Chemistry: An Atoms-Focused Approach

Thomas R. Gilbert, Rein V. Kirss, Natalie Foster

Chapter 11

Properties of Solutions: Their Concentrations and Colligative Properties - all with Video Answers

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Chapter Questions

Problem 1

Figure P11.1 provides 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.
(IMAGE CANNOT COPY)
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 $X$

Shubham Kumar

Shubham Kumar

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Problem 2

Figure $\mathrm{P} 11.2$ provides a particle-level view of a sealed 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 X.
d. If $Y$ were not present, there would be fewer total particles in the gas above the liquid solution.
(IMAGE CANNOT COPY)

Anatole Borisov

Anatole Borisov

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Problem 3

Figure $\mathrm{P} 11.3$ provides particle-level views of $0.001 M$ aqueous solutions of the following four solutes: $\mathbf{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ $\mathrm{NaCl}, \mathrm{MgCl}_{2},$ and $\mathrm{K}_{3} \mathrm{PO}_{4} .$ The blue spheres represent
particles of solute. Which compounds are represented in images (a)-(d)?
(a)(IMAGE CANNOT COPY)
(b)(IMAGE CANNOT COPY)
(c)(IMAGE CANNOT COPY)
(d)(IMAGE CANNOT COPY)

Anatole Borisov

Anatole Borisov

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Problem 4

(IMAGE CANNOT COPY)
Which of the four solutions in Figure P11.3 has the highest (a) vapor pressure; (b) boiling point; (c) freezing point; (d) osmotic pressure compared to pure solvent?

Anatole Borisov

Anatole Borisov

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Problem 5

Use the graph in Figure $\mathrm{P} 11.5$ to estimate the normal boiling points of substances $\mathrm{X}$ and $\mathrm{Y}$. Molecules of which substance experience the stronger intermolecular forces?
(GRAPH CANNOT COPY)

Anatole Borisov

Anatole Borisov

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Problem 6

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 $P 11.6$ shows such a membrane separating fluids of various compositions.
a. In which direction does the water flow in each solution?
b. In which direction do the sodium ions flow in each solution?
c. In which direction do the potassium ions flow in each solution?
(I)(IMAGE CANNOT COPY)
(II)(IMAGE CANNOT COPY)

Anatole Borisov

Anatole Borisov

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Problem 7

The arrow in Figure $P 11.7$ indicates the direction of solvent flow through a semipermeable membrane in equipment designed to measure osmotic pressure. Which solution, $\mathrm{A}$ or $\mathrm{B},$ is the more concentrated? Explain your answer.
(FIGURE CANNOT COPY)

Anatole Borisov

Anatole Borisov

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Problem 8

Which of the images in Figure P11.8 represents the gas with the greatest Henry's law constant, $k_{\mathrm{H}} ?$
(a)(IMAGE CANNOT COPY)
(b)(IMAGE CANNOT COPY)
(c)(IMAGE CANNOT COPY)

Anatole Borisov

Anatole Borisov

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Problem 9

Which of the images in Figure $\mathrm{P} 11.9$ best describes the effect of pressure on the solubility of a gas?
(a)(IMAGE CANNOT COPY)
(b)(IMAGE CANNOT COPY)
(c)(IMAGE CANNOT COPY)

Anatole Borisov

Anatole Borisov

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Problem 10

Use representations [A] through [I] in Figure $P 11.10$ to answer questions a-f.
a. Which compound, $[\mathrm{B}],[\mathrm{C}],$ or $[\mathrm{F}]$ has the highest boiling point?
b. Between $[\mathrm{A}]$ and $[\mathrm{I}],$ which has the higher vapor pressure?
c. Between [A] and [I], which has the lower freezing point?
d. If solutions $[A]$ and [1] were separated by a semipermeable membrane, as shown in [E], what molecules or ions would flow across the membrane and in what direction?
e. Name two variables that could be changed to increase the solubility of the gas in [D].
f. Which beaker of water, $[\mathrm{G}]$ or $[\mathrm{H}]$, is at a lower temperature?
A (IMAGE CANNOT COPY)
B (IMAGE CANNOT COPY)
C (IMAGE CANNOT COPY)
D (IMAGE CANNOT COPY)
E (IMAGE CANNOT COPY)
F (IMAGE CANNOT COPY)
G (IMAGE CANNOT COPY)
H (IMAGE CANNOT COPY)
I (IMAGE CANNOT COPY)

Shubham Kumar

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Problem 11

What is a semipermeable membrane?

