This writer has a corresponding program for the TI-591 PC-100A combination which will accept as input any n, T, and one or several pairs of A and K'values; it will then automatically print the amount for each point andlor plot a complete curve for a s i n ~ l substance e or a mixture, based on the equation above. u p t o 81 points (for a two-component mixture) can be obtained. An additional feature permits suppression of initial and final hlank uortion and exoansion of the remainder over the full number of points. T h e brogram is very fast and makes possible a fascinating study of distrihution processes as a function of the various parameters. Interested readers may obtain the program on a card and instructions by sending a self-addressed stamped envelope and a hlank magnetic card. Practical Applications of Calculator Simulations David Holdsworth University of Papua New Guinea Vogel notes that a calculator oronram ( 1 4 ) to disulay . . . the masses of solute in each tube after countercurrent extraction can operate to a maximum of 69 solvent transfers (70 tuhes) with most availahle pocket calculators. This limitation is of little disadvantage in mactice since few machines are built with over 50 tubes. However a calculator program can he readily modified to control overflow hy a factor adjustment and the calculator overflows when "C,=,/2 > 10loOin the hinomial. This occurs after 329 transfers (330 tubes). Manual inspection can allow further transfers, though this is slow with the calculator operating in semiautomatic mode. Students heing introduced to countercurrent extraction appreciate the distrihution is hinomial by first choosing K = 1and nlottine distrihution curves re ore sent in^ a few solvent transfkrs. A &aph representing the Heparation of p-hydroxyhenzoic acid and gallic acid in an ether-water system after fifteen transfers is sufficient to show complete separation (14). For such a program using a simple calculator, without a factorial key, the data required for the sixteen plots is displayed
in about 2l12 minutes. The data required to plot the purification of henzylpenicillin in 70 tubes using an HP-67 (or HP-97) instrument, with a factorial key, is displayed or printed in ahout two minutes for each solute. Each point on the graph can he readily checked if necessary. This time factor is reduced in Vogel's continuous plot program, but the mass in each tube, beginning from tuhe 1, must he displayed in turn, the display series cannot easily he initiated a t any selected tuhe, and the mass in a particular tuhe cannot he directly examined or checked if the student makes a graphical error. Consequently the student may not appreciate that the mass in any selected tuhe can he readily calculated by a hinomial expression. Vogel's statistical expression is an interesting one. However, it proved to be inaccurate for the class uses I mentioned in illustrating the principles of countercurrent distrihution. I t has the disadvantage that for most students the calculator hecomes a number-disolavine . " "blackbox." The derivation of the expression programmed, the program, and its application could confuse manv and daunt all hut the bravest teachers and students. I prefer to have the calculator evaluate expressions that students can derive and use themselves. Literature Cited (1) Wuzniak, S., "The AppleII," Hyts.215). 34 (May 19771. (2) Sauitiky, A, and Onlay,M. J. E.,Anal. Chem., 36, 1627 (18641. (a) criffith3.rcter R.. " ~ ~ ~ ~ ~~e /~ ho nri pmu in a schemistry." plenum PW, 1978. (4) Murgieh. J., J. CHEM.EDUC.,SW!. 421 (1877). .I. P.."Qu~ntumChemi~tiv."Academic Reas. New York. 1978. Aooendix 10. 15) LOWP. (6) Fleser. L. F: Williamson. K, I.'"organic Erperimmt.?4th ed., ~ e & , i e r i n g t o n ,
Maaarchu~etts,Experiment 54. , New York, 1969, Chapter 14. (7) Sukal, R. 8 . andRohlT, F.J.. R m m ~ i r yFreeman, (81 Day, R. A . Jr.. and Underwood, A. L.. "Quantitative Analysis: 2nd ed., Prentice-HnU, Englewood Cliffs, New .leraey. 1971. (9) Kerni~han,B. W., and Piauger, P. J., "Software Tools..' Addison-Wesley. Readinp. Masachoaetta, 1978. (10) Munn, R. I.. and Stewart. I. M.. "RATMAC: Kernighan and Plaueor's Structured FORTRAN Prnerammine Laneuaee."TR-675. Camouter Science Center. Universitv M ~ ~c & ~ pa&, ~I ~~1 9 i s~- ~ , 111) Munn. R. J.. and Stewart. d. M.. "RATMAC Primer: TR-804. C o m o u t e ~Science Center. University of Maryland, College Park, 1979. (12) ~ o b i n s ~ A. n . I . . , s c ~ PZ~ O~ ~T . , 119no). ~ ~ 113) Demidavlch, B. 1'. and Mamn. I. A . "Computational Mathematics? MIR Pub..
Computer Series Reprint Volume Available The Division of Chemical Education is pleased to announce the publication of "Iteratiuns: Computing in the Journal Computer Series. of Chemical Education" edited by John W. Moore, the current editor of the JOUHNAL'S The first 16 articles from the Computer Series together with a dozen more full-lengthdescriptions of computer applications from the 1979through April 1981issues of the JOURNALare contained in this volume. It begins with an introduction to amputers, educational applications,and sources of materials. Also included are a thorough treatment of computer-assisted instruction, computer graphics, microcomputers and desktop computers, simulation and data analysis, computers and testing, and information storsee and retrieval. Aoolications of oocket calculators. use of com~utersin ohvsieal and organic chemistrv me comprehensive reference. This paperback is available postpaid for $9.75. Address prepaid orders to Journal of Chemical Education, 238 Kent Road, Springfield,PA 19064.
Volume 58 Number 9
Seotember 1981
697
