Using VB theory and the Lewis structure model, determine the bond order in (a) $\mathrm{H}_2$, (b) $\mathrm{Na}_2$, (c) $\mathrm{S}_2$, (d) $\mathrm{N}_2$ and (e) $\mathrm{Cl}_2$. Is there any ambiguity with finding the bond orders by this method?

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 $=$ $\left.218 \mathrm{~kJ} \mathrm{~mol}^{-1}\right]$

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.

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

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

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

Show that the VSEPR model is in agreement with the following molecular shapes:

$$\begin{array}{ll}\mathrm{BF}_3 & \text { trigonal planar } \\ {\left[\mathrm{IF}_5\right]^{2-}} & \text { pentagonal planar } \\ {\left[\mathrm{NH}_4\right]^{+}} & \text {tetrahedral } \\ \mathrm{SF}_6 & \text { octahedral } \\ \mathrm{XeF}_4 & \text { square planar } \\ \mathrm{AsF}_5 & \text { trigonal bipyramidal } \\ {\left[\mathrm{AlCl}_4\right]^{-}} & \text {tetrahedral }\end{array}$$

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. $\left.339 ; 315 ; 294 \mathrm{kJmol}^{-1}\right]$

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

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. $\left.339 ; 315 ; 294 \mathrm{kJmol}^{-1}\right]$

What, according to the mainstream theory of the business cycle, is the most common source of recession: a decrease in aggregate demand, a decrease in aggregate supply, or both? Which is the most likely component of aggregate demand to start a recession? How does the aggregate demand multiplier influence a recession?

Use the following information. Economist Arthur Laffer argues that beyond a certain percent $p_m$, increased taxes will produce less government revenue. His theory is illustrated in the graph below.

Use your graph to find the tax rate that yields $\$ 600$ million of revenue.

The hyponitrite ion, ${ }^{-} \mathrm{O}-\mathrm{N}=\mathrm{N}-\mathrm{O}^{-}$, exists in solid compounds as the trans isomer. Using valence bond theory, explain why cis-trans isomers might be expected for this ion. Draw structural formulas of the cis-trans isomers.

Joe Perverse has invented a new law of gravitation. In this theory, the force exerted on a mass $m$ at $(x, y, z)$ by a mass $M$ at the origin is $\mathbf{F}=-J M m \mathbf{r} / r^5$, where $J$ is Joe's constant. Find $V$ such that $\mathbf{F}=-\boldsymbol{\nabla} V$ and verify that $\mathbf{F}$ is orthogonal to the level surfaces of $V$.