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Unformatted text preview: Problems L Concentration Units 7.1 How many grams of w
solution by weight? 7.2 What is the molarity of a 2.12 mol kg solution is 1.30 g dm‘3. 7.3 Calculate the molality of a 1.50 M aqueous ethanol solution. The density of the solution is 0.980 g cm”.
7.4 The concentrated sulfuric acid we use in the laboratory is 98.0% sulfuric acid by weight. Calculate the molality and molarity of concentrated sulfuric acid if the density of the solution is 1.83 g cm‘3. 7.5 Convert a 0.25 mol kg"l sucrose solution into percent by weight. The density. of the solution is 1.2 g cm’3. 7.6 For dilute aqueous solutions in which the density of the solution is roughly equal to that of the
pure solvent, the molarity of the solution is equal to its molality. Show that this statement is correct for a 0.010 M aqueous urea [(NH2)2CO] solution. 7.7 The blood sugar (glucose) level of a diabetic patient is approximately 0.140 g of glucose/100 mL
of blood. Every time the patient ingests 40 g of glucose, her blood glucose level rises to
approximately 0.240 g/ 100 mL of blood. Calculate the number of moles of glucose per milliliter of blood and the total number of moles and grams of glucose in the blood before and after
consumption of glucose. (Assume that the total volume of blood in her body is 5.0 L.) 7.8 The strength of alcoholic beverages is usually described in terms of “proof,” which is deﬁned as
twice the percentage by volume of ethanol. Calculate the number of grams of alcohol in 2
quarts of 75proof gin. What is the molality of the gin? (The density of ethanol is 0.80 g cm‘3; 1 quart = 0.946 L.) ater must be added to 20.0 g of urea to prepare a 5.00% aqueous urea ‘1 aqueous sulfuric acid solution? The density of this Thermodynamics of Mixing 7.9 Liquids A and B form a nonideal solution. Provide a molecular interpretation for each of the
following situations: AmixH > 0, AmixH < 0, AmixV > 0, AmixV < 0. 7.10 Calculate the changes in entropy for the following processes: (a) mixing of 1 mole of nitrogen and 1 mole of oxygen, and (b) mixing of 2 moles of argon, 1 mole of helium, and 3 moles of
hydrogen. Both (a) and (b) are carried out under conditions of constant temperature (298 K) and constant pressure. Assume ideal behavior. 7.11 At 25 °C and 1 atm pressure, the absolute thirdlaw entropies of methane and ethane are
186.19 J K‘1 mol‘1 and 229.49 J K‘1 mol—1, respectively, in the gas phase. Calculate the
absolute thirdlaw entropy of a “solution” containing 1 mole of each gas. Assume ideal behavior. Henry’s Law 7.12 Prove the statement that an alternative way to express Henry’s law of gas solubility is to say that
the volume of gas that dissolves in a ﬁxed volume of solution is independent of pressure at a
given temperature. 7.13 A miner working 900 ft below the surface had a soft drink beverage during the lunch break. To
his surprise, the drink seemed very ﬂat (that is, not much effervescence was observed upon
removing the cap). Shortly after lunch, he took the elevator up to the surface. During the trip up, he felt a great urge to belch. Explain. 7.14 The Henry’s law constant of oxygen in water at 25 °C is 773 atm mol‘1 kg of water. Calculate
the molality of oxygen in water under a partial pressure of 0.20 atm. Assuming that the granaﬁmwiwmjw“was sum: 24:: 4;; , .1. up _ nng mammal...” mvmqw . Problems solubility of oxygen in blood at 37 °C is roughly the same as that in water at 25 °C, comment on
the prospect for our survival without hemoglobin molecules. (The total volume of blood in the
human body is about 5 L.) 7.15 The solubility of N2 in blood at 37 °C and a partial pressure of 0.80 atm is 5.6 x 10‘4 mol L“. A
deepsea diver breathes compressed air with a partial pressure of N2 equal to 4.0 atm. Assume
that the total volume of blood in the body is 5.0 L. Calculate the amount of N2 gas released (in liters) when the diver returns to the surface of water, where the partial pressure of N2 is
0.80 atm. J A Chemical Potential and Activity 7.16 Which of the following has a higher chemical potential? If neither, answer “same.” (a) H20(s) or
H20(l) at water’s normal melting point, (b) H20(s) at —5 °C and 1 bar or H20(l) at —5 °C and
1 bar, (c) benzene at 25 °C and 1 bar or benzene in a 0.1 M toluene solution in benzene at 25 °C
and 1 bar. 7.17 A solution of ethanol and npropanol behaves ideally. Calculate the chemical potential of
ethanol in solution relative to that of pure ethanol when its mole fraction is 0.40 at its boiling point (78.3 °C).
