Important ConceptsMolecular view of the solution processAttractive forces and randomness in the solution processSolubility related to attractive forcesConcentration units, particularly molarity and molalityColligative propertiesOsmotic pressure

Important EquationsM = moleslliter solutionm = moles/kg solvent!:J.T=-~m!:J.T=~mrrv= nRTd = grams/ern"

Practice ExercisesL

Multiple-ChoiceFor the first four problems below, one or more of the following responses willapply; each response may be used more than once or not at all in these questions.