SCATCHARD PLOT N O . l
SCATCHARD PLOT N 0 . 3 161
v 10
BOUND Figure 7. k, = 1 X los. "1 = 1, k9 = 1 X lo3, n2 = 1. Thisplotexaminesa high and low affinity site for a single ligand. This case is likened tothe association of a protein to a drug which allows for increased binding due to higher drug concentration.
SCATCHARD PLOT N 0 . 2
Figwe 8. k, = 1 X lo5. nr = 1, k* = 1 X to3, n2 = 10. Scatchard plot ofa single high affinity site wia a number of mspecifii sites at higher ligard mncenlration. This might be illustrative of a proteinsteroid or protein-lipid interaction.
Figureg. k, = 1 X to5, n, = 1. k2 = 1 X lo3, n, = 50.Thisisanexbemecase of a Single site wilh massive nonspecific sites at high ligand concenhation.
program requires the input of k~,nl,kz,nzvalues, then asks for values on the hound axis of line 2. These values are used in the program to produce the appropriate points on line 1and then on the final curved line. SCATSUM output includes the input h and n values as well as three columns of numbers. Column one lists the generated values on the hound axis of line two as a reference. Columns two and three list bound and boundlfree values on the composite curve. Plotting the values in columns three versus two gives the resultant nonlinear Scatchard plot, for class demonstration. The line s h a ~ e of s three d o t s of e s he plots different h and n values are given in ~ i ~ u r7-9. were ~roducedon the Warme Droeram Scientific Plotter (31). when invariant h values are given, the program will produce a linear d o t as ex~ected. ~ e c a & ethis produces precise values along the curved Scatchard dot, the student can use the generated data to determine the i a n d n values. This exercise on the student's part will be an informative homework problem. SCATSUM is available as Apple Disk # 16 from Project SERAPHIM. Send a check for $4 made out to Project SERAPHIM, acct. 20350, to John W. Moore, Department of Chemistry, Eastern Michigan University, Ypsilanti, MI 48197.
Computer Simulation of Mass Spectral Envelopes of Polyisotopic Elements trate the effects of variation ink, the association constant, and n , the number of binding sites, on the Scatchard line shape. In this discussion it is usually pointed out that a linear Scatchard plot results when binding involves a single class of equivalent and independent sites. Such a plot has a slope of -k, an intercept on the hound axis of n a i d an intercept on the boundlfree axis of nh. In contrast, a nonlinear Scatchard plot is produced when two or more non-equivalent hinding sites exist. In this type of plot, the intercept on the bound axis becomes the sum of the n values, ( n l + nz . . . n,) and the intercept on the boundlfree axis is now the sum of the nh oroducts ( m h , nqhl+ - - . . . n.h.). .. .. he simpl'est t-xample of a nonlinear Scatrhard plot involves the case of two classes of indevendmt sires. T o produce this type of plot precisely, a smali program, SCATSUM in Apulesoft Basic. is offered below. SCATSUM uses the curve peeling method of Rosenthal(3OJ as a model to construct the rrsultant Scatchard curve from twostraiaht Scatchard lines. This task is achieved by vector addition of points on each straight line. Rosenthal offers a full explanation of this procedure which she uses graphically to deconvolute a cuived Scatchard plot into its straight line components. In SCATSUM the binding line with the larger h association value is identified as line 1.Line 2 has the lower h value. The
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+
528
Journal of Chemical Education
R. A.
Geanangel
University of Houston University Park, Houston. TX 77004
In work dealing with organotin compounds, we found i t necessary to examine isotopic abundance ratios in order to identify the compounds responsible for spectral envelopes. We sought to compare peak envelopes with profiles predicted from the isotopic abundances of the constituents of the cluster ions oroduced in the snectrometer (32).While the calculation of such ahundancrs is straightforward ( 3 3 - X I ,the presence of tin with 10 stable isotooes alone with other oolvisotooic elements in our reactions made the &culation of ihekxpecied oeak lenethv and tedious.. and.. therefore, we sought . ~rofiles computer software fk the purpose. Despite indications &at such software exists (37) none that was compatible with hardware available to us was located. Therefore, we undertook to write a Droeram that would calculate themass numbers and relative ibundances expected for a cluster ion given the number of atoms, the mass numbers, and the ahundanws ofthr iiotopes of each atom. The mathematical modeldescrihed hy Hugentohlrr and ldliger (.%)was chosen as the basis for the program because of the general approach employed and the flexibility i t permits. The ahun-
Figure 10. Parent ion envelope in the mass spectrum of boron trichloride (33): (a) experimental: (b) calculated.
dances and mass numhers of the isotopes of an atom in a cluster are expressed as the coefficients and exponents, respectively, of the variable in a polynomial known as the generating function for that particular atom. For a simple diatomic cluster AB, the generating function for atom A has the form of eqn. (1) where h., is the abundance of isotope 1of atom A and Ma1 is the mass number of the same isotope. A similar generating function can be written for each atom in the cluster, and it can he shown that the generating function for the cluster is the product of the atomic generating functions (eqn. (2)).
Figure 11. Mass spectrum of HgBr2+: (a) Adapted from spectrum shown in ref. (38):(b) calculated.
In the general case of an isotopic cluster such as A,B,C,
.. .,where each type of atom may appear one or more times, eqn. (3) applies. Pabc = (Ps(~))m(Pb(~))"(Pc(~))o. ..
