University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009

HONOURS PHYSICAL CHEMISTRY – CHEM731 Duration: 3 hours

Total Marks: 100

Internal Examiners:

Professor T A Ford Professor S B Jonnalagadda Professor B S Martincigh

External Examiner:

Professor S O Paul UNISA

INSTRUCTIONS: 1.

This paper is divided into three sections. Answer each section in a separate answer book.

2.

Answer five of the six questions.

3.

Programmable calculators may be used but all working must be shown.

4.

The marks shown are for guidance only. Extra credit may be given for answers showing originality of thought and for relevant information from sources outside this course.

5.

This paper consists of 12 pages. Please make sure you have them all.

6.

Graph paper is provided.

7.

A periodic table and data sheet are attached at the end of this question paper.

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 2

SECTION A QUESTION 1 (a)

The structures of the molecules (i) fluoroacetylene, HCCF (linear), (ii) fluoroform, CHF3 (tetrahedral) and (iii) tetrafluoroethylene, C2F4 (planar) are shown below.

(i)

(ii)

(iii)

Sketch each of the molecules, drawing in their labelled Cartesian coordinate axes, according to the standard convention. Hence identify all the symmetry elements of each molecule, including the identity element. (6) (b)

The phosphoryl chloride molecule, OPCl3, belongs to the C3v point group. Its equilibrium structure is illustrated below. The z axis coincides with the P=O bond and the x axis lies in one of the OPCl planes.

The nine normal modes of vibration are illustrated below.

mode 1 (1322 cm-1)

mode 2 (590 cm-1)

mode 3 (590 cm-1)

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 3

mode 4 (481 cm-1)

mode 5 (333 cm-1)

mode 6 (333 cm-1)

mode 7 (266 cm-1)

mode 8 (187 cm-1)

mode 9 (187 cm-1)

Using the character table for the C3v point group given, assign each normal vibration to its correct irreducible representation (symmetry species). Describe the nature of each vibration (stretching, bending, symmetric, antisymmetric, etc.) and indicate the infrared and Raman activities, and any degeneracies, in each case.

(14) [20]

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 4 QUESTION 2 (a)

Consider the three molecules (i) hydrazine, N2H4 (non-planar), (ii) oxalic acid, (COOH)2 (planar) and (iii) silane, SiH4 (tetrahedral), illustrated below. By recognizing the presence of their symmetry elements, assign each molecule to its correct point group. A point group flow chart is provided.

(i)

(ii)

(iii)

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 5

(6)

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 6 (b)

The structure of the molecule furan, C4H4O, of C2v symmetry, is shown below.

The z axis of the molecule lies in the molecular plane, passes through the O atom and bisects the opposite C4C5 bond. The y axis lies in the plane of the molecule and the x axis is perpendicular to this plane. The energies and occupancies of molecular orbitals 6 to 29 are given in the table below, along with the major contributing atomic orbitals. (Orbitals 1 to 5 are core 1s orbitals of the O and C atoms.) A number of selected molecular orbitals are shown below. Using the C2v character table (provided), assign each of these molecular orbitals to its correct irreducible representation (symmetry species) and identify it as being either bonding, non-bonding or antibonding, and either σ or π. Number 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Energy/H -1.39474 -1.01732 -0.93780 -0.73784 -0.72222 -0.67695 -0.55876 -0.53913 -0.51444 -0.49596 -0.45103 -0.32249 -0.26076 0.28579 0.38402 0.57652 0.62014 0.63736 0.68378 0.75155 0.77223 0.93322 0.93530 1.12704

Occupancy 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0

Major atomic orbital contributions O1:2s + C2:2s + C3:2s C4:2s + C5:2s C2:2s – C3:2s + C4:2s – C5:2s O1:2py + C2:2pz – C3:2pz C2:2s + C3:2s + H6:1s + H7:1s C2:2py – C3:2py – C4:2pz – C5:2pz O1:2px + C2:2px + C3:2px – C2:2py – C3:2py – H6:1s + H7:1s C4:2pz – C5:2pz – H8:1s + H9:1s C4:2py – C5:2py + H8:1s + H9:1s O1:2s + O1:2pz O1:2px – C2:2px – C3:2px – C4:2px – C5:2px C2:2px – C3:2px + C4:2px – C5:2px – O1:2px + C2:2px + C3:2px – C4:2px – C5:2px – C2:2px + C3:2px + C4:2px – C5:2px O1:2s – O1:2pz + C2:2py – C2:2pz – C3:2py – C3:2pz C2:2s + C3:2s – H6:1s – H7:1s O1:2py + C2:2py + C3:2py – C2:2s + C3:2s – H6:1s + H7:1s C2:2s – C3:2s – H6:1s + H7:1s C4:2s + C5:2s – H8:1s – H9:1s C2:2pz – C3:2pz + C4:2py + C5:2py C2:2py – C3:2py + C4:2pz + C5:2pz C2:2pz + C3:2pz + C4:2s + C4:2pz – C5:2s – C5:2pz

