Chapter 4 Multiple Choice Questions

Fundamental constants

Planck's constant h = 6.626 10-34 J s
Boltzmann's constant kB = 1.381 10-23 J K-1
Vacuum permeability ?0 = 4? x 10-7 J s2 C-2 m-1
Gas constant R = 8.314 J K-1 mol-1

Magnetogyric ratios
Magnetogyric ratios of common nuclides can be found in Table 1.3, page 3.

. Two carbons in a molecule undergo symmetrical two-site exchange. Their chemical shifts in the absence of exchange are 21.6 ppm and 56.8 ppm. What is the value of the rate constant when the linebroadening, measured on a spectrometer with a 9.4 T magnet, is 1.0 Hz under conditions of fast-exchange?

. The rate constant for N=O flipping in dimethylnitrosamine (Fig. 4.1) is given by an Arrhenius equation with activation energy 96.0 kJ mol-1 and pre-exponential factor 7.0 x 1012 s-1. The 1H resonance frequencies of the two methyl groups differ by 26 Hz. At what temperature would the two signals just merge into one?

. A molecule undergoes symmetrical two-site exchange with an activation energy of 100 kJ mol-1. In the slow exchange regime, the linebroadening arising from the exchange is 5.30 Hz at 37 °C. Calculate the linebroadening at 27 °C.

. PCl2F3 is trigonal bipyramidal (D3h symmetry). At sufficiently high temperature, all five halogen atoms exchange rapidly between axial and equatorial positions. Which multiplets would be seen in (i) the 19F spectrum and (ii) the 31P spectrum?

. A molecule undergoes unsymmetrical two-site exchange, A ⇌ B. Under conditions of fast exchange, when the equilibrium constant K = 1.0 x 10-3, the spectrum contains a single line at 6.68 ppm. Given that the chemical shift of A in the absence of exchange is 6.70 ppm, calculate the chemical shift of B in the absence of exchange.

. The three-bond J-couplings between the α proton and the two β protons of an amino acid are 3.7 Hz and 6.7 Hz. Using the Karplus relation Jαβ = 4.7 - 0.5cosφ + 4.5cos2φ determine the fractional populations of the three rotamers.

. The rotamer of CHX2-CHY2 in which the protons are trans has a lower energy than the gauche rotamer. The rotation around the C-C bond is fast. Which of the following statements is true?

. Processes are often said to be fast or slow 'on the NMR timescale'. Which of the following statements most accurately describes what determines the NMR timescale?

. Which of the following statements most accurately explains why faster exchange processes can often be studied using 13C rather than 1H NMR.

. A molecule X undergoes the electron exchange reaction X + X•- ⇌ X•- + X in which X•- is the anion radical form of X. The forward and backward reactions have equal second order rate constants. In the absence of X•-, the spin relaxation rate of a proton in X is 1 s-1. The spin relaxation rate of the same proton in X•- is 104 s-1 as a result of its interaction with the electron spin. Under conditions of fast exchange, when the concentration of X is 1 mM, the spin relaxation rate of the proton is found to be 10 s-1. Assuming that relaxation rates obey an equation similar to eqn 4.7, calculate the concentration of X•-. See Chapter 5 for more information on spin relaxation processes.

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