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chemistry
physical chemistry

Questions and Answers of Physical Chemistry

F. Luo, G.c. McBane, G. Kim, cr. Giese, and W.R. Gentry (J. Chem. Phys. 98, 3564 (1993)) reported experimental observation of the He2 complex, a species that had escaped detection for a long time.
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 symmetries of the normal modes of
Show that the moment of inertia of a diatomic molecule composed of atoms of masses mA and mB and bond length R is equal to meffR2, where meff= mAmB/(mA + mB)'
In the group theoretical language developed in Chapter 12, a spherical rotor is a molecule that belongs to a cubic or icosahedral point group, a symmetric rotor is a molecule with at least a
The protein haemerythrin is responsible for binding and carrying 0, in some invertebrates. Each protein molecule has two Fe'+ ions that are in very close proximity and work together to bind one
The moments of inertia of the linear mercury (II) halides are very large, so the °and S branches of their vibrational Raman spectra show little rotational structure. Nevertheless, the peaks of both
In Problem 10.27, we saw that Doppler shifts of atomic spectral lines are used to estimate the speed of recession or approach of a star. From the discussion in Section 13.3a, it is easy to see that
There is a gaseous interstellar cloud in the constellation Ophiuchus that is illuminated from behind by the star ζ Ophiuci. Analysis of the electronic-vibrational-rotational absorption lines
The space immediately surrounding stars, also called the circumstellar space, is significantly warmer because stars are very intense black -body emitters with temperatures of several thousand kelvin.
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| Discuss.
Explain the origin of the term symbol 32:~for the ground state of Dioxygen.
How do the band heads in P and R branches arise? Could the Q branch show ahead?
Describe the mechanism of fluorescence. To what extent is a fluorescence spectrum not the exact mirror image of the corresponding absorption spectrum
Describe the principles of laser action, with actual examples.
The molar absorption coefficient of a substance dissolved in hexane is known to be 327 dm3 mol-1 cm-1 at 300 nm calculate the percentage reduction in intensity when light of that wavelength passes
When light of wavelength 400 nm passes through 3.5 mm of a solution of an absorbing substance at a concentration 0.667 mmol dm-3, the transmission is 65.5 per cent. Calculate the molar absorption
The molar absorption coefficient of a solute at 440 nm is 323 dm2 mol-1 cm-1 when light of that wavelength passes through a 7.50 mm cell containing a solution of the solute 52.3 per cent of the light
The absorption associated with a certain transition begins at 199 nm, peaks sharply at 220 nm, and ends at 275 nm. The maximum value of the molar absorption coefficient is 2.25 x 104 dm3 mol-1 cm-1.
1, 3, 5-hexatriene (a kind of 'linear' benzene) was converted into benzene itself. On the basis of a free-electron molecular orbital model (in which hexatriene is treated as a linear box and benzene
The following data were obtained for the absorption by a dye dissolved in methylbenzene using a 2.50 mm cell. Calculate the molar absorption coefficient of the dye at the wavelength
A 2.50-mm cell was filled with a solution of a dye. The concentration of the dye was 15.5 mmol dm-3 Calculate the molar absorption coefficient of benzene at this wavelength given that the
Given that the maximum molar absorption coefficient of a molecule containing a carbonyl group is 30 dm3 mol-1 cm3 near 280 nm, calculate the thickness of a sample that will result in (a) Half the
The electronic absorption band of a compound in solution had a Gaussian lineshape and a half-width at half-height of 4233 cm-1 and E max = 1.54 X 104 dm3 mol-1 cm-1. Estimate the integrated
The photo ionization of F2 by 21 eV photons produces Pr. would you expect the 2 f- 0 transition to be weaker or stronger than the 0 f- 0 transition? Justify your answer.
