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 $0.0258 \mathrm{~J} \mathrm{~g}^{\circ} \mathrm{C}^{-1}$.

The first step in the industrial recovery of copper from the copper sulfide ore is roasting, that is, the conversion of CuS to CuO by heating:

$$\begin{array}{r} 2 \mathrm{CuS}(s)+3 \mathrm{O}_2(g) \longrightarrow 2 \mathrm{CuO}(s)+2 \mathrm{SO}_2(g) \\ \Delta H=-805.6 \mathrm{~kJ} / \mathrm{mol} \end{array}$$

Calculate the heat evolved per gram of CuS roasted.

A 0.1375-g sample of solid magnesium is burned in a constant-volume bomb calorimeter that has a heat capacity of 3024 J/°C. The temperature increases by 1.126 °C. Calculate the heat given off by the burning Mg, in kJ/g and in kJ/mol.

A 44.0-g sample of an unknown metal at 99.0 °C was placed in a constant-pressure calorimeter containing 80.0 g of water at 24.0 °C. The final temperature of the system was found to be 28.4 °C. Calculate the specific heat of the metal. (The heat capacity of the calorimeter is 12.4 J/°C.)

A buffer contains significant amounts of acetic acid and sodium acetate. Write equations showing how this buffer neutralizes added acid and added base.

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 $98.0^{\circ} \mathrm{C}$ ?

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 $98.0^{\circ} \mathrm{C}$ ?

A gas undergoes two processes. In the first, the volume remains constant at $0.200 m^{3}$ and the pressure increases from $2.00 \times 10^{5} \mathrm{Pa}$ to $5.00 \times 10^{5} \mathrm{Pa}$. The second process is a compression to a volume of $0.120 \mathrm{m}^{3}$ at a constant pressure of $5.00 \times 10^{5} \mathrm{Pa}$. (a) In a pV-diagram, show both processes. (b) Find the total work done by the gas during both processes.

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?

An experimenter adds 970 J of heat to 1.75 mol of an ideal gas to heat it from $10.0^{\circ} \mathrm{C}$ to $25.0^{\circ} \mathrm{C}$ at constant pressure. The gas does +223 J of work during the expansion. (a) Calculate the change in internal energy of the gas. (b) Calculate $\gamma$ for the gas.

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.