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# 27.E: More about Spectroscopy (Exercises)

Exercise 27-1 The lifetime for rotation about the $$\ce{C-C}$$ bond in ethanol is $$\sim 10^{-10} \: \text{sec}$$ at room temperature. Approximately what (large) chemical-shift difference, in $$\ce{Hz}$$, would a given hydrogen (marked with *) have to have between $$4$$ and either of the conformations $$5$$ and $$6$$ to permit the observation of separate chemical shifts for the $$\ce{CH_3}$$ hydrogens in these conformations? Show your reasoning.

Exercise 27-2 The $$\ce{^{19}F}$$ NMR spectrum of 1,2-difluorotetrachloroethane shows two peaks with unequal areas separated by about $$0.90 \: \text{ppm}$$ at $$-120^\text{o}$$ but a single sharp resonance at room temperature. Explain this change in the spectrum.

Exercise 27-3 The NMR spectrum of the tert-butyl protons of 3,3-dibromo-2,2-dimethylbutane is shown as a function of temperature in Figure 27-4. Explain the two peaks observed at $$-64^\text{o}$$. Calculate the approximate mean lifetime of the process that causes the lines to coalesce at $$-33^\text{o}$$.

Figure 27-4: Proton spectra of 3,3-dibromo-2,2-dimethylbutane in $$\ce{CF_2Cl_2}$$ as solvent at various temperatures.

Exercise 27-4 Referring to Figure 9-8, we see that the microwave spectrum of 1-iodopropane shows separate rotational peaks for the trans and gauche forms. Peaks about $$0.35 \: \text{GHz}$$ apart are clearly resolved. What lower limit can we then put on $$\Delta t$$ for the lifetime of interconversion of the trans and gauche forms of 1-iodopropane? Show your reasoning.

Exercise 27-5 Figure 9-29 shows some rather remarkable changes in the spectrum of ethanol as a function of concentration in $$\ce{CCl_4}$$ solution.

a. Explain the origin of the approximately $$5 \: \text{Hz}$$, 1:2:1 triplet observed for the $$\ce{HO}$$ proton at $$10\%$$ concentration.

b. The washing-out of the triplet splitting of the $$\ce{HO}$$ resonance in $$100\%$$ ethanol is a consequence of intermolecular $$\ce{HO}$$ proton exchange $$\left( \ce{C_2H_5OH}^* + \ce{C_2H_5OH} \rightleftharpoons \ce{C_2H_5OH} + \ce{C_2H_5OH}^* \right)$$. Any given proton then experiences a $$+5 \: \text{Hz}$$ spin-spin interaction on some molecules, a net of zero spin-spin interaction on other molecules, and a $$-5 \: \text{Hz}$$ spin-spin interaction on still others. Notice that the $$\ce{HO}$$ resonance in $$100\%$$ ethanol in Figure 9-29 is quite broad in comparison with that in Figure 9-23, which is of ethanol containing a trace of $$\ce{HCl}$$ to make the exchange very fast. Calculate an approximate lifetime before exchange, $$\Delta t$$, for the hydroxyl proton in $$100\%$$ ethanol that is in accord with the spectrum of Figure 9-29.

c. Explain why the $$\ce{CH_2}$$ resonance in $$100\%$$ ethanol in Figure 9-29, but not in Figure 9-23, is much less sharp than the $$\ce{CH_3}$$ resonance.

Exercise 27-6* Notice that Figures 27-5 and 27-6 show that the total magnetic energy for the protons in the $$+\frac{1}{2}$$, $$-\frac{1}{2}$$ state is $$60 \: \text{MHz}$$ less than for those in the $$-\frac{1}{2}$$, $$+\frac{1}{2}$$ state. Why then should we expect the observed transitions from $$+\frac{1}{2}$$, $$+\frac{1}{2}$$ to $$+\frac{1}{2}$$, $$-\frac{1}{2}$$ and the transition from $$-\frac{1}{2}$$, $$+\frac{1}{2}$$ to $$-\frac{1}{2}$$, $$-\frac{1}{2}$$, to have the same intensity? (Review Section 9-10A.)

