
(a)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•

Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | |||||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
The character of
Therefore,
Therefore, there are four Raman-active vibrations and two IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
(b)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•

Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | |||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
The character of
Therefore,
The
Therefore, there are six Raman-active vibrations and six IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
(c)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•

Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | ||||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Therefore,
The
The
The
Therefore, there are nine Raman-active vibrations and eight IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
(d)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•

Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | |||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
The character of
Therefore,
The
Therefore, there are six Raman-active vibrations and six IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
(e)
Interpretation:
The number of Raman-active vibrations for the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•

Answer to Problem 14.94E
The number of Raman-active vibrations for the
Explanation of Solution
The symmetry of
The character table for point group
operations | |||||
This reducible representation reduced using great orthogonality theorem as shown below.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
•
•
•
•
•
The order of the group is
The great orthogonality theorem orthogonality of the irreducible representation of
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
The character of
Therefore,
Therefore, there are four Raman-active vibrations and two IR-active vibrations would be observed by
Therefore, the number of Raman-active vibrations for the
The number of Raman-active vibrations for the
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Chapter 14 Solutions
Physical Chemistry
- Experiment 27 hates & Mechanisms of Reations Method I visual Clock Reaction A. Concentration effects on reaction Rates Iodine Run [I] mol/L [S₂082] | Time mo/L (SCC) 0.04 54.7 Log 1/ Time Temp Log [ ] 13,20] (time) / [I] 199 20.06 23.0 30.04 0.04 0.04 80.0 22.8 45 40.02 0.04 79.0 21.6 50.08 0.03 51.0 22.4 60-080-02 95.0 23.4 7 0.08 0-01 1970 23.4 8 0.08 0.04 16.1 22.6arrow_forward(15 pts) Consider the molecule B2H6. Generate a molecular orbital diagram but this time using a different approach that draws on your knowledge and ability to put concepts together. First use VSEPR or some other method to make sure you know the ground state structure of the molecule. Next, generate an MO diagram for BH2. Sketch the highest occupied and lowest unoccupied MOs of the BH2 fragment. These are called frontier orbitals. Now use these frontier orbitals as your basis set for producing LGO's for B2H6. Since the BH2 frontier orbitals become the LGOS, you will have to think about what is in the middle of the molecule and treat its basis as well. Do you arrive at the same qualitative MO diagram as is discussed in the book? Sketch the new highest occupied and lowest unoccupied MOs for the molecule (B2H6).arrow_forwardQ8: Propose an efficient synthesis of cyclopentene from cyclopentane.arrow_forward
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- Q5: Predict major product(s) for the following reactions. Note the mechanism(s) of the reactions (SN1, E1, SN2 or E2). H₂O דיי "Br KN3 CH3CH2OH NaNH2 NH3 Page 3 of 6 Chem 0310 Organic Chemistry 1 HW Problem Sets CI Br excess NaOCH 3 CH3OH Br KOC(CH3)3 DuckDuckGarrow_forwardQ4: Circle the substrate that gives a single alkene product in a E2 elimination. CI CI Br Brarrow_forwardPlease calculate the chemical shift of each protonsarrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage Learning