Charles Thomas

Numerade Educator

Problem 12

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 13

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 14

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

Allea Cauilan

Numerade Educator

Problem 15

What is reverse osmosis? List the basic components of equipment used to purify seawater by reverse osmosis.

Shubham Kumar

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Problem 16

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

Allea Cauilan

Numerade Educator

Problem 17

Why is it important to know if a substance is a strong electrolyte before predicting its effect on the osmotic pressure of a solution?

Anatole Borisov

Anatole Borisov

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Problem 18

Why is the van 't Hoff factor for solutions of acetic acid, $\mathrm{CH}_{3} \mathrm{COOH},$ slightly greater than 1 but far short of $i=2 ?$

Anatole Borisov

Anatole Borisov

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Problem 19

Why are theoretical and experimental van 't Hoff factors of electrolytes sometimes different?

Anatole Borisov

Anatole Borisov

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Problem 20

Can an experimentally measured value of a van 't Hoff factor be greater than the theoretical value? Why or why not?

Shubham Kumar

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Problem 21

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

Anatole Borisov

Anatole Borisov

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Problem 22

The following pairs of aqueous solutions are separated by
a semipermeable membrane. In which direction will the solvent flow?
a. $A=0.48 M N_{a} C l ; B=55.85 \mathrm{g}$ of $N a C 1$ 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 $6.56 \mathrm{mM} \mathrm{MgSO}_{4} ; \mathrm{B}=5.24 \mathrm{g}$ of
$\mathrm{MgCl}_{2}$ in $250 \mathrm{mL}$ of solution

Anatole Borisov

Anatole Borisov

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Problem 23

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 24

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 25

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 ethanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)$
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 $\mathrm{CaCl}_{2}, i=2.47$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 26

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 $\left[\mathrm{H}_{2} \mathrm{NC}(\mathrm{O}) \mathrm{NH}_{2}\right]$
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 $\mathrm{KI}, i=1.90$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 27

Which of the three curves of osmotic pressure versus temperature in Figure P11.27 represents a strong electrolyte if the concentrations of solutions $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$ are all $1.21 \times 10^{-5} \mathrm{MP}$
(GRAPH CANNOT COPY)

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 28

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 29

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

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 30

Alpetin is a compound found in Alpinia speciosa, a tropical evergreen used historically for treating cold, flu, fever, flatulence, and indigestion. A $54.1 \mathrm{mg}$ sample of alpetin is dissolved in $75.0 \mathrm{mL}$ of water. The osmotic pressure of the solution is 0.0657 atm at $27^{\circ} \mathrm{C}$ Assuming that alpetin is a nonelectrolyte, calculate the molar mass of alpetin.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 31

After $100.0 \mathrm{mL}$, of a solution of physiological saline $(0.90 \%$ 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 $37^{*} \mathrm{C} ?$ Assume that $\mathrm{NaCl}$ dissociates completely into $\mathrm{Na}^{+}(a q)$ and $\mathrm{Cl}^{+}(a q)$.

Anatole Borisov

Anatole Borisov

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Problem 32

An unknown compound $(152 \mathrm{mg})$ is dissolved in water to make $75.0 \mathrm{mL}$ of solution. The solution does not conduct electricity and has an osmotic pressure of
0.328 atm at $27^{\circ} \mathrm{C} .$ Elemental analysis reveals the substance to be $78.90 \% \mathrm{C}, 10.5996 \mathrm{H},$ and $10.5196 \mathrm{O}$.
Determine the molecular formula of this compound.

Anatole Borisov

Anatole Borisov

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Problem 33

Use kinetic molecular theory to explain why the vapor pressure of a liquid increases with increasing temperature.

Anatole Borisov

Anatole Borisov

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Problem 34

Why is the vapor pressure of neopentane (its condensed molecular structure is shown in Figure $P 11.34$ ) higher than that of pentane at the same temperature?
(FIGURE CANNOT COPY)

Anatole Borisov

Anatole Borisov

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Problem 35

Generally speaking, how is the vapor pressure of a liquid affected by the strength of intermolecular forces?