The vibrational wave number of the oxygen molecule in its electronic ground state is 1580 cm3, whereas that in the first excited state (B 3L), to which there is an allowed electronic transition, is
A lot of information about the energy levels and wave functions of small inorganic molecules can be obtained from their ultraviolet spectra. An example of a spectrum with considerable vibrational
Aromatic hydrocarbons and 12 form complexes from which charge transfer electronic transitions are observed the hydrocarbon acts as an electron donor and 12 as an electron acceptor the energies hvmax
Consider some of the precautions that must be taken when conducting single-molecule spectroscopy experiments.(a) What is the molar concentration of a solution in which there is, on average, one
Suppose that you are a colour chemist and had been asked to intensify the colour of a dye without changing the type of compound, and that the dye in question was a polyene. Would you choose to
Estimate the oscillator strength (see Problem 14.16) of a charge transfer transition modeled as the migration of an electron from an His orbital on one atom to another His orbital on an atom a
The fluorescence spectrum of anthracene vapour shows a series of peaks of increasing intensity with individual maxima at 440 nm, 410 nm, 390 nm, and 370 nm followed by a sharp cut-off at shorter
Spin angular momentum is conserved when a molecule dissociates into atoms. What atom multiplicities are permitted when? (a) An 02 molecule (b) An N, molecule dissociates into atoms?
The flux of visible photons reaching Earth from the North Star is about 4 x 103 mm-2 S-I. Of these photons, 30 per cent are absorbed or scattered by the atmosphere and 25 per cent of the surviving
Ozone absorbs ultraviolet radiation in a part of the electromagnetic spectrum energetic enough to disrupt DNA in biological organisms and that is absorbed by no other abundant atmospheric
G.C.G. Wachewsky, R. Horansky, and V. Vaida (J. Phys. Chem. 100, 11559 (1996)) examined the UV absorption spectrum ofCH3I, a species of interest in connection with stratospheric ozone chemistry. They
One of the principal methods for obtaining the electronic spectra of unstable radicals is to study the spectra of comets, which are almost entirely due to radicals. Many radical spectra have been
Discuss in detail the origins of the local, neighbouring group, and solvent contributions to the shielding constant.
Suggest a reason why the relaxation times of BC nuclei are typically much longer than those of IH nuclei.
Discuss how the Fermi contact interaction and the polarization mechanism contribute to spin-spin couplings in NMR and hyperfine interactions in EPR.
Suppose a uniform disk-shaped organ is in a linear field gradient, and that the MRI signal is proportional to the number of protons in a slice of width Oxat each horizontal distance x from the centre
What is the resonance frequency of a proton in a magnetic field of 14.1 T?
33S has a nuclear spin of% and a nuclear g-factor of 0.4289 calculate the energies of the nuclear spin states in a magnetic field of7.500 T.
Calculate the frequency separation of the nuclear spin levels of a 14N nucleus in a magnetic field of 15.4 T given that the magnetogyricrati ratio is 1.93 X 107 T-1 s-l
In which of the following systems is the energy level separation the largest? (a) A 14Nnucleus in (for protons) a 600 MHz NMR spectrometer, (b) An electron in a radical in a field of 0.300 T
Calculate the magnetic field needed to satisfy the resonance condition for unshielded protons in a 150.0 MHz radiofrequency field.
Use Table 15.2 to predict the magnetic fields at which (a) 14N,(b) 19F, and (c) 31p comes into resonance at (i) 300 MHz, (ii) 750 MHz.
Calculate the relative population differences (oN/N) for 13Cnuclei in fields of (a) 0.50 T, (b) 2.5 T, and (c) 15.5 T at 25°C.
What are the relative values of the chemical shifts observed for nuclei in the spectrometers mentioned in Exercise 15.8a in terms of? (a) Values, (b) Frequencies?
The chemical shift of the CH3 protons in diethyl ether is, = 1.16 and that of the CH2 protons is 3.36. What is the difference in local magnetic field between the two regions of the molecule when the
Sketch the appearance of the IH-NMR spectrum of diethyl ether using J = 6.97 Hz and the data in Exercise 15.9b in a spectrometer operating at (a) 350 MHz, (b) 650 MHz.
