d.H
by
WALTER A. WOLF Eisenhower College Seneca Falls. New York 13148
suburban locations situated on the circumferences of circles of three and six mile radii, and centered at the city center. Students readily agree that the number of suburban locations must steadily increase along the circumferences of larger and lareer circles. From this. it is a straiehtforward conclusion that two opposing factors must be weighted in computing the number of persons residing a t a specified distance from the city center: the population density steadily decreases with increasine- r.. while the number of suburban locations of anv specified size increases with increasing r. A maximum value for the number of Dersons livine a t a s~ecifieddistance from the city center is therefore expeged a t Bome finite value of the distance; this is exactly analogous to the maximum value found for the radial probability at the Bohr radius.
Compact Compacts
Probability Density and Maximum Radial Probability for the Is Orbital: An Analogy with Population Density and Distribution in Cities A. D. B a k e r City University of New York, Queens College Flushing, New York 11367 Many students have difficulty in reconciling the following facts: (1)when W* or $2 . is .lotted aeainst distance.. r.. from nucleus, for the hydrogen 1s wavefunrtion, the graph shows the maximum value of$$- or $:at the nucleui ( r = 0): (21 the distance from the nucl& a t which the electronis m&tlikely to be found is a t the Bohr radius, 0.539 A, and not at r = 0. The students' difficulties invariably stem from a failure to realize that the maximum probability distance referred to in (2) is derived from a summation of +5.* or 5.2 for a11 possible volume elements centered distance r from the nucleus. The distinction between probability per unit volume and radial probability is illustrated fairly clearly by consideration of population density and distribution around a city. The maximum population density (peoplelunit area) is expected at the city center, and wiU then decrease on moving intothe suburbs. This is analogous to the behavior of 5.2. However if one wishes to compare the number of people a t varying distances from the city center (analogous to radial probability)-say at three and six miles-one must add up the contributions from all 516 I Journal of Chemical Education
J o h n W. Hill and Lyle C. Hall of the University of Wisconsin, River Falls, Wisconsin, report that for several years they have used the synthesis of soap as an interest-enhancing end-of-term activity in freshman chemistry. Now they have found a cheap and easy way to color the soap (ordinary food colors, which are water soluble, do not work very well). Fat collected from cookina is used for the svnthesis. T o color the soap, merely add a cra),on t c g the fat at ;he itart uf the procedure (1 g ofcrayon to 7 5 E of f a t ) . The darker colored cravons work best, producing attractive pastel shades in the soap. Perfume, if desired, may be added with the water a t the last washing. Grace Chiu, of the University of West Florida, Pensacola, Florida, has noticed that in the study of buffers, many students have difficulty associating the chemistry with the algebra. T o help students understand this topic, and acid-base chemistry in general, an experiment was designed. The student is to prepare 100 ml of approximately 1M buffer solutions of pH 5.0 and 8.0. The only information provided is a table of dissociation constants of acids and bases. After selecting the appropriate conjugate acid-base pair for each buffer and calculating the amounts of reagents required, the student prepares the solutions. The pH is measured and adjusted to the nominal value, if necessary. Then the effects of dilution and of the addition of small amounts of strong acid or base on the pH of the buffers and other solutions are studied. The results are compared to each other and to theory, if desired. This experiment may be introduced in general or analytical chemistry. It could be comdeted in a 3-hour ~ e r i o dA . more detailed procedure may be-obtained upon request This column is devoted to brief announcements of new ideas in chemical education. These consist of succinct statements of the key ideas of the authors along with possible information on obtaininp furthermaterial related ta the subject upon request. Authors who wish to submit articles for consideration far oublieation should send the manuscripts (one double-spaced, typewritten page) and the supporting materials to Dr. Walter A. Wolf, Editor, Chem Ed Compacts, Department of Chemistry, Eisenhower College, Seneca Falls, New York 13148.
