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chemistry
physical chemistry

Questions and Answers of Physical Chemistry

Thallium, a neurotoxin, is the heaviest member of Group 13 of the periodic table and is found most usually in the +1 oxidation state. Aluminum, which causes anaemia and dementia, is also a member of
Compare the approximations built into valence-bond theory and molecular-orbital theory.
Distinguish between the Pauling and Mulliken electro negativity scales.
Discuss the approximations built into the Huckel method.
Use concepts of molecular orbital theory to describe the biochemical reactivity of O2, N2, and NO.
Give the ground-state electron configurations of (a) H-2 (b) N2, and (c) Oz.
Give the ground-state electron configurations of (a) CIF, (b) CS, and (c) 0-2.
Which of the molecules N2, NO, 02, C2, F2, and CN would you expect to be stabilized by (a) The addition of an electron to form AB-, (b) The removal of an electron to form AB+?
Sketch the molecular orbital energy level diagrams for BrCI and deduce its ground-state electron configurations. Is BrCl likely to have a shorter bond length than BrCl-?
Arrange the species 0+2, 02, 0-2, O2-2 in order of increasing bond length.
Normalize the molecular orbital ΨA + λ ΨB in terms of the parameter λ and the overlap integral S.
Can the function Ψ = x2 (L - 2x) be used as a trial wave function for the n = 1 state of a particle with mass m in a one-dimensional box of length L? If the answer is yes, then express the
Suppose that the function Ψ= Ae€”ar2 with A being the normalization constant and a being an adjustable parameter, is used as a trial wave function for the is orbital of the hydrogen
What is the energy of an electron that has been ejected from an orbital of ionization energy 4.69 eV by a photon of radiation of wavelength 584 nm?
Construct the molecular orbital energy level diagrams of ethene (acetylene) on the basis that the molecule is formed from the appropriately hybridized CH2 or CH fragments.
Predict the electronic configurations of (a) The benzene anion, (b) The benzene cation. Estimate the π-electron binding energy in each case.
Use mathematical software to estimate the π-electron binding energy of (a) Anthracene (8), (b) Phenanthrene (9) within the Huckel approximation.
Suppose that a molecular orbital has the form N (O.l45A + 0.844B). Find a linear combination of the orbitals A and B that is orthogonal to this combination.
Show that, if a wave cos kx centred on A (so that x is measured from A) interferes with a similar wave cos k'» centred on B (with x measured from B) a distance R away, then constructive interference
Before doing the calculation below, sketch how the overlap between a is orbital and a 2p orbital can be expected to depend on their separation. The overlap integral between an H Is orbital and an H2p
Repeat the calculation in Problem 11.4but plot the probability densities of the two orbitals. Then form the difference density, the difference between Ψ2 and ½| Ψ 2a + Ψ2b|
Imagine a small electron-sensitive probe of volume 1.00 pm3 inserted into an H+2 molecule-ion in its ground state. Calculate the probability that it will register the presence of an electron at the
The same data as in Problem 11.8 may be used to calculate the molecular potential energy curve for the antibonding orbital, which is given by
Rydberg molecules are molecules with an electron in an atomic orbital with principal quantum number 11 one higher than the valence shells of the constituent atoms. Speculate about the existence of
Set up and solve the Huckel secular equations for the n electrons of NO-3. Express the energies in terms of the Coulomb integrals ao and aN and the resonance integral 13. Determine the delocalization
The FEMO theory (Problem 11.14) of conjugated molecules is rather crude and better results are obtained with simple Huckel theory.(a) For a linear conjugated polyene with each of N carbon atoms
If you have access to mathematical software that can perform matrix diagonalization, use it to solve Problems 11.15 and 11.16, disregarding the expressions for the energies and coefficients given
Electronic excitation of a molecule may weaken or strengthen some bonds because bonding and antibonding characteristics differ between the HOMO and the LUMO. For example, a carbon-carbon bond in a
An sp2 hybrid orbital that lies in the xy-plane and makes an angle of 1200 to the x-axis has the formUse hydrogenic atomic orbitals to write the explicit form of the hybrid orbital. Show that it has
Derive eqns 11.11 and 11.14 by working with the normalized LCAO-MOs for the H+2 molecule-ion (Section 11.3a). Proceed by evaluating the expectation value of the Hamiltonian for the ion. Make use of
We saw in Section 11.5 that, to find the energies of the bonding and antibonding orbitals of a heteronuclear diatomic molecule, we need to solve the secular determinant where aA et aB and we have
There is some indication that other hydrogen ring compounds and ions in addition to H3 and D3 species may play a role in interstellar chemistry. According to J.S. Wright and G.A. DiLabio (J. Phys.
Molecular orbital calculations may be used to predict trends in the standard potentials of conjugated molecules, such as the quinones and flavins that are involved in biological electron transfer
Explain how a molecule is assigned to a point group.
Explain the symmetry criteria that allow a molecule to be polar?
Explain what is meant by(a) A representative and(b) A representation in the context of group theory.
Explain how spectroscopic selection rules arise and how they are formulated by using group theory.
