(a) Construct an MO diagram for the formation of $\mathrm{O}_2$; use only the valence orbitals of the oxygen atoms. (b) Use the diagram to rationalize the following trend in $\mathrm{O}-\mathrm{O}$ bond distances: $\mathrm{O}_2, 121 \mathrm{pm} ;\left[\mathrm{O}_2\right]^{+}, 112 \mathrm{pm}$; $\left[\mathrm{O}_2\right]^{-}, 134 \mathrm{pm} ;\left[\mathrm{O}_2\right]^{2-}, 149 \mathrm{pm}$. (c) Which of these species are paramagnetic?

Use electronegativity values in Table $2.2$ to confirm that each of the following molecules is polar. Draw diagrams to show the directions of the molecular dipole moments.

$$\mathrm{Br}-\mathrm{F}$$

S ClC(Cl)Cl

Show that the VSEPR model is consistent with a trigonal planar structure for $\mathrm{SO}_3$.

Show that each atom in each of the following molecules obeys the octet rule: $\mathrm{NF}_3, \mathrm{CF}_4, \mathrm{OF}_2, \mathrm{~F}_2$. Draw Lewis structures for the molecules and confirm that the bond order of each bond is one.

Given that $D(\mathrm{H}-\mathrm{H}), D(\mathrm{Cl}-\mathrm{Cl}), D(\mathrm{Br}-\mathrm{Br})$ and $D(\mathrm{I}-\mathrm{I})$ in $\mathrm{H}_2, \mathrm{Cl}_2, \mathrm{Br}_2$ and $\mathrm{I}_2$ are $436,242,193$ and $151 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively, estimate (by the above method) values of $D(\mathrm{H}-\mathrm{X})$ in $\mathrm{HCl}, \mathrm{HBr}$ and $\mathrm{HI}$.

Using Fig. $2.10$ as a basis, account for the fact that $\left[\mathrm{N}_2\right]^{+}$ is paramagnetic.

Why does a $\sigma$-MO formed by the overlap of two $2 p_x$ orthitak (Fig. 2.7a) have the label $\sigma_g$ ?

Figure shows the emission spectrum of sodium. Low-pressure sodium street lamps depend upon this bright yellow emission from sodium atoms excited by an electrical discharge. Figure shows a simple spectrum (see figure caption), but the National Institute of Standards and Technology (NIST) atomic spectra database lists 5888 lines in the emission spectrum of sodium. Suggest three reasons why no other lines are visible in Fig. (b) The wavelengths of the yellow lines in Fig. are close to $589 \mathrm{~nm}$. To what frequency does this correspond? (c) Give a general explanation of how a series of spectral lines such as those in Fig. arises.

(a) Write down an equation that defines the process to which the value of $I E_4$ of $\mathrm{S} n$ refers. Is this process exothermic or endothermic? (b) To what overall process does a value of $\left(I E_1+I E_2+I E_3\right)$ for $\mathrm{Al}$ refer?

Draw the structures of the two isomers of octahedral $\left[\mathrm{Cr}\left(\mathrm{OH}_2\right)_4 \mathrm{Cl}_2\right]^{+}$and give labek that distinguish the isomers.

Use the following data to estimate the bond dissociation enthalpy of $\mathrm{BrCl}: D(\mathrm{Br}-\mathrm{Br})=224 \mathrm{~kJ} \mathrm{~mol}^{-1}$; $D(\mathrm{Cl}-\mathrm{Cl})=242 \mathrm{~kJ} \mathrm{~mol}^{-1} ; \chi^{\mathrm{P}}(\mathrm{Br})=3.0 ; \chi^{\mathrm{P}}(\mathrm{Cl})=3.2$. $\left[\right.$ Ans. $\approx 237 \mathrm{~kJ} \mathrm{~mol}^{-1} ;$ actual experimental value $=$ $\left.218 \mathrm{~kJ} \mathrm{~mol}^{-1}\right]$

Show that $\left[\mathrm{SiF}_6\right]^{2-}$ and $\left[\mathrm{PF}_6\right]^{-}$are iscelectronic.

The bond length in HF is $92 \mathrm{pm}$, and the dipole moment is $1.83 \mathrm{D}$. Determine the charge distribution in the molecule.

$$\left[\mathrm{Ans} . \stackrel{+0.41}{\mathrm{H}}-\mathrm{-0.41}^{\mathrm{F}}\right]$$

Given that $D(\mathrm{H}-\mathrm{H}), D(\mathrm{CH}-\mathrm{Cl}), D(\mathrm{Br}-\mathrm{Br})$ and $D(\mathrm{I}-\mathrm{I})$ in $\mathrm{H}_2, \mathrm{Cl}_2, \mathrm{Br}_2$ and $\mathrm{I}_2$ are $436,242,193$ and $151 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively, estimate (by the above method) values of $D(\mathrm{H}-\mathrm{X})$ in $\mathrm{HCl}, \mathrm{HBr}$ and $\mathrm{HI}$. $\left[\right.$ Ans. $\left.339 ; 315 ; 294 \mathrm{kJmol}^{-1}\right]$