Chapter 12

Why do two gases spontaneously mix when they are brought into contact?

When substances form liquid solutions, what two factors are involved in determining the solubility of the solute in the solvent?

Methanol, \(\mathrm{CH}_{3} \mathrm{OH},\) and water are miscible in all proportions. What does this mean? Explain how the OH unit in methanol contributes to this.

Hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) and water are immiscible. What does this mean? Explain why they are immiscible in terms of structural features of their molecules and the forces of attraction between them.

Explain how ion-dipole forces help to bring potassium chloride into solution in water.

Explain why potassium chloride will not dissolve in carbon tetrachloride, \(\mathrm{CCl}_{4}\)

Water and dichloromethane, \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\), are immiscible; however, when enough methanol is added, the three are soluble in each other. What properties of methanol allows the three liquids to form a homogeneous mixture?

Which would be expected to have the larger hydration energy, \(\mathrm{Al}^{3+}\) or \(\mathrm{Li}^{+}\) ? Why? (Both ions are about the same size.)

Suggest a reason why the value of \(\Delta H_{\text {soln }}\) for a gas such as \(\mathrm{CO}_{2},\) dissolving in water, is negative.

The value of \(\Delta H_{\text {saln }}\) for the formation of an acetonewater solution is negative. Explain this in general terms using intermolecular forces of attraction.

The value of \(\Delta H_{\text {soln }}\) for the formation of an ethanolhexane solution is positive. Explain this in general terms that involve intermolecular forces of attraction.

When a certain solid dissolves in water, the solution becomes cool. Is \(\Delta H_{\text {waln }}\) for this solute positive or negative? Explain your reasoning. Is the solubility of this substance likely to increase or decrease with increasing temperature? Explain your answer using Le Châtelier's principle.

If the value of \(\Delta H_{\text {saln }}\) for the formation of a mixture of two liquids \(A\) and \(B\) is zero, what does this imply about the relative strengths of \(A-A, B-B,\) and \(A-B\) intermolecular attractions?

What is Henry's law?

Mountain streams often contain fewer living things than equivalent streams at sea level. Give one reason why this might be true in terms of oxygen solubilities at different pressures.

Why does a bottled carbonated beverage fizz when you take the cap off?

Write the definition for each of the following concentration units: (a) mole fraction, (b) mole percent, (c) molality, (d) percent by mass. What are the maximum possible values for the units in (a), (b), and (d)?

Suppose a \(1.0 \mathrm{~m}\) solution of a solute is made using a solvent with a density of \(1.15 \mathrm{~g} / \mathrm{mL}\). Will the molarity of this solution be numerically larger or smaller than 1.0 ? Justify your conclusion mathematically.

What specific fact about a physical property of a solution must be true to call it a colligative property?

Why does a nonvolatile solute decrease the vapor pressure of a solvent?

When octane is mixed with methanol, the vapor pressure of the octane over the solution is higher than what we would calculate using Raoult's law. Why? Explain the discrepancy in terms of intermolecular attractions.

Will a solution of pentane and hexane have an ideal Raoult's law vapor pressure curve? Explain your answer in terms of intermolecular attractions.

Explain why a nonvolatile solute dissolved in water makes the system have (a) a higher boiling point than water, and \((b)\) a lower freezing point than water.

What is the key difference between dialyzing and osmotic membranes?

At a molecular level, explain why, in osmosis, there is a net migration of solvent from the side of the membrane less concentrated in solute to the side more concentrated in solute.

Two glucose solutions of unequal molarity are separated by an osmotic membrane. Which solution will lose water, the one with the higher molarity or the one with the lower molarity?

What is the difference berween a bypertonic solution and a hypotonic solution?

Why are colligative properties of solutions of ionic compounds usually more pronounced than those of solutions of molecular compounds of the same molalities?

What is the van't Hoff factor? What is its expected value for all nondissociating molecular solutes? If its measured value is slightly larger than 1.0 , what does this suggest about the solute? What is suggested by a van't Hoff factor of approximately \(0.5 ?\)

Which aqueous solution, if either, is likely to have the higher boiling point, \(0.50 \mathrm{~m} \mathrm{Nal}\) or \(0.50 \mathrm{~m} \mathrm{Na}_{2} \mathrm{CO}_{3} ?\)

What is the Tyndall effect?

What is a micelle, and why does it form?

For an ionic compound dissolving in water, \(\Delta H_{\text {soln }}=\) \(-56 \mathrm{k} \mathrm{J} \mathrm{mol}^{-1}\) and the hydration energy is \(-894 \mathrm{~kJ} \mathrm{~mol}^{-1}\) Estimate the lattice energy of the ionic compound.

Consider the formation of a solution of aqueous potassium chloride. Write the thermochemical equations for (a) the conversion of solid KCl into its gaseous ions and (b) the subsequent formation of the solution by hydration of the ions. The lattice energy of \(\mathrm{KCl}\) is \(-715 \mathrm{~kJ} \mathrm{~mol}^{-1}\), and the hydration energy of the ions is \(-686 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Calculate the enthalpy of solution of \(\mathrm{KCl}\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\)

If the solubility of a gas in water is \(0.010 \mathrm{~g} \mathrm{~L}^{-1}\) at \(25^{\circ} \mathrm{C}\) with the partial pressure of the gas 1. 0 atm, predict the solubility of the gas at the same temperature but at double the pressure.

At 740 torr and \(20.0^{\circ} \mathrm{C}\), nitrogen has a solubility in water of \(0.018 \mathrm{~g} \mathrm{~L}^{-1}\). At 620 torr and \(20.0{ }^{\circ} \mathrm{C}\), its solubility is \(0.015 \mathrm{~g} \mathrm{~L}^{-1}\). Show that nitrogen obeys Henry's law.

