G. Dana Brabson and David W. SeegmiIIer United States Air Force Academy
Colorado 80840
1I
Programmable C U ~ C U ~ Add O~S a New Dimension to Laboratories
W i t h the advent of the digital computer, many problems in chemistry which were previously intractable or at best extraordinarily time-consuming have become easily soluble. The eventual impact of such computers on undergraduate chemistry instruction and in particular on laboratory courses is difficult to foresee. Several schools are including basic computer familiarization courses in their chemistry curricula. At the U.S. Air Force Academy all cadets are required to take one semester of digital computer programming; thus, by the time cadets enroll in physical chemistry and instrumental analysis laboratory courses they are firmly grounded in the use and programming of large scale digital computers. However, even under these most favorable circumstances, the authors have found that the large digital computer is not ideally suited to aid the undergraduate student as he labors with the tedious calculations required for physical chemistry and instrumental analysis laboratory reports. Recently, a much smaller instrument, the programmable calculator, has become available. Because of its reasonable cost and computational ability, it promises to add a new dimension to undergraduate laboratory courses. In essence, the instrument is, as the name implies, a calculator; however, it is a vastly more capable instrument than the familiar mechanical desk calculator. Various machines, of course, have different capabilities; however, most can perform, in addition to the common operations (addition, subtraction, multiplication and division), operations such as In x,eZ, &, x2. Some are able to automatically evaluate trigonometric functions. The great power of the programmable calculator, however, lies in its capability to automatically carry out a sequence of operations. In this sense it is capable of performing many of the functions of a true computer. A Typical Application
Many physical chemistry and instrumental analysis laboratory experiments require that rather extensive computations be carried out for each of several data sets. Often, each computation yields a single point which is then used in a graphical representation. A case in point is the study of the homogeneous NzOa-NO2 equilibrium.' Briefly the experiment is performed as follows 1) The weight of an evacuated glass bulb is determined; the same bulb is then weighed again after having been filled with laboratory air. From these measurements and the cdculrtted DANII:LS,F., CORNWELL, C. D., WILLIAMS, J. W., BENDER, AL~ERTY 1%. , A,, "Experimental Physical Chemistry," (6th ed.), McGraw-Hill Book Company, Inc., New York, 1962, pp. 96-100. I
P.,
AND
Equations for NsOn-NOz Equilibrium
Table 1.
PnUP= PBST -Pmr
v
0001818 t - .0000130 (t - 1,) 1 .0001818 t
['
+
=
W"
M e -W R T =
PV 92.06
(3)
-M
M
(4)
(5) AH'
=
-2.303 R
-
Yd;z:l
W"
= room temperature in 'C = scale calibration temperature in ' C = vnlnme o f hnlh .-. -. = weight of laborstory air contained by
R
= =
t t8
V
r
- -- - - -
~ e r c e n relative t humiditv
(6)
hulb
pas constant TR, = room temperature ("K) p"n,o = saturstion water vapor pressure at temperature TB, Pa.. = harometrio Dressure M = apparent m6lecular weight of the N20,-NO. mixture W = weight of N80,-NO1 mixture T = equilibrium temperature in OK = degree of dissociation of N.0, = eauilihrium constant AH" = hiat of reaction density of the laboratory air, the volume of the bulb is etahlished. 2) The bulb is evacuated and then a small amount of N104 condensed into it. At each of approximately 20 temperature between 25 and 60°C, the hulb contents are allowed to equilibrate; the bulb is periadicdly vented to the atmosphere, thus maintaining an equilibrium pressure equal to that of the atmosphere. The gas density is determined at esch temperature by weighing the bulb with its contents.
Several calculations, ideally suited for a programmable calculator, are required to reduce the data. The pertinent calculations are listed in Table 1. The first step in the calculations is to make a scale expansion correction to the barometric pressure, eqn. (1). Next, using the corrected pressure, the density of the laboratory air and the volume of the bulb are computed; this combined calculation can be expressed as eqn. (2); about 75 program operations are needed for this step. Next, for each of the 20 temperatures a t which data were obtained, logloK is calculated by sequentially solving eqns. (3), (4),and (5); about 75 program operations are required for these calculations. Finally, loaoK is plotted versus 1/T, the method of least squares is used to determine the best straight line fit of the data points, and AH is calculated from the slope of the least squares line; the least squares procedure requires about 75 program operations. Volume 47, Number 2, February 1970 / 1 17
In addition to the experiment discussed, Table 2 lists a few of the other programs which the authors are currently using in their classes. Table 2.
Typical Applications
" .
Phvsical Chemistm Exoeriments N104-NO*Equilibrium Molecular Weieht-Dumas Method (Ideal and Berthelot BeITe,rt oi (:c,~zat,u*tion-RonlII Calorimetry l'nrtial hllolecdar \\'eiyht by Boiliq Point Elevatim Temperature Dependence of E M F Instrumental Analysis Experiments Analysis of Emission Spectrograph Films Treatment of log [(id - i)/i] vemus E Data in Polarography Quantitative Analysis of Gas Mixtures fram Mass Spectrometric Data Pmgrems of General Utility Mean, Variance, and Standard Deviation bz Least Squares Fit t o y = a Least Squares Fit to y = a bz cz2 Solution of Three Simultaneous Eauations
+ + +
Table 3.
Company Friden Division The Singer Company 2350 Washington Ave. Ssn Leandro, Calif. 94577 Hewlett-Packard Co. Loveland Division P.O. Box 301 Loveland, Colo. 80537 I M E Sales Corporation One IME Plaza North Bergen, N.J. 07047 Monroe International 550 Central Ave. Orange, N.J. 07051 ~livetti-underwood One Park Avenue New York, N.Y. 10016 Smith-Corona Marchant 299 Park Avenue New York, N.Y. 10017 Wan Laboratories 836 orth Street Tewksburry, Mass. 01876
fi
Instrument designation
Method qf* programnung Kevboard
IME 86s or I M E 86SR with DG 308 Epic 3000
NumStoragec ber of6 steps registers 30
Keyboard or Mag- 19614n netic Card Keyboard or Mag- 392-14n netic Card 512 Keyboard or Punched Card Keyboard
42
Processingd registers
Output
1
4
Printed Tape
+
3
n 2 O
