Considering only the molecular orbitals formed by combinations of the 2s atomic orbitals, how many molecular orbitals can be formed by 1000 Li atoms? In the lowest energy state, how many of these orbitals will be populated by pairs of electrons and how many will be empty?

To melt an ionic solid, energy must be supplied to disrupt the forces between ions so the regular array of ions collapses. Predict (and explain) how the melting point is expected to vary as a function of the distance between cation and anion.

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

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

Predict the trend in lattice energy, from least negative to most negative, for the following compounds based on the ion charges and ionic radii: LiI, LiF, CaO, RbI.

A unit cell of cesium chloride is illustrated in Figure 12.8. The density of the solid is 3.99 g/cm$^3$, and the radius of the Cl$^−$ ion is 181 pm. Calculate the radius of the Cs$^+$ ion in the center of the cell. (Assume that the Cs$^+$ ion touches all of the corner Cl$^−$ ions.)

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.)

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

The manager of the concert production company regarded in earlier exercises considers the regression of Total Revenue on Ticket Sales and calculates the Durbin-Watson statistic, obtaining a value of $0.51$.

b) Specify what this statistic tests and what the test says about these data.

Vitamin A has a molar mass of 286.4 g/mol and a general molecular formula of $\mathrm{C}_{x} \mathrm{H}_{y} \mathrm{E},$ where E is an unknown element. If vitamin A is 83.86% C and 10.56% H by mass, what is the molecular formula of vitamin A?

Solve using any strategy.

A lot measures $50 \text{ft}$ by $100 \text{ft}$. The house on the lot GPS measures $25 \text{ft}$ by $50 \text{ft}$. What is the area of the lawn?

Expected Value for Deal or No Deal The television game show Deal or No Deal begins with individual suitcases containing the amounts of $15, \$ 1, \$ 5, \$ 10, \$ 25, \$ 50, \$ 75$, $\$ 100, \$ 200, \$ 300, \$ 400, \$ 500, \$ 750, \$ 1000, \$ 5000, \$ 10,000, \$ 25,000, \$ 50,000, \$ 75,000$, $\$ 100,000, \$ 200,000, \$ 300,000, \$ 400,000, \$ 500,000, \$ 750,000$, and $\$ 1,000,000$. If a player adopts the strategy of choosing the option of "no deal" until one suitcase remains, the payoff is one of the amounts listed, and they are all equally likely.

a. Find the expected value for this strategy.

You perform 1000 significance tests using $\alpha=0.05$. Assuming that all null hypotheses are true, about how many of the test results would you expect to be statistically significant? Explain how you obtained your answer.

How is it possible to obtain the structure of a molecule using x-ray diffraction from the molecular crystal?