Chapter 9

Suppose you are standing on the end of a pier watching the waves and, between your position and a buoy \(200 \mathrm{~m}\) straight out, you count 15 wave crests. Further, suppose a wave crest comes by every 15 seconds. Calculate \(\nu\) in \(\mathrm{Hz}, \lambda\) in \(\mathrm{m}, c\) in \(\mathrm{m} \mathrm{sec}^{-1}\), and \(\bar{\nu}\) in \(\mathrm{km}^{-1}\).

Blue light has \(\bar{\nu}=20,800 \mathrm{~cm}^{-1}\). Calculate \(\nu\) in \(\mathrm{Hz}\) and \(\lambda\) in \(\mathrm{nm}\).

Calculate the energy in \(\mathrm{kcal} \mathrm{mol}^{-1}\) that corresponds to the absorption of 1 einstein of light of \(589.3 \mathrm{~nm}\) (sodium \(D\) line) by sodium vapor. Explain how this absorption of light by sodium vapor may have chemical utility.

Which compound in each group would have the most intense infrared absorption band corresponding to stretching vibrations of the bonds indicated? Give your reasoning. a. \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{O},\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{CH}_{2}\) (multiple bond) b. \(\mathrm{CH}_{3}-\mathrm{CH}_{3}, \mathrm{CH}_{3}-\mathrm{O}-\mathrm{CH}_{3}(\mathrm{C}-\mathrm{C}\) vs. \(\mathrm{C}-\mathrm{O})\) c. \(\mathrm{CH}_{3} \mathrm{C} \equiv \mathrm{CH}, \mathrm{CH}_{3} \mathrm{C} \equiv \mathrm{CCH}_{3}\) (multiple bond) d. \(\mathrm{H}-\mathrm{Cl}, \mathrm{Cl}-\mathrm{Cl}\)

How many vibrational modes are possible for (a) \(\mathrm{CS}_{2}\) (linear), (b) \(\mathrm{BeCl}_{2}\) (linear), and (c) \(\mathrm{SO}_{2}\) (angular)? Show your reasoning.

Classify the following molecules according to the general characteristics expected for their infrared and Raman spectra: a. \(\mathrm{HC} \equiv \mathrm{CH}\) b. \(\mathrm{ICl}\) c. \(\mathrm{CO}\) d. \(\mathrm{CF}_{2}=\mathrm{CH}_{2}\) (double-bond stretch only) e. \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{CH}_{2}\) f. \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{3}\)

Explain why the absorption band at \(227.3 \mathrm{~nm}\) for trimethylamine, \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}\), disappears in acid solution.

A solution containing the two forms of the important coenzyme nicotinamide adenine dinucleotide (abbreviated \(\mathrm{NAD}^{\oplus}\) and NADH; see Section \(15-6 \mathrm{C}\) for structures) has an absorbance in a \(1-\mathrm{cm}\) cell of \(0.311\) at \(340 \mathrm{~nm}\) and \(1.2\) at \(260 \mathrm{~nm}\). Both \(\mathrm{NAD}^{\oplus}\) and NADH absorb at \(260 \mathrm{~nm}\), but only NADH absorbs at \(340 \mathrm{~nm}\). The molar extinction coefficients are $$ \begin{array}{lll} \text { Compound } & \underline{260 \mathrm{~nm}} & \underline{340 \mathrm{~nm}} \\ \hline \mathrm{NAD}^{\oplus} & 18,000 & \sim 0 \\ \mathrm{NADH} & 15,000 & 6220 \end{array} $$ Calculate the proportions of \(\mathrm{NAD}^{\oplus}\) and NADH in the mixture.

In nmr experiments, structural inferences sometimes are drawn from differences in resonance frequencies as small as \(1 \mathrm{~Hz}\). What difference in energy in kcal \(\mathrm{mol}^{-1}\) does \(1 \mathrm{~Hz}\) represent?

a. Identify the protons with different chemical shifts in each of the structures shown. Use letter subscripts \(\mathrm{H}_{A}, \mathrm{H}_{B}\), and so on, to designate nonequivalent protons. Use models if necessary. (i) cis- and trans-2-butene (ii) 1,3-butadiene (iii) 1 -chloro-2,2-dimethylbutane (iv) 2-butanol (v) trans-1,2-dibromocyclopropane b.* Why does 3-methyl-2-butanol have three methyl resonances with different chemical shifts in its proton \(\mathrm{nmr}\) spectrum? c. \(^{*}\) For the compounds in Part a designated those protons (if any) that are enantiotopic or diastereotopic.

If the \(-\mathrm{NH}_{2}\) protons of 2 -aminoethanol, \(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\), have a shift of \(1.1 \mathrm{ppm}\) and the \(-\mathrm{OH}\) proton has a shift of \(3.2 \mathrm{ppm}\), what will be the observed average \(\left(-\mathrm{NH}_{2},-\mathrm{OH}\right)\) proton shift if exchange is very fast?

In reasonably concentrated solution in water, ethanoic acid (acetic acid) acts as a weak acid (less than \(1 \%\) dissociated). Ethanoic acid gives two proton nmr resonance lines at 2 and 11 ppm, relative to TMS, whereas water gives a line at \(5 \mathrm{ppm} .\) Nonetheless, mixtures of ethanoic acid and water are found to give only two lines. The position of one of these lines depends on the ethanoic acid concentration, whereas the other one does not. Explain how you would expect the position of the concentration-dependent line to change over the range of ethanoic acid concentrations from \(0-100 \%\).