Anatole Borisov

Anatole Borisov

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Problem 36

Is vapor pressure an intensive or extensive property of a volatile substance?

Shubham Kumar

Numerade Educator

Problem 37

Rank the following compounds in order of increasing vapor pressure at $298 \mathrm{K}:$ (a) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH},$ (b) $\mathrm{CH}_{3} \mathrm{OCH}_{3},$ and
(c) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}$.

Vishal Sharma

Numerade Educator

Problem 38

Rank the compounds in Figure $\mathrm{P} 11.38$ in order of increasing vapor pressure at $298 \mathrm{K}$.
(a)(FIGURE CANNOT COPY)
(b)(FIGURE CANNOT COPY)
(c)(FIGURE CANNOT COPY)

Shubham Kumar

Numerade Educator

Problem 39

Pine Oil The smell of fresh-cut pine is due in part to the cyclic alkene pinene, whose carbon-skeleton structure is shown in Figure P11.39. Use the data in the table to calculate the heat of vaporization, $\Delta H_{\mathrm{vap}},$ of pinene.
(FIGURE and TABLE CAN'T COPY)

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 40

Almonds and Cherries Almonds and almond extracts are common ingredients in baked goods. Almonds contain the compound benzaldehyde (shown in Figure $\mathrm{P} 11.40$ ), which accounts for the odor of the nut. Benzaldehyde is also partly responsible for the aroma of cherries. Use the data in the table to calculate the heat of vaporization, $\Delta H_{\mathrm{vap}},$ of benzaldehyde.
(FIGURE and TABLE CAN'T COPY)

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 41

High-Octane Gasoline Gasoline is a complex mixture of hydrocarbons. It is sold with a variety of octane ratings that are based on the comparison of the gasoline with the combustion propertics of isooctanc, a compound with the molecular formula $\mathrm{C}_{8} \mathrm{H}_{18} .$ The Lewis structures of isooctane and another compound with molecular formula $\mathrm{C}_{8} \mathrm{H}_{18}$ are shown in Figure $\mathrm{P} 11.41,$ along with their
(FIGURE CANNOT COPY)
normal boiling points and heats of vaporization. Determine the vapor pressure of each isomer on a day when the temperature is $38^{\circ} \mathrm{C}$.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 42

Portable lanterns and stoves used for camping and backpacking often use a mixture of $\mathbf{C}_{5}$ and C hydrocarbons known as "white gas." Figure P11.42 shows the carbon-skeleton structure of pentane, $\mathrm{C}_{5} \mathrm{H}_{12},$ along with its normal boiling point and heat of vaporization. Determine the vapor pressure of pentane on a morning when the temperature is $5.0^{\circ} \mathrm{C}$.
(FIGURE CANNOT COPY)

Anatole Borisov

Anatole Borisov

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Problem 43

What physical property of the components of crude oil is used to separate them?

Anatole Borisov

Anatole Borisov

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Problem 44

What is the difference between simple distillation and fractional distillation?

Anatole Borisov

Anatole Borisov

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Problem 45

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 46

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

Anatole Borisov

Anatole Borisov

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Problem 47

At $20^{\circ} \mathrm{C},$ the vapor pressure of ethanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)$ is
45 torr and the vapor pressure of methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ 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?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 48

A bottle is half-filled with a 50: 50 (by moles) 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 octane 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.

Anatole Borisov

Anatole Borisov

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Problem 49

Explain how nearly all the water ends up in one compartment in Figure 11.17

Anatole Borisov

Anatole Borisov

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Problem 50

A dam separates the freshwater of the Charles River from the seawater of Boston Harbor. If the two bodies of water are at the same temperature, which one evaporates faster on
a hot summer day?

Shubham Kumar

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Problem 51

What is the difference between molarity and molality?

Amy Jiang

Numerade Educator

Problem 52

As a solution of NaCl becomes more concentrated, does the difference between its molarity and its molality increase or decrease?

Shubham Kumar

Numerade Educator

Problem 53

Why does seawater freeze at a lower temperature than normal saline?

