Chemistry The Science in Context

Thomas R. Gilbert

Chapter 11

Solutions: Properties and Behavior - all with Video Answers

Educators

AZ

Chapter Questions

Problem 1

Figure P11.1 shows a particle-level view of a sealed container partially filled with a solution that has two components: $X$ (blue spheres) and $Y$ (red spheres). Which of the following statements about substances $X$ and $Y$ are true?
a. $X$ is the solvent in this solution.
b. Pure $Y$ is a volatile liquid.
c. If $Y$ were not present, there would be fewer X particles in the gas above the liquid solution.
d. The presence of $Y$ increases the vapor pressure of $X$.

AZ

Alison Zhitkov

Numerade Educator

Problem 2

Figure $\mathrm{P} 11.2$ shows a particle-level vicw of a scaled container partially filled with a solution of two miscible liquids: X (blue spheres) and $Y$ (red spheres). Which of the following statements about substances $\mathrm{X}$ and $\mathrm{Y}$ are true?
a. Y is the solvent in this solution.
b. Pure $Y$ has a higher vapor pressure than pure X.
c. The presence of $Y$ in the solution lowers the vapor pressure of $\mathrm{X}$.
d. If $Y$ were not present, there would be fewer total particles in the gas above the liquid solution.

Allea Cauilan

Numerade Educator

Problem 3

Figure $P 11.3$ shows particle-level vicws of $0.001 M$ aqueous solutions of the following four solutes: $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}, \mathrm{NaCl}$ $\mathrm{MgCl}_{2},$ and $\mathrm{K}_{3} \mathrm{PO}_{4} .$ The blue spheres represent particles of solute.
a. Which compounds are represented in images (I)-(IV)?
b. Which of the four solutions in Figure $P 11.3$ has the highest (i) vapor pressure; (ii) boiling point; (iii) freezing point; (iv) osmotic pressure?

Charles Thomas

Numerade Educator

Problem 4

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?

Allea Cauilan

Numerade Educator

Problem 5

The graph in Figure $P 11.5$ shows the decrease in the freezing point of water $\Delta T_{\mathrm{f}}$ for solutions of two different substances, A (triangles) and B (circles), in water. Explain how you can reasonably conclude that (a) $\mathrm{A}$ and $\mathrm{B}$ are nonelectrolytes and (b) the freezing point depression constant $K_{\mathrm{f}}$ of water is independent of the solute's identity.

Charles Thomas

Numerade Educator

Problem 6

The arrow in Figure P11.6 indicates the direction of solvent flow through a semipermeable membrane in equipment designed to measure osmotic pressure. Which solution, A or B, is more concentrated? Explain your answer.

Allea Cauilan

Numerade Educator

Problem 7

Kidney Dialysis Semipermeable membranes of the sort used in kidney dialysis do not allow large molecules and cells to pass but do allow small ions and water to pass. Figure $P 11.7$ shows such a membrane separating fluids of various compositions.
a. In which direction does the water
flow in each apparatus?
b. In which direction do sodium ions Aow in each apparatus?
c. In which direction do the potassium ions flow in each apparatus?

AZ

Alison Zhitkov

Numerade Educator

Problem 8

Use representations [A] through [I] in Figure P11.8 to answer questions a-f about the formation of an aqueous solution of potassium chloride from potassium $[\mathrm{K}(s),$ purple spheres] and chlorine $\left[\mathrm{Cl}_{2}(g),$ green spheres]. \right.
a. Which process depicts the formation of a compound from its elements?
b. Which processes require the breaking of bonds?
c. Which processes depict transfer of electrons?
d. Which representation illustrates ion-dipole interactions?
e. Which processes require the input of energy to overcome intermolecular forces?
F. Which processes are exothermic?

Allea Cauilan

Numerade Educator

Problem 9

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

AZ

Alison Zhitkov

Numerade Educator

Problem 10

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

Allea Cauilan

Numerade Educator

Problem 11

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

Charles Thomas

Numerade Educator

Problem 12

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

Allea Cauilan

Numerade Educator

Problem 13

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

Charles Thomas

Numerade Educator

Problem 14

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

Allea Cauilan

Numerade Educator

Problem 15

Which has the higher melting point, LiF or MgO?

