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1.6: Problems

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    1. Write octet structures (including formal charges, bond order, and molecular shape) for SeO32-, SeF4, XeF4, HClO3 (= HOClO2), NO3-, and ClO2+.

    2. Write octet structures (including formal charges, bond order, and molecular shape) for Al2Cl6, SnCl3-, BrF4-, HOClO, SO3, and NO2+.

    3. Show using resonance why the S-O bond is slightly shorter in SO2F2 than in SO2.

    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) O3, (b) BF, (c) CO32-, and (d) N3-.

    6. Name three well known molecules or ions that are isoelectronic with (a) CN-, (b) H2O, (c) BF3, and (d) CO2.

    7. The N-N bond distance is 1.10 Å in N2. Using the Pauling bond length – bond strength formula, D(n) = D(1) - 0.6 log(n), calculate the bond distance in the N2+ cation.

    8. In hydroxylamine, H2NOH, the N-O bond distance is 1.46 Å. Using the Pauling bond length - bond strength formula, estimate the N-O bond distances in NO2 and NO3-.

    9. While PF5 and SF6 are stable molecules, NF5 and OF6 are unknown. Can you draw octet structures for these compounds? Why would these molecules be unstable?

    10. Consider the compounds NH3 and PH3. The H-N-H bond angle in ammonia is 108o (close to the tetrahedral angle, 109.5o), but the analogous angle in PH3 is 93o. Why is the angle in PH3 closer to 90o than it is to the tetrahedral angle?

    11. Two hypothetical structures for the N2F3+ ion are [N-NF3]+ and [F-N-NF2]+. Which one is more stable? Explain. (Note: lines in the formulas can represent either single or multiple bonds)

    12. Krypton difluoride, KrF2, decomposes at dry ice temperature to Kr and F2. However, several salts of the [KrF]+ ion are relatively stable. Draw valence bond pictures for KrF2 and [KrF]+, showing lone pairs, possible resonance structures, formal charges, bond orders, and bond angles. Why is [KrF]+ more stable than KrF2?

    13. Consider the molecule ClF3O2 (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 BrF3 and BrF5.

    15. The B-H bond distances are about the same in BH3 and BH4-. however, the B-F bond distance in BF3 is shorter than that in the BF4- ion. Explain.

    16. The N-N bond dissociation energy in hydrazine (H2N-NH2) is 159 kJ/mol. The dissociation energy of the N-N triple bond in N2 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 N2.

    17. Show that a set of three sp2 hybrid orbitals satisfies the following criteria: (a) any two orbitals in the sp2 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 S4N3+ 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 F2 is a much stronger oxidizing agent than Cl2, 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.

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