7.18 Derive the phase rule (Equation 6.23) in terms of chemical potentials. 7.19 The following data give the pressures for carbon disulﬁde—acetone solutions at 35.2 °C. Calculate
the activity coefﬁcients of both components based on deviations from Raoult’s law and Henry’s
law. (Hint: First determine Henry’s _1aw constants graphically.) xcsZ 0 0.20 0.45 0.67 0.83 1.00
Pcsz/torr ‘ 0 272 390 438 465 512
PCJHGO/torr 344 291 250 217 180 0 7.20 A solution is made up by dissolving 73 g of glucose (C6H1206; molar mass 180.2 g) in 966 g of
water. Calculate the activity coefﬁcient of glucose in this solution if the solution freezes at
*0.66 °C. 7.21 A certain dilute solution has an osmotic pressure of 12.2 atm at 20 °C. Calculate the difference
between the chemical potential of the solvent in the solution and that of pure water. Assume
that the density is the same as that of water. (Hint: Express the chemical potential in terms of
mole fraction, x1, and rewrite the osmotic pressure equation as 7rV = anT, where n2 is the
number of moles of the solute and V = l L.) 7.22 At 45 °C, the vapor pressure of water for a glucose solution in which the mole fraction of glucose
is 0.080 is 65.76 mmHg. Calculate the activity and activity coefﬁcient of the water in the
solution. The vapor pressure of pure water at 45 °C is 71.88 mmHg. 7.23 Consider a binary liquid mixture A and B, where A is volatile and B is nonvolatile. The
composition of the solution in terms of mole fraction is xA = 0.045 and x}; = 0.955. The vapor
pressure of A from the mixture is 5.60 man, and that of pure A is 196.4 mmHg at the same
temperature. Calculate the activity coeﬂicient of A at this concentration. Colligative Properties
7.24 List the important assumptions in the derivation of Equation 7.39. 7.25 Liquids A (bp = T 1:) and B (bp = T13) form an ideal solution. Predict the range of boiling points
of solutions formed by mixing different amounts of A and B. 7.26 A mixture of ethanol and npropanol behaves ideally at 36.4 °C. (a) Determine graphically the
mole fraction of npropanol in a mixture of ethanol and npropanol that boils at 36.4 °C and
72 mmHg. (b) What is the total vapor pressure over the mixture at 36.4°C when the mole 245 Chapter 7: Nonelectrolyte Solutions fraction of npropanol is 0.60? (c) Calculate the composition of the vapor in (b). (The
equilibrium vapor pressures of ethanol and npropanol at 36.4 0C are 108 mmHg and 40.0 mmHg, respectively.) 7.27 Two beakers, 1 and 2, containing 50 mL of 0.10 M urea and 50 mL of 0.20 M urea, respectively, are placed under a tightly sealed bell jar at 298 K. Calculate the mole fraction of urea in the
solutions at equilibrium. Assume ideal behavior. (Hint: Use Raoult’s law and note that at equilibrium, the mole fraction of urea is the same in both solutions.) awater is 22.98 mmHg. 3 7.28 At 298 K, the vapor pressure of pure water is 23.76 mmHg and that of se
(Hint: Sodium chloride Assuming that seawater contains only NaCl, estimate its concentration. is a strong electrolyte.) 7.29 Trees in cold climates may be subjected to temperatures as low as —60 °C. Estimate the
concentration of an aqueous solution in the body of the tree that would remain unfrozen at this temperature. Is this a reasonable concentration? Comment on your result. 7.30 Explain why jams can be stored under atmospheric conditions for long periods of time without spoilage.
7.31 Provide a molecular interpretation for the positive and negative deviations in the boilingpoint
curves and the formation of azeotropes. 7.32 The freezingpointdepression measurement of benzoic acid in acetone yields a molar mass of
122 g; the same measurement in benzene gives a value of 242 g. Account for this discrepancy. (Hint: Consider solvent—solute and solute—solute interactions.) 7.33 A common antifreeze for car radiators is ethylene glycol, CH2(OH)CH2(OH). How many
milliliters of this substance would you add to 6.5 L of water in the radiator if the coldest day in winter is —20 °C? Would you keep this substance in the radiator in the summer to prevent the
water from boiling? (The density and boiling point of ethylene glycol are 1.11 g cm‘3 and 470 K, respectively.)
