MODULE No.9 : Symmetry and optical activity and dipole moment. Paper No 13 Applications of Group Theory

Transcription

1 1 Subject Chemistry Paper No and Title Paper No 13 Applications of Group Theory Module No and Title 9 :Symmetry and optical activity and dipole moment Module Tag CE_P13_M9 CEMISTRY 1

2 2 TABLE O CONTENTS 1. Learning outcome: 2. Introduction 3. Meaning of optical activity in terms of symmetry 3.1 Examples of dissymmetric molecule having optical activity 3.2 Examples of molecules lacking σ and I but still optically inactive 3.3 Conditions for optical activity 4. Symmetry and optical activity 4.1 Symmetry properties of molecules 4.2 Examples of finding DPM using symmetry criteria 5. Summary CEMISTRY 2

3 3 1. Learning Outcomes After studying this module, you shall be able to 2. Introduction o Know about optical activity o Symmetry aspects of optical activity o Examples of dissymmetric molecules o That absence of S n axis of any order means compound is optically active o Conditions for optical activity o Know about DPM o Know about symmetry and dipole moment o General symmetry criteria for DPM in a molecule o Some examples of finding DPM Optical activity has both classical and quantum mechanical roots, Of all the natural phenomenon observed in nature, none has so profound effect on chemical thoughts as that of natural optical rotatory power.(leiher, A.D., J. Phys-Chem, 1964, 40, 1965). Chirality or optical activity can be applied to molecular structures as well as to individual molecular species. In 1813 Jean Baptiste Biot noticed that plane-polarized light was rotated either to the right or the left when it passed through single crystals of quartz or aqueous solutions of tartaric acid or sugar. Substances that can rotate plane-polarized light are said to be optically active. Those that rotate the plane clockwise are said to be dextrorotatory those that rotate the plane counterclockwise are called levorotatory. Louis Pasteur in 1848 noted that sodium ammonium tartrate forms two different kinds of crystals that are mirror images of each other and rotate the plane polarised light. In this module details of optical activity will not be discussed. 3. Meaning of optical activity in terms of symmetry Criterion for optical activity of a molecule involves the test of superismposability of its mirror image on the original one. igure.1 shows non-superimposability of mirror image arrangement of tetrahedrons with different substituents. CEMISTRY 3

4 4 a a c d b b d c Br Cl Mirror Cl Br mirror ig.1 Reflection of two tetrahedrons through a mirror The tetrahedron I and tetrahedron II are not superimposable and thus are optically active. Take II tetrahedron and try to rotate or manipulate in other way it can not be superimposed on tetrahedron I.Non superimposable mirror images are optically compound and known as enantiomers. It is always easy to draw the mirror image of a structure, but to test whether or not the mirror image is superimposable on the original is very difficult exercise. This type of comparison of original and mirror image is still made for more difficult by the practice of using various projection formulae for the molecules. or example 2- iodobutane C 4 9 I can be written in different projection forms as shown in figure.2 C 3 I C 3 i C 3 C 3 iii C 3 C 3 ii C 3 iv C 3 ig.2 Various projection formulae for 2-iodobutane. In three dimensional projection forms the spatial position of each substituent is fixed. So any type of rotation or manipulation will not change the relative position of the substituents. In the projection form of type iii with its mirror image one is temped to rotate the molecule about dotted line and try to super impose original and its mirror image on each other as shown in figure.3 CEMISTRY 4

5 5 C 3 C 3 a C 3 b C 3 rotate C 3 C 3 iii c ig.3 Mirror images of 2-iodobutane in projection form iii ere a and b are the mirror images and c is the rotated image. Rotated image c now can be superimposed on a projection form and hence the molecule looks to be optically inactive which is not so. Thus this form of projection can miss lead to wrong result. The error arises due to the fact that during such rotations the groups which were forward earlier now go backward and backward groups come forward. rom projection formulas it is not clear. Superimposability test can be easily performed for simple molecules but when complicated molecules are examined such visualizations become more difficult and cumbersome and time consuming. Is there is a simple way of looking whether molecule will be optically active or not? Symmetry properties of the molecules can help in this direction.the earlier definition of a molecule to be optically active nor not was that it should be asymmetric and should not have any symmetry element in it. or a molecule to be optically active it should not have mirror plane and centre of inversion. This definition has been modified. All molecules which lack S n axis of any order will be dissymmetric and optically active i.e. molecule and its mirror image cannot be superimposed in any manner i.e. by rotational or translational motion of the whole molecule. We know that S 1 = σ and S 2 = i. So molecules having S 1 and S 2 axes respectively means that these have σ and i respectively and thus cannot be optically active. Optically compound need not be asymmetric. These may have symmetry axes 3.1 Examples of dissymmetric molecules having optical activity: Let us examine this new definition by taking the example of substituted cyclopropane. The example we take is that of cis- and trans -1, 2-dichlorocyclopropane. Cis-form has S 1 = σ so can not be optically active Trans-form has axis in the plane of three member ring system bisecting C-C bond bearing Cl atoms and passing through C which has two hydrogen atoms attached to it, i.e. ethylene carbon atom. igure.4 shows these symmetry elements in these two forms of 1, 2-choloropropane. CEMISTRY 5

