The molar mass of benzoic acid $\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{COOH}\right)$ determined by measuring the freezing-point depression in benzene is twice what we would expect for the molecular formula, $\mathrm{C}_7 \mathrm{H}_6 \mathrm{O}_2$. Explain this apparent anomaly.

A solution is prepared by condensing 4.00 L of a gas, measured at $27^{\circ} \mathrm{C}$ and 748 mmHg pressure, into 58.0 g of benzene. Calculate the freezing point of this solution.

How many liters of the antifreeze ethylene glycol $\left[\mathrm{CH}_2(\mathrm{OH}) \mathrm{CH}_2(\mathrm{OH})\right]$ would you add to a car radiator containing $6.50 \mathrm{~L}$ of water if the coldest winter temperature in your area is $-20^{\circ} \mathrm{C}$ ? Calculate the boiling point of this water-ethylene glycol mixture. (The density of ethylene glycol is $1.11 \mathrm{~g} / \mathrm{mL}$.)

The elemental analysis of an organic solid extracted from gum arabic (a gummy substance used in adhesives, inks, and pharmaceuticals) showed that it contained $40.0$ percent $\mathrm{C}, 6.7$ percent $\mathrm{H}$, and $53.3$ percent O. A solution of $0.650 \mathrm{~g}$ of the solid in $27.8 \mathrm{~g}$ of the solvent diphenyl gave a freezing-point depression of $1.56^{\circ} \mathrm{C}$. Calculate the molar mass and molecular formula of the solid. $\left(K_{\mathrm{f}}\right.$ for diphenyl is $8.00^{\circ} \mathrm{C} \mathrm{m}^{-1}$.)

The elemental analysis of an organic solid extracted from gum arabic (a gummy substance used in adhesives, inks, and pharmaceuticals) showed that it contained 40.0 percent C, 6.7 percent H, and 53.3 percent O. A solution of 0.650 g of the solid in 27.8 g of the solvent diphenyl gave a freezing-point depression of $1.56^{\circ} \mathrm{C}$. Calculate the molar mass and molecular formula of the solid. ( $K_{\mathrm{f}}$ for diphenyl is $8.00^{\circ} \mathrm{C} / \mathrm{m}$.)

Pheromones are compounds secreted by the females of many insect species to attract males. One of these compounds contains $80.78 \% \mathrm{~C}, 13.56 \% \mathrm{~H}$, and $5.66 \%\mathrm{~O}$. A solution of $1.00 \mathrm{~g}$ of this pheromone in $8.50 \mathrm{~g}$ of benzene freezes at $3.37^{\circ} \mathrm{C}$. What are the molecular formula and molar mass of the compound?

The vapor pressures of ethanol $\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\right)$ and 1-propanol $\left(\mathrm{C}_3 \mathrm{H}_7 \mathrm{OH}\right)$ at $35^{\circ} \mathrm{C}$ are $100 \mathrm{~mmHg}$ and $37.6\mathrm{~mmHg}$, respectively. Assume ideal behavior and calculate the partial pressures of ethanol and 1-propanol at $35^{\circ} \mathrm{C}$ over a solution of ethanol in 1-propanol, in which the mole fraction of ethanol is $0.300$.

Consider the statement: “The equilibrium constant of a reacting mixture of solid NH4Cl and gaseous NH3 and HCl is 0.316.” List three important pieces of information that are missing from this statement.

The solubility of $\mathrm{N}_2$ in blood at $37^{\circ} \mathrm{C}$ and at a partial pressure of $0.80 \mathrm{~atm}$ is $5.6 \times 10^{-4} \mathrm{~mol} / \mathrm{L}$. A deepsea diver breathes compressed air with the partial pressure of $\mathrm{N}_2$ equal to $4.0 \mathrm{~atm}$. Assume that the total volume of blood in the body is $5.0 \mathrm{~L}$. Calculate the amount of $\mathrm{N}_2$ gas released (in liters) when the diver returns to the surface of the water, where the partial pressure of $\mathrm{N}_2$ is $0.80 \mathrm{~atm}$.

Calculate the molality, molarity, and mole fraction of NH3 in an 8.00 mass % aqueous solution (d = 0.9651 g/mL).

Osmium (Os) is the densest element known (density = 22.57 g/cm3 ). Calculate the mass in pounds and in kilograms of an Os sphere 15 cm in diameter (about the size of a grapefruit). See Problem 1.57 for volume of a sphere.

The unit “troy ounce” is often used for precious metals such as gold (Au) and platinum (Pt). (1 troy ounce = 31.103 g.) (a) A gold coin weighs 2.41 troy ounces. Calculate its mass in grams. (b) Is a troy ounce heavier or lighter than an ounce? (1 lb =16 oz; 1 lb = 453.6 g.)

The surface area and average depth of the Pacific Ocean are $1.8 \times 10^8 \mathrm{~km}^2$ and $3.9 \times 10^3 \mathrm{~m}$, respectively. Calculate the volume of water in the ocean in liters.

The surface area and average depth of the Pacific Ocean are 1.8 $\times 10^8$ km2 and 3.9 $\times 10^3$ m, respectively. Calculate the volume of water in the ocean in liters.