
(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
- Determine if the following salt is neutral, acidic or basic. If acidic or basic, write the appropriate equilibrium equation for the acid or base that exists when the salt is dissolved in aqueous solution. If neutral, simply write only NR. Be sure to include the proper phases for all species within the reaction LiNO3arrow_forwardAn unknown weak acid with a concentration of 0.410 M has a pH of 5.600. What is the Ka of the weak acid?arrow_forward(racemic) 19.84 Using your reaction roadmaps as a guide, show how to convert 2-oxepanone and ethanol into 1-cyclopentenecarbaldehyde. You must use 2-oxepanone as the source of all carbon atoms in the target molecule. Show all reagents and all molecules synthesized along the way. & + EtOH H 2-Oxepanone 1-Cyclopentenecarbaldehydearrow_forward
- R₂ R₁ R₁ a R Rg Nu R₂ Rg R₁ R R₁₂ R3 R R Nu enolate forming R₁ R B-Alkylated carbonyl species or amines Cyclic B-Ketoester R₁₁ HOB R R₁B R R₁₂ B-Hydroxy carbonyl R diester R2 R3 R₁ RB OR R₂ 0 aB-Unsaturated carbonyl NaOR Aldol HOR reaction 1) LDA 2) R-X 3) H₂O/H₂O ketone, aldehyde 1) 2°-amine 2) acid chloride 3) H₂O'/H₂O 0 O R₁ R₁ R R₁ R₁₂ Alkylated a-carbon R₁ H.C R₁ H.C Alkylated methyl ketone acetoacetic ester B-Ketoester ester R₁ HO R₂ R B-Dicarbonyl HO Alkylated carboxylic acid malonic ester Write the reagents required to bring about each reaction next to the arrows shown. Next, record any regiochemistry or stereochemistry considerations relevant to the reaction. You should also record any key aspects of the mechanism, such as forma- tion of an important intermediate, as a helpful reminder. You may want to keep track of all reactions that make carbon-carbon bonds, because these help you build large molecules from smaller fragments. This especially applies to the reactions in…arrow_forwardProvide the reasonable steps to achieve the following synthesis.arrow_forwardIdentify which compound is more acidic. Justify your choice.arrow_forward
- Provide the reasonable steps to achieve the following synthesis.arrow_forwardWhen anisole is treated with excess bromine, the reaction gives a product which shows two singlets in 1H NMR. Draw the product.arrow_forward(ii) Draw a reasonable mechanism for the following reaction: CI NaOH heat OH (hint: SNAr Reaction) :arrow_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