Exercise 27-7* Suppose you have three kinds of protons with chemical-shift differences of $$100 \: \text{Hz}$$, $$60 \: \text{Hz}$$, and $$40 \: \text{Hz}$$ from TMS. Suppose the $$+\frac{1}{2}$$, $$+\frac{1}{2}$$ state of the $$100$$, $$60 \: \text{Hz}$$ pair is destabilized by a mutual spin-spin magnetic interaction of $$5 \: \text{Hz}$$; the $$+\frac{1}{2}$$, $$+\frac{1}{2}$$ state of the $$100$$, $$40 \: \text{Hz}$$ pair is destabilizing by $$3 \: \text{Hz}$$; and the $$+\frac{1}{2}$$, $$+\frac{1}{2}$$ state of the $$60$$, $$40 \: \text{Hz}$$ pair has zero interaction. Draw energy diagrams analogous to Figures 27-5 and 27-6 showing the total energy for the three nuclei (the levels correspond to $$+\frac{1}{2}$$, $$+\frac{1}{2}$$, $$+\frac{1}{2}$$; $$-\frac{1}{2}$$, $$+\frac{1}{2}$$, $$+\frac{1}{2}$$; $$+\frac{1}{2}$$, $$-\frac{1}{2}$$, $$+\frac{1}{2}$$; $$+\frac{1}{2}$$, $$+\frac{1}{2}$$, $$-\frac{1}{2}$$; and so on), first without and then with correction for the spin-spin interactions. You should have eight energy levels for each diagram. Now calculate and plot the transition energies as in Figure 27-7. What are the resulting $$J$$ values? What relative intensities would you expect for the lines? (If you work through this problem, you will understand the simple basis of spin-spin splitting. You also will see why it is desirable to carry forward the calculations for more complicated systems with a digital computer.)

Exercise 27-8 Explain why the irradiation of 3,3-dimethyl-2-butanone might be expected to lead to $$\ce{C-C}$$ bond cleavage between the $$\ce{C_2}$$ and $$\ce{C_3}$$ carbons rather than between the $$\ce{C_1}$$ and $$\ce{C_2}$$ carbons. What products would you expect to observe in the irradiation of 2-propanone (acetone)? Would CIDNP be expected?

Exercise 27-9* The photoelectron spectrum of ethyne in Figure 27-10 shows vibrational fine structure for the carbon-carbon bond in ionization at about $$18.5 \: \text{eV}$$ with spacings of about $$0.27 \: \text{eV}$$. Explain how one could decide whether the observed vibrational spacings are more associated with the ionized excited state of ethyne rather than the ground state. Review Section 9-7B.

Exercise 27-10 The purpose of this exercise is to investigate the importance of the uncertainty principle for some kinds of spectroscopy other than NMR, as discussed in Section 27-1. (You may wish to use the wavelength-energy conversion factors given in Sections 9-3 and 9-4.)

a. The lifetime of an excited $$\ce{^{57}Fe}$$ nucleus undergoing $$\gamma$$-ray absorption in a Mössbauer experiment is $$9.9 \times 10^{-8} \: \text{sec}$$. Calculate the range in $$\Delta \Delta E$$ in frequency units and $$\text{kcal mol}^{-1}$$ that this corresponds to, and also the ratio of the uncertainty of the energy of the quantum absorbed to its total energy $$\left( 14,400 \: \text{eV} \right)$$.

b. When a sodium atom in the vapor state absorbs radiation of $$589.3 \: \text{nm}$$ (sodium D line; Section 9-4) the lifetime of the excited state is $$1.5 \times 10^{-8} \: \text{sec}$$. Calculate the $$\Delta \nu$$ that corresponds to the lifetime of the excited state and convert this into a $$\Delta \lambda$$ for the line width of the absorption in $$\text{nm}$$.

