Chapter 11

The graph in Figure P11.4 describes the volume of distillate collected during the fractional distillation of a liquid. Answer the following questions about the process: (a) Is the sample a pure liquid or a mixture? (b) If it is a mixture: (i) how many components are in the mixture? (ii) What are the relative ratios of the volumes in the mixture? (iii) What are their approximate boiling points?

Indicate the substance that contains the largest anion. (a) \(\mathrm{BaCl}_{2} ;\) (b) \(\mathrm{AlF}_{3} ;\) (c) \(\mathrm{KI} ;\) (d) \(\mathrm{SrBr}_{2}\)

Indicate the substance that contains the smallest cation. (a) \(\mathrm{BaCl}_{2} ;\) (b) \(\mathrm{Al}_{2} \mathrm{O}_{3} ;\) (c) \(\mathrm{Mg}_{3} \mathrm{N}_{2} ;\) (d) SrS

Why is CaSO, less soluble in water than \(\mathrm{NaCl}\) ?

Does the strength of an ion-ion attraction depend on the number of ions in the compound? Explain your answer.

Rank the following ionic compounds in order of increasing attraction between their ions: \(\mathrm{KBr}, \mathrm{SrBr}_{2}, \mathrm{CsBr}\).

Rank the following ionic compounds in order of increasing attraction between their ions: \(\mathrm{BaO}, \mathrm{BaCl}_{2}, \mathrm{CaO}\)

Which has the higher melting point, LiF or MgO?

Which has the higher boiling point, \(\mathrm{NaCl}\) or \(\mathrm{CaCl}_{2}\) ?

Explain why trends in lattice energies for ionic compounds parallel trends in melting points and are opposite to the trends in water solubility.

In the formula \(U=k Q_{1} Q_{2} / d\) for the different lattice energies of a pair of ionic compounds such as LiCl and MgO, which factor dominates- -the charge product \(Q_{1} Q_{2}\) or the distance \(d\) between the ion nuclei?

Explain why it might be difficult to measure the enthalpy of hydration of a single ion.

How do the melting points of the series of sodium halides \(\mathrm{NaX}(\mathrm{X}=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I})\) relate to the atomic number of \(\mathrm{X} ?\)

Rank the following ionic compounds in order of (a) increasing melting point and (b) increasing water solubility: \(\mathrm{BaF}_{2}, \mathrm{CaCl}_{2}, \mathrm{MgBr}_{2},\) and \(\mathrm{SrI}_{2}\)

Which substance has the least negative lattice energy? (a) \(\mathrm{Mg} \mathrm{I}_{2} ;\) (b) \(\mathrm{MgBr}_{2} ;\) (c) \(\mathrm{Mg} \mathrm{Cl}_{2} ;\) (d) \(\mathrm{Mg} \mathrm{F}_{2}\)

Rank the following from lowest to highest lattice energy: \(\mathrm{NaBr}, \mathrm{MgBr}_{2}, \mathrm{CaBr}_{2},\) and \(\mathrm{KBr}\)

Use a Born-Haber cycle to calculate the lattice energy of potassium chloride (KC1) from the following data: Ionization energy of \(\mathrm{K}(g)=425 \mathrm{kJ} / \mathrm{mol}\) Electron affinity of \(\mathrm{Cl}(g)=-349 \mathrm{kJ} / \mathrm{mol}\) Energy to sublime \(\mathrm{K}(s)=89 \mathrm{kJ} / \mathrm{mol}\) Bond energy of \(\mathrm{Cl}_{2}(g)=240 \mathrm{kJ} / \mathrm{mol}\) \(\Delta H_{f}\) for \(\mathrm{K}(s)+\frac{1}{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{KCl}(s)=-438 \mathrm{kJ} / \mathrm{mol}\)

