
(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
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- What are the missing reagents for the spots labeled 1 and 3? Please give a detailed explanation and include the drawings and show how the synthesis proceeds with the reagents.arrow_forwardPlease provide the complete mechanism for the reaction below and include all appropriate arrows, formal charges, and intermediates. Please draw out the answerarrow_forwardPredict the major organic product for this reaction.arrow_forward
- help me with the rf value i am so confusedarrow_forwardPredict the major organic product for this reaction.arrow_forward3) The following molecule, chloral is a common precursor to chloral hydrate, an acetal type molecule that was a first-generation anesthetic. Draw a mechanism that accounts for tis formation and speculate why it does not require the use of an acid catalyst, like most hemiacetal and acetal reaction: (10 pts) H H₂Oarrow_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

