calculate the rate constant and give a rate plot. CONINFIN was tested on 22 sets of raw data taken from kinetics textbooks and from the literature.' In all hut one case, the R obtained using the calculated A, was a t least equal to, and, in most cases, greater than that obtained using the experimental A,. In all cases improvement in as ranged from 0 to 97%, with an average of 7.4%. The difference between reported and calculated Am's and k's seems to be randomly positive and negative, suggesting the absence of any bias in the CONINFIN aleorithm. Two methods exist for obviating the need to measure A, in a first-order reaction. These are the Guggenheim method (8) and that reported independently by Kezdy ( 9 ) ,hy Mangelsdorf (10) and by Swinbourne ( l l ) , which accordingly will henceforth he called the KMS method. Both of these methods reauire that data ooints he taken a t aconstant time interval, T , which are rapid reactions could prove troublesome. Furthermore, in order to yield results of high precision, r should he two to three rimes the half-life of the reaction-especially fur the Guyyenheim method. Not only might this cause experimental (ltfficulryin very slow reactions, t ~ u it t means also that reactions must remain first-order over several half-lives. Thus the Guggenheim and K M S methods are in theory not suitnhle for measuring initial rates in reactions which depart from first-order behaiior after one half-life or so. A comparison of these methods with CONINFIN for ten first-order reactions showed that the Gueeenheim method is the least . .,. dependable of the three. In all cases, this method gave a lower II and a hieher o. than theothers. though this must at least in part be d;le to small T used in eight of ;he cases. In contrast, rhe K M S method seems insentitive to the magnitude of the i/tll2 ratio. Of the KMS and CONINFIN methods, the latter vielded rate constants of ereater orecision in most cases, judging by the values of o, and the mean y-residual. Though the KMS method comoares auite favorablv with the CONINFIN method, the requirement for even spacing of data ooints in the former case remains an inconvenience. In addition, Swinbourne (11) has noted that the KMS method is not narticularlv sensitive to reaction order. Consequently, one should t n k e c a r e ~ v e r i fthat ~ the reaction is indeeh firscorder before armlvine .. - this techn~aue.This orohlem is nor expected to he as severe when CONINFIN is used, since when rate data are plotted in the normal manner, f(A, - At) versus t, an ~~
~~
~~~~~~
~~~
~
~
improper plotting function is more obvious. In Figure 5 are compared first-order plots of second-order data using CONINFIN and the KMS method. In the former case, the sigmoidal distribution of the data points about the hest-fit line is apparent, while in the KMS plot, the nonlinearity is nearly obscured by the scatter, and one could easily be misled if one did not compare first- and second-order plots of the same data. Proeram CONINFIN is available either in IBM VSPC interactrve, free-format FORTRAN (109 statements, 38 comments) or in standard FORTRAN-GI (265 statements, 93 comments). Students run the standard version using cards. The output of the standard version includes a listing of the input and a printer plot of the rate curve. Execution requires less than 128K. 32-bit words on an IBM 370-158. No card decks are available, but complete documentation including listing, sample output, and tables of comparisons with the other methods discussed may he had by sending a check for $2.50, to cover duplicating and postage, to Dr. John J. Houser.
Plots of Potential Curves and Vibrational Levels Jacques Llevln Laboratoire de Chimie Physique Moleculaire Faculte des Sciences CP.160, Universite Libre de Bruxelles 1050 Bruxelles, Belgium
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~
lComplete references and tabulated resuits supplied with program documentation.
A computer program has been developed to produce plots of electronic potential energy curves and of vibrational energy levels for diatomic molecules from spectroscopic data. We hope that these graphs may be useful to undergraduate students performing the vibrational and eventually the rotational analysis of diatomic molecules' spectra (see, for example, the description of such spectroscopic experiments in THIS JOURNAL for the 12, Cz, CH and HCI molecules (12-16)). The plots will help students to visualize the physical meaning of parameters determined from the analysis of a spectrum (electronic terms, dissociation energies, shapes of the potential wells, energetic dependence of vibrational levels) and to discuss the validitv of the theoretical models used for this analysis (harmonic and anharmonic oscillator approximations, Biree-Snooner extranolation. Franck-Condon orinci~le). . . Teachers can also use the program to illustrate a course on molecular spectroscopy with some concrete examples, taking the required data in the literature (17). The . oroeram is desiened to draw on the same e r a ~ the h " " Morse potential energy curves of an optional number, n, of electronic states of a diatomic molecule. The Morse ~otential is calculated as -
A
E ( R ) = T.
+ D,(1 - e-fl(R-R=))2
(1)
with
The Birge-Spooner extrapolation gives: D, =-
w.
