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Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437

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BuyFindarrow_forward

Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437
Chapter 13, Problem 13.30E
Textbook Problem
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Structural isomers can have very different point groups. Determine the point groups of 1 , 4 cyclohexadiene and 1 , 3 cyclohexadiene , which both have the molecular formula C 6 H 8 .

Interpretation Introduction

Interpretation:

The point groups of 1,4cyclohexadiene and 1,3cyclohexadiene is to be identified.

Concept introduction:

Group theory is the area of mathematics, which deals with symmetry and point groups.

A group is a collection of operations that satisfies certain mathematical characteristics.

In a molecule, the collection of symmetry elements forms a point group. All molecules possess structure that belongs to one of the recognised point groups.

Explanation of Solution

Structural isomers consist of same chemical formula but the sequence of atoms to each other is different. The compounds 1,4cyclohexadiene and 1,3cyclohexadiene, both have the molecular formula C6H8 and are structural isomers of each other.

The isomer 1,4cyclohexadiene has the following elements of symmetry:

Identity element E, the proper rotational axis C2 and two vertical planes of symmetry σv and σv'.

Figure 1

Therefore, using the flowchart, which determines the point groups, it belongs to the C2v point group

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Chapter 13 Solutions

Physical Chemistry
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Ch. 13 - In the answer to exercise 13.10, part a, what does...Ch. 13 - List the mathematical properties of a group.Ch. 13 - Use equation 13.18 to construct the matrix...Ch. 13 - What are the number of classes and the order of...Ch. 13 - What are the number of classes and the order of...Ch. 13 - a Show that the C3v point group satisfies the...Ch. 13 - a In the Td point group, an S41 improper rotation...Ch. 13 - Determine which single symmetry operation of the...Ch. 13 - What symmetry operations are the inverse of the...Ch. 13 - What symmetry operations are the inverse of the...Ch. 13 - Group theory requires that symmetry operations...Ch. 13 - Figure 13.27 shows the structure of the molecule...Ch. 13 - In Example 13.3e, we are assuming that resonance...Ch. 13 - Identify all the symmetry elements present in the...Ch. 13 - Point groups are called such because all of the...Ch. 13 - Determine the point groups of the following...Ch. 13 - Determine the point group of the following...Ch. 13 - Determine the point groups of the following...Ch. 13 - Determine the point groups of the following...Ch. 13 - Structural isomers can have very different point...Ch. 13 - Structural isomers can have very different point...Ch. 13 - Chlorination of methane yields CH3Cl,CH2Cl2,CHCl3...Ch. 13 - Identify the point group of the wave functions of...Ch. 13 - Identify the point group of the wave functions of...Ch. 13 - a What would be the formulas of possible molecules...Ch. 13 - Determine if the following species have permanent...Ch. 13 - Determine if the following species have permanent...Ch. 13 - Which of the following species will not have...Ch. 13 - Determine if the following species have permanent...Ch. 13 - Explain why a molecule with a center of inversion...Ch. 13 - a Unlike methane, bromochlorofluoromethane...Ch. 13 - Write out explicitly the 1212 matrices that...Ch. 13 - For NH3, write out explicitly the three 1212...Ch. 13 - Show that the irreducible representations of the...Ch. 13 - Show that the irreducible representations of the...Ch. 13 - Show that any two of the irreducible...Ch. 13 - Show that any irreducible representation of these...Ch. 13 - Explain why this proposed irreducible...Ch. 13 - Using the character tables in Appendix 3, can you...Ch. 13 - Show by using an example that the sum of the...Ch. 13 - Why is it unnecessary to consider whether an...Ch. 13 - Explain why the characters for the proper and...Ch. 13 - Use the expressions in Rh(3) to determine the...Ch. 13 - a What are the symmetry elements present in a plot...Ch. 13 - What are the symmetry elements present in a plot...Ch. 13 - What point groups must the wavefunctions of all...Ch. 13 - The bonds in the ethylene molecule can be...Ch. 13 - Consider the bonds in ethylene shown in the...Ch. 13 - Reduce the following reducible representations...Ch. 13 - Determine the resulting representations for the...Ch. 13 - Determine the resulting representations for the...Ch. 13 - Without using the great orthogonality theorem,...Ch. 13 - Assume that you are evaluating the integral of...Ch. 13 - Assume that you are evaluating the integral of...Ch. 13 - Assume that x- polarized light can be assigned an...Ch. 13 - Show that ss transitions are not allowed in the...Ch. 13 - The ground electronic state of ozone, O3, a C2v...Ch. 13 - The five d orbitals in transition metals can be...Ch. 13 - Determine the symmetry labels of the H-like p...Ch. 13 - Determine the symmetry labels of the H-like f...Ch. 13 - Construct the symmetry-adapted linear combination...Ch. 13 - Referring to exercise 13.71: How would the...Ch. 13 - In Example 13.13, several of the molecular...Ch. 13 - Should the molecular orbitals for H2O found in...Ch. 13 - How many SALCs can be constructed for CH4 using...Ch. 13 - Construct a list comparing and contrasting VB...Ch. 13 - Why might one not be surprised to find that the...Ch. 13 - Suppose you use p0,p1 and p+1 along with s...Ch. 13 - Show that the individual sp orbitals, as written...Ch. 13 - Show that the individual sp3 orbitals, as written...Ch. 13 - What is the rough hybridization of the carbon...Ch. 13 - Determine the symmetry species of the D3h point...Ch. 13 - Determine the D3h symmetry species of the sp3d...Ch. 13 - Determine the Oh symmetry species of the sp3d2...Ch. 13 - In propene CH3CH=CH2, the first carbon has sp3...Ch. 13 - Justify the fact that the nitrogen atom in ammonia...Ch. 13 - What symmetry species is assigned to the lone p...Ch. 13 - Construct 90 probability surface diagrams for sp,...

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