6 6 Cl Cl Trans- Cl Trans- Cl (ii) (i) Mirror images are superimposable Cl Cl Cl Cl Cis- Cis- Mirror images are superimposable Mirror images are not superimposable ig.4 Optical activity of trans- 1,2- dichlorocyclopropane The trans- 1, 2-dichlorocyclopropane (ii) does not have S 1 (= σ ) or S 2 (= i ) axis so it is optically active. But trans- form and its mirror image have -axis i.e. do not lack symmetry.these are dissymmetric but not asymmetric (without symmetry element). The only symmetry element that dissymmetric (optically active) compounds can have are one or more C n axes. Many dissymmetric compounds have axis. Most optically active compounds are asymmetric as well as dissymmetric and hence have only C 1 axis. S n axis (n>2) is difficult to find. 3.2 Examples of molecules lacking σ and i still optically inactive : Let us take an example of a molecule which does not have S 1 ( σ ) or S 2 ( i ) axis in it but still it is optically inactive. The example we take here is that of spiro compound 3, 4, 3, 4 - tetramethyl spiro (1, 1) bipyrrolidinium ion. This molecule does not have S 1 (σ ) or S 2 ( i ) and so it should be optically active but it is not so as it contains S 4 axis coinciding with axis ig.5 shows the presence of S 4 axis in this molecule. Molecule does not have σ but combination of σ and C 4 axis results in S 4 axis. Thus the molecule is optically inactive even if it does not have σ. As it contains S 4 axis so it is optically inactive. CEMISTRY 6

7 + 7 C 3 3 C C 3 3 C 3 C N + σ C 3 S 4 3 C N + C 3 3 C C 4 C 3 N C 3 3 C ig.5 Presence of S 4 axis in 3, 4, 3, 4 - tetramethyl spiro (1, 1) bipyrrolidinium ion Let us another similar example of a molecule which does not have σ or i in it but still it is optically inactive. Example we take is that of 1,3,5,7-tetrafluorocyclooctatetraene. It lacks both σ and i. It is not optically active. This molecule has a axis and S 4 axis along this axis as shown in figure.6 CEMISTRY 7

8 C 4 along σ C 4 S ig. S 4 in 1,3,5,7-tetrafluorocyclooctatetraene. Thus the molecule has S 4 axis so it is optically inactive 3.3 Condition for optical activity: conditions for optical activity,asymmetry and dissymmetry can be summarized as: (i) If the molecule possesses only C n axis it is dissymmetric and optically active (ii) If n=1 in C n the molecule is asymmetric as well as dissymmetric (iii) If molecule possesses S n axis of any order it cannot be optically active. S 1 means σ and S 2 means i. 4. Symmetry and optical activity: ow to determine that a molecule has dipole moment? (i) Draw correct Lewis dot structure of the molecule. (ii) Draw geometry according to VSPER theory. (iii) ind whether the molecule is totally symmetrical or not. (iv) Polarity in a bond means pull in a particular direction. If the pull is equal the there will be no polarity. Criteria for dipole moment (i) If the molecule is diatomic and atoms are different then there will be DPM in it. (ii) A molecule which just has one electron pair in it will have DPM. CEMISTRY 8

9 9 (iii) If all end atoms are similar and there is no lone pair in it, then the molecule will be no polar (iv) If the molecule is unsymmetrical it will have DPM. Thus we see that if we want to know whether the molecule has DPM or not we have to go through these points and come to a conclusion. ere symmetry property of the molecule comes to our rescue and just by noting the presence of symmetry elements one can easily predict whether the molecule will have the DPM or not 4.1 Symmetry properties of molecules : Dipole moment (DPM) is vector property.it has both magnitude and direction and it results from unequal sharing of electrons between atoms of a bond in molecule. It is a stationary and not a dynamic property. Stationary properties must remain unchanged by every symmetry operation of the molecule. In order that dipole moment remains unchanged, dipole moment vector must lie in each of the symmetry elements of the molecule. Some of the main points about dipole moment and symmetry are given as : (i) Molecules having i can not have DPM, as vector can not lie in a point. (ii) Molecules having C n axis only have DPM vector along C n axis. (iii) Molecules having σ, have DPM vector in this plane. (iv Molecules which have more than one C n axis (n>1) cannot have DPM, as vector can not lie along each and every axis at the same time. (v) Molecules belonging to C 1, and σ v have dipole moment along C n and σ v. CEMISTRY C s, C n, C nv only can have DPM i.e. molecules having C n (vi) If DPM of a molecule is known symmetry of the molecule can be predicted. (vii) Symmetry arguments can only fix the direction of DPM vector. It can not give its magnitude and can not tell about the +ve and ve ends of it. If one knows these points about dipole moment and symmetry elements present in the molecules then one can immediately predict the structure or direction of magnitude in the molecule. 4.2 Examples of finding DPM using symmetry criteria Let us take (i) CO 2 (ii) 2 O (iii) CCl 4 (iv) 2 SO (i) CO 2 belongs to D h point group it. It has C axis and has n C axes perpendicular to C axis. DPM vector can not lie in each and every axis so molecule has no DPM. (ii) 2 O molecule belongs to v point group has axis and two σ v. DPM will be along axis and will lie in these planes only. (iii) CCl 4 molecule is highly symmetrical and has multiple axes of several order. DPM can not lie in each every axis. So molecule has no DPM. 9

10 10 (iv) 2 SO molecule S O has only one mirror plane and belongs to C s point group and hence it will have DPM in the plane only. 5.Summary In brief optical activity in molecules explained Symmetry aspects of optical activity explained by taking suitable examples Example of dissymmetric molecule cis- and trans- 1,2-dicholoro cyclopropane was discussed Criteria for optical activity ie absence of S n axis explained by taking suitable examples. Some conditions for optical activity are given Symmetry and DPM explained by taking suitable examples Some main points about symmetry and DPM given and explained with the help of examples CEMISTRY 10