Which data set contains the extra random errors?
Please submit results to the author, and include a description of the data processing approach used for the calculations. Give literature references if appropriate. The Reward
If a varietv of scholars resuond we will all benefit hv the t ~ m p l r i s moire>ulth~ h t d l n r dI!, dlvrr+ nl1pruacl1t.n10 tliia ~ m ~ ~ t and ~ r ttatii~l~dr , ~ ~ ~~t ~ r ~ ~ lrh ~ krns!*t r n .o i the 1n111.ishtd methods really work? perhaps we will learn something about the limitations of calculation methods as well as illustrate the limitations of typical potentiometric measurements. Participants may wish to counter this challenge with one of their own, providing data on some other type of system or data obtained by a different type of experimental measurement. Perhaps by working together we may accumulate a set of "standard" eauilihrium problems that researchers can use as benchmarks in testing new data processing ideas. I
