# 1.6: Problems

- Page ID
- 183294

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.