Exercise 27-11 The chemical-ionization mass spectrum produced from octadecane $$\left( \ce{C_{18}H_{38}} \right)$$ by attack of the ions produced by electron impact on $$\ce{CH_4}$$ is shown in Figure 27-14.

a. Why are $$\ce{M} + 29$$ and $$\ce{M} + 41$$ peaks not visible in this spectrum?

b. Would you expect $$\ce{C_{17}H_{35}CH_2^+}$$ or an ion such as $$\ce{C_{16}H_{33}} \overset{\oplus}{\ce{C}} \ce{HCH_3}$$ to be the most likely $$\left( \ce{M} - 1 \right)^+$$ ion formed from $$\ce{C_{18}H_{38}}$$ and $$\ce{CH_5^+}$$? Why?

c. Account for the many, but evenly spaced, fragmentation peaks in the spectrum seen at $$m/e =$$ 57, 71, 85, 99, 113, 127, 141, 155, 169, 183, 197, 211, 225, and 239 by reasonable decomposition reactions of the $$\left( \ce{M} - 1 \right)^+$$ ion(s).

Figure 27-14: Chemical ionization mass spectrum of octadecane. (Kindly supplied by the Finnegan Corporation.) See Exercise 27-11.

Exercise 27-12 Electron impact on 1,2-dibromoethane produces a positive ion of mass 188, which is converted rapidly to a rather positive ion of mass 108 diminishes in concentration and the equivalent amount of a new positive ion of mass 136 appears. What are the likely structures of these ions? Explain how they are formed and why the one of mass 136 is formed at the expense of the one of mass 108.

Exercise 27-13 The ESR spectrum shown in Figure 27-18 is a first-derivative curve of the absorption of a radical produced by x irradiation of 1,3,5-cycloheptatriene present as an impurity in crystals of naphthalene. Sketch this spectrum as it would look as an absorption spectrum and show the structure of the radical to which it corresponds. Show how at least one isomeric structure for the radical can be eliminated by the observed character of the spectrum.

Figure 27-18: Electron-spin resonance spectrum of cycloheptatrienyl radical produced by x irradiation of 1,3,5-cycloheptatriene. See Exercise 27-13.

Exercise 27-14 Diphenylmethanone (benzophenone) in diethyl ether solution adds an electron from a sodium atom and forms a radical anion:

The ESR of the radical anion shows splitting of the electron resonance by the ring protons and a small splitting by sodium ($$\ce{^{23}Na}$$ with $$I = \frac{3}{2}$$) that gives four lines. When excess diphenylmethanone is added, fast electron exchange occurs. This exchange wipes out the splitting by the protons but not the splitting by the $$\ce{^{23}Na}$$ nuclei.

a. What can you say about the degree of ionic dissociation of the $$\ce{-O-Na}$$ bond $$\left( \ce{-O-Na} \rightleftharpoons \ce{-} \overset{\ominus}{\ce{O}} + \overset{\oplus}{\ce{Na}} \right)$$ in the radical anion in the absence of excess diphenylmethanone? Why? [Notice that there is no $$\ce{^{23}Na}$$ splitting of the electron resonance of sodium naphthalenide in 1,2-dimethoxyethane, but such splittings are observed in oxacyclopentane (tetrahydrofuran); see Sections 8-7F and 15-11E for discussion of possible differences between solvents in their ion-solvating powers.]

b. Write a mechanism for the electron-exchange in diethyl ether that is consistent with the loss of the electron-proton splitting but retention of the electron-sodium splitting. Why does the electron-sodium splitting disappear when 1,2-dimethoxyethane is the solvent?

## Contributors

• John D. Robert and Marjorie C. Caserio (1977) Basic Principles of Organic Chemistry, second edition. W. A. Benjamin, Inc. , Menlo Park, CA. ISBN 0-8053-8329-8. This content is copyrighted under the following conditions, "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format."