Calculate the lattice energy of sodium oxide \(\left(\mathrm{Na}_{2} \mathrm{O}\right)\) from the following data: Ionization energy of \(\mathrm{Na}(g)=495 \mathrm{~kJ} / \mathrm{mol}\) Electron affinity of \(\mathrm{O}(g)\) for 2 electrons \(=603 \mathrm{~kJ} / \mathrm{mol}\) Energy to sublime \(\mathrm{Na}(s)=109 \mathrm{~kJ} / \mathrm{mol}\) $$ \begin{aligned} &\text { Bond energy of } \mathrm{O}_{2}(g)=499 \mathrm{~kJ} / \mathrm{mol}\\\ &\Delta H_{\mathrm{f}} \text { for } 2 \mathrm{Na}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{Na}_{2} \mathrm{O}(s)=-416 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$

Explain the term nonvolatile solute.

Which has the higher vapor pressure at constant temperature, pure water or seawater? Explain your answer.

Why does the vapor pressure of a liquid increase with increasing temperature?

A solution contains 4.5 moles of water, 0.3 moles of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right),\) and 0.2 moles of glucose. Sucrose and glucose are nonvolatile. What is the mole fraction of water in this solution? What is the vapor pressure of the solution at \(35^{\circ} \mathrm{C},\) given that the vapor pressure of pure water at \(35^{\circ} \mathrm{C}\) is 42.2 torr?

Another way of stating Raoult's law is that the fractional lowering of the vapor pressure of a solvent \(\left(P_{\text {solicat }}^{*}-P_{\text {solicant }}\right)^{\prime}\) \(P_{\text {solvent }}^{o l}\) is equal to the mole fraction of the solute, \(X_{\text {soluter }} .\) Use Equation 11.6 to show that this is true.

Why does the boiling point of a mixture of volatile hydrocarbons increase over time during a simple distillation?

Would you expect a solution of cyclohexane, \(\mathrm{C}_{6} \mathrm{H}_{12},\) in benzenc, \(\mathrm{C}_{6} \mathrm{H}_{6},\) to behave ideally? Explain your answer.

Explain the origin of negative deviations from Raoult's law for the predicted vapor pressure of a solution of two volatile liquids.

At \(20^{\circ} \mathrm{C},\) the vapor pressure of cthanol is 45 torr and the vapor pressure of methanol is 92 torr. What is the vapor pressure at \(20^{\circ} \mathrm{C}\) of a solution prepared by mixing \(25 \mathrm{g}\) of methanol and \(75 \mathrm{g}\) of ethanol?

At \(90^{\circ} \mathrm{C},\) the vapor pressure of styrene \(\left(\mathrm{C}_{8} \mathrm{H}_{8}\right)\) is 134 torr and that of ethylbenzene \(\left(\mathrm{C}_{8} \mathrm{H}_{10}\right)\) is 183 torr. What is the vapor pressure of a solution of \(38 \%\) by weight styrene and \(62 \%\) by weight ethylbenzene at \(90^{\circ} \mathrm{C} ?\)

A bottle is half-filled with a 50: 50 (mole-to-mole) mixture of heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}\right)\) and octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) at \(25^{\circ} \mathrm{C} .\) What is the mole ratio of heptane vapor to octanc vapor in the air space above the liquid in the bottle? The vapor pressures of heptane and octane at \(25^{\circ} \mathrm{C}\) are 31 torr and 11 torr, respectively.

Explain why freezing point depression, boiling point clevation, and the osmotic pressure of ionic solutes cannot be used to measure their formula masses.

What is the definition of the concentration scale called molality that is used to determine the molar mass of a nonvolatile solute by measuring the solute's effect on the freezing and boiling points of the solvent? Why must a mass- based concentration scale and not molarity be used?

As a solution of \(\mathrm{NaCl}\) is heated from \(5^{\circ} \mathrm{C}\) to \(90^{\circ} \mathrm{C},\) does the difference between its molarity and its molality increase or decrease? Explain your answer.

Why is it important to know if a substance is a molecular compound or an ionic compound before predicting its effect on the boiling and freczing points of a solvent?