Charles Thomas

Numerade Educator

Problem 16

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

Allea Cauilan

Numerade Educator

Problem 17

Define the terms in the relation $\Delta H_{\text {tolution }}=\Delta H_{\text {hrdration }}-U$

Charles Thomas

Numerade Educator

Problem 18

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

Allea Cauilan

Numerade Educator

Problem 19

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?

Charles Thomas

Numerade Educator

Problem 20

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

Allea Cauilan

Numerade Educator

Problem 21

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 $\mathrm{X} ?$

AZ

Alison Zhitkov

Numerade Educator

Problem 22

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 $\mathrm{SrI}_{2}$

Allea Cauilan

Numerade Educator

Problem 23

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) $\mathrm{Mg} \mathrm{F}_{2}$

Charles Thomas

Numerade Educator

Problem 24

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

Allea Cauilan

Numerade Educator

Problem 25

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 $\mathrm{K}(s)+\frac{1}{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{KCl}(s)=-438 \mathrm{kJ} / \mathrm{mol}$

Charles Thomas

Numerade Educator

Problem 26

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 $\mathrm{Na}(s)=109 \mathrm{~kJ} / \mathrm{mol}$
$$
\begin{aligned}
&\text { Bond energy of } \mathrm{O}_{2}(g)=499 \mathrm{~kJ} / \mathrm{mol}\\
&\Delta H_{\mathrm{f}} \text { for } 2 \mathrm{Na}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{Na}_{2} \mathrm{O}(s)=-416 \mathrm{~kJ} / \mathrm{mol}
\end{aligned}
$$

Allea Cauilan

Numerade Educator

Problem 27

Using the values in Table 11.4 and $\Delta H_{\text {rolution }}=19.9 \mathrm{kJ} / \mathrm{mol}$ for KBr, calculate the lattice energy of KBr.

Charles Thomas

Numerade Educator

Problem 28

Using the values in Table 11.4 and $\Delta H_{\text {solution }}=-17.7 \mathrm{kJ} / \mathrm{mol}$ for KF, calculate the lattice energy of KF.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 29

Explain the term nonvolatile solute.

Charles Thomas

Numerade Educator

Problem 30

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

Allea Cauilan

Numerade Educator

Problem 31

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

Charles Thomas

Numerade Educator

Problem 32

In the experiment shown in Figure 11.7 , the vapor pressure of one of the solutions remains constant throughout the experiment, whereas the vapor pressure of the other solution changes. Which solution is which?

Allea Cauilan

Numerade Educator

Problem 33

An experiment like that shown in Figure 11.7 is set up with the compartment containing pure ethanol full to the brim and the compartment containing a solution of sugar in ethanol half-full. Explain why the compartment that contains the ethanol-sugar solution will eventually overflow.

Charles Thomas

Numerade Educator

Problem 34

Explain to a nonscientist how the water gets from one compartment to the other in the experiment depicted in Figure 11.7

Allea Cauilan

Numerade Educator

Problem 35

A solution contains 3.5 moles of water and 1.5 moles of nonvolatile glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right) .$ What is the mole fraction of water in this solution? What is the vapor pressure of the solution at $25^{\circ} \mathrm{C},$ given that the vapor pressure of pure water at $25^{\circ} \mathrm{C}$ is 23.8 torr?

Charles Thomas

Numerade Educator

Problem 36

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?

Allea Cauilan

Numerade Educator

Problem 37

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.

Charles Thomas

Numerade Educator

Problem 38

Use the statement of Raoult's law in Problem 11.37 to determine the mole fraction of glucose in Problem 11.35

Allea Cauilan

Numerade Educator

Problem 39

In an equimolar mixture of $\mathrm{C}_{5} \mathrm{H}_{12}$ and $\mathrm{C}_{7} \mathrm{H}_{16},$ which compound is present in higher concentration in the vapor above the solution?

Charles Thomas

Numerade Educator

Problem 40

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

Allea Cauilan

Numerade Educator

Problem 41

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.

Charles Thomas

Numerade Educator

Problem 42

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

Allea Cauilan

Numerade Educator

Problem 43

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?

Charles Thomas

Numerade Educator

Problem 44

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 $90^{\circ} \mathrm{C} ?$

Allea Cauilan

Numerade Educator

Problem 45

The mixture described in Problem 11.44 is separated by fractional distillation at reduced pressure so that it begins to boil when the solution in the distillation flask reaches $90^{\circ} \mathrm{C}$
a. What is the ratio of ethylbenzene to styrene in the vapor phase as the mixture first begins to boil?
b. What will be the temperature of the first distillate that comes off the top of the column? (i) lower than $90^{\circ} \mathrm{C}$
(ii) $90^{\circ} \mathrm{C}$
(iii) higher than $90^{\circ} \mathrm{C}$

Charles Thomas

Numerade Educator

Problem 46

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.

