In a police forensics lab, you examine a package that may contain heroin. However, you find the white powder is not pure heroin but a mixture of heroin $\left(\mathrm{C}_{21} \mathrm{H}_{23} \mathrm{O}_5 \mathrm{~N}\right)$ and lactose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$. To determine the amount of heroin in the mixture, you dissolve $1.00 \mathrm{~g}$ of the white powdery mixture in water in a $100.0-\mathrm{mL}$ volumetric flask. You find that the solution has an osmotic pressure of $539 \mathrm{~mm} \mathrm{Hg}$ at $25^{\circ} \mathrm{C}$. What is the composition of the mixture?

A tree is exactly $10 \mathrm{~m}$ tall.
What must be the total molarity of the solutes if sap rises to the top of the tree by osmotic pressure at $20^{\circ} \mathrm{C}$? Assume the groundwater outside the tree is pure water and that the density of the sap is $1.0 \mathrm{~g} / \mathrm{mL}$. $\left(1 \mathrm{~mm} \mathrm{Hg}=13.6 \mathrm{~mm} \mathrm{H}_2 \mathrm{O}\right.$.)

Arrange the following aqueous solutions in order of decreasing the freezing point. (The last three are all assumed to dissociate completely into ions in water.)
$0.20 \mathrm{~m}$ ethylene glycol (a nonvolatile, nonelectrolyte)

To make homemade ice cream, you cool the milk and cream by immersing the container in ice and a concentrated solution of rock salt (NaCl) in water. If you want to have a water–salt solution that freezes at −10. $^o$C, what mass of NaCl must you add to 3.0 kg of water? (Assume the van’t Hoff factor, i, for NaCl is 1.85.)

Use the following data to calculate the enthalpy of solution of sodium perchlorate, $\mathrm{NaClO}_4$ : $\Delta_f H^{\circ}(\mathrm{s})=-382.9 \mathrm{~kJ} / \mathrm{mol}$ and

$$\begin{align*} \Delta_f H^{\circ}(\mathrm{aq}, 1 \mathrm{~m})=-369.5 \mathrm{~kJ} / \mathrm{mol} \end{align*}$$

Silver ion has an average concentration of $28 \mathrm{ppb}$ (parts per billion) in U.S. water supplies.
What is the molality of the silver ion?

If one is very careful, it is possible to float a needle on the surface of the water. (If the needle is magnetized, it will turn to point north and south and become a makeshift compass.) What would happen to the needle if a drop of liquid soap is added to the solution? Explain the observation.

You are given a flask filled with a colored liquid. Suggest several tests that would allow you to determine whether this is a solution or a colloid.

If a carbonated beverage is bottled under $1.5 \mathrm{bar} \mathrm{CO}_2$ pressure, what will be the concentration of dissolved $\mathrm{CO}_2$ in that beverage? ( $k_{\mathrm{H}}$ for $\mathrm{CO}_2$ is $0.034 \mathrm{~mol} / \mathrm{kg}$ bar.) After the pressure is released what fraction of the dissolved gas will escape before an equilibrium with the $\mathrm{CO}_2$ in the atmosphere is reached?

The Henry's law constant for $\mathrm{N}_2 \mathrm{O}$ is $2.4 \times 10^{-2}$ $\mathrm{mol} / \mathrm{kg} \cdot$ bar. (Nitrous oxide, $\mathrm{N}_2 \mathrm{O}$, laughing gas, is used as an anesthetic). Determine the mass of $\mathrm{N}_2 \mathrm{O}$ that will dissolve in $500\mathrm{mL}$ of water, under an $\mathrm{N}_2 \mathrm{O}$ pressure of $1.00$ bar. What is the concentration of $\mathrm{N}_2 \mathrm{O}$ in this solution, expressed in $\operatorname{Ppm}\left(d\left(\mathrm{H}_2 \mathrm{O}\right)=1.00 \mathrm{~g} / \mathrm{mL}\right)$?

A compound is known to be a potassium halide, KX. If $4.00 \mathrm{~g}$ of the salt is dissolved in exactly $100 \mathrm{~g}$ of water, the solution freezes at $-1.28{ }^{\circ} \mathrm{C}$. Identify the halide ion in this formula.

Methanol is a polar solvent and heptane is a nonpolar solvent. In which of these two solvents are each of the following solutes more likely to be soluble?

a. KCl, ionic

b. Rubbing alcohol, polar

c. Gasoline, nonpolar

d. $\text{NaNO}_3$, ionic

Indicate whether each of the following actions will increase or decrease the rate of the dissolving of a sugar cube in water. a. Cooling the sugar cube–water mixture b. Stirring the sugar cube–water mixture c. Breaking the sugar cube up into smaller “chunks” d. Crushing the sugar cube to give a granulated form of sugar

You want to prepare an aqueous solution of ethylene glycol, $\mathrm{HOCH}_2 \mathrm{CH}_2 \mathrm{OH}$, in which the mole fraction of solute is $0.125$. What mass of ethylene glycol, in grams, should you combine with $955 \mathrm{~g}$ of water? What is the molality of the solution?