7.34 For intravenous injections, great care is taken to ensure that the concentration of solutions to be injected is comparable to that of blood plasma. Why? 7.35 The tallest trees known are the redwoods in California. Assuming the height of a redwood to be
105 in (about 350 ft), estimate the osmotic pressure required to push water up from the roots to the treetop. 7.36 A mixture of liquids A and B exhibits ideal behavior. At 84°C, the total vapor pressure of a
solution containing 1.2 moles of A and 2.3 moles of B is 331 mmHg. Upon the addition of
another mole of B to the solution, the vapor pressure increases to 347 mmHg. Calculate the vapor pressures of pure A and B at 84°C. 7.37 Fish breathe the dissolved air in water through their gills. Assuming the partial pressures of
oxygen and nitrogen in air to be 0.20 atm and 0.80 atm, respectively, calculate the mole
fractions of oxygen and nitrogen in water at 298 K. Comment on your results. 7.38 Liquids A (molar mass 100 g mol“) and B (molar mass 110 g mol‘l) form an ideal solution. At
55 °C, A has a vapor pressure of 95 mmHg and B a vapor pressure of 42 mmHg. A solution is
prepared by mixing equal weights of A and B. (a) Calculate the mole fraction of each
component in the solution. (b) Calculate the partial pressures of A and B over the solution at
55 °C. (c) Suppose that some of the vapor described in (b) is condensed to a liquid. Calculate
the mole fraction of each component in this liquid and the vapor pressure of each component above this liquid at 55 °C. 7.39 Lysozyme extracted from chicken egg white has a molar mass of 13,930 g mol‘l. Exactly 0.1 g of
this protein is dissolved in 50 g of water at 298 K. Calculate the vapor pressure lowering, the depression in freezing point, the elevation of boiling point, and the osmotic pressure of this
solution. The vapor pressure of pure water at 298 K is 23.76 mmHg. 7.40 The following argument is frequently used to explain the fact that the vapor pressure of the
solvent is lower over a solution than over the pure solvent and that lowering is proportional to 7.41 7.42 7.43 7.44 7.45 7.46 7.47 7.48 Problems the concentration. A dynamic equilibrium exists in both cases, so that the rate at which
molecules of solvent evaporate from the liquid is always equal to that at which they condense.
The rate of condensation is proportional to the partial pressure of the vapor, whereas that of
evaporation is unimpaired in the pure solvent but is impaired by solute molecules in the surface
of the solution. Hence the rate of escape is reduced in proportion to the concentration of the
solute, and maintenance of equilibrium requires a corresponding lowering of the rate of
condensation and therefore of the partial pressure of the vapor phase. Explain why this
argument is incorrect. [Source K. J. Mysels, J. Chem. Educ. 32, 179 (1955).] A compound weighing 0.458 g is dissolved in 30.0 g of acetic acid. The freezing point of the
solution is found to be 1.50 K below that of the pure solvent. Calculate the molar mass of the
compound. Two aqueous urea solutions have osmotic pressures of 2.4 atm and 4.6 atm, respectively, at a
certain temperature. What is the osmotic pressure of a solution prepared by mixing equal
volumes of these two solutions at the same temperature? A forensic chemist is given a white powder for analysis. She dissolves 0.50 g of the substance in
8.0 g of benzene. The solution freezes at 3.9 °C. Can the chemist conclude that the compound is
cocaine (C17H21NO4)? What assumptions are made in the analysis? The freezing point of
benzene is 5.5 °C. “Timerelease” drugs have the advantage of releasing the drug to the body at a constant rate so
that the drug concentration at any time is not high enough to have harmful side eifects or so
low as to be ineffective. A schematic diagram of a pill that works on this basis is shown below.