Hydrogen gas has a solubility in water of \(0.00157 \mathrm{~g} \mathrm{~L}^{-1}\) under 1.00 atm of \(H_{2}\) pressure at \(25^{\circ} \mathrm{C}\). At 0.85 atm and \(25^{\circ} \mathrm{C}\), its solubility is \(0.00133 \mathrm{~g} \mathrm{~L}^{-1}\). Does hydrogen gas obey Henry's law?

Helium gas can be used to displace other gases from a solvent by bubbling He through the solvent, a process called sparging, and leaving an atmosphere of helium above the solvent. At 760 torr of He, the concentration of He in water is \(0.00148 \mathrm{~g} \mathrm{~L}^{-1}\) at \(298 \mathrm{~K}\). What is Henry's law constant for \(\mathrm{He}\) at \(298 \mathrm{~K} ?\)

Muriatic acid is the commercial name for hydrochloric acid that can be purchased from hardware stores as a solution that is \(30 \%(\mathrm{w} / \mathrm{w}) \mathrm{HCl}\). What mass of this solution contains \(7.5 \mathrm{~g}\) of \(\mathrm{HCl}\) ?

Hydrofluoric acid dissolves glass and must be stored in plastic containers. What mass of a \(45 \%(\mathrm{w} / \mathrm{w})\) solution of \(\mathrm{HF}(a q)\) contains \(1.5 \mathrm{~g}\) of \(\mathrm{HF}\) ?

In order to conduct three experiments that required different amounts of chloride ions, what mass of a \(0.150 \mathrm{~m}\) \(\mathrm{NaCl}\) solution is needed to obtain (a) \(0.00100 \mathrm{~mol} \mathrm{Cl}^{-}\) (b) \(0.00500 \mathrm{~mol} \mathrm{Cl}\), (c) \(0.0200 \mathrm{~mol} \mathrm{Cl}^{-}\) ?

What is the molality of \(\mathrm{NaCl}\) in a solution that is \(3.000 \mathrm{M}\) \(\mathrm{NaCl}\), with a density of \(1.07 \mathrm{~g} \mathrm{~mL}^{-1}\) ?

The mole fraction of neon in the air is about \(2.6 \times 10^{-5}\). If the average molar mass of air is \(28.96 \mathrm{~g} / \mathrm{mol}\), what is the concentration of neon in air in \(\mathrm{ppm}\) ?

A solution of fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) a sugar found in many fruits, is made by dissolving \(24.0 \mathrm{~g}\) of fructose in \(1.00 \mathrm{~kg}\) of water. For this solution, what are (a) the molal con- centration, (b) the mole fraction, (c) the mass percent, and (d) the molarity of fructose if the density of the solution is \(1.0078 \mathrm{~g} / \mathrm{mL}\)

If you dissolved \(11.5 \mathrm{~g}\) of \(\mathrm{NaCl}\) in \(1.00 \mathrm{~kg}\) of water, \((\mathrm{a})\) what would be its molal concentration? (b) What are the mass percent \(\mathrm{NaCl}\) and the mole percent \(\mathrm{NaCl}\) in the solution? The volume of this solution is virtually identical to the original volume of the \(1.00 \mathrm{~kg}\) of water. (c) What is the molar concentration of \(\mathrm{NaCl}\) in this solution? (d) What would have to be true about any solvent for one of its dilute solutions to have essentially the same molar and molal concentrations?

In an aqueous solution of sulfuric acid, the concentration is \(1.89 \mathrm{~mol} \%\) of acid. The density of the solution is \(1.0645 \mathrm{~g} \mathrm{~mL}^{-1}\). Calculate the following: (a) the molal concentration of \(\mathrm{H}_{2} \mathrm{SO}_{4},\) (b) the mass percent of the acid, and (c) the molarity of the solution.

At \(25^{\circ} \mathrm{C}\) the vapor pressures of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) and toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right)\) are 93.4 and 26.9 torr, respectively. A solution made by mixing \(35.0 \mathrm{~g}\) of benzene and \(65.0 \mathrm{~g}\) of toluene is prepared. What is the vapor pressure of this solution?

A solution containing \(8.3 \mathrm{~g}\) of a nonvolatile, nondissociating substance dissolved in \(1.00 \mathrm{~mol}\) of chloroform, \(\mathrm{CHCl}_{3},\) has a vapor pressure of 511 torr. The vapor pressure of pure \(\mathrm{CHCl}_{3}\) at the same temperature is 526 torr. Calculate (a) the mole fraction of the solute, (b) the number of moles of solute in the solution, and (c) the molecular mass of the solute.

At \(21.0^{\circ} \mathrm{C},\) a solution of \(18.26 \mathrm{~g}\) of a nonvolatile, nonpolar compound in \(33.25 \mathrm{~g}\) of ethyl bromide, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}\), had a vapor pressure of 336.0 torr. The vapor pressure of pure ethyl bromide at this temperature is 400.0 torr. Assuming an ideal solution, what is the molecular mass of the compound?

(a) Show that the following equation is true. Molar mass of solute \(=\frac{\text { (grams of solute) } R T}{\Pi \mathrm{V}}\) (b) An aqueous solution of a compound with a very high molecular mass was prepared in a concentration of \(2.0 \mathrm{~g} \mathrm{~L}^{-1}\) at \(25^{\circ} \mathrm{C}\). Its osmotic pressure was 0.021 torr. Calculate the molecular mass of the compound.