Two groups of protons are made equivalent by the isomerization of a fluxional molecule. At low temperatures, where the interconversion is slow, one group has 0=5.5 and the other has 0=6.8. At what
From the data in Table 15.2, predict the frequency needed for 31p_ NMR in an NMR spectrometer designed to observe proton resonance at 500 MHz. Sketch the proton and 31presonances in the NMR spectrum
Sketch the form of an A2M2XS spectrum, where A, M, and X are protons with distinctly different chemical shifts and JhM > JAX > JMX'
Which of the following molecules have sets of nuclei that are chemically but not magnetically equivalent? (a) CHZ=C=CP1, (b) cis- and trans-[Mo (CO) 4(PHJ) 2]
The duration of a 90° or 180° pulse depends on the strength of the 'El field. If a 180° pulse requires 12.5 us, what is the strength of the 'El field? How long would the corresponding 90° pulse
Some commercial EPR spectrometers use 8 mm microwave radiation (the Q band). What magnetic field is needed to satisfy the resonance condition?
The centre of the EPR spectrum of atomic deuterium lies at 330.02 mT in a spectrometer operating at 9.2482 GHz. What is the g-value of the electron in the atom?
A radical containing three equivalent protons shows a four-line spectrum with an intensity distribution 1:3:3:1. The lines occur at 331.4 mT, 333.6 mT, 335.8 mT, and 338.0 mT. What is the hyperfine
A radical containing three in equivalent protons with hyperfine constants 2.11 mT, 2.87 m'T and 2.89 mT gives a spectrum centred on 332.8 mT. At what fields do the hyperfine lines occur and what are
Predict the intensity distribution in the hyperfine lines of the EPR spectra of (a) ·CH1H3, (b) ·CD2CD3.
The naphthalene radical anion has g = 2.0024. At what field should you search for resonance in a spectrometer operating at? (a) 9.312 GHz,(b) 33.88 GHz?
The EPR spectrum of a radical with two equivalent nuclei of a particular kind is split into five lines of intensity ratio 1:2:3:2: 1. What is the spin of the nuclei?
Sketch the form of the hyperfine structures of radicals XHJ and XDJ, where the nucleus X has I =3/2
A scientist investigates the possibility of neutron spin resonance, and has available a commercial NMR spectrometer operating at 300 MHz. What field is required for resonance? What is the relative
Suppose that the PID in Pig. 15.31 was recorded in a 300 MHz spectrometer, and that the interval between maxima in the oscillations in the PID is 0.10 s. What is the Larmor frequency of the nuclei
Various versions of the Karplus equation (eqn 15.27) have been used to correlate data on vicinal proton coupling constants in systems of the type RjR2CHCHR3R4. The original version, (M. Karplus, f.
Figure 15.64 shows the proton COSY spectrum of l-nitro propane. Account for the appearance of off-diagonal peaks in the spectrum
The hyperfine coupling constant in ·CH3 is 2.3 mT. Use the information in Table 15.3 to predict the splitting between the hyperfine lines of the spectrum of ·CD what are the overall widths of the
When an electron occupies a 2s orbital on an N atom it has a hyper fine interaction of 55.2 mT with the nucleus. The spectrum of N02 shows an isotropic hyper fine interaction of 5.7 mT. For what
When an electron occupies a 2s orbital on an N atom it has a hyperfine interaction of 55.2 mT with the nucleus. The spectrum ofN02 shows an isotropic hyperfine interaction of 5.7 mT. For what
The z-component of the magnetic field at a distance R from a magnetic moment parallel to the z-axis is given by eqn 15.28. In a solid, a proton at a distance R from another can experience such a
The shape of a spectral line, J(w), is related to the free induction decay signal G(t) by where a is a constant and 'Re' means take the real part of what follows. Calculate the lineshape
EPR spectra are commonly discussed in terms of the parameters that occur in the spin-Hamiltonian, a Hamiltonian operator that incorporates various effects involving spatial operators (like the
When interacting with a large biopolymer or even larger organelle, a small molecule might not rotate freely in all directions and the dipolar interaction might not average to zero. Suppose a molecule
Sketch the EPR spectra of the di-tert-butyl nitroxide radical (10) at 292 K in the limits of very low concentration (at which electron exchange is negligible), moderate concentration (at which
Describe the physical significance of the partition function.
