A quantity of $7.480 \mathrm{~g}$ of an organic compound is dissolved in water to make $300.0 \mathrm{~mL}$ of solution. The solution has an osmotic pressure of $1.43$ atm at $27^{\circ} \mathrm{C}$. The analysis of this compound shows that it contains $41.8$ percent $\mathrm{C}$, $4.7$ percent $\mathrm{H}, 37.3$ percent $\mathrm{O}$, and $16.3$ percent $\mathrm{N}$. Calculate the molecular formula of the compound.

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.

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 $31.8 \mathrm{mmHg}$ )

A 3.20-g sample of a salt dissolves in $9.10 \mathrm{~g}$ of water to give a saturated solution at $25^{\circ} \mathrm{C}$. What is the solubility (in $\mathrm{g}$ salt/ $/ 00 \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{O}$ ) of the salt?

A compound X undergoes two simultaneous first-order reactions as follows: X$\to$ Y with the rate constant k1 and X$\to$ Z with rate constant k2. The ratio of k1/k2 at 40 degree C is 8.0. What is the ratio at 300 degree C. Assume that the frequency factor of the two reactions are the same.

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 $0.80 \mathrm{~atm}$.

Order the following species with respect to the carbon-oxygen bond length (longest to shortest):

$$\mathrm { CO } , \mathrm { CO } _ { 2 } , \mathrm { CO } _ { 3 } ^ { 2 } , \mathrm { CH } _ { 3 } \mathrm { OH }$$

What is the order from the weakest to the strongest carbon-oxygen bond?

A solution containing $0.8330 \mathrm{~g}$ of a polymer of unknown structure in $170.0 \mathrm{~mL}$ of an organic solvent was found to have an osmotic pressure of $5.20 \mathrm{mmHg}$ at $25^{\circ} \mathrm{C}$. Determine the molar mass of the polymer.

Tetrahydrofuran, an organic substance used as a solvent in many pharmaceutical processes, has the formula C$_4$ H$_8$ O. In tetrahydrofuran, the four C atoms are bonded in a row, each C atom is bonded to two H atoms, each H atom is bonded to one C atom, and the O atom is bonded to two C atoms. Write a structural formula for tetrahydrofuran.

A solution of $2.50 \mathrm{~g}$ of a compound having the empirical formula $\mathrm{C}_6 \mathrm{H}_5 \mathrm{P}$ in $25.0 \mathrm{~g}$ of benzene is observed to freeze at $4.3^{\circ} \mathrm{C}$. Calculate the molar mass of the solute and its molecular formula.

The mass of an organic compound was found to be 58.077 46 by mass spectrometry. Is the sample C$_2$H10, C$_2$H$_2$O, or C$_2$H$_2$N$_2$? Exact masses of elements are 1.0 0 7 8 2 5 ($^1$ H); 12.000 00 ($^{12}$ C); 14.003 074 ($^{14}$N); and 15.994 915 ($^{16}$O).

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

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.