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Unformatted text preview: Chapter 4 4.1 Draw sketches of C, axes and a planes? (a) NH 3 ? In the drawings below, the circle represents the nitrogen atom of ammonia and the diamonds represent the hydrogen atoms. The mirror plane drawn is in the plane of the page, and it contains the nitrogen atom and the hydrogen atom on the left. The other two hydrogen atoms are out of this plane, one behind the page and one in front. (b) The PtC1 4 2- ion? In the drawings below, the circle represents the platinum atom of the tetrachloroplatinate anion and the diamonds represent the chlorine atoms. The mirror plane drawn is in the plane of the page, and it contains all five atoms. This plane is also drawn on its side, so that all five atoms seem to lie on a single line. In addition, there are four more mirror planes perpendicular to the first plane. 4 .2 S 4 or i : (a) C0 2 ? This linear molecule has a center of inversion. There are only two point groups for linear molecules, D h (has i ) or C (does not have i ). Therefore, the point group is D h . (b) C 2 H 2 ? This linear molecule also has i . The point group is D h . (c) BF 3 ? This molecule possesses neither i nor S 4 . It belongs to the D 3h point group. (d) SO 4 2- ? This ion has three different S 4 axes, which are coincident with three C 2 axes, but there is no i . The point group is T d . 4.3 Assigning point groups: (a) NH 2 C1? The only element of symmetry that this molecule possesses other than E is a mirror plane that contains the N and Cl atoms and bisects the H-N-H bond angle. The set of symmetry elements (E, ) corresponds to the point group C s (the subscript comes from the German word for mirror, Spiegel). (b) C0 3 2- ? The carbonate anion is planar, so it possesses at least one plane of symmetry. Since this plane is perpendicular to the major proper rotation axis, C 3 , it is called h . In addition to the C 3 axis, there are three C 2 axes coinciding with the three C-O bond vectors. There are also other mirror planes and improper rotation axes, but the elements listed so far (E, C 3 , ah, 3C 2 ) uniquely correspond to the D 3h point group (note that CO 3 2- ) has the same symmetry as BF 3 ). A complete list of symmetry elements is E, C 3 , 3C 2 , S 3 , h , and 3 v ....
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