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 7

orbital 6

orbital 8

orbital 13

orbital 16

orbital 18

orbital 19

orbital 21

orbital 24

orbital 27 (14) [20]

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 8

SECTION B QUESTION 3 (a)

The hydrolysis of ethyl acetate in the presence of sodium hydroxide was investigated in the temperature range 20 oC to 50 oC and the frequency factor and energy of activation for the reaction were found to be 1.25 x 1013 dm3 mol-1 s-1 and 104 kJ mol-1 respectively. Use absolute reaction rate theory to calculate ΔH≠and ΔS≠ at 30 oC for the reaction. (6)

(b)

Derive the Brρnsted equation to predict the effect of ionic strength on the reaction between charged species. (6)

(c)

Show that for a first-order first order reversible reaction, the relaxation time is given by τ = 1/(k1 + k-1).

(8) [20]

QUESTION 4 (a)

(b)

For the reaction between two charged species in solution, show that ln kr α 1/ε, where kr is the rate constant and ε is the dielectric constant. Use the 'Double sphere' model.

(8)

Fick's law states that flux is proportional to the concentration gradient. Derive the rate constant for the diffusion-controlled reaction between two reactants, which are not influenced by electrostatic interactions. (8)

(c)

(i) Show that for a diffusion-controlled reaction between non-charged species, the rate coefficient, kd, is independent of the reacting species and is equal to 8RT/3η, where η is the viscosity of the solvent. (2) (ii) Calculate the magnitude of the diffusion-controlled rate constant at 298 K for the recombination of two moles of such reactants in water. (Viscosity of water, η = 0.89 x 10-3 kg m-1 s-1) (2) [20]

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 9

SECTION C QUESTION 5 The diagram below shows the potential energy curves for the Br2 molecule. Where possible use the diagram to illustrate your answers to the questions which follow.

(a)

(b)

What are the selection rules for an optical transition for a diatomic molecule such as Br2?

(2)

What is meant by optical dissociation? (3)

(c)

What is meant by predissociation? (4)

(d)

Explain the following observations as fully as possible: (i) Absorption of light of 6300 Å produces two ground-state atoms (2P3/2). (ii)

(3)

Absorption at 4662 Å produces both ground- and excited-state atoms but not in equal numbers. (3)

(iii)

Absorption at 3471 Å produces two ground-state atoms. (1½)

(iv)

(e)

Vacuum ultraviolet photolysis of Br2 produces excited bromine atoms (5s, P5⁄2, 4P3⁄2).

4

2

(1½)

2

Estimate the energy difference between the P3/2 and P1⁄2 states of atomic bromine.

(2) [20]

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 10 QUESTION 6 When exposed to ultraviolet light, m-nitroanisole (I) in aqueous solution is excited to the S1 state and then 100% of the excited molecules undergo rapid intersystem crossing to the T1 state. In the presence of hydroxide ion, OH¯, and a triplet quencher, Q, the molecule in the T1 state has one of the following fates: (i) (ii) (iii)

radiationless decay to the ground state of I (rate constant k1) attack by OH¯ leading initially to m-nitrophenol (II) as indicated in the equation below (with rate constant k2) quenching by Q leading to the ground state of I (rate constant k3) NO2

NO2 +

+

OH

CH3O

OH

OCH3

I

II

The quantum yield Ν of the reaction to produce (II) varies with the triplet quencher concentration as follows; the OH¯ concentration is held constant. [Q]/10-3 mol dm-3

Ν (a)

0 0.37

1.7 0.32

3.3 0.28

5.0 0.25

6.9 0.22

9.8 0.19

What is meant by “intersystem crossing” and what are the selection rules for such a transition? (4)

(b)

Draw a Jablonski diagram to illustrate the intramolecular processes mentioned above. (2)

(c)

(d)

Write a mechanism for the above processes and then derive an expression for the quantum yield of the reaction in terms of the rate constants k1, k2 and k3.

(9)

By drawing an appropriate graph, show that the quantum yield data are consistent with this expression. (5) [20]

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 11

University of KwaZulu-Natal, Westville Campus, Durban Examinations: June 2009 Honours Physical Chemistry – CHEM731 Page 12