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 $\mathrm{O}$. 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. ( $K_{\mathrm{f}}$ for diphenyl is $8.00^{\circ} \mathrm{C} / \mathrm{m}$.)

How many grams of urea $\left[\left(\mathrm{NH}_2\right)_2 \mathrm{CO}\right]$ must be added to $450 \mathrm{~g}$ of water to give a solution with a vapor pressure $2.50 \mathrm{mmHg}$ less than that of pure water at $30^{\circ} \mathrm{C}$ ? (The vapor pressure of water at $30^{\circ} \mathrm{C}$ is $31.8 \mathrm{mmHg}$ )

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 $8.00^{\circ} \mathrm{C} / \mathrm{m}$.)

How many grams of sucrose must be added to 552 g of water to give a solution with a vapor pressure 2.0 mmHg less than that of pure water at $20^{\circ} \mathrm{C}$ ?

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 $0.300$.

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 $0.80 \mathrm{~atm}$.

How many grams of sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ must be added to $552 \mathrm{~g}$ of water to give a solution with a vapor pressure $2.0 \mathrm{~mmHg}$ less than that of pure water at $20^{\circ} \mathrm{C}$ ?

How many grams of sucrose C12H22O11 are in 1.55 L of 0.758 M sucrose solution?

Explain why we cannot use osmotic pressure to determine both molar mass and percent ionization for an unknown monoprotic acid.

Use the fourth-order method to solve the problem as stated

Calculate the difference in osmotic pressure (in atm) at the normal body temperature between the blood plasma of a diabetic patient and that of a healthy adult. Assume that the sole difference between the two people is due to the higher glucose level in the diabetic patient. The glucose levels are $1.75$ and $0.84 \mathrm{~g} / \mathrm{L}$, respectively. Based on your result, explain why such a patient frequently feels thirsty.

Calculate the osmotic pressure of a $0.0500 \mathrm{MgSO}_4$ solution at $25^{\circ} \mathrm{C}$. (Hint: See Table 13.3.)

What are the boiling point and freezing point of a $2.47 \mathrm{~m}$ solution of naphthalene in benzene? (The boiling point and freezing point of benzene are $80.1^{\circ} \mathrm{C}$ and $5.5^{\circ} \mathrm{C}$, respectively.)

A solution is prepared by dissolving 396 g of sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ in 624 g of water. What is the vapor pressure of this solution at $30^{\circ} \mathrm{C}$ ?