T o the Editor: On page 476 of the September, 1962, issue, a simplified calculation of the tetrahedral bond angle is presented. This reminds me of a similar treatment which we heard in our lectures a t Graz and which gives this angle directly. It is based on an application of the principles of vector calculations, viz., that the scalar product of two vectors is given by the product of their lengths times the cosine of the angle between them. Starting from the same point as Dr. McCullough, we may write r,, r2, r,, and r, for the four vectors of the C H dipole moments; and because the dipole moment of methane is zero, we get rt T, ?a . 74 = 0 If we multiply with one of those vectors, say r,, we get
+ +
rr.r,
+
+ +ra
n . 7 ~
f n.7, = 0
If we designate a as the length of all four C-H moments and a as the tetrahedral angle, we have immediately aa
+ aP.eosa + a2.coS a + a3.cos a = 0
which simplifies to 3 cos a hence, cos a
= -1 = -I/3
This means that the angle must he between 90 and 180° (more than 180' would be identical with an angle measured the other way around, and i t would then be smaller than 180°) and so we find the same value of 109' 28'. This treatment, which is in fact equivalent to the one above, shows more elegantly the equivalence of all four C-H bonds. G. SXATZKE ORGANISCH-CHEMI~CHES INsTITDT UNIVERSITXT BONN.WEST GERMANY
To the Editor: In the September, 1962, issue, T. McCullough (THIS JOURNAL, 39,476 (19fi2)) gave a mechanical derivation of the tetrahedral bond angle. A very simple derivation follows from an elementary property of the tetrahedron, namely that the centroid divides each median in the ratio 3 : 1. I n the diagram, A E B is a plane which contains the centroid G, the two bonds G A and GB, and the line GH. AGF is a median of the tetrahedron. < -4GH = < AFB = 9 0 ° . < H G B = < G B F = a.
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Journol o f Chemical Education
To the Editor: Textbook errors can be psychological as well as chemical. For example, in the reaction between dilute sulfuric acid and zinc, hydrogen gas is liberated. Under certain conditions we have been able to detect measnrable amounts of hydrogen sulfide gas in the hydrogen. For the beginner in chemistry, the important product is hydrogen. It would be a psychological error to detract from the main reaction and the accompanying introduction to the activity series by calling attention to the side reaction or reactions. The point made by Bostrup, Demandt, and Hansen in Textbook Errors, 41, The Thermal Decomposition of KC103, 39, 573 (November, 1962) is quite comparable. The catalyzed decomposition of KC1O3 does indeed produce several side reactions, and the liberated oxygen is far from the pure colorless, odorless gas the textbook described. On the other hand, it would he a psychological error to draw the student's attention from the essential path of the reaction. Let him learn for the first time about the effect of a catalyst without cluttering up a big idea by calling attention to side reactions. E. GERALD MEYER NEW MEXICOHIGHLANDS UNIV. Las VEOAB,N. M.
ELBERTC. WEAVER PHILLIPSACADEMY ANDOVER, MASSAC~BETTS
EDITOR'SNOTE: Readers should turn to p. 78 for more information on the subjects discussed in these letters. To the Editor: The article, "The Thermal Decomposition of KC108" in the November, 1962 JOURNAL came a t a very opportune time. The Chemistry Club was organizing a program on the topic, oxygen, for the next meeting. Two test tube generators were set up with equal weights of high grade potassium chlorate. One was mixed with reagent grade MnOr and the other with the same weight of the technical grade. The gases from each were collected in bottles placed in 2 liter beakers containing the same volume of a dilute solution of KI and starch. The evolution of oxygen from the generator with the impure catalyst was rapid even with less heat than applied to the generator with pure chemicals. The solution colors in the collectiug beakers contrasted markedly. The solution in the beaker using the pure chemical was a pale blue. The other solution was an intensely dark blue. A comparison of the amount of chlorine liberated could be made by diluting the darker solution to match the lighter one. Others may use or modify this experiment. It shows that the technical grade MnOn has greater catalytic power and also liberates more chlorine and/or chlorine dioxide in the decomposition of the potassium chlorate.