Allea Cauilan

Numerade Educator

Problem 47

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

Charles Thomas

Numerade Educator

Problem 48

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?

Allea Cauilan

Numerade Educator

Problem 49

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.

Charles Thomas

Numerade Educator

Problem 50

Diet Soft Drinks The thermostat in a refrigerator filled with cans of soft drinks malfunctions and the temperature of the refrigerator drops below $0^{\circ} \mathrm{C}$. The contents of the cans of dict soft drinks freeze, rupturing many of the cans and causing an awful mess. However, none of the cans containing reqular, nondiet soft drinks rupture. Why?

Allea Cauilan

Numerade Educator

Problem 51

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?

Charles Thomas

Numerade Educator

Problem 52

Refer to the phase diagram in Figure 11.17 and explain in your own words why the change in the vapor pressure of a solution caused by a nonvolatile solute results in a higher boiling point and a lower melting point.

Allea Cauilan

Numerade Educator

Problem 53

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.

Charles Thomas

Numerade Educator

Problem 54

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

Allea Cauilan

Numerade Educator

Problem 55

What is a semipermeable membrane?

Charles Thomas

Numerade Educator

Problem 56

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?

Allea Cauilan

Numerade Educator

Problem 57

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?

Charles Thomas

Numerade Educator

Problem 58

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

Allea Cauilan

Numerade Educator

Problem 59

Explain the principle of reverse osmosis.

Charles Thomas

Numerade Educator

Problem 60

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

Allea Cauilan

Numerade Educator

Problem 61

Aqueous solutions of physiological saline (NaCl) and dextrose (glucose) are used to deliver intravenous medications. Why must their molar concentrations differ by a factor of two?

Charles Thomas

Numerade Educator

Problem 62

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

Allea Cauilan

Numerade Educator

Problem 63

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

Charles Thomas

Numerade Educator

Problem 64

Table 4.1 lists molaritics of major ions in seawater. Using a density of $1.022 \mathrm{g} / \mathrm{mL}$ for seawater, convert the concentrations into molalities.

Charles Thomas

Numerade Educator

Problem 65

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, $\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH} ;(\mathrm{c}) 1.07 \mathrm{m} \mathrm{CaCl}_{2}$

Charles Thomas

Numerade Educator

Problem 66

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

Allea Cauilan

Numerade Educator

Problem 67

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 $1.00 \mathrm{g} / \mathrm{mL}$

Charles Thomas

Numerade Educator

Problem 68

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.

Allea Cauilan

Numerade Educator

Problem 69

Cinnamon Cinnamon owes its flavor and odor to cinnamaldehyde (C $_{9} \mathrm{H}_{8} \mathrm{O}$ ). Determine the boiling point clevation of a solution of 100 mg of cinnamaldehyde dissolved in $1.00 \mathrm{g}$ of carbon tetrachloride $\left(K_{\mathrm{b}}=5.02^{\circ} \mathrm{C} / \mathrm{m}\right)$

Charles Thomas

Numerade Educator

Problem 70

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 $\left(K_{\mathrm{b}}=2.34^{\circ} \mathrm{C} / \mathrm{m}\right)$

Allea Cauilan

Numerade Educator

Problem 71

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

Charles Thomas

Numerade Educator

Problem 72

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

Allea Cauilan

Numerade Educator

Problem 73

Saccharin Determine the melting point of an aqueous solution made by adding $186 \mathrm{mg}$ of saccharin $\left(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{NS}\right)$
to $\left.1.00 \mathrm{mL} \text { of water (density }=1.00 \mathrm{g} / \mathrm{mL}, K_{f}=1.86^{\circ} \mathrm{C} / \mathrm{m}\right)$

Charles Thomas

Numerade Educator

Problem 74

Determine the boiling point of an aqueous solution that is $2.50 \mathrm{m}$ ethylene glycol $\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right) ; K_{\mathrm{b}}$ for water
is $0.52^{\circ} \mathrm{C} / \mathrm{m} .$ Assume that the boiling point of pure water is $100.00^{\circ} \mathrm{C}$