Explain how it works. Elastic
impermeable
membrane Semipermeable
membrane\ Saturated
NaCl solution ' \Rigld wall
containing tiny holes A nonvolatile organic compound, Z, was used to make up two solutions. Solution A contains
5.00 g of Z dissolved in 100 g of water, and solution B contains 2.31 g of Z dissolved in 100 g of
benzene. Solution A has a vapor pressure of 754.5 mmHg at the normal boiling point of water,
and solution B has the same vapor pressure at the normal boiling point of benzene. Calculate
the molar mass of Z in solutions A and B, and account for the difference. Acetic acid is a polar molecule that can form hydrogen bonds with water molecules. Therefore, it
has a high solubility in water. Yet acetic acid is also soluble in benzene (C6H5), a nonpolar
solvent that lacks the ability to form hydrogen bonds. A solution of 3.8 g of CH3COOH in 80 g
C6H6 has a freezing point of 3.5 °C. Calculate the molar mass of the solute, and suggest what
its structure might be. (Hint: Acetic acid molecules can form hydrogen bonds among
themselves.) At 85 °C, the vapor pressure of A is 566 torr and that of B is 250 torr. Calculate the composition
of a mixture of A and B that boils at 85 °C when the pressure is 0.60 atm. Also, calculate the
composition of the vapor mixture. Assume ideal behavior. Comment on whether each of the following statements is true or false, and brieﬂy explain your
answer: (a) If one component of a solution obeys Raoult’s law, then the other component must
also obey the same law. (b) Intermolecular forces are small in ideal solutions. (c) When 15.0 mL
of an aqueous 3.0 M ethanol solution is mixed with 55.0 mL of an aqueous 3.0 M ethanol
solution, the total volume is 70.0 mL. 247 248 Chapter 7: Nonelectrolyte Solutions 7.49 Liquids A and B form an ideal solution at a certain temperature. The vapor pressures of pure A
and B are 450 torr and 732 torr, respectively, at this temperature. (a) A sample of the solution’s
vapor is condensed. Given that the original solution contains 3.3 moles of A and 8.7 moles of
B, calculate the composition of the condensate in mole fractions. (b) Suggest a method for
measuring the partial pressures of A and B at equilibrium. 7.50 Nonideal solutions are the result of unequal intermolecular forces between components. Based
on this knowledge, comment on whether a racemic mixture of a liquid compound would
behave as an ideal solution. 7.51 Calculate the molal boilingpoint elevation constant (Kb) for water. The molar enthalpy of
vaporization of water is 40.79 kJ mol‘1 at 100 °C. 7.52 Explain the following phenomena. (a) A cucumber placed in concentrated brine (saltwater)
shrivels into a pickle. (b) A carrot placed in fresh water swells in volume. Additional Problems 7.53 Calculate the change in the Gibbs energy at 37 °C when the human kidneys secrete 0.275 mole of
urea per kilogram of water from blood plasma to urine if the concentrations of urea in blood
plasma and urine are 0.005 mol kg‘1 and 0.326 mol kg“1, respectively. 7.54 (a) Which of the following expressions is incorrectas a representation of the partial molar
volume of component A in a twocomponent solution? Why? How would you correct it? (95) (aﬁ)
anA T.P,n3 axA T,P,XB (b) Given that the molar volume of this mixture (Vm) is given by
Vm = 0.34 + 3.6xAxB + 0.4xB(1— xA) Lmol—1 derive an expression for the partial molar volume for A at xA = 0.20. 7.55 The partial molar volumes for a benzene—carbon tetrachloride solution at 25 °C at a mole
fraction of 0.5 are: 7b = 0.106 L mol‘1 and 7c 2 0.100 L mol‘l, respectively, where the
subscripts b and c denote C6H6 and CCl4. (a) What is the volume of a solution made up of one
mole of each? (h) Given that the molar volumes are: C5H5 = 0.089 L mol‘1 and CC14 =
0.097 L mol“, what is the change in volume on mixing 1 mole each of C6H6 and CC14? (c) What can you deduce about the nature of intermolecular forces between C6H6 and CC14? 7.56 The osmotic pressure of poly(methyl methacrylate) in toluene has been measured at a series of
concentrations at 298 K. Determine graphically the molar mass of the polymer. n/atm 8.40 x 10—4 1.72 x 10—3 2.52 x 10‘3 3.23 X 10‘3 7.75 x 10‘3
c/g  L‘1 8.10 12.31 15.00 18.17 28.05 7.57 Benzene and toluene form an ideal solution. Prove that to achieve the maximum entropy of
mixing, the mole fraction of each component must be 0.5. 7.58 Suppose 2.6 moles of He at 0.80 atm and 25 °C are mixed with 4.1 moles of Ne at 2.7 atm and
25 °C. Calculate the Gibbs energy change for the process. Assume ideal behavior. 7.59 Two beakers are placed in a closed container. Beaker A initially contains 0.15 mole of
naphthalene (Cloﬂg) in 100 g of benzene (C6H6) and beaker B initially contains 31 g of an
unknown compound dissolved in 100 g of benzene. At equilibrium, beaker A is found to have
lost 7.0 g. Assuming ideal behavior, calculate the molar mass of the unknown compound. State
any assumptions made. ...
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 Fall '07
 MCCRACKEN

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