Problem 2
Calculate the reduced masses of (a) an HD molecule,(b) \(a^{12} C-H\) unit and\((\mathrm{c}) \mathrm{a}^{13} \mathrm{C}^{16} \mathrm{O}\)molecule. Exact masses: \(^{1} \mathrm{H}, 1.01 ;^{2} \mathrm{H}, 2.01 ;^{12} \mathrm{C}\) \(12.00 ;^{13} \mathrm{C}, 13.00 ;^{16} \mathrm{O}, 15.99\)
Problem 3
The force constants for the bonds in ClF, BrF and \(\mathrm{BrCl}\) are 448,406 and \(282 \mathrm{Nm}^{-1}\) respectively. Predict the trend in their bond enthalpies.
Problem 4
The stretching mode of NO gives rise to an absorption in the IR spectrum at \(1903 \mathrm{cm}^{-1} .\) What is the force constant of the bond?
Problem 5
(a) Determine the reduced masses of \(\mathrm{H}^{35} \mathrm{Cl}\) and \(\mathrm{H}^{37} \mathrm{Cl}\); exact masses \(^{1} \mathrm{H}=1.01\) \(^{35} \mathrm{Cl}=34.97 ;^{37} \mathrm{Cl}=36.97 .\) (b) If the force constants of the bonds are the same, is the ratio of the reduced masses sufficient to cause a shift in the IR absorption assigned to the \(\mathrm{H}-\mathrm{Cl}\) stretch? (c) Would you expect to see any chemical differences between \(\mathrm{H}^{35} \mathrm{Cl}\) and \(\mathrm{H}^{37} \mathrm{Cl} ?\)
Problem 7
What shapes are (a) \(\mathrm{HCN},(\mathrm{b}) \mathrm{CS}_{2},(\mathrm{c}) \mathrm{OCS}\) and \((\mathrm{d})\) \(\mathrm{XeF}_{2} ?\) Are the symmetric stretching, asymmetric stretching and bending modes of these molecules IR active?
Problem 13
(a) What is the molecular shape of \(\mathrm{SO}_{3} ?\) (b) Draw a diagram to show the symmetric stretching mode of vibration of \(\mathrm{SO}_{3}\) (c) Is this mode IR active?
Problem 15
The IR spectrum of \(\mathrm{H}_{2} \mathrm{O}\) shows bands at 3756 (asymmetric stretch), 3657 (symmetric stretch) and \(1595 \mathrm{cm}^{-1}(\text {scissoring }) .\) In \(\mathrm{D}_{2} \mathrm{O},\) the corresponding vibrational modes give rise to absorptions at 2788 2671 and \(1178 \mathrm{cm}^{-1}\). Account for these observations.
Problem 18
Find the moments of inertia \(I_{A}, I_{B}\) and \(I_{C}\) of \(^{79} \mathrm{Br}^{19} \mathrm{F}\) (bond length \(=176 \mathrm{pm} ;\) accurate masses: \\[ \left.^{79} \mathrm{Br}=78.92 ;^{19} \mathrm{F}=19.00\right) \\]
Problem 20
Explain why a pure rotational spectrum is observed for HCl but not for \(\mathrm{H}_{2}\) or for \(\mathrm{Cl}_{2}\).
Problem 22
Explain what is meant by (a) the vibrational ground state and (b) the rotational ground state of a diatomic molecule.
