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.

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

A 262-mL sample of a sugar solution containing $1.22 \mathrm{~g}$ of the sugar has an osmotic pressure of $30.3 \mathrm{mmHg}$ at $35^{\circ} \mathrm{C}$. What is the molar mass of the sugar?

A solution of 6.85 g of a carbohydrate in 100.0 g of water has a density of 1.024 g/mL and an osmotic pressure of 4.61 atm at $20.0^{\circ} \mathrm{C}$. Calculate the molar mass of the carbohydrate.

What is the osmotic pressure of a 1.36 M aqueous solution of urea at $22.0^{\circ} \mathrm{C}$ ?

Calculate the osmotic pressure of a $0.0500 \mathrm{M}$ $\mathrm{MgSO}_4$ solution at $25^{\circ} \mathrm{C}$.

Using the experimental van't Hoff factor from Table 13.4, determine the freezing point of a $0.100-m$ aqueous solution of $\mathrm{NaCl}$. (Assume that the van't Hoff factors do not change with temperature.)

The vapor pressure of benzene is $100.0 \mathrm{~mmHg}$ at $26.1^{\circ} \mathrm{C}$. Calculate the vapor pressure of a solution containing $24.6 \mathrm{~g}$ of camphor $\left(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}\right)$ dissolved in $98.5 \mathrm{~g}$ of benzene.

The vapor pressure of benzene is 100.0 mmHg at $26.1^{\circ} \mathrm{C}$. Calculate the vapor pressure of a solution containing 24.6 g of camphor dissolved in 98.5 g of benzene.

Calculate the molality of each of the following aqueous solutions: (a) $2.50~M\mathrm{~NaCl}$ solution, (b) $48.2$ percent by mass $\mathrm{KBr}$ solution.

Calculate the molality of each of the following aqueous solutions: (a) 2.50 M NaCl solution, (b) 48.2 percent by mass KBr solution.

An aqueous solution contains the amino acid glycine. Assuming that the acid does not ionize in water, calculate the molality of the solution if it freezes at $-1.1^{\circ} \mathrm{C}$.

Calculate the molalities of the following aqueous solutions: (a) 1.22 M sugar solution, (b) 0.87 M NaOH solution, (c) 5.24 M $\mathrm{NaHCO}{ }_3$ solution.

Calculate the molalities of the following aqueous solutions: (a) $1.22 \mathrm{M}$ sugar $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ solution (density of solution $=1.12 \mathrm{~g} / \mathrm{mL}$ ), (b) $0.87 \mathrm{M} \mathrm{NaOH}$ solution (density of solution $=1.04 \mathrm{~g} / \mathrm{mL}$ ), (c) $5.24 M$ $\mathrm{NaHCO}_3$ solution (density of solution $=1.19 \mathrm{~g} / \mathrm{mL}$ ).