Anatole Borisov

Anatole Borisov

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Problem 54

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 diet soft drinks freeze, rupturing many of the cans and causing an awful mess. However, none of the cans containing regular, nondiet soft drinks freeze and rupture. Why?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 55

A solution contains 3.5 mol of water and 1.5 mol of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right) .$ What is the mole fraction of water in the 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?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 56

A solution contains 4.5 mol of water, 0.3 mol of sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right),$ and 0.2 mol of glucose. Sucrose and glucose are nonvolatile. What is the mole fraction of water in the 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?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 57

Calculate the molality of each of the following solutions:
a. 0.875 mol of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ in $1.5 \mathrm{kg}$ of water
b. 11.5 mmol of acctic acid $\left(\mathrm{CH}_{3} \mathrm{COOH}\right)$ in $65 \mathrm{g}$ of water
c. 0.325 mol of baking soda $\left(\mathrm{NaHCO}_{3}\right)$ in $290.0 \mathrm{g}$ of water

Chareen Guzman

Numerade Educator

Problem 58

Calculate the molality of each of the following solutions:
a. $11.7 \mathrm{g}$ of $\mathrm{NaCl}$ in $1.0 \mathrm{kg}$ of water
b. $4.99 \mathrm{g}$ of $\mathrm{CuSO}_{4}$ in $265 \mathrm{g}$ of water
c. $6.41 \mathrm{g}$ of $\mathrm{CH}_{3} \mathrm{OH}$ in $375 \mathrm{g}$ of water

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 59

Calculate the molality of each of the following aqueous solutions:
a. $1.30 M \mathrm{CaCl}_{2}(d=1.113 \mathrm{g} / \mathrm{mL})$
b. $2.02 M$ fructose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}, d=1.139 \mathrm{g} / \mathrm{mL}\right)$
c. $8.94 M$ ethylene glycol (antifreeze, $\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}$, $d=1.069 \mathrm{g} / \mathrm{mL})$
d. $1.97 M$ LiCl $(d=1.046 \mathrm{g} / \mathrm{mL})$

Shubham Kumar

Numerade Educator

Problem 60

Table 8.1 lists molar concentrations of the major ions in seawater. Using a density of $1.025 \mathrm{g} / \mathrm{mL}$ for seawater, convert the concentrations into molalities.

Shubham Kumar

Numerade Educator

Problem 61

What mass of the following solutions contains 0.100 mol of solute? (a) $0.334 \mathrm{m} \mathrm{NH}_{4} \mathrm{NO}_{3} ;$ (b) $1.24 \mathrm{m}$ ethylene glycol, $\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH} ;(\mathrm{c}) 5.65 \mathrm{m} \mathrm{CaCl}_{2}$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 62

How many moles of solute are there in the following solutions?
a. $0.150 \mathrm{m}$ glucose solution made by dissolving the glucose
in $100.0 \mathrm{kg}$ of water
b. $0.028 m \mathrm{Na}_{2} \mathrm{CrO}_{4}$ solution made by dissolving the $\mathrm{Na}_{2} \mathrm{CrO}_{4}$ in $1000.0 \mathrm{g}$ of water
c. $0.100 \mathrm{m}$ urea solution made by dissolving the urea in $500.0 \mathrm{g}$ of water

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 63

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

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 64

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 65

Cinnamon owes its flavor and odor to cinnamaldehyde (C $_{9} \mathrm{H}_{8} \mathrm{O}$ ). Determine the freezing point of a solution of 75 mg of cinnamaldehyde dissolved in $1.00 \overline{\mathrm{g}}$ of benzene $\left(K_{f}=4.3^{\circ} \mathrm{C} / \mathrm{m} ; \text { normal freezing point }=5.5^{\circ} \mathrm{C}\right)$.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 66

Determine the boiling point elevation of a solution of 125 mg of carvone $\left(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O},$ 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 67

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 68

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

Allea Cauilan

Numerade Educator

Problem 69

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

Charles Thomas

Numerade Educator

Problem 70

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 71

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 72

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

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 73

Which one of the following aqueous solutions should have the highest boiling point: $0.0400 \mathrm{m} \mathrm{NH}_{4} \mathrm{NO}_{3}, 0.0165 \mathrm{m}$
LiCl, or $0.0105 \mathrm{m} \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} ?$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 74

