second chance is allowed if the first response is incorrect, the final grade awarded the student reflects all incorrect answers. Students indicate that the programs are demanding, interesting, and helpful. The seven THERM programs and a library program, XLIBRE, are written in PASCAL, the versim being DECUS 10-271. In these programs two functions that are not in the Revised Pascal R e ~ o r hv t N. Wirth. RANDOM and TIME. are used. The eighi pro&ms average 80 lines and 10 comments each. Execution rewires 9K :%bit words on aDEC-10. the programs. i'hese mater& may he obtained at no charge by writing to: Dr. .John Chamberlin, Department of Chemistry, Western Kentucky University, Bowling Green. KY 42101.
An Introduction to X-ray Crystallography-Two Computer Programs M. Webder The Unlverslty Southampton SO9 5NH. United Kingdom
As single crystal X-ray structure determination assumes the role of a routine technique it remains important to intn)duce the elements of the subject to students of the physical sciences. This is conventionally done through an introduction to the powder method, often of cubic substances, and a numher of exoeriments have been described (12-14). Students ftom our biochemistry department have two lahorat~rryexercises to complement the lectures. In the first of t.hese powder photographs of cubic substances are recorded on film and used to establish cell dimensions, the number of molecules per cell, and the lattice type. A second related exercise involves comparine. the intensity . . .pattern uf a different substance with that calculated for an assumed structure. The intensities (again recorded on film) can he measured using a microdensitometer or estimated by eye. These exercises, particularly the calculation of intensities, henefit from t,he use nftwo computer programs. Student response to the laboratory exercises has been favorable and ~enerallvthe programs have stood the test of time well over the last five years. The first ororram . .. calculates 2H. ninW from the ~ o s i t i o nof the line on the film and then under student control seeks relationshio amonr sin2H values such that all the values are an (The photogaphs are produced on a Unicam 19-cm camera and minor changes would allow the program to he used with other film or diffractometer set,-ups.) The second program inputs the unit cell dimension, wavelength, atomic scattering factors, and structural type. After each ih, h , 1 ) value is entered, the Lp factor, multiplicity and intensity, is calculated 1151. There is orovision for chaneine ., ..the structure tvoe . . and the atomic temperature factors while retaining the atom types. The structural types dealt with are NaCI, ZnS, CsCI, and CaFa and the monatomic lattices P, I, and F. A number of compounds and elements have been used but particularly instructive are the body-centered n-W, KCI, and the Group IIIIV c o m ~ o u n d ssuch as lnSh where the choice The programs have been used on a DEC PDP 11145 with the time-sharing RSTS/E operating system. Interactive BASIC with instructions via the terminal a t execution time. Documentation for the program POWDER (109 statements including 18 comments, 5K) and CIJBIND (65 statements including 9 comments, 4 K) is a source listing of some test jobs and is availahle free dcharge.
A Computer Program to Calculate Alkalinity via Gran's Plot Method Kenneth Wed and Patricia Flath Paul Smith's College Paul Smiths. NY The computer program descrihed here is an aid for calculation by the Gran's Plot method (16, 17) of the alkalinity of natural water systems. Carbonates, bicarbonates, and hydroxides are the most common sources of alkalinity in natural waters, and the levels and types of alkalinity are directly dependent on the source of the water. Adirondack lakes generally have very little huffering ability due to the hase-deficient soil and hedrock common to this region, and with an increase of acid precipitation, there is agreat concern over the ahility of these lakes to continue to support biological systems. "Acidification has proceeded to levels lethal to fish in certain lakes due to low acid neutralizing capacity" (18). I t is estimated that. 56% of the lakes above the 2,000-foot level have no fish, tiny aquatic life, plants or animals (19). As part of our Environmental Technology .. Laboratory course, we require each freshman student to determine the alkalinity of a standard sodium hicarbonate solution and then determine the alkalinity fur a natural water sample. The method employed is that descrihed hy Schufield (18) and re. quires the execution of the following equation: ~
where
V,
= sample volume
in ml
V. = cumulative acid volume in rnl
FI values are plotted against volume of hydrochloric acid titrated and a dope andintercept calculat-ed. This is most efficiently done by a linear regression computation. The computer program is designed to input volume titrated and resultant pH values. The calculated FI values are used in a linear repression equation, with slope, intercept, and correlation values printed. The program includes a visual display of the linear rerressim data. which reinforces the Gran's Plot method, and gives a visual check on the input data. The program is written in HASIC, specifically for a Level I1 16K TRS-80 Microcomputer. The student can request instructions for use of the program. The method has heen tried with a class of 60 stude;ts (and one computer) and has been beneficial to students and faculty. We have also tested the program in our research on alkalinity-poor water supplies, and find that the .program eliminates time-consuming calcula. tions. We have a listing of the program and a description of the experimental method. A TRS-80 cassette tape is available for $10 (check or money order). Send requests to: Professor Patricia C. Flath, Ecolugy and Environmental Technology Division, Paul Smith's College, Paul, Smiths, NY 12970. We would also be interested in trading other computer programs in the environmental and general chemistry areas.
A Comprehensive Treatment of Acid-Base Equilibria on a Pocket Calculator Brian W. Clare School of Mathematical and Physical Sciences. Murdoch University Murdoch. Western Australia 6150 Acid-base equilibria problems are among the first calculations encountered in introdurtorv chemistry courses. In such courses, prohlems are usually solved by recourse to gross apnroximatk,ns. which are valid onlv over limited concentration ranges. This may lead to skepticism on the part of the student, whu when confronted with such a problem has little feeling tor ~ h t i ~t ~ ~ ) l ) r c ~ x i he t ~ wt1111d i . ~ t ~l~w ~p t i l~i r d 111 u>!n;. Xlorv I W ~ I I W I I I ~-!I,. I) ,IS thnt gkvn In I{utlvr 121,t.still ;~dvaa~ced Volume 58 Number 7
July 1981
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