Enumerate the ways by which the parameter f3 may be identified with 1/kT.
Explain what is meant by an ensemble and why it is useful in statistical thermodynamics.
What is the temperature of a two-level system of energy separation equivalent to 300 cm-I when the population of the upper state is one-half that of the lower state?
Calculate the ratio of the translational partition functions of xenon and helium at the same temperature and volume.
A certain atom has a doubly degenerate ground level, a triply degenerate electronically excited level at 1250 cm3, and a doubly degenerate level at 1300 cm3. Calculate the partition function of these
Calculate the electronic contribution to the molar internal energy at 2000 K for a sample composed of the atoms specified in Exercise 16.4b.
A certain molecule has a doubly degenerate excited state lying at 360 cm3 above the non-degenerate ground state. At what temperature will is per cent of the molecules be in the upper state?
A nitrogen nucleus spin can adopt any of three orientations in a magnetic field, and its energies are 0, ±YNn'13, where YN is the magnetogyricrati ratio of the nucleus. Deduce an expression for the
Consider a system of distinguishable particles having only three no degenerate energy levels separated by an energy which is equal to the value of kTat 25.0 K. Calculate (a) The ratio of populations
At what temperature would the population of the first excited rotational level ofHCl are lie times its population of the ground state?
Calculate the standard molar entropy of xenon gas at (a) 100 K,(b) 298.15 K.
Calculate the vibrational contribution to the entropy of Br, at 600 K given that the wave number of the vibration is 321 cm3,
Identify the systems for which it is essential to include a factor of 1/N on going from Q to q: (a) A sample of carbon dioxide gas, (b) A sample of graphite, (c) A sample of diamond, (d) Ice.
Consider a system A consisting of subsystems Al and A2, for which WI = 1 X 1020 and W2 = 2 X 1020 what is the number of configurations available to the combined system? Also, compute the entropies 5,
By what factor does the number of available configurations increase when 100 J of energy is added to a system containing 1.00 mol of particles at constant volume at 298 K?
Explore the conditions under which the 'integral' approximation for the translational partition function is not valid by considering the translational partition function of an Ar atom in a cubic box
(a) Calculate the electronic partition function of a tellurium atom at (i) 298 K, (ii) 5000 K by direct summation using the following data:(b) What proportion of the Te atoms are in the ground term
The No molecule has a doubly degenerate excited electronic level 121.1 cm-1 above the doubly degenerate electronic ground term. Calculate and plot the electronic partition function of NO from T= 0 to
Calculate, by explicit summation, the vibrational partition function and the vibrational contribution to the molar internal energy of is molecules at (a) 100 K, (b) 298 K given that its vibrational
A sample consisting of five molecules has a total energy SE. Each molecule is able to occupy states of energy jE, with j = 0, 1,2, .... (a) Calculate the weight of the configuration in which the
The most probable configuration is characterized by a parameter we know as the 'temperature'. The temperatures of the system specified in Problems 16.13 and 16.14 must be such as to give a mean value
Consider a system with energy levels Ej =jE and N molecules. (a) Show that if the mean energy per molecule is ae, then the temperature is given byEvaluate the temperature for a system in which the
Here you will use the zipper model discussed in Impact I16.1 to explore the helix-coil transition in polypeptides.(a) Investigate the effect of the parameter s on the distribution of random coil
For gases, the canonical partition function, Q, is related to the molecular partition function q by Q = q NIN!. Use the expression for q and general thermodynamic relations to derive the perfect gas

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