The CCl4 molecule belongs to the point group Td. List the symmetry elements of the group and locate them in the molecule.
Which of the following molecules may be polar? (a) CH3Cl (C3J, (b) HW2 (CO)10 (D4h), (c) SnCl4 (Td).
Use symmetry properties to determine whether or not the integral f Px zPz dτ is necessarily zero in a molecule with symmetry D6
Is the transition A1g → E2u forbidden for electric dipole transitions in a D6h molecule?
Show that the function xyz has symmetry species AI in the group D2.
Molecules belonging to the point groups Th or Td cannot be chiral. Which elements of these groups rule out chirality’s?
The group C4v consists of the elements E, 2C4, C2, and 2σv, 2σd construct the group multiplication table.
Identify the point groups to which the following objects belong: (a) A sharpened cylindrical pencil, (b) A three-bladed propeller, (c) A four-legged table, (d) Yourself (approximately).
List the symmetry elements of the following molecules and name the point groups to which they belong: (a) Naphthalene, (b) Anthracene, (c) The three dichlorobenzenes.
Assign the following molecules to point groups:(a) HF,(b) IF7 (pentagonal bipyramid),(c) XeO2F2, (see-saw),(d) Fe,(CO)9 (22),(e) Cubane, C8H8,(f) Tetrafluorocubane, C8H4F4 (23)
Which of the molecules in Exercises 12.9b and 12.10b can be? (a) Polar, (b) Chiral?
Consider the C3Yion NO;. Is there any orbital of the central N atom that can have a nonzero overlap with the combination 2pz (A) – pz (B) – pz (C) of the three O atoms (with z perpendicular to
The CIO2 molecule (which belongs to the group C, 2v) was trapped in a solid. Its ground state is known to be BJ• Light polarized parallel to the y-axis (parallel to the 00 separation) excited the
What states of(a) Anthracene,(b) Coronene (24) may be reached by electric dipole transitions from their (totally symmetrical) ground states?
Determine whether the integral over /J and /, in Exercise 12.15a is zero over a symmetrical range about e = 0 in the group C3v
List the symmetry elements of the following molecules and name the point groups to which they belong: (a) Staggered CH3CH3, (b) Chair and boat cyclohexane, (c) B, H6, (d) [Co (en) 3J3+, where
The group D 1h has a C, axis perpendicular to the principal axis and a horizontal mirror plane. Show that the group must therefore have a centre of inversion.
Confirm that the z-component of orbital angular momentum is a basis for an irreducible representation of A, symmetry in C3v'
Construct the multiplication table of the Pauli spin matrices, CY, and the 2 x 2 unit matrix:Do the four matrices form a group under multiplication?
Suppose that a methane molecule became distorted to (a) C3v symmetry by the lengthening of one bond, (b) C2v symmetry, by a kind of scissors action in which one bond angle opened and another
R. Eujen, B. Hoge, and D.J. Brauer (Inorg. Chem. 36, 1464 (1997» prepared and characterized several square-planar Ag (III) complex anions. In the complex anion [trans-Ag (CF3)2 (CN), 2|-, the
The algebraic forms of the [orbitals are a radial function multiplied by one of the factors (a) z (5z2 - 3r2), (b) y (5y2 - 3r2), (c) x (5x2 - 3r2), (d) Z(x2 – Y2), (e) Y(x2- z2), (f) x (z2
The NO2, molecule belongs to the group C2v' with the C2 axis bisecting the ONO angle. Taking as a basis the N2s, N2p, and 02p orbitals, identify the irreducible representations they span, and
The phenanthrene molecule (29) belongs to the group C2v with the C, axis in the plane of the molecule.(a) Classify the irreducible representations spanned by the carbon 2pz orbitals and find their
The H3 molecular ion, which plays an important role in chemical reactions occurring in interstellar clouds, is known to be equilateral triangular. (a) Identify the symmetry elements and determine
Some linear polyenes, of which ,6-carotene is an example, are important biological co-factors that participate in processes as diverse as the absorption of solar energy in photosynthesis (Impact
Describe the physical origins of line widths in the absorption and emission spectra of gases, liquids, and solids.
Discuss the physical origins of the gross selection rules for rotational and vibrational Raman spectroscopy.
Suppose that you wish to characterize the normal modes of benzene in the gas phase. Why is it important to obtain both infrared absorption and Raman spectra of your sample?
Calculate the ratio of the Einstein coefficients of spontaneous and stimulated emission, A and B, for transitions with the following characteristics:(a) 500 MHz radiofrequency radiation,(b) 3.0 cm
At what speed of approach would a red (660 nm) traffic light appear green (520 mu)?
Estimate the lifetime of a state that gives rise to a line of width (a) 100 MHZ (b) 2.14 cm-1
A molecule in a gas undergoes about 1.0 X 109 collisions in each second. Suppose that (a) Every collision is effective in deactivating the molecule rotationally and (b) That one collision in 10
Calculate the frequency of the J = 3 f-- 2 transition in the pure rotational spectrum of 12CI60. The equilibrium bond length is 112.81 pm.