Which one of the following aqueous solutions should have the lowest freezing point: $0.0500 \mathrm{m} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}, 0.0450 \mathrm{m}$
$\mathrm{NaI},$ or $0.0125 \mathrm{m} \mathrm{K}_{2} \mathrm{SO}_{4} ?$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 75

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

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 76

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

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 77

The freezing point of a solution prepared by dissolving 150 mg of caffeine in $10.0 \mathrm{g}$ of camphor is lower by $3.07^{\circ} \mathrm{C}$ than that of pure camphor $\left(K_{f}=39.7^{\circ} \mathrm{C} / \mathrm{m}\right)$
What is the molar mass of caffeine? Elemental analysis of caffeine yields the following results: $49.49 \%$ C, $5.15 \% \mathrm{H}$ $28.8796 \mathrm{N},$ and the remainder is $\mathrm{O} .$ What is the molecular formula of caffeine?

Shubham Kumar

Numerade Educator

Problem 78

One of the ingredients in the Native American stomachache remedy derived from common chokecherry is caffeic acid.
a. Combustion of 100 mg of caffeic acid yielded $220 \mathrm{mg}$ $\mathrm{CO}_{2}$ and $40.3 \mathrm{mg} \mathrm{H}_{2} \mathrm{O} .$ Determine the empirical formula of caffeic acid.
b. $A$ solution of $0.272 \mathrm{g}$ caffeic acid in $10.0 \mathrm{g}$ carbon tetrachloride causes the freezing point of the solution to decrease by $4.47^{\circ} \mathrm{C} .$ Given that $K_{\mathrm{f}}$ for $\mathrm{CCl}_{4}$ is $29.8^{\circ} \mathrm{C} / \mathrm{m}$
and that caffeic acid is a nonelectrolyte, calculate the molar mass and molecular formula of caffeic acid.

Shubham Kumar

Numerade Educator

Problem 79

Why is the Henry's law constant for $\mathrm{CO}_{2}$ so much larger than those for $\mathrm{N}_{2}$ and $\mathrm{O}_{2}$ at the same temperature? Hint:
Docs CO $_{2}$ react with water?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 80

The values of $k_{\mathrm{H}}$ for $\mathrm{NO}$ and $\mathrm{CO}$ gas in water at $20^{\circ} \mathrm{C}$ are $1.4 \times 10^{-3} \mathrm{M} / \mathrm{atm}$ and $7.4 \times 10^{-3} \mathrm{M} / \mathrm{atm},$ respectively.
Why is CO more soluble in water?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 81

As water in a beaker is heated, bubbles form inside the beaker at temperatures well below the boiling point of water. What gas is in the bubbles?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 82

Air is primarily a mixture of nitrogen and oxygen. Is the Henry's law constant for the solubility of air in water the sum of $k_{\mathrm{H}}$ for $\mathrm{N}_{2}$ and $k_{\mathrm{H}}$ for $\mathrm{O}_{2}$ ? Explain why or why not.

David Collins

Numerade Educator

Problem 83

Arterial blood contains about $0.25 \mathrm{g}$ of oxygen per liter at $37^{\circ} \mathrm{C}$ and standard atmospheric pressure. What is the Henry's law constant, in $\operatorname{mol} /(\mathrm{L} \cdot \mathrm{atm}),$ for $\mathrm{O}_{2}$ dissolution in blood at $37^{\circ} \mathrm{C} ?$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 84

Nitrous oxide, $\mathrm{N}_{2} \mathrm{O},$ is used in dental clinics as an anesthetic. The solubility of $\mathrm{N}_{2} \mathrm{O}$ in water is $1.1 \mathrm{g} / \mathrm{L}$ at an atmospheric pressure of 1 atm and a temperature
of $20^{\circ} \mathrm{C}$
a. Calculate the Henry's law constant of $\mathrm{N}_{2} \mathrm{O}$ at $20^{\circ} \mathrm{C}$.
b. Compare the value for $k_{\mathrm{H}}$ for $\mathrm{N}_{2} \mathrm{O}$ with the value for $\mathrm{O}_{2}$ in Table $11.1 .$ Why are they different?

