Chapter 6 - Group Theory ( Test )

Question 1

Briefly describe symmetry

Answer 1

Is very important in chemistry researches and group theory is the tool that is used to determine symmetry

Question 2

What is group theory

Answer 2

Is the mathematical application of symmetry to an object to obtain knowledge of its physical properties

Question 3

Purpose of Group Theory

Answer 3

How the symmetry of a molecule is related to its physical properties and provides a quick simple method to determine the relevant physical information of the molecule

Question 4

Explain Symmetry Operations

Answer 4

• When we perform an operation to a molecule, if we cannot tell any difference before and after we do the operation, we call this operation a symmetry operation
• This means that the molecule seems unchanged before and after a symmetry operation

Question 5

What are two basic and important concepts in group theory

Answer 5

Symmetry operations and symmetry elements

Question 6

Explain Symmetry Elements

Answer 6

• For different molecules, there are different kinds of symmetry operations we can perform
• To finish a symmetry operation, we may rotate a molecule on a line as an axis, reflect it on a mirror plane, or invert it through a point
  located in the center
• These lines, planes, or points are called symmetry elements. There may be more then one symmetry operations associated with a particular symmetry

Question 7

Explain Identity E

Answer 7

• The molecule does not move and all atoms of the molecule stay at the same place when we apply an identity operation, E, on it
• All molecules have the identity operation
• Identity operation can also be a combination of different operations when the molecule returns to its original position after these operations are performed

Question 8

Explain frequencies

Answer 8

• Different covalent bonds have different strengths due to the masses of different atoms at either end of the bond
• As a result, the bonds vibrate at different frequencies
• The frequency of vibration can be found by detecting when the molecules absorb electro-magnetic radiation
• Various types of vibration are possible

Examples include… STRETCHING and BENDING

Question 9

Explain the identification of compounds by direct comparison of spectra

Answer 9

• The only way to completely identify
  a compound using IR is to compare
  its spectrum with a known sample
• The part of the spectrum known as
  the ‘Fingerprint Region’ is unique to each compound

Question 10

What are the uses of the inra red spectra

Answer 10

1. Identification of particular bonds in a molecule
2. Identification of compounds by direct comparison of spectra

Question 11

Why is the infra red spectra complex

Answer 11

• Due to the many different vibrations taking
  place in each molecule
• Total characterisation of a substance based only on its IR spectrum is almost impossible unless one has computerised data handling facilities for comparison of the obtained spectrum with one in memory
• The technique is useful when used in conjunction with other methods - nuclear magnetic resonance spectroscopy and mass spectroscopy

Question 12

Peak position depends on…

Answer 12

1. Bond strength
2. Masses of the atoms joined by the bond

Question 13

Strong bonds and light atoms…

Answer 13

Absorb at lower wavenumbers

Question 14

Weak bonds and heavy atoms…

Answer 14

Absorb at high wavenumbers

Question 15

Explain the fingerprint region

Answer 15

• rganic molecules have a lot of C-C and C-H bonds within their structure

-Spectra obtained will have peaks in the 1400 cm-1 to 800 cm-1 range

• The pattern obtained is characteristic of a particular compound the frequency of any absorption is also affected by adjoining atoms or groups

Question 16

Explain IR Spectrum of a carbonyl compound

Answer 16

• Show a sharp, strong absorption between 1700 and 1760 cm-1
• This is due to the presence of the C=O bond

Question 17

Explain IR Spectrum of an alcohol

Answer 17

• Show a broad absorption between 3200 and 3600 cm-1
• This is due to the presence of the O-H bond
• O-H STRETCH

Question 18

Explain IR Spectrum of a carboxylic acid

Answer 18

• Show a broad absorption between 3200 and 3600 cm-1
• This is due to the presence of the O-H bond
• They also show a strong absorption around 1700 cm-1
• This is due to the presence of the C=O bond
• O-H STRETCH AND C=O STRETCH

Question 19

Explain IR Spectrum of an ester

Answer 19

• Show a strong absorption between 1750 cm-1 and 1730 cm-1
• This is due to the presence of the C=O bond

Question 20

What stretch is there in aldehydes

Answer 20

C = O Stretch

Question 21

Explain the C-H bond

Answer 21

• Alkane
• 2965 - 2850
• Strong

Question 22

Explain Idnetity E more

Answer 22

• All molecules have Identity
• This operation leaves the entire molecule unchanged
• A highly asymmetric molecule such as a
  tetrahedral carbon with 4 different groups attached has only identity, and no other symmetry elements

Question 23

Explain n-fold rotation

Answer 23

• Water has a 2-fold axis of rotation.
• When rotated by 180 degrees, the hydrogen atoms trade places, but the molecule will look exactly the same

Question 24

Explain n-fold Axis of Rotation of ammonia

Answer 24

• Ammonia has a C3 axis.
• Note that there are two operations associated with the C3 axis. Rotation by 120 degrees in a clockwise or a counterclockwise direction provide two different orientations of the molecule

Question 25

Explain Mirror Planes for a water molecule

Answer 25

- The reflection of the water molecule in either of its two mirror planes results in a molecule that looks unchanged - The subscript “v” in σv, indicates a vertical plane of symmetry - This indicates that the mirror plane includes the principal axis of rotation (C2)

Question 26

Explain the mirror planes of a benzene ring

Answer 26

- The benzene ring has a C6 axis as its principal axis of rotation - The molecular plane is perpendicular to the C6 axis, and is designated as a horizontal plane, σh - The vertical planes, σv, go through the carbon atoms, and include the C6 axis - The planes that bisect the bonds are called dihedral planes, σd

Question 27

Explain Improper Rotation

Answer 27

An improper rotation is rotation, followed by reflection in the plane perpendicular to the axis of rotation

Question 28

Explain Inversion

Answer 28

The inversion operation projects each atom through the center of inversion, and across to the other side of the molecule

Question 29

Explain symmetry

Answer 29

- Is the property of a molecule (or object) by which it appears unchanged after a certain operation is performed on it — such as rotation, reflection, or inversion - In other words, a molecule has symmetry if some part of it can be transformed and the molecule still looks identical to its original orientation

Question 30

The Five Basic Types of Symmetry Operations

Answer 30

1. Identity (E) 2. Rotation (Cₙ) – rotation by 360°/n about an axis 3. Reflection (σ) – reflection through a mirror plane 4. Inversion (i) – inversion through a center 5. Improper rotation (Sₙ) – rotation by 360°/n followed by reflection through a plane perpendicular to that axis

Question 31

Of the five basic types of symmetry operations, two are not independent (i.e. they can be expressed by two of the three others). Name the two operations and explain why they are not independent

Answer 31

1. Inversion (i) 2. Improper rotation (Sₙ) Reason: - Both can be expressed in terms of combinations of other symmetry operations: - The inversion (i) operation is equivalent to a rotation (C₂) followed by a reflection (σh) in some cases. - The improper rotation (Sₙ) is defined as a rotation (Cₙ) followed by a reflection (σh) perpendicular to the rotation axis. - Thus, both depend on combinations of other symmetry operations and are not independent