Chapter 10

Convert a wavelength of 450 nm to (a) wavenumber, (b) frequency, and (c) energy. (Section 10.2 )

The yellow colour of sodium emission in a flame is due to emission at \(589.0 \mathrm{nm}\) and \(589.6 \mathrm{nm}\). Calculate the difference in energy between the photons emitted at these two wavelengths. (Section 10.2 )

What wavelength of radiation would provide sufficient energy to break a C-H bond in methane, where the bond dissociation energy is \(+439 \mathrm{kJ} \mathrm{mol}^{-1} ?(\text { Section } 10.2)\) \\[ \mathrm{CH}_{4} \rightarrow \mathrm{CH}_{3}^{*}+\mathrm{H}^{*} \\]

Calculate the energy difference between the \(n=1\) and \(n=2\) levels for an electron in a one-dimensional box with a length of \(4.0 \times 10^{-10} \mathrm{m} .\) At what wavelength would a transition between these levels appear? (Section 10.2 )

Using the one-dimensional particle in a box model, calculate the first four electronic energy levels for 1,3,5 -hexatriene. Assume that a \(2 p\) electron can move freely along the delocalized \(\pi\) system. At what wavelength would the lowest energy electronic transition appear? Assume the average carbon- carbon distance to be \(0.15 \mathrm{nm}\). (Section 10.2 )

Calculate the energy differences, \(\Delta E,\) and the relative populations of the upper and lower energy levels for transitions giving rise to absorption of the following at \(298 \mathrm{K}\) (Section 10.3 ): (a) an IR photon with wavenumber \(2000 \mathrm{cm}^{-1}\) (b) a microwave photon with frequency \(20 \mathrm{GHz}\); (c) visible light with wavelength 500 nm; (d) an X-ray with wavelength \(4 \mathrm{nm}\); (e) a radio wave with frequency \(10 \mathrm{MHz}\). (Assume the degeneracy of all the levels is \(g=1\).)

What are the transmittance and absorbance of a solution that absorbs: (a) \(10 \% ;\) (b) \(90 \% ;\) (c) \(99 \%\) of the incident radiation? (Section \(10.3)\)

\(\mathrm{A} 5.0 \times 10^{-4} \mathrm{mol} \mathrm{dm}^{-3}\) solution of \(\mathrm{Br}_{2}\) in \(\mathrm{CCl}_{4}\) absorbed \(64 \%\) of the incident light when placed in a \(2.0 \mathrm{cm}\) cell at a wavelength where \(\mathrm{CCl}_{4}\) does not absorb. Calculate the molar absorption coefficient of \(\mathrm{Br}_{2}\). (Section 10.3 )

Explain why a rotational spectrum is observed for ICl but not for \(\left.I_{2} \text { or } \mathrm{Cl}_{2} \text { . (Section } 10.4\right)\)

HBr shows an IR absorption at \(2650 \mathrm{cm}^{-1}\). The HBr bond length is \(0.141 \mathrm{nm}\). Calculate the force constant of the bond. (Section \(10.5)\)

The radiation absorbed by \(^{12} \mathrm{C}^{16} \mathrm{O}\) during a vibrational transition occurs at \(2168 \mathrm{cm}^{-1}\). (Section 10.5 ) (a) Caiculate the ground state vibrational energy in \(\mathrm{kJmol}^{-1}\) (b) What is the ratio of the number of molecules in the first vibrational excited state \((\mathrm{v}=1)\) compared with the ground state \((\mathrm{v}=0)\) at \(298 \mathrm{K} ?\) (c) Calculate the force constant of the bond, assuming \(^{12} \mathrm{C}^{16} \mathrm{O}\) behaves as a simple harmonic oscillator. (d) Estimate the change in the position of the peak if \(^{12} \mathrm{C}\) was replaced by \(^{13} \mathrm{C}\)

Phenolphthalein is used as an indicator in acid-base titrations. In solutions at high \(\mathrm{pH}\), it is a bright magenta colour with a peak at \(553 \mathrm{nm}\) in the absorption spectrum; at low pH phenolphthalein is colourless. (Section 10.6 ) (a) In terms of absorption and transmission of light, explain the colour of phenolphthalein at high pH. (b) At high pH, phenolphthalein is ionized; it is unionized at low pH. Suggest a reason for the colour change. (c) Does the absorption move to higher energy or lower energy at low pH?

Predict the splitting patterns in the \(^{1} \mathrm{H}\) NMR spectra of the following molecules (Section \(10.7)\) (a) propanone \(\left(\mathrm{CH}_{3} \mathrm{COCH}_{3}\right)\) (b) 1 -bromopropane \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br}\right)\) (c) 1,1 -dichloroethene \(\left(\mathrm{CCl}_{2}=\mathrm{CH}_{2}\right)\) (d) \(E-1,2\) -dichloroethene \((\mathrm{CHC})=\mathrm{CHC} \mathrm{C}\); \((\mathrm{Z} \text { and } E \text { isomers })\) (e) nitrobenzene; (1) 1,2 -dinitrobenzene (g) 1,3 -dinitrobenzene (h) 1,4 -dinitrobenzene.

The magnetogyric ratio for a \(^{1} \mathrm{H}\) nucleus is \(26.7519 \times 10^{7} \mathrm{T}^{-1} \mathrm{s}^{-1}\) Calculate the magnetic field strength (in tesla) required to give a Larmor frequency of \(400 \mathrm{MHz}\). (Section 10.7 ) Further questions on using IR and NMR spectroscopies in the context of structure elucidation are given at the end of Chapter 12 \((p .606)\)