edltwd by
WALTER A. WOLF Eisenhower College
Seneca Falls. New York 13\40
Calculators, Slide Rules, and Significant Figures Thomas McCullough, CSC. St. Edward's University Austin, Texas 78704 As Shakespeare so brilliantly demonstrated, an outstanding success can often carry with it the ingredients for tragedy. A common example is the acquisition of power, political or often corrupts those who poesess it, slowly otherwise, for perhaps but inexorahly. In the field of science, a corrupting power is the pocket calculator which easily, quickly, and accurately performs all manner of mathematical operations a t the push of a button or two. Unfortunately the calculator does not know how to manipulate significant figures properly and imparts this ignorance to the unwary student who dutifully and naively records all the pretty luminous numbers as they appear in the read-out. The absurdity of obtaining eight or nine significant figures when dividing a pair of numbers having only two or three is seldom grasped by the proud new owner of the marvelous calculator. And it really is a marvel when compared to the slide rule or the drudgery of hand computation. But even marvels must be treated properly. Before entrusting students with a calculator, practical pedagogy suggests that a brief encounter with a slide rule is in order. The slide rule does have the advantage of usually yielding the proper number of significant figures, especially when dealing with such common chemical numbers as 22.4, 273.16.0. etc.. for what you see is what you get. Not so with the calculator, which is fartoo generous in handing out numbers, thus . preying~ on the students' instinct to believe anything that appears in "print".
Acid-Base Half-Reactions-A Useful Formalism for Review Lessons G. F. Atkinson Uniuersity of Waterloo Waterloo, Ontario Canada N2L 3GI The following is an effective way to draw analogies between acid-hase and redox effects while reviewinr both. I r introduces students to the notion of acid-base half-reactions. Lowrv-Bronsted acids are proton donors, and bases are proton &-eptors. An acid halfrenction and a base half-reacIton ran he written separately, then combined ro eliminate prt~ronsjust a i rcdox halt'-reartima we comhinnl to eliminate rlertruns. In the reacrionul'lI~Iwith kH~.a"stronger"arid and hase react to e k e as ~roductsa 'wenkt.rn acid (NH.,') and hase (Cl-), againYanalo&sly to redox. Just as it is conventional to tabulate redox half-reactions as reductions, and to cite reduction potentials, so acid-base half-reactions are tabulated as acid half-reactions with acidity constants. The Henderson-Hasselhach equation is now clearly anal238 1 Journal of Chemical Education
ogous to the Nernst equation. Just as the redox couple creates a poised (electron-buffered) system a t potentials near the standard potential when both members are present, so the conjugate acid-base pair creates a proton-buffered system a t pH values near the pK. value. Both equations have the general form: tabulated property (measured quantity) = of the system I
+ (factor)log
ratio of pair of constituent forms, concentrations
Since standard redox potentials may he plotted along a number-line of voltages, and pK,,'s may he plotted similarly on a number-line of pH, and since the definition of zero on both scales arises from a single experimental device-the srnndnnl hydrogen electrude . i r is c~mvenientro use the scales ac axes from a rummon point to lay OUI a plane in which anv solution lies at a ~ o i n tsince . anv solution must have a DH and a redox poten&. p his lays the groundwork for the later introduction of the usefulness in analvtical work of Pourbaix diagrams, which are constructed in such a plane.
A Model to Illustrate the Infinite Nature of a Crystalline Compound C. H. L. Kennard Uniuersity o f Queensland Brisbane, Australia, 4067 A model to represent the infinite and periodic nature of face-centered cubic crystalline compounds has been constructed. A black acrylic box is fitted with a highly reflecting gold-plated glass op (an offcut from reflecting window glass used to clad skys~rapers).Two rigid square frames (cut out from circuit hoards) fit into slots parallel to the glass top at % and 2 / ~of the model's depth. These each contain two-dimensional arrays of nine equally spaced and alternnre yelhw and red lieht (wittine diodes 5 I . K I ) I in $1 fnce centered ar" rangement. An ordinary flat mirror forms the internal hase of the box. The LED's in the top array (four yellow and five red) all face toward the reflecting glass top or "see through" mirror and those in the bottom (five yellow and four red) are in the alternate arrangement and are directed toward the mirror in the base. All metal connectors and the bottoms of the LED's are coated with a non-reflectine black paint to eliminate extraneous light. The only light seen when viewing into the box is from the top of the LED's. This arrangement gives an optical effect of an infinite face centered cihic arraneement of vellow and red LED's. i p o w e r su{ply is necessary for the low voltage LED's. Care must be taken to mount the LED's in the rigid board to make the two boards parallel to the top and bottom mirrors, and to add shims to overcome any curvature of the mirrors. The author wishes to acknowledge the constructional and technical assistance given to him by Wilson Turner, Les Bretherton, George Spatny, and Miki Jankovits. Editors note: There are commercially available light "sculptures" hased upon this principle.