Explain how the theoretical value of the van 't Hoff factor i for substances such as \(\mathrm{CH}_{3} \mathrm{OH}, \mathrm{NaBr},\) and \(\mathrm{K}_{2} \mathrm{SO}_{4}\) can be predicted from their formulas.

Is it possible for an experimentally measured value of a van 't Hoff factor to be greater than the theoretical value? Explain your answer.

What is a semipermeable membrane?

A pure solvent is separated from a solution containing the same solvent by a semipermeable membrane. In which direction does the solvent flow across the membrane, and why?

A dilute solution is separated from a more concentrated solution containing the same solvent by a semipermeable membrane. In which direction does the solvent tend to flow across the membrane, and why?

How is the osmotic pressure of a solution related to its molar concentration and its temperature?

Explain the principle of reverse osmosis.

Explain how the minimum pressure for purification of seawater by reverse osmosis can be estimated from its composition.

Why do red blood cells undergo hemolysis when they are placed in pure water?

Calculate the molality of each of the following solutions: a. 0.433 mol of sucrose \(\left(C_{12} H_{22} O_{11}\right)\) in 2.1 kg of water b. 71.5 mmol of acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) in \(125 \mathrm{g}\) of water c. 0.165 mol of baking soda \(\left(\mathrm{NaHCO}_{3}\right)\) in \(375.0 \mathrm{g}\) of water

What mass of the following solutions contains 0.100 mol of solute? (a) \(0.135 \mathrm{m} \mathrm{NH}_{4} \mathrm{NO}_{3} ;\) (b) \(3.92 \mathrm{m}\) ethylene glycol, \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH} ;(\mathrm{c}) 1.07 \mathrm{m} \mathrm{CaCl}_{2}\)

How many moles of solute are there in the following solutions? a. \(0.750 \mathrm{m}\) glucose solution made by dissolving the glucose in \(10.0 \mathrm{kg}\) of water b. \(0.183 \mathrm{m} \mathrm{Na}_{2} \mathrm{CrO}_{4}\) solution made by dissolving the \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) in \(900.0 \mathrm{g}\) of water c. \(1.425 \mathrm{m}\) urea solution made by dissolving the urea in \(750.0 \mathrm{g}\) of water

Fish Kills High concentrations of ammonia (NH \(_{3}\) ), nitrite ion, and nitrate ion in water can kill fish. Lethal concentrations of these species for rainbow trout are \(1.1 \mathrm{mg} / \mathrm{L}, 0.40 \mathrm{mg} / \mathrm{L},\) and \(1361 \mathrm{mg} / \mathrm{L},\) respectively. Express these concentrations in molality units, assuming a solution density of \(1.00 \mathrm{g} / \mathrm{mL}\)

The concentrations of six important elements in a sample of river water are \(0.050 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Al}^{3+}, 0.040 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Fe}^{3+}, 13.4 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Ca}^{2+}, 5.2 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Na}^{+}, 1.3 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{K}^{+}\), and \(3.4 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Mg}^{2+} .\) Express each of these concentrations in molality units.

Spearmint Determine the boiling point elevation of a solution of 125 mg of carvone \(\left(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O}, \text { oil of spearmint }\right)\) dissolved in \(1.50 \mathrm{g}\) of carbon disulfide \(\left(K_{\mathrm{b}}=2.34^{\circ} \mathrm{C} / \mathrm{m}\right)\)

What molality of a nonvolatile, nonelectrolyte solute is needed to lower the melting point of camphor by \(1.000^{\circ} \mathrm{C}\) \(\left(K_{f}=39.7^{\circ} \mathrm{C} / m\right) ?\)

What molality of a nonvolatile, nonelectrolyte solute is needed to raise the boiling point of water by \(7.60^{\circ} \mathrm{C}\) \(\left(K_{\mathrm{b}}=0.52^{\circ} \mathrm{C} / m\right) ?\)