(3)
The calculation of the isotopic abundance ratios in\r)lves first obtaining the specific equntion resulting from eqn. r;O tor the Volume 61
Number 6
June 1984
529
Table 2. Calculated Relative lntensftles for The Cluster Ion HgBr2+ Mass Number
Relative %'
354 356
0.167 11.799 19.281 49.100 52.878 96.949 48.099 100.000 14.500 48.037 7.513
357 358 359 360 361 362 363 364 366
'Isotwic abvndancestaken horn ref. (39).
isotopic cluster in question, e.g., AzB3, then extracting from that equation the abundance expected for each mass number possible for the cluster. Recognition that the form of the equation involved will differ with the number of atoms present in the cluster led us t o write subprograms for 2-atom, 3-atom, 4-atom, . . . etc. clusters rather than attemptine to write self-modifvine code to facilitate such calculation. i m a x i m u m 6-atom capibility has proved to be adeauate for our needs althouah modification to accommudrrte larger numhers of atoms is-easily possible rivcn thereneralitv of the approach. This was true in part, at feast, because envelopes are &ten identified by tbeir-profile as much as by their actual mass numbers. It is therefore possible to omit monoisotopic elements such as fluorine or iodine from the cluster formula without changing the envelope profile that reduces the total number of atoms that must beincluded in the cluster formula. Once the choice of a particular subprogram has been made, the program requests as user input the numher of isotopes that exist for each atom of the cluster and the mass numher and percent ahundance of each isotope. These values are stored in annronriate .. . arrav variables that are then used to calculate mass number sums and ahundance products for all possible cluster isotope combinations. Finally, all contributions to each allowed cluster mass number are summed and the totals normalized to 100%. Output in the form of mass numherabundance values is sent to the console screen and, optionally, to the printer. An ahundance histogram is constructed in a vertical format on a single page with a maximum of 20 or 33 peaks depending.on whether an 80 or 132 column printer is &ailable. Figure 10a represents the parent ion envelope observed in the mass spectrum of BCb (33)('OB = 19.78%,llB = 80.22%. W 1 = 75.53%, 37CI = 24.47%) compared to the envelope produced by the ABCD.BAS program (Fig. lob). The histogram-plotting routine in the program scales the vertical peak height to 50 lines for the 100% RA ion in order to keep the plot on a single page. For that reason abundances less than 2% are not disnlaved in the histoeram as can he seen for the small peak at'm/k 121, calculated"ahundance ON%, visible in Figure 10a hut absent in lob. Otherwise a close correspondence can be seen between the experimental and calculated spectra. Often metal halide com~oundsprovide examples of cluster ions detected in their mass specira. One such instance involving polyisotopic elements is HgBr%+,the spectrum of which (Fig. l l a ) was reported by Glocking (38). The calculated profile for the ion (Fie. l l b ) clearly resembles the experimental profile in spite i f small differences in relative intensity for mle 361,363,365, and 366. Glocking points out that mass spectra of even very pure metal halide; often give the impression that impurities are present in the sample with extra peaks and unexpected relative intensities of peaks in the spectra owing to facile chemical interchange between the 530
Journal of Chemical Education
sample and the ion source contaminants. We believe this phenomenon is responsible for the differences noted above since %RAvalues seem lareer for the experimental spectrum in every case where there is a difference. There are numerous factors that can and often do cause differences hetween the spectral envelopes obtained experimentallv and tw calculation. Some of these orieinate from the instrum&t, h i t probably more common areufactors arising from the sample, such as impurities or other sample components which overlap or interfere with the envelope of the component of interest. Our experience with the prozrams so far suggests that obtaining c~eHnmass spectral ehveiopes for comparison is not as easy as one might wish. Nevertheless, calculated profiles have helped us identify solution species on several occasions even when interfering ions were present. The five programs described are written in MBASIC (Microsoft Basic), hut an effort was made to avoid dialect-specific constructs so that translation to other versions of BASIC should not require major rewriting. Each program requires about 4 K of disk storage. Memory requirement during execution is somewhat greater owing to storage of the input and calculated parameters. Execution time varies from almost no delay in a case such as CO to a few minutes for 6-atom clusters with numerous isotooes. Printout of the relative ahundances and histogram is opiional. Copies of the programs on 5.25-in. diskettes along with listings and program notes can be obtained for $20 to cover the costs of media and shipping. We can provide the programs on diskettes with North Star format (10 hard sectors) single or double density and Morrow Micro Decision MD2 format (soft sector). We can also write the programs onto disks previously formated by the Osborne 1(single density) or Xerox 820 hut cannot format those here. Checks or money orders should be made out to the University of Houston-Department of Chemistry a t the above address. Acknowledgment
The author gratefully acknowledges support of this work by the Robert A. Welch Foundation under grant E-439.
The MINC Computer in the Physical Chemistry Laboratory Geoffrey S. Waldo, Carol A. Schulre, and Rubln BaHlno Wright State University Dayton. OH 45435
We purchased a MINC computer system (Digital Equipment Corp.) including a printer, X-Y recorder, and dual 8-in. disk drives several years ago on an NSF cost-sharing grant. The intent was to modernize our physical chemistry laboratory using this system. First, all students taking the laboratory courseare required to learn BASIC and to work on the machine. A set of detailed eet on the machine and includine notes to heln the students to " sample exercises is given out at the beginning of the course. The computer is used a t several levels: for teachine Drogramming, for doing selective homework problems f r o g the lecture part of the course, and for routine data processing for several of the experiments. In particular, we have written programs to process the data for a bomb calorimeter experiment where students manually record time-temperature data for subsequent keying into the computer. Temperatures are determined using a DVM output from a transducer that linearizes the signal from a thermistor to give 0-1 V in the range 20-30°C. The output from our Parr solution calorimeter is recorded directly into a file in the computer. This stored data is then processe-d with programs that-will calculate the heat capacity uf the system (using THIS, a calorimeter standnrd)
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