Allea Cauilan

Numerade Educator

Problem 75

Which aqueous solution has the lowest freezing point:
$0.5 \mathrm{m}$ glucose, $0.5 \mathrm{m} \mathrm{NaCl},$ or $0.5 \mathrm{m} \mathrm{CaCl}_{2} ?$

Charles Thomas

Numerade Educator

Problem 76

Which aqueous solution has the highest boiling point:
$0.5 \mathrm{m}$ methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right), 0.5 \mathrm{m} \mathrm{KI},$ or $0.5 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4} ?$

Allea Cauilan

Numerade Educator

Problem 77

Which of the following aqueous solutions should have the highest boiling point: $0.0200 \mathrm{m}$ ethanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)$ $0.0125 \mathrm{m} \mathrm{LiClO}_{4},$ or $0.0100 \mathrm{m} \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2} ?$

Charles Thomas

Numerade Educator

Problem 78

Which of the following aqueous solutions should have the lowest freezing point: $0.0500 \mathrm{m} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}, 0.0300 \mathrm{m} \mathrm{KBr}$
or $0.0150 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4} ?$

Allea Cauilan

Numerade Educator

Problem 79

Arrange the following aqueous solutions in order of increasing boiling point:
a. $0.06 \mathrm{m} \mathrm{FeCl}_{3}(i=3.4)$
b. $0.10 m \mathrm{MgCl}_{2}(i=2.7)$
c. $0.20 \mathrm{m} \mathrm{KCl}(i=1.9)$

Charles Thomas

Numerade Educator

Problem 80

Arrange the following solutions in order of increasing freezing point depression:
a. $0.10 \mathrm{m} \mathrm{MgCl}_{2}$ in water, $i=2.7, K_{f}=1.86^{\circ} \mathrm{C} / \mathrm{m}$
b. $0.20 \mathrm{m}$ toluene in diethyl ether, $i=1.00, K_{f}=$ $1.79^{\circ} \mathrm{C} / \mathrm{m}$
c. $0.20 \mathrm{m}$ ethylene glycol in ethanol, $i=1.00, K_{\mathrm{f}}=$ $1.99^{\circ} \mathrm{C} / \mathrm{m}$

Allea Cauilan

Numerade Educator

Problem 81

The following pairs of aqueous solutions are scparated by
a semipermeable membrane. In which direction will the solvent flow?
a. $A=1.25 M N_{a} C l ; B=1.50 M K C l$
b. $A=3.45 M C a C l_{2} ; B=3.45 M_{a} B_{r}$
c. $A=4.68 M$ glucose; $B=3.00 M N a C 1$

Charles Thomas

Numerade Educator

Problem 82

The following pairs of aqueous solutions are separated by
a semipermeable membrane. In which direction will the solvent flow?
a. $A=1.00 \mathrm{L}$ of $0.48 M \mathrm{NaCl} ; \mathrm{B}=55.85 \mathrm{g}$ of $\mathrm{NaCl}$
dissolved in $1.00 \mathrm{L}$ of solution
b. $A=100 \mathrm{mL}$ of $0.982 M \mathrm{CaCl}_{2} ; \mathrm{B}=16 \mathrm{g}$ of $\mathrm{NaCl}$ in
$100 \mathrm{mL}$ of solution
c. $A=100 \mathrm{mL}$ of $6.56 \mathrm{m} M \mathrm{MgSO}_{4} ; \mathrm{B}=5.24 \mathrm{g}$ of $\mathrm{Mg} \mathrm{Cl}_{2}$
in 250 mL of solution

Allea Cauilan

Numerade Educator

Problem 83

Calculate the osmotic pressure of each of the following aqueous solutions at $20^{\circ} \mathrm{C}:$
a. $2.39 M$ methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$
b. $9.45 \mathrm{mM} \mathrm{MgCl}_{2}$
c. $40.0 \mathrm{mL}$ of glycerol $\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right)$ in $250.0 \mathrm{mL}$ of aqueous solution (density of glycerol $=1.265 \mathrm{g} / \mathrm{mL}$ )
d. $25 \mathrm{g}$ of $\mathrm{CaCl}_{2}$ in $350 \mathrm{mL}$ of solution

