Examine the trends in lattice energy in the table below. The value of the lattice energy becomes somewhat more negative on going from NaI to NaBr to NaCl, and all are in the range from -700 to -800 kJ/mol. Propose a reason for the observation that the lattice energy of ${NaF}\left(\Delta_{\text {lattice }} U=-926 {~kJ} / {mol}\right)$ is much more negative than those of the other sodium halides.

Lattice Energies of Some Ionic Compounds

$$\begin{array}{l|r} \hline \text { Compound } & \begin{array}{r} \Delta_{\text {lattice }} U \\ (\mathrm{~kJ} / \mathrm{mol}) \end{array} \\ \hline \mathrm{LiF} & -1037 \\ \hline \mathrm{LiCl} & -852 \\ \hline \mathrm{LiBr} & -815 \\ \hline \mathrm{Lil} & -761 \\ \hline \mathrm{NaF} & -926 \\ \hline \mathrm{NaCl} & -786 \\ \hline \mathrm{NaBr} & -752 \\ \hline \mathrm{Nal} & -702 \\ \hline \mathrm{KF} & -821 \\ \hline \mathrm{KCl} & -717 \\ \mathrm{KBr} & -689 \\ \mathrm{KI} & -649 \\ \hline \end{array}$$

Based on a C-C distance of 139 pm, determine the side-to-side dimension of a planar, ${C}_6$ ring.

Determine how many tin atoms are contained in the tetragonal crystal lattice unit cell of $\beta$-tin. How many tin atoms are contained in the cubic crystal lattice unit cell of $\alpha$-tin?

What mass of lithium can be acquired from 73 million metric tons of lithium carbonate? (1 metric ton = 1000 kg.)

A flexible connection consisting of rubber pads (thickness $t=9\ \mathrm{mm}$) bonded to steel plates. The pads are 160 mm long and 80 mm wide. (a) Find the average shear strain $\gamma_{\text { aver }}$ in the rubber if the force $P=16\ \mathrm{kN}$ and the shear modulus for the rubber is $G=1250\ \mathrm{kPa}$. (b) Find the relative horizontal displacement $\delta$ between the interior plate and the outer plates.

Which element would you expect to be more metallic?

Ca or Rb,

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Which compound in each of the following pairs has the larger lattice energy? Note: $\mathrm{Mg}^{2+}$ and $\mathrm{Li}^{+}$have similar radii; $\mathrm{O}^{2-}$ and $\mathrm{F}^{-}$have similar radii. Explain your choices. (a) $\mathrm{MgO}$ or $\mathrm{MgSe}$ (b) $\mathrm{LiF}$ or $\mathrm{MgO}$ (c) $\mathrm{Li}_2 \mathrm{O}$ or $\mathrm{LiCl}$ (d) $\mathrm{Li}_2 \mathrm{Se}$ or $\mathrm{MgO}$

Compute the overall thermal resistance of a wall made up of 100 mm brick (1920 kg/m$^3$) and 200 mm normal weight concrete block with a 20 mm air gap between. There is 13 mm of gypsum plaster on the inside. Assume a 7 m/s wind velocity on the outside and still air inside.

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Divide. Write the answer in simplest form. 2/3 ÷ 3

How would each of the following scenarios affect a firm's cost of debt, $r_d(1-T)$; its cost of equity, $\mathrm{r}_{\mathrm{s}}$; and its WACC? Indicate with a plus $(+)$, a minus $(-)$, or a zero $(0)$ whether the factor would raise, lower, or have an indeterminate effect on the item in question. Assume for each answer that other things are held constant, even though in some instances this would probably not be true. Be prepared to justify your answer but recognize that several of the parts have no single correct answer. These questions are designed to stimulate thought and discussion.

Point $(x, y)$ is a lattice point if both $x$ and $y$ are integers. For the given values of $x$, graph the lattice points that satisfy each equation.

$y=\frac{1}{3} x+\frac{1}{3}$, where $x \in\{0,2,4,5,6,8\}$

If $f^{\prime}(t)$ and $g^{\prime}(t)$ are continuous functions, and if no segment of the curve

$$x=f(t), \quad y=g(t) \quad(a \leq t \leq b)$$

is traced more than once, then it can be shown that the area of the surface generated by revolving this curve about the $x$-axis is

$$S=\int_a^b 2 \pi y \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t$$

and the area of the surface generated by revolving the curve about the $y$-axis is

$$S=\int_a^b 2 \pi x \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t$$

[The derivations are similar to those used to obtain Formulas (4) and (5) in Section Use the formulas above in these exercises.

Find the area of the surface generated by revolving the curve $x=e^t \cos t, y=e^t \sin t(0 \leq t \leq \pi / 2)$ about the $x$-axis.