Calculate the molar enthalpy change when $H_2O(l)$ is cooled from $48.3^{\circ} \mathrm{C}$ to $25.2^{\circ} \mathrm{C}$.

The value of $K_{sp}$ for $\mathrm { Cd } ( \mathrm { OH } ) _ { 2 }$ is $2.5 \times 10 ^ { - 14 }$ What is the molar solubility of $Cd(OH)_2?$

(a) A sample of $1.00 \mathrm{~mol} \mathrm{H}_2 \mathrm{O}(\mathrm{g})$ is condensed isothermally and reversibly to liquid water at $100^{\circ} \mathrm{C}$. The standard enthalpy of vaporization of water at $100^{\circ} \mathrm{C}$ is $40.656 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Find $w, q, \Delta U$, and $\Delta H$ for this process.

(b) A sample of $2.00 \mathrm{~mol} \mathrm{CH}_3 \mathrm{OH}(\mathrm{g})$ is condensed isothermally and reversibly to liquid at $64^{\circ} \mathrm{C}$. The standard enthalpy of vaporization of methanol at $64^{\circ} \mathrm{C}$ is $35.3 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Find $w, q, \Delta U$, and $\Delta H$ for this process.

What is the molar mass of C$_{37}$H$_{34}$N$_2$Na$_2$O$_9$S$_3$ (brilliant blue FCF)?

What is the molar mass of diazepam (Valium), $\mathrm{C}_{16} \mathrm{H}_{13} \mathrm{ClN}_2 \mathrm{O}$ ?

Use values of $K_{sp}$ for Agl and $K_f$ for $Ag(CN)_2 ^-$ to determine the molar solubility of Agl in a 0.100 M NaCN solution.

In above Chapter you learned about the colligative properties of solutions. Which of the colligative properties is suitable for determining the molar mass of a polymer? Why?

What is the molar solubility of $\mathrm{Pb}(\mathrm{OH})_2$ in a $0.138-\mathrm{M}$ solution of $\mathrm{CH}_3 \mathrm{NH}_2$ ?

Calculate the molar mass of a gas at 388 torrs and $45^{\circ} \mathrm{C}$ if 206 ng occupies $0.206 \mu \mathrm{L}$.

A closed rigid vessel initially contains a gaseous mix. ture at $25^{\circ} \mathrm{C}, 1 \mathrm{~atm}$ with the molar analysis of $25 \%$ ethylene $\left(\mathrm{C}_2 \mathrm{H}_4\right), 75 \%$ oxygen $\left(\mathrm{O}_2\right)$. The mixture burns completely and the products are cooled to $500 \mathrm{~K}$. Find the heat transfer between the vessel and its surroundings, in $\mathrm{kJ}$ per $\mathrm{kmol}$ of fuel present initially, and the final pressure, in atm.

Show that the difference between the molar heat capacities at constant pressure and at constant volume is equal to the gas constant $R$ for an ideal gas whose internal energy relies only upon temperature $T$ : $C {P, m}-C {V, m}=R$. 33.7 At first, the top layers of a lake's water are at mathrm $0^{\circ} \mathrm{C}$. The surface of the lake is kept at a temperature $\Delta T$ below $0^{\circ} \mathrm{C}$. by the onset of a chilly breeze. (a)If the heat loss needed to lower the temperature of the ice that has already formed is substantially less than the heat loss needed to generate new ice, then find the rate of rise of the thickness of the ice $d z / d t$. (Also assume that the ice's temperature varies linearly with depth.) (b) Determine the thickness of the ice $z$ one hour after freezing starts if $\Delta T=10^{\circ} \mathrm{C}$.. Use the answer of section Use: thermal conductivity of ice: $\kappa=2.0 \ mathrm{~W} \ mathrm{~m}^{-1} \ mathrm{~K}^{-1}$, latent heat of ice formation: $L=3.3 \times 10^5 \ mathrm{~J} \mathrm{~kg}^{-1}$.

Ethanol $\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right)$ melts at $-114^{\circ} \mathrm{C}$ and boils at $78^{\circ} \mathrm{C}$. The enthalpy of fusion of ethanol is $5.02 \mathrm{~kJ} / \mathrm{mol}$, and its enthalpy of vaporization is $38.56 \mathrm{~kJ} / \mathrm{mol}$. The specific heats of solid and liquid ethanol are $0.97 \mathrm{~J} / \mathrm{g}-\mathrm{K}$ and $2.3 \mathrm{~J} / \mathrm{g}-\mathrm{K}$, respectively. How much heat is required to convert $75.0 \mathrm{~g}$ of ethanol at $-120^{\circ} \mathrm{C}$ to the vapor phase at $78^{\circ} \mathrm{C}$ ?

What is an alternative term for the reactant that makes the least amount of product?

(a) stoichiometric amount

(b) limiting reagent

(c) molar mass

(d) excess reagent

We have learned that the enthalpy of vaporization of a liquid is generally a function of temperature. If we wish to take this temperature variation into account, we cannot use the Clausius-Clapeyron equation in the form given in the text (that is, equation 12.2). Instead, we must go back to the differential equation upon which the Clausius-Clapeyron equation is based and reintegrate it into a new expression. Our starting point is the following equation describing the rate of change of vapor pressure with temperature in terms of the enthalpy of vaporization, the difference in molar volumes of the vapor $\left(V_g\right)$, and liquid $\left(V_1\right)$, and the temperature.

$$\frac{d P}{d T}=\frac{\Delta_{\mathrm{vap}} H}{T\left(V_{\mathrm{g}}-V_{\mathrm{I}}\right)}$$

Because in most cases the volume of one mole of vapor greatly exceeds the molar volume of liquid,we can treat the $V_1$ term as if it were zero. Also, unless the vapor pressure is unusually high, we can treat the vapor as if it were an ideal gas; that is, for one mole of vapor, $P V=R T$. Make appropriate substitutions into the above expression, and separate the $P$ and $d P$ terms from the $T$ and $d T$ terms. The appropriate substitution for $\Delta_{\text {vap }} H$ means expressing it as a function of temperature. Finally, integrate the two sides of the equation between the limits $P_1$ and $P_2$ on one side and $T_1$ and $T_2$ on the other. (a) Derive an equation for the vapor pressure of $\mathrm{C}_2 \mathrm{H}_4(1)$ as a function of temperature, if $\Delta_{\mathrm{vap}} \mathrm{H}=$ $15,971+14.55 T-0.160 T^2$ (in J mol ${ }^{-1}$ ).