Portable hot packs are available for skiers and people engaged in other outdoor activities in a cold climate. The air-permeable paper packet contains a mixture of powdered iron, sodium chloride, and other components, all moistened by a little water. The exothermic reaction that produces the heat (the rusting of iron) is

$$4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{O}_2(\mathrm{~g}) \longrightarrow 2 \mathrm{Fe}_2 \mathrm{O}_3(s)$$

When the outside plastic envelope is removed, $\mathrm{O}_2$ molecules penetrate the paper, causing the reaction to begin. A typical packet contains $250 \mathrm{~g}$ of iron to warm your hands or feet for up to 4 hours. How much heat (in $\mathrm{kJ}$ ) is produced by this reaction? (Hint: See Appendix 2 for $\Delta H_{\mathrm{f}}$ values.)

A quantity of $0.020$ mole of a gas initially at $0.050 \mathrm{~L}$ and $20^{\circ} \mathrm{C}$ undergoes a constant-temperature expansion until its volume is $0.50 \mathrm{~L}$. Calculate the work done (in joules) by the gas if it expands
against a constant pressure of $0.20$ bar.

A quantity of $0.020$ mole of a gas initially at $0.050 \mathrm{~L}$ and $20^{\circ} \mathrm{C}$ undergoes a constant-temperature expansion until its volume is $0.50 \mathrm{~L}$. Calculate the work done (in joules) by the gas if it expands
against a vacuum.

The molar enthalpy of vaporization of a liquid $\left(\Delta H_{\text {vap }}\right)$ is the energy required to vaporize $1.00 \mathrm{~mol}$ of the liquid. In one experiment, $60.0 \mathrm{~g}$ of liquid nitrogen (boiling point $-196^{\circ} \mathrm{C}$ ) is poured into a Styrofoam cup containing $2.00 \times 10^2 \mathrm{~g}$ of water at $55.3^{\circ} \mathrm{C}$. Calculate the molar enthalpy of vaporization of liquid nitrogen if the final temperature of the water is $41.0^{\circ} \mathrm{C}$.

Producer gas (carbon monoxide) is prepared by passing air over red-hot coke:

$$\mathrm{C}(\mathrm{s})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}(\mathrm{g})$$

Water gas (a mixture of carbon monoxide and hydrogen) is prepared by passing steam over redhot coke:

$$\mathrm{C}(\mathrm{s})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{CO}(\mathrm{g})+\mathrm{H}_2(\mathrm{~g})$$

For many years, both producer gas and water gas were used as fuels in industry and for domestic cooking. The large-scale preparation of these gases was carried out alternately, that is, first producer gas, then water gas, and so on. Using thermochemical reasoning, explain why this procedure was chosen.

A 1.00-mole sample of ammonia at $14.0$ bar and $25^{\circ} \mathrm{C}$ in a cylinder fitted with a movable piston expands against a constant external pressure of $1.00$ bar. At equilibrium, the pressure and volume of the gas are $1.00$ bar and $23.5 \mathrm{~L}$, respectively.
Calculate $q, w$, and $\Delta U$ for the process. The specific heat capacity of ammonia is $0.0258 \mathrm{~J} \mathrm{~g}^{\circ} \mathrm{C}^{-1}$.

A 1.00-mole sample of ammonia at $14.0$ bar and $25^{\circ} \mathrm{C}$ in a cylinder fitted with a movable piston expands against a constant external pressure of $1.00$ bar. At equilibrium, the pressure and volume of the gas are $1.00$ bar and $23.5 \mathrm{~L}$, respectively.
Calculate the final temperature of the sample.

Show that the work required for the reversible and isothermal expansion of $n$ moles of a van der Waals gas (Equation $5.42$ ) from an initial volume $V_1$ to a final volume $V_2$ is given by

$$w=n R T \ln \frac{V_1-n b}{V_2-n b}+a n^2\left(\frac{1}{V_1}-\frac{1}{V_2}\right)$$

The combustion of what volume of ethane $\left(\mathrm{C}_2 \mathrm{H}_6\right)$, measured at $23.0^{\circ} \mathrm{C}$ and $752 \mathrm{~mm} \mathrm{Hg}$, would be required to heat $855 \mathrm{~g}$ of water from $25.0^{\circ} \mathrm{C}$ to $98.0^{\circ} \mathrm{C}$ ?

Calculate the work done (in joules) when 1.0 mole of water vaporizes at 1.0 atm and 100$\degree$C. Assume ideal gas behavior and that the volume of liquid water is negligible compared with that of steam at 100$\degree$C.

The heat of fusion of ice at the standard melting point $\left(0^{\circ} \mathrm{C}\right)$ is $6.01 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Determine the heat of fusion at $-10^{\circ} \mathrm{C}$ using data from Appendix 2.

The enthalpy of vaporization is found to decrease with increasing temperature for a certain substance. What information does this give you about the relative properties of the liquid and vapor phases?

The molar enthalpies of fusion and vaporization of water at $298 \mathrm{~K}$ are $6.01$ and $44.01 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively. Use these values to estimate the molar enthalpy of sublimation of ice.

The molar enthalpies of fusion and sublimation of molecular iodine are $15.27$ and $62.30 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively. Estimate the molar heat of vaporization of liquid iodine.