If the wave number of the J = 1 f-- 0 rotational transition of IH81Br considered as a rigid rotator is 16.93 cm-1, what is (a) The moment of inertia of the molecule, (b) The bond length?
Given that the spacing of lines in the microwave spectrum of 35Cjl9p is constant at 1.033 cm-1, calculate the moment of inertia and bond length of the molecule (me(35Cl) = 34.9688 u, m(19F) = 18.9984
The rotational constant of 12/16OC is 0.39021 cm. Calculate the bond length of the molecule (m (l2C) = 12 u exactly, m (16O) = 15.9949 u).
Determine the CO and CS bond lengths in OCS from the rotational constants B(16Ol2C32S) = 6081.5 MHz, B(16012C34S) = 5932.8 MHz.
The wave number of the incident radiation in a Raman spectrometer is 20623 cm-1. What is the wave number of the scattered Stokes radiation for the J = 4 f- 2 transition of 160O2?
The rotational Raman spectrum of 19F2 (m (19F) = 18.9984 u) shows a series of Stokes lines separated by 3.5312 cm-1 and a similar series of anti-Stokes lines. Calculate the bond length of the
Which of the following molecules may show a pure rotational microwave absorption spectrum? (a) H20, (b) H202, (c) NH4 (d) N20?
Which of the following molecules may show a pure rotational Raman spectrum? (a) CH2Cl2 (b) CH3CH3, (c) SP6, (d) N2O?
An object of mass 2.0 g suspended from the end of a spring has a vibrational frequency of 3.0 Hz. Calculate the force constant of the spring.
Calculate the percentage difference in the fundamental vibration wave number of IH35Cl and 2H37CIon the assumption that their force constants are the same.
The wave number of the fundamental vibrational transition of 79BrB1Bris 323.2 cm-1, Calculate the force constant of the bond (mC9Br) = 78.9183 u, m(8IBr) = 80.9163 u).
Calculate the relative numbers of Br, molecules (v = 321 cm-1) in the second and first excited vibrational states at (a) 298 K, (b) 800 K.
Prom the data in Exercise 13.18a, predict the fundamental vibrational Wave numbers of the deuterium halides.
For 14N2 ∆G values for the transitions v = 1 ← 0, 2 ← 0, and 3 ← 0 are, respectively, 2345.15, 4661.40, and 6983.73 cm-1. Calculate v and xe- Assume ye to be zero.
The first five vibrational energy levels of HI are at 1144.83, 3374.90, 5525.51, 7596.66, and 9588.35 cm-1 Calculate the dissociation energy of the molecule in reciprocal centimeters and electron
Infrared absorption by I H81 12 Br gives rise to an R branch from v = O. What is the wave number of the line originating from the rotational state with J = 2? Use the information in Table 13.2.
Which of the following molecules may show infrared absorption spectra? (a) CH3CH3, (b) CH4, (c) CH3CI, (d) N2
How many normal modes of vibration are there for the following molecules: (a) C6H6, (b) C6H6CH3, (c) HC=C-C=CH.
Which of the vibrations of an AB3 molecule are infrared or Raman active when it is (a) Trigonal planar, (b) Trigonal pyramidal?
Consider the vibrational mode that corresponds to the boat-like bending of a benzene ring. Is it (a) Raman, (b) Infrared active?
A carbon disulfide molecule belongs to the point group D_h. The nine displacements of the three atoms span A1g+ AIU+ A2g+ 2E1u+ E1g.What are the symmetries of the normal modes of vibration?
Use mathematical software to evaluate the Planck distribution at any temperature and wavelength or frequency, and evaluate integrals for the energy density of the radiation between any two
The collision frequency z of a molecule of mass m in a gas at a pressure pis z = 4(J (kTlnm) 1/2p/kT, where o is the collision cross-section. Find an expression for the collision-limited lifetime of
The rotational constant for CO is 1.9314 cm-1 and 1.6116 cm-1 in the ground and first excited vibrational states, respectively. By how much does the intern clear distance change as a result of this
Rotational absorption lines from 1H35CI gas were found at the following wave numbers (R.1, Hausler and R.A. Oetjen, f. Chem. Phys. 21, 1340 (1953)): 83.32, 104.13, 124.73, 145.37, 165.89, 186.23,
Thermodynamic considerations suggest that the copper monohalides CuX should exist mainly as polymers in the gas phase, and indeed it proved difficult to obtain the monomers in sufficient abundance to
In a study of the rotational spectrum of the linear Fe CO radical, K. Tanaka, M. Shirasaka, and T. Tanaka (J. Chem. Phys. 106,6820 (1997)) report the following J+ I (,- J transitions: J 24 25
Predict the shape of the nitronium ion, NO from its Lewis structure and the VSEPR model. It has one Raman active vibrational mode at 1400 cm-1, two strong IR active modes at 2360 and 540 cm-1, and
The HCI molecule is quite well described by the Morse potential with De = 5.33 eV, V = 2989.7 cm-1, and XV = 52.05 cm-I. Assuming that the potential is unchanged on deuteration, predict the

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