Charles Thomas

Numerade Educator

Problem 84

Calculate the osmotic pressure of each of the following aqueous solutions at $27^{\circ} \mathrm{C}$
a. $10.0 \mathrm{g}$ of $\mathrm{NaCl}$ in $1.50 \mathrm{L}$ of solution
b. $10.0 \mathrm{mg} / \mathrm{L}$ of $\mathrm{LiNO}_{3}$
c. $0.222 M$ glucose
d. $0.00764 M \mathrm{K}_{2} \mathrm{SO}_{4}$

Allea Cauilan

Numerade Educator

Problem 85

Determine the molarity of each of the following solutions from its osmotic pressure at $25^{\circ} \mathrm{C} .$ Include the van 't Hoff factor for the solution when the factor is given.
a. $\Pi=0.674$ atm for a solution of cthanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)$
b. $I I=0.0271$ atm for a solution of aspirin $\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)$
c. $\Pi=0.605$ atm for a solution of $\mathrm{CaCl}_{2}, i=2.47$

Charles Thomas

Numerade Educator

Problem 86

Determine the molarity of each of the following solutions from its osmotic pressure at $25^{\circ} \mathrm{C} .$ Include the van 't Hoff factor for the solution when the factor is given.
a. $\Pi=0.0259$ atm for a solution of urea $\left[\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\right]$
b. $\Pi=1.56$ atm for a solution of sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$
c. $\Pi=0.697$ atm for a solution of $\mathrm{KI}, i=1.90$

Allea Cauilan

Numerade Educator

Problem 87

Is the following statement true or false? For solutions of the same reverse osmotic pressure at the same temperature, the molarity of a solution of NaCl will always be less than the molarity of a solution of $\mathrm{CaCl}_{2} .$ Explain your answer.

Charles Thomas

Numerade Educator

Problem 88

Suppose you have $1.00 M$ aqueous solutions of each of the following solutes: glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right), \mathrm{NaCl},$ and acetic acid (CH $_{3} \mathrm{COOH}$ ). Which solution has the highest pressure requirement for reverse osmosis?

Allea Cauilan

Numerade Educator

Problem 89

What cffect does dissolving a solute have on the following properties of a solvent? (a) its osmotic pressure; (b) its freezing point; (c) its boiling point

Charles Thomas

Numerade Educator

Problem 90

How can measurements of osmotic pressure, freezing point depression, and boiling point elevation be used to find the molar mass of a solute? Why are such determinations usually carried out on molecular substances as opposed to ionic ones?

Allea Cauilan

Numerade Educator

Problem 91

Throat Lozenges A 188 -mg sample of a nonelectrolyte isolated from throat lozenges was dissolved in enough water to make $10.0 \mathrm{mL}$ of solution at $25^{\circ} \mathrm{C} .$ The osmotic pressure of the resulting solution was 4.89 atm. Calculate the molar mass of the compound.

Charles Thomas

Numerade Educator

Problem 92

Antibiotic An unknown compound $(27.40 \mathrm{mg})$ with antibiotic properties was dissolved in water to make $100.0 \mathrm{mL}$ of solution. The solution did not conduct clectricity and had an osmotic pressure of 9.94 torr at $23.6^{\circ} \mathrm{C} .$ Elemental analysis revealed the substance to

Allea Cauilan

Numerade Educator

Problem 93

Cloves Eugenol is one of the compounds responsible for the flavor of cloves. A 111 -mg sample of eugenol was dissolved in $1.00 \mathrm{g}$ of chloroform $\left(K_{\mathrm{b}} 53.63^{\circ} \mathrm{C} / \mathrm{m}\right),$ increasing the boiling point of the chloroform by $2.45^{\circ} \mathrm{C} .$ Calculate eugenol's molar mass. Eugenol is $73.1796 \mathrm{C}, 7.32 \%$ H, and $19.51 \%$ O by mass. What is the molecular formula of eugenol?

Charles Thomas

Numerade Educator

Problem 94

Caffeine The freezing point of a solution prepared by dissolving 150 mg of caffeine in $10.0 \mathrm{g}$ of camphor is lower than that of pure camphor $\left(K_{f}=39.7^{\circ} \mathrm{C} / \mathrm{m}\right)$ by $3.07^{\circ} \mathrm{C}$
What is the molar mass of caffeine? Elemental analysis of caffeine yields the following results: $49.49 \%$ C $, 5.15 \% \mathrm{H}$ $28.87 \% N,$ and the remainder O. What is the molecular formula of caffeine?