Shubham Kumar

Numerade Educator

Problem 85

Use the Henry's law constant for $\mathrm{O}_{2}$ dissolved in arterial blood from Problem 11.83 to calculate the solubility of $\mathrm{O}_{2}$ in the blood of $(\mathrm{a}) \mathrm{a}$ climber on Mt. Everest $\left(P_{\text {atm }}=0.35 \text { atm }\right)$ and (b) a scuba diver breathing air at a depth of 20 meters $(P \approx 3.0 \text { atm })$.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 86

An air sample contains $1.89 \times 10^{-4} \%$ of methane gas (CH $_{4}$ ). The Henry's law constant for methane in water is approximately $1.3 \times 10^{-3} \mathrm{M}$ at $20^{\circ} \mathrm{C}$ and 1.0 atm.
a. Calculate the solubility of methane in water under a pure methane atmosphere of 1.0 atm.
b. Calculate the maximum solubility of the methane found in the air sample.

Shubham Kumar

Numerade Educator

Problem 87

Melting Ice $\mathrm{CaCl}_{2}$ is 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 $70.1 \mathrm{g} \mathrm{CaCl}_{2} / 100.0 \mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O}$
and that the van 't Hoff factor for a saturated solution of $\mathrm{CaCl}_{2}$ is 2.5.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 88

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 Ib 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.

Shubham Kumar

Numerade Educator

Problem 89

The freczing 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?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 90

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

Shubham Kumar

Numerade Educator

Problem 91

Eugenol is one of the compounds responsible for the flavor of cloves. A 111 mg sample of eugenol is dissolved in $1.00 \mathrm{g}$ of chloroform $\left(K_{\mathrm{b}}=3.63^{\circ} \mathrm{C} / \mathrm{m}\right)$
increasing the boiling point of chloroform by $2.45^{\circ} \mathrm{C}$ Calculate eugenol's molar mass. Eugenol is $73.17 \% \mathrm{C}$ $7.32 \% \mathrm{H},$ and $19.51 \% \mathrm{O}$ by mass. What is the molecular formula of eugenol?

Shubham Kumar

Numerade Educator

Problem 92

Suppose $100.0 \mathrm{mL}$ of $2.50 \mathrm{m} M \mathrm{NaCl}$ 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.

Shubham Kumar

Numerade Educator

Problem 93

A solution of 7.50 mg of a small protein in $5.00 \mathrm{mL}$ 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 94

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 allows small ions, urea, and water but not large protein molecules and cells 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 to those in blood?

Allea Cauilan

Numerade Educator

Problem 95

The Henry's law constant for the solubility of a gas and the van der Waal's constants $a$ and $b$ in Equation 10.27 depend on intermolecular forces. a. Plot the values of $a$ and $b$ in Table 10.5 as a function of
$k_{\mathrm{H}}(\text { Table } 11.1)$ for $\mathrm{He}, \mathrm{O}_{2}, \mathrm{N}_{2}, \mathrm{CH}_{4},$ and $\mathrm{CO}_{2} .$ Which
gas seems to be an outlicr?
b. Why might this gas be an outlier?

Narayan Hari

Numerade Educator

Problem 96

Xanthotoxin is a natural product extracted from the fruits of Heracleum persicum that seems to have some success in treating a skin discase known as psoriasis.
a. Combustion of $0.0100 \mathrm{g}$ of xanthotoxin in excess oxygen yielded $0.0244 \mathrm{g} \mathrm{CO}_{2}$ and $0.00333 \mathrm{g} \mathrm{H}_{2} \mathrm{O}$
Calculate the empirical formula of xanthotoxin.
b. A solution of $0.250 \mathrm{g}$ xanthotoxin in $10.0 \mathrm{g}$ carbon tetrachloride causes the freezing point of the solution to decrease by $3.46^{\circ} \mathrm{C} .$ Given that $K_{f}$ for $\mathrm{CCl}_{4}$ is $29.8^{\circ} \mathrm{C} / \mathrm{m}$ and that xanthotoxin is a nonelectrolyte, calculate the molar mass and molecular formula of xanthotoxin.

Shubham Kumar

Numerade Educator