4w.xe
(3)
where T,,D,, were and Re represent the electronic term, the dissociation energy, the vibrational frequency, the single anharmonicity constant and the equilibrium distance. Optionally, a numher, n,, of vibrational term values calculated in the Morse anharmonic oscillator approximation can he plotted. For an energy level of quantum numher u , the term value is Figure 5. Secand-orderrate data plmed as tirst-orderusing CONINFIN and the KMS melhad. (Houser)
and the internuclear distances a t the turning points are Volume 59
Number 9
SeDtember 1982
777
Program POTCURV is written in FORTRAN IV extended and run on a CDC Cyber 170-750with 30000 (octal) words of 60 bits. I t contains103 statements. Plots are drawn by a CALCOMP digital plotter, by calls to original FORTRANoriented software. The transportability of the program to another graphics system can he made easily owing to an extensive description of the calling sequences of the plotting routines given in the documentation. Listing, description of the program, and sample executions can be obtained, free of charge, by writing to Dr. J. Lievin. The author is grateful to Dr. J. Olhregts and Mr. J. Breulet for critical reading of the manuscript.
Microcomputer-Simulated Liquid Chromatography James E. DlNunzlo Wright State University Dayton, OH 45435
and X'&+ Figure 6. Potential curves of the .HIovt
states of I?. (Lievin)
Another option to he activated is the plot of an harmonic potential curve of the form with the force constant k related to the vihrational frequency by the expression (17) The following data are t o be entered interactively: the number of states, n, the energy scale, and for each state the values of T., D., Re, /3, k , n,, we and wax.. An example of plot is given in Figure 6 where the potential curves of the B3n,,+ and X'Z: states of the I2 molecule are drawn. We suggest that students discuss the following relevant features appearing on such a graph: 1) The differences hetween the vibrational frequencies, anhar-
monieities, and dissociation energies of the two electronic . + . t n .
2, The relative positions of the powntial minima. 3) The region of validit). of the hdrrnunicosrillstorapproximation. 4, The different aturnic orudurts dissorintiun limlr (dircusr the
Wigner-Witmer rules).'
5) The displacements of the turning points of the vibrational levels between the two states (discussthe Franck-Condon principle).The students can also draw different Morse potential curves for the
same electronic state by calculating the dissociation energy in several ways: 1)Birge-Spooner extrapolation (eqn. (3)),2) using (18) the Morse-Pekeri expression for the a. constant, 3) using hands convergence (observed in same eases (12),electronic term and atomic excitation energy. Using one of the two last ways to determine D. will provide potential curves with a more correct shape a t long-range distances. However, it is important to note that a parallel correction of the vibrational constants we and w,x, is not possible and that the values of these constants obtained from a Birge-Spooner graph are only valid for small values of the vibrational auantum number. Therefore.. the oromam . " will use as independent data the values of D. and we, o,x, to plot modified Morse ootential curves toeether with fust vibrational energy levels. 778
Journal of Chemical Education
Liquid chromatography is a powerful technique, useful in many areas of chemistry. If this technique is used, a large number of parameters can be varied in order to achieve adesired goal, i.e., separation of a group of solutes. Because of time limitations in the normal laboratory schedule, it is impossible for students to obtain actual exoerience in all asoects of liauid chromatography. In many cases, students obtain only avague idea of its power. The purpose of the computer program described here is to allow students to observe the full potential of liquid chromatography within the time limits of a normal laboratory period. The program is designed to be used in a iunior-senior analvtical instrumentation course. In order tooperare the program, the student is required to obtain from the literaturean articledealing with the separation of components hy liquid-liquid partition chromatography. This article must meet the t'ollou,ina requirements. The article must deal with the separation of a t least three solutes. The separation should be performed by reverse phase liquid chromatography (preferably methanol and water as mobile phase solvents). Data must be available for the separation of the solutes using a t least two mobile phases containing different proportions of the same solvents. This data can be given in terms of tabulated values of capacity factors a t various mobile phase compositions or actual chromatograms from which the capacity factors can be measured. When the program is initiated, the student is asked to enter the caoacitv nercent volume of or. .factor and corresoondine". ganic solvent in the mobile phase for each solute at each of two different mohile phase compositions. All the data for each solute is entered in turn. After the student enters the data for each solute, the computer will calculate and display the capacity factors for that solute over the mobile phase composition of 0-100% organic solvent in 5% steps. After all the data have been entered, the student is asked to oerform several exoeriments. First, using a set of standard ch;omatographic codditions written into t h e programs the student examines the influence of the mobile phase composition on the separation of the chosen solutes. This is done by selecting several mobile phase compositions by entering the selected percent organic solvent and obtaining the chromatographic data. In a similar manner, the student examines the influence of the stationary phase particle size, column length, and mobile phase flow rate on the separation. These parameters are examined using an optimum mobile phase composition selected from the results obtained in the first experiment. The total time reauired to run the . oromam is about three hours. The chromatoeraohic data from each exoeriment are displayed hy the micr&omputer in two ways: First, after each oarameter is entered. the chromatoeram is dis~laved eranh. . . ically. This is a usefu
