3.6: Problems
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1. Write octet structures (including formal charges, bond order, and molecular shape) for SeO 3 2 - , SeF 4 , XeF 4 , HClO 3 (= HOClO 2 ), NO 3 - , and ClO 2 + .
2. Write octet structures (including formal charges, bond order, and molecular shape) for Al 2 Cl 6 , SnCl 3 - , BrF 4 - , HOClO, SO 3 , and NO 2 + .
3. Show using resonance why the S-O bond is slightly shorter in SO 2 F 2 than in SO 2 .
4. Give the formulas for five stable molecules and/or ions that are isoelectronic with ammonia.
5. Name three well known molecules or ions that are isoelectronic with (a) O 3 , (b) BF, (c) CO 3 2- , and (d) N 3 - .
6. Name three well known molecules or ions that are isoelectronic with (a) CN - , (b) H 2 O, (c) BF 3 , and (d) CO 2 .
7. The N-N bond distance is 1.10 Å in N 2 . Using the Pauling bond length – bond strength formula, D(n) = D(1) - 0.6 log(n), calculate the bond distance in the N 2 + cation.
8. In hydroxylamine, H 2 NOH, the N-O bond distance is 1.46 Å. Using the Pauling bond length - bond strength formula, estimate the N-O bond distances in NO 2 and NO 3 - .
9. While PF 5 and SF 6 are stable molecules, NF 5 and OF 6 are unknown. Can you draw octet structures for these compounds? Why would these molecules be unstable?
10. Consider the compounds NH 3 and PH 3 . The H-N-H bond angle in ammonia is 108 o (close to the tetrahedral angle, 109.5 o ), but the analogous angle in PH 3 is 93 o . Why is the angle in PH 3 closer to 90 o than it is to the tetrahedral angle?
11. Two hypothetical structures for the N 2 F 3 + ion are [N-NF 3 ] + and [F-N-NF 2 ] + . Which one is more stable? Explain. (Note: lines in the formulas can represent either single or multiple bonds)
12. Krypton difluoride, KrF 2 , decomposes at dry ice temperature to Kr and F 2 . However, several salts of the [KrF] + ion are relatively stable. Draw valence bond pictures for KrF 2 and [KrF] + , showing lone pairs, possible resonance structures, formal charges, bond orders, and bond angles. Why is [KrF] + more stable than KrF 2 ?
13. Consider the molecule ClF 3 O 2 (with Cl the central atom). How many isomers are possible? Which is the most stable?
14. The Br-F bond distance in the interhalogen compound BrF is 1.76 Å. Use this information to estimate the average bond lengths in BrF 3 and BrF 5 .
15. The B-H bond distances are about the same in BH 3 and BH 4 - . however, the B-F bond distance in BF 3 is shorter than that in the BF 4 - ion. Explain.
16. The N-N bond dissociation energy in hydrazine (H 2 N-NH 2 ) is 159 kJ/mol. The dissociation energy of the N-N triple bond in N 2 is 941 kJ/mol, i.e., much greater than three times the N-N single bond dissociation energy in hydrazine. Explain why the N-N bond in hydrazine is so weak, and why this effect is not seen in N 2 .
17. Show that a set of three sp 2 hybrid orbitals satisfies the following criteria: (a) any two orbitals in the sp 2 set are orthogonal, and (b) the orbitals are properly normalized.
18. Quantum mechanically, the momentum (p) of a particle traveling in a specific direction (e.g., the x direction) can be obtained by operating on its wavefunction \(\psi\) with the momentum operator :
\[ \hat{p}\psi = p\psi , \: \textrm{where} \: \hat{p} = -i \hbar \frac{\delta}{\delta x}\]
Knowing the correct form of this operator was the key to Schrödinger's formulation of the Hamiltonian operator, \( \hat{H} = \frac{\hat{p}^{2}}{2m} + V\), which operates on a wavefunction to give the total energy. The momentum operator must also be consistent with the de Broglie relation , \( p = \frac{h}{\lambda}\), which relates the momentum to the particle wavelength.
By analogy to electromagnetic waves, Schrödinger knew that a wavelike particle (such as an electron) traveling in free space in the x-direction could be described by the wavefunction:
\[ \psi(x, t) = Ae^{i(kx - \omega t + \varphi)}\]
where the wavenumber k is inversely related to the particle's de Broglie wavelength λ by \( k = \frac{2\pi}{\lambda}\). Here A is a normalization constant, ω is the frequency of the wave, and \(\varphi\) represents its phase.
Show using the momentum operator \(\hat{p}\) that the value of the momentum p we obtain for a free particle from \(\hat{p}\psi = p\psi\) is consistent with the de Broglie relation, \(p= \frac{h}{\lambda}\).
(Hint: k, ω, and \(\varphi\) are independent of x)
19. Which S-N bonds in the cyclic S 4 N 3 + ion would you predict to be the shortest? The atomic connectivity in the ring is: -S-S-N-S-N-S-N-. [ Hint: determine the number of π-bonds in the molecule by electron counting and then find the most stable resonance structures].
20. F has a higher electronegativity than Cl, and F 2 is a much stronger oxidizing agent than Cl 2 , despite the fact that the electron affinity of fluorine (-328 kJ/mol) is weaker than that of chlorine (-349 kJ/mol). Explain this apparent contradiction.
21. (a) Explain why C-H, N-H, and O-H bonds in chemical compounds are stronger than Si-H, P-H, and S-H bonds, respectively. (b) Explain why C-F, N-F, and O-F single bonds follow the opposite trend, namely, they are weaker than Si-F, P-F, and S-F single bonds, respectively.