Physical Chemistry
2nd Edition
ISBN: 9781285969770
Author: Ball
Publisher: Cengage
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Chapter 13, Problem 13.27E
Determine the point group of the following molecules. (a)
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Draw the shape of the PF5 molecule and answer the following questions:
Does the molecule have σh mirror plane(s)? If so, how many?
(v) Does the molecule have σv mirror plane(s)? If so, how many?
(vi) Does the molecule have σd mirror plane(s)? If so, how many?
(vii) What is the point group of the PF5 molecule?
(viii) WhatistheorderofthepointgroupofthePF5molecule?
(ix) Using symmetry criteria, predict
if the PF5 molecule is polar or non-polar.
(x) Using symmetry criteria, predict if the PF5 molecule is chiral or non-chiral.
(i)
the point group to which pyridine (C5H§N) belongs;
(ii)
the number of internal degrees of freedom for pyridine;
(ii)
the irreducible representation for pyridine;
(iv)
the number of IR active C-H stretching modes for pyridine;
(v)
the number of Raman active C-H stretching modes for pyridine.
Chapter 13 Solutions
Physical Chemistry
Ch. 13 - In your own words, explain why an object that has...Ch. 13 - Identify the symmetry elements present in the...Ch. 13 - Identify the symmetry elements present in the...Ch. 13 - Prob. 13.4ECh. 13 - Prob. 13.5ECh. 13 - Prob. 13.6ECh. 13 - Prob. 13.7ECh. 13 - Prob. 13.8ECh. 13 - Any axis of symmetry Cn that rotates an object by...Ch. 13 - Prob. 13.10E
Ch. 13 - Prob. 13.11ECh. 13 - Prob. 13.12ECh. 13 - Prob. 13.13ECh. 13 - What are the number of classes and the order of...Ch. 13 - Prob. 13.15ECh. 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 - Prob. 13.19ECh. 13 - Prob. 13.20ECh. 13 - Prob. 13.21ECh. 13 - Figure 13.27 shows the structure of the molecule...Ch. 13 - Prob. 13.23ECh. 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 - Prob. 13.32ECh. 13 - Identify the point group of the wave functions of...Ch. 13 - Identify the point group of the wave functions of...Ch. 13 - Prob. 13.35ECh. 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 - Prob. 13.39ECh. 13 - Explain why a molecule with a center of inversion...Ch. 13 - a Unlike methane, bromochlorofluoromethane...Ch. 13 - Prob. 13.42ECh. 13 - Prob. 13.43ECh. 13 - Prob. 13.44ECh. 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 - Prob. 13.49ECh. 13 - Prob. 13.50ECh. 13 - Why is it unnecessary to consider whether an...Ch. 13 - Prob. 13.52ECh. 13 - Prob. 13.53ECh. 13 - Prob. 13.54ECh. 13 - Prob. 13.55ECh. 13 - Prob. 13.56ECh. 13 - Prob. 13.57ECh. 13 - Prob. 13.58ECh. 13 - Reduce the following reducible representations...Ch. 13 - Determine the resulting representations for the...Ch. 13 - Prob. 13.61ECh. 13 - Without using the great orthogonality theorem,...Ch. 13 - Assume that you are evaluating the integral of...Ch. 13 - Prob. 13.64ECh. 13 - Assume that x- polarized light can be assigned an...Ch. 13 - Prob. 13.66ECh. 13 - Prob. 13.67ECh. 13 - Prob. 13.68ECh. 13 - Prob. 13.69ECh. 13 - Prob. 13.70ECh. 13 - Construct the symmetry-adapted linear combination...Ch. 13 - Prob. 13.72ECh. 13 - Prob. 13.73ECh. 13 - Prob. 13.74ECh. 13 - Prob. 13.75ECh. 13 - Prob. 13.76ECh. 13 - Prob. 13.77ECh. 13 - Suppose you use p0,p1 and p+1 along with s...Ch. 13 - Show that the individual sp orbitals, as written...Ch. 13 - Prob. 13.80ECh. 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 - Prob. 13.84ECh. 13 - In propene CH3CH=CH2, the first carbon has sp3...Ch. 13 - Prob. 13.87ECh. 13 - Prob. 13.88ECh. 13 - Prob. 13.89E
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- Consider the molecule CH3Cl. (a) To what point group does the molecule belong? (b) How many normal modes of vibration does the molecule have? (c) What are the symmetry species of the normal modes of vibration of this molecule? (d) Which of the vibrational modes of this molecule are infrared active? (e) Which of the vibrational modes of this molecule are Raman active?arrow_forwarddetermine:(i) the point group to which thiophene (C 4 H 4 S) belongs;(ii) the number of internal degrees of freedom for thiophene;(iii) the irreducible representation for thiophene;(iv) the number of IR active C-H stretching modes for thiophene;(v) the number of Raman active C-H stretching modes for thiophene.arrow_forwardNeopentane, C(CH3)4, has Tď symmetry, with character table provided below. Suppose the characters of a reducible representation of this point group are x(E) = 17, x(C3) = 2, x(C₂) = 5, x(S4) = -3, and x(od) = -5 (this is shown explicitly in the last row of the character table). (a) Use the T₁ irreducible representation to determine the order of the point group using the Little Orthogonality Theorem (Vallance Eq. 1.15.13, see Problem 3). (b) Determine how many times each irreducible representation in Ta is contained in this reducible representation. Td A₁ A₂ E Τ1 T₂ r E 1 1 2 3 3 17 8C3 1 1 -1 1 0 0 2 3C₂ 1 1 2 -1 6S4 1 -1 1 101 1.5 7 0 1 713 7. 1.5 -1 -1 60d -3 -1 -1 -5arrow_forward
- P10C.8 Consider the molecule F2C=CF2 (point group D2h), and take it as lying in the xy-plane, with x directed along the C–C bond. (a) Consider a basis formed from the four 2pz orbitals from the fluorine atoms: show that the basis spans B1u, B2g, B3g, and Au. (b) By applying the projection formula to one of the 2pz orbitals, generate the SALCs with the indicated symmetries. (c) Repeat the process for a basis formed from four 2px orbitals (the symmetry species will be different from those for 2pz).arrow_forwardConsider the octahedral species CrCl63- (point group Oh). What point group results by (a) removing one Cl (b) replacing one Cl with one Br (c) removing two trans Cl’sarrow_forwardDetermine the point groupof the following molecules Ethene Tetraphenylmethane , C(C6H5)4arrow_forward
- (a) Identify the principal (z) rotational axis for all molecules provided below. (b) Provide a complete list of symmetry operations for each of the following molecules. (c) Which molecules posses identical sets of symmetry operations? C Me Me Me Me Me ÇI HN FoNH H3N CI NH3 NO CO Fo CO co Fo CO co OC ON čo čoarrow_forward1. Find the point groups of the following shapes, interpreting (a) as a square and (b)-(p) as derivatives with lines perpendiarrow_forward(a) Identify the symmetry elements in ethene and in allene, and assign each molecule to a point group. (b) Consider the biphenyl molecule, Ph–Ph, in which different conformations are possible according to the value of the dihedral angle between the planes of the two benzene rings: if this angle is 0°, the molecule is planar, if it is 90°, the two rings are perpendicular to one another. For each of the following dihedral angles, identify the symmetry elements present and hence assign the point group: (i) 0°, (ii) 90°, (iii) 45°, (iv) 60°.arrow_forward
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