D. P. G. Hamon University of Adelaide Adelaide, South Australia 5001
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T h e Walden inversion is a fundamental principle of the organic chemistry which requires considerable descriptive ability on the part of a teacher in order to impart the concept to beginners studying the subject. A number of teachers have expressed the opinion that a model, which really demonstrates the principle, would greatly assist them. It is the purpose of this article to describe such a model which, in the opinion of the author, goes a long way towards satisfying this requirement. The design for the model is illustrated in the accompanying diagrams. Basically it consists of three segments of a hollow sphere held together by some expanding device (rubber bands, etc.), sliding over the surface of an inner sphere. It holds its shape by virtue of the fact that the combined segments, when held together by the rubber bands, constitute more than a hemisphere and therefore the inner sphere cannot fall out. The segments are designed so that rods protruding from the center of each segment, and normal to the surface, point to three apexes of a tetrahedron. The fourth rod is attached to a cone which fits into the inner sphere and points to the fourth apex of the tetrahedron. When an identical cone is pushed from the side opposite from that of the fourth rod this rod is pushed out and the three segments are caused t o slide around the inner sphere so that the sides which were not in contact now become so. If the model is correctly constructed, the four rods have taken up another tetrahedral arrangement in which the configuration is inverted. Let us consider the geometry of the system in more detail. If one views a sphere, which has rods protruding from its center in a tetrahedral arrangement, from the side directly opposite one of those rods then one sees that, in a two dimensional sense, these rods are
398 / lournol o f Chemicol Education
A Model to Demonstrate the Walden Inversion disposed at an angle of 120' to one another. Therefore it is seen that the rods must be attached to segments of a sphere that subtend an angle of 120' to an axis of that sphere when viewed from immediately behind the fourth rod. It should also be realized that this requirement is necessary when the inverted configuration is viewed. Therefore one is dealing with a symmetrical system in which the rod is situated at the center. However, the rods are tetrahedrally disposed on the surface of the sphere, and hence one can calculate the length of the chord which joins the points where the axis intersects the surface (A Figure I), and where the rod intersects the surface (B Figure I), of the sphere. By trigonometry this chord AB equals twice the radius of the sphere multiplied by the sine of the angle 54' 44'. The geometry of the required segment is that of the
@ G
B
----f
,'
A
Figure 1. Segment of sphere reouired to At between tetrohedrolly ipaced mdr
Figure 2.
Detail of innor sphere.
Figure.3. Armnbled model ond rod with cone which locks Wle fourth bond in place.
Figure 4. Modcis o f more accumte design.
curved surface of the solid segment shown in Figure 1. The angle A E D is 109' 28'; the angle between the planes D F E and DEG is 120'; and the angle between the planes F A E and AEG is also 120". The sides DF, DG, G A , and F A are equal in length. Three of these segments are of course required for each model and they should fit around an inner sphere into which conic holes have been bored. Details of the inner sphere are shown in cross-sectional representation by the shaded area in Figure 2. The cone and rod, which represent the fourth bond, can be seen in Figure 3. The extension of the cone into a rod, which fits through the model and just protrudes as a rounded knob, allows for correct positioning of the segments and acts as a lock to hold the fourth rod in place. The actual sequence of inversion involves pushing out the cone already in place by an identical cone which is pressed against the small protruding knob, the side of the cone then spreads the three segments at the same time causing them to slide around the inner sphere to give the inverted configuration. The point at which the three rods attached to the segments become coplanar can be used to construct trigonal carbon atoms by the use of a spindle with two end washers as shown schematically in Figure 2. The ends of the spindle, where the washers fit, are of smaller diameter than the center section so that the inserting rod, which represents "attack" on the trigonal carbon atom, can be pushed through the near washer. This discards the spindle and far washer enabling the atom to take up the tetrahedral arrangement. Because of the design this can, of course, occur from either side. Having discussed the basic parts of the model, it is desirable to illustrate some of the concepts that can be demonstrated by it. By far the most useful demonstration is that of the Waldeu inversion itself. A model for this purpose only is relatively simple to construct since the accuracy of the tetrahedral angles is not very important. The author, in fact, made the segments for the first model, for demonstrating this inversion, from a hollow plastic toy-hall. The inner sphere was a wooden ball turned on a lathe to the correct diameter and bored out as required. The inserting cones were turned on a lathe from aluminum rod. The expand-
ing device, holding the segments together, was sections of rubber tubing fitting over pieces of welding rod let into the surface of the segment and glued with epoxy resin. The rods from the surface of the segment were of plastic glued to the surface. The result is shown in Figure 3. For more sophisticated demonstrations, models of more accurate design are needed and these require considerable engineering competence and are much more time consuming to construct. The models shown (Fig. 4) were made to be used in conjunction with the models previously described by Professor L. F. Fieser.' They enable one to extend his models, which ably demonstrate geometrical and couformational aspects of molecules before and after reactions, into ones which also demonstrate configurational changes which occur during reactions at both tetrahedral and trigonal centers. For instance, they can be used to demonstrate both the stereochemical requirements for SN2 displacement and the stereochemical consequences of S N displacement ~ of an axial or an equatorial leaving group in a six-memhered ring. The model in the trigonal arrangement can represent a carbony1 group and will allow the demonstration, for example, of such topics as the consequences of stericapproach control versus product-development contro1.z It can, of course, also be used t o represent a carbonium ion. Two trigonal carbon atoms can be used to represent a double bond and thus to demonstrate the stereochemical requirements and consequences of additions to such a system. It should be noted that to maintain restricted rotation about the double bond it is necessary to insert a peg through the bond joining the two trigonal atoms and that this should be removed before converting to the tetrahedral configuration to allow the necessary rotation about that bond. One most important aspect of these n~odels,from the demonstrator's point of view, is that each of these reactions can be shown with reagents "attacking" the carbon atom involved, followed by progress through the transition state to the final product, without the necessity of pulling models to bits. The suspicion of a sleight-of-hand trick, which accompanies the presentation of such reactions by other models available at the moment, is thus avoided. Whether this is sufficient justification for the effort involved in constructing the more accurate models is debatable. I am indebted to Mr. Kevin Newton for technical assistance in the preparation of the models.
(1965). l F o r a discussion of this topic see Housn, H. O., "Modern Synthetic Reactions," W. A. Benjamin, Inc., New York, 1965, p. 30. See also CHEREST, M., AND FELKIN, H., Tetrahedron Lelt k , 2205 (1968).
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Volume 47, Number 5, May 1970
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399
