Show that both the valence bond method and molecular orbital theory provide an explanation for the existence of the covalent molecule $\mathrm{Na}_2$ in the gaseous state. Would you predict $\mathrm{Na}_2$ by the Lewis theory?

Draw Lewis structures for two different molecules with the formula $\mathrm{C}_3 \mathrm{H}_4$. Is either of these molecules linear? Explain.

Between which two levels of the hydrogen atom must an electron fall to produce light of wavelength $1876 \mathrm{~nm}$?

A mixture of $\mathrm{H}_2(\mathrm{~g})$ and $\mathrm{O}_2(\mathrm{~g})$ is prepared by electrolyzing $1.32 \mathrm{~g}$ water, and the mixture of gases is collected over water at $30^{\circ} \mathrm{C}$ and $748 \mathrm{mmHg}$. The volume of "wet" gas obtained is $2.90 \mathrm{~L}$. What must be the vapour pressure of water at $30^{\circ} \mathrm{C}$ ?

$$2 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \stackrel{\text { electrolysis }}{\longrightarrow} 2 \mathrm{H}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g})$$

What volume of air, measured at $298 \mathrm{~K}$ and $101 \mathrm{kPa}$, is required to burn $2.00 \mathrm{~kg} \mathrm{C}_8 \mathrm{H}_{18}$ ? Air is approximately $78.1 \% \mathrm{~N}_2$ and $20.9 \% \mathrm{O}_2$, by volume. Other gases make up the remaining $1.0 \%$.

Gas cylinder A has a volume of $48.2 \mathrm{~L}$ and contains $\mathrm{N}_2(\mathrm{~g})$ at $8.35 \mathrm{~atm}$ at $25^{\circ} \mathrm{C}$. Gas cylinder $\mathrm{B}$, of unknown volume, contains $\mathrm{He}(\mathrm{g})$ at $9.50 \mathrm{~atm}$ and $25^{\circ} \mathrm{C}$. When the two cylinders are connected and the gases mixed, the pressure in each cylinder becomes $8.71$ atm. What is the volume of cylinder B?

A mixture of $1.00 \mathrm{~g} \mathrm{H}_2$ and $8.60 \mathrm{~g} \mathrm{O}_2$ is introduced into a $1.500 \mathrm{~L}$ flask at $25^{\circ} \mathrm{C}$. When the mixture is ignited, an explosive reaction occurs in which water is the only product. What is the total gas pressure when the flask is returned to $25^{\circ} \mathrm{C}$? (The vapor pressure of water at $25^{\circ} \mathrm{C}$ is $23.8 \mathrm{mmHg}$.)

Ammonium nitrite, $\mathrm{NH}_4 \mathrm{NO}_2$, decomposes according to the chemical equation below.

$$\mathrm{NH}_4 \mathrm{NO}_2(\mathrm{~s}) \longrightarrow \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$$

What is the total volume of products obtained when $128 \mathrm{~g} \mathrm{NH}_4 \mathrm{NO}_2$ decomposes at $819^{\circ} \mathrm{C}$ and $101 \mathrm{kPa}$ ?

Two evacuated bulbs of equal volume are connected by a tube of negligible volume. One of the bulbs is placed in a constant-temperature bath at $225 \mathrm{~K}$ and the other bulb is placed in a constant-temperature bath at $350 \mathrm{~K}$. Exactly $1 \mathrm{~mol}$ of an ideal gas is injected into the system. Calculate the final number of moles of gas in each bulb.

Can this bonding be described by either $s p^2$ or $s p^3$ hybridization of the $\mathrm{N}$ atoms? Can bonding in $\mathrm{N}_2$ be described in terms of unhybridized orbitals? Explain.

Several factors are involved in determining the cooking times required for foods in a microwave oven. One of these factors is specific heat capacity. Determine the approximate time required to warm $250 \mathrm{~mL}$ of chicken broth from $4^{\circ} \mathrm{C}$ (a typical refrigerator temperature) to $50^{\circ} \mathrm{C}$ in a $700 \mathrm{~W}$ microwave oven. Assume that the density of chicken broth is about $1 \mathrm{~g} / \mathrm{mL}$ and that its specific heat capacity is approximately $4.2 \mathrm{Jg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$.

Use data from Table 7.3 and Appendix D to determine the standard enthalpy change in the following reaction. $\mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow \mathrm{Al}(\mathrm{OH})_3(\mathrm{~s}) \quad \Delta_{\mathrm{r}} \mathrm{H}^0=?$

Ants release formic acid $(\mathrm{HCOOH})$ when they bite. Use the data in Table 7.2 and the standard enthalpy of combustion for formic acid $\left(\Delta_{\mathrm{r}} H^{\circ}=-255 \mathrm{~kJ} / \mathrm{mol}\right)$ to calculate the standard enthalpy of formation for formic acid.

Use standard enthalpies of formation from Table $7.2$ to determine $\Delta_{\mathrm{r}} H^{\circ}$ at $25^{\circ} \mathrm{C}$ for the following reaction.