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 $41.0^{\circ} \mathrm{C}$.

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.

How much heat (in kJ) is needed to convert $866 \mathrm{~g}$ of ice at $-10^{\circ} \mathrm{C}$ to steam at $126^{\circ} \mathrm{C}$ ? (The specific heat capacities of ice and steam are $2.03$ and $1.99 \mathrm{~J} \mathrm{~g}^{-1}$ ${ }^{\circ} \mathrm{C}^{-1}$, respectively.)

Calculate the amount of heat (in $\mathrm{kJ}$ ) required to convert $74.6 \mathrm{~g}$ of water to steam at $100^{\circ} \mathrm{C}$.

Calculate the work done when $50.0 \mathrm{~g}$ of tin dissolves in excess acid at $1.00$ bar and $25^{\circ} \mathrm{C}$

$$\mathrm{Sn}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Sn}^{2+}(a q)+\mathrm{H}_2(\mathrm{~g})$$

Assume ideal gas behavior.

Use the bond enthalpy values in Table $7.6$ to calculate the enthalpy of combustion for ethane $\left(\mathrm{C}_2 \mathrm{H}_6\right)$ :

$$\mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})+\frac{7}{2} \mathrm{O}_2(g) \longrightarrow 2 \mathrm{CO}_2(g)+3 \mathrm{H}_2 \mathrm{O}(g)$$

Use the bond enthalpy data in Table $7.6$ to calculate the enthalpies of formation of the following gases:
$\mathrm{H}_2 \mathrm{NCl}$.