Sketch the proton chemical shifts in ppm and \(\mathrm{Hz}\) as well as the integral you would expect for each of the following substances at \(60 \mathrm{MHz}\). (The spin-spin splitting of the resonance lines evident in Figures 9-23 and 9-27, but not seen in Figure \(9-31\), can be safely neglected with all of the compounds listed.) a. \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCH}_{2} \mathrm{OCH}_{3}\) b. \(\mathrm{CH}_{2} \mathrm{COC}\left(\mathrm{CH}_{3}\right)_{3}\) c. \(\mathrm{HCOC}\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHO}\) d. e. \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{CCl}_{2}\) f. \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COC} \equiv \mathrm{CH}\) g. \(\left(\mathrm{CH}_{2} \mathrm{Cl}\right)_{3} \mathrm{CCO}_{2} \mathrm{H}\) h.* cis-1-methyl-4-tert-butyl-1,2,2,3,3,4,5,5,6,6-decachlorocyclohexane

Write structures for compounds with the following descriptions (There may be more than one correct answer, but only one answer is required.) a. \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\) with one proton \(\mathrm{nmr}\) shift b. \(\mathrm{C}_{6} \mathrm{H}_{12}\) with one proton nmr shift c. \(\mathrm{C}_{5} \mathrm{H}_{12}\) with one proton \(\mathrm{nmr}\) shift d. \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}\) with two different proton \(\mathrm{nmr}\) shifts e. \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}\) with three different proton \(\mathrm{nmr}\) shifts f. \(\mathrm{C}_{4} \mathrm{Cl}_{8}\) with two different \({ }^{13} \mathrm{C} \mathrm{nmr}\) shifts

Sketch the proton \(\mathrm{nmr}\) spectrum and integral expected at \(60 \mathrm{MHz}\), with TMS as standard, for the following substances. Show the line positions in \(\mathrm{Hz}\); neglect spin-spin couplings smaller than 1 to \(2 \mathrm{~Hz}\) and all second-order effects. Remember that chlorine, bromine, and iodine (but not fluorine) act as nonmagnetic nuclei. a. \(\mathrm{CH}_{3} \mathrm{Cl}\) b. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}\) c. \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCl}\) d. \(\mathrm{CH}_{3} \mathrm{CCl}_{2} \mathrm{CH}_{2} \mathrm{Cl}\) e. \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCl}\) f. \(\mathrm{CHCl}_{2} \mathrm{CHBr}_{2}\) g. \(\mathrm{CH}_{3} \mathrm{CHClCOCH}_{3}\) h. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) i. \(\mathrm{ClCH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{I}\) j. \(\left(\mathrm{ClCH}_{2}\right)_{3} \mathrm{CH}\)

a. Show how the assignment of \(J_{A B}=J_{B C}=2 J_{A C}\) leads to the prediction of four equally spaced and equally intense lines for the methyl resonance of 2 -phenylpropene. b. What would the splittings of the alkenic and methyl protons look like for trans-1-phenylpropene if \(J_{A B}=16 \mathrm{~Hz}\), \(J_{A C}=4 \mathrm{~Hz}\), and \(J_{B C}=0 \mathrm{~Hz} ?\)

Explain how a mass spectrometer, capable of distinguishing between ions with \(m / e\) values differing by one part in 50,000 , could be used to tell whether an ion of mass 29 is \(\mathrm{C}_{2} \mathrm{H}_{5}^{+}\) or \(\mathrm{CHO}^{+}\).

a. Calculate the relative intensities of the \((\mathrm{M}+1)^{+}\) and \((\mathrm{M}+2)^{+}\) ions for a molecule of elemental composition \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NO}_{2}\) b. The \(\mathrm{M}^{+},(\mathrm{M}+1)^{+}\), and \((\mathrm{M}+2)^{+}\) ion intensities were measured as \(100,8.84\), and \(0.54\) respectively, and the molecular weight as 120 . What is the molecular formula of the compound? c. In our example of how natural \({ }^{13} \mathrm{C}\) can be used to determine the number of carbon atoms in a compound with \(\mathrm{M}^{+}=86\) and a \((\mathrm{M}+1)^{+} / \mathrm{M}^{+}\) ratio of \(6.6 / 100\), we neglected the possible contribution to the \((\mathrm{M}+1)^{+}\) peak of the hydrogen isotope of mass 2 (deuterium). The natural abundance of deuterium is \(0.015 \%\) For a compound of composition \(\mathrm{C}_{6} \mathrm{H}_{14}\), how much do you expect the deuterium to contribute to the intensity of the \((\mathrm{M}+1)^{+}\) peak relative to the \(\mathrm{M}^{+}\) peak?

The mass spectrum of propylbenzene has a prominent peak at mass number 92. With (3,3,3trideuteriopropyl)benzene, this peak shifts to 93. Write a likely mechanism for breakdown of propylbenzene to give a fragment of mass number 92 .

The mass spectra of alcohols usually show peaks of \((\mathrm{M}-18)\), which correspond to loss of water. What kind of mechanisms can explain the formation of \((\mathrm{M}-18)\) peaks, and no \((\mathrm{M}-19)\) peaks, from 1,1-dideuterioethanol and \(1,1,1,3,3-\)pentadeuterio-2-butanol?

What is the likely structure for the major fragment ion with \(m / e=45\) derived from methoxyethane (methyl ethyl ether) on electron impact?

A certain halogen compound gave a mass spectrum with molecular ion peaks at \(m / e 136\) and 138 in about equal intensities. The nmr spectrum of this compound gave only a single resonance around \(1.2 \mathrm{ppm}\). What is the structure of the compound? Give your reasoning.