Allea Cauilan

Numerade Educator

Problem 95

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

Charles Thomas

Numerade Educator

Problem 96

Explain why the boiling point of pure sodium chloride is much higher than the boiling point of an aqueous solution of sodium chloride.

Allea Cauilan

Numerade Educator

Problem 97

Melting lce $\mathrm{CaCl}_{2}$ is often used to melt ice on sidewalks. Could $\mathrm{CaCl}_{2}$ melt ice at $-20^{\circ} \mathrm{C}$ ? Assume that the solubility of $\mathrm{CaCl}_{2}$ at this temperature is $70.1 \mathrm{g}$ of $\mathrm{CaCl}_{2} / 100.0 \mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O}$ and that the van 't Hoff factor for a saturated solution of $\mathrm{CaCl}_{2}$ is 2.5

Charles Thomas

Numerade Educator

Problem 98

Making Ice Cream A mixture of table salt and ice is used to chill the contents of hand-operated ice-cream makers. What is the melting point of a mixture of 2.00 lb of $\mathrm{NaCl}$ and 12.00 lb of ice if exactly half of the ice melts? Assume that all the NaCl dissolves in the melted ice and that the van 't Hoff factor for the resulting solution is 1.44

Allea Cauilan

Numerade Educator

Problem 99

The freezing points of $0.0935 \mathrm{m}$ ammonium chloride and $0.0378 \mathrm{m}$ ammonium sulfate in water were found to be $-0.322^{\circ} \mathrm{C}$ and $-0.173^{\circ} \mathrm{C},$ respectively. What are the values of the van 't Hoff factors for these salts?

Charles Thomas

Numerade Educator

Problem 100

The following data were collected for three compounds in aqueous solution. Determine the value of the van 't Hoff factor for each salt $\left(K_{f} \text { for water }=1.86^{\circ} \mathrm{C} / \mathrm{m}\right)$

Allea Cauilan

Numerade Educator

Problem 101

Physiological Saline One hundred milliliters of a solution of physiological saline $(0.92 \%$ NaCl by mass) is diluted by the addition of $250.0 \mathrm{mL}$ of water. What is the osmotic pressure of the final solution at $37^{\circ} \mathrm{C} ?$ Assume that $\mathrm{NaCl}$ dissociates completely into $\mathrm{Na}^{+}(a q)$ and $\mathrm{Cl}^{-}(a q)$

Charles Thomas

Numerade Educator

Problem 102

One hundred milliliters of $2.50 \mathrm{mM} \mathrm{NaCl}$ is mixed with $80.0 \mathrm{mL}$ of $3.60 \mathrm{mM} \mathrm{MgCl}_{2}$ at $20^{\circ} \mathrm{C} .$ Calculate the
osmotic pressure of each starting solution and that of the mixture, assuming that the volumes are additive and that both salts dissociate completely into their component ions.

Allea Cauilan

Numerade Educator

Problem 103

A solution of 7.50 mg of a small protein in 5.00 mL of aqueous solution has an osmotic pressure of 6.50 torr at $23.1^{\circ} \mathrm{C} .$ What is the molar mass of the protein?

Charles Thomas

Numerade Educator

Problem 104

Kidney Dialysis Hemodialysis, a method of removing waste products from the blood if the kidneys have failed, uses a tube made of a cellulose membrane that is immersed in a large volume of aqueous solution. Blood is pumped through the tube and is then returned to the patient's vein. The membrane does not allow passage of large protein molecules and cells but does allow small ions, urea, and water to pass through it. Assume that a physician wants to decrease the concentration of sodium ion and urea in a patient's blood while maintaining the concentration of potassium ion and chloride ion in the blood. What materials must be dissolved in the aqueous solution in which the dialysis tube is immersed? How must the concentrations of ions in the immersion fluid compare with those in blood?

Allea Cauilan

Numerade Educator

Problem 105

IN Solution Another solution used clinically in the hospital setting for IV administration is Ringer's lactate,
a solution of sodium, potassium, and calcium cations and chloride and lactate anions. This solution is isotonic with
0.996 saline and D5W described in Section $11.5 .$ Write a mathematical statement that indicates the relationship between the concentrations of cations and anions in this solution compared with $0.9 \%$ saline.

Charles Thomas

Numerade Educator

Problem 106

Injections The injection of pharmaceutical solutions that are hypertonic in relation to human plasma can cause considerable pain at the site of injection. Why?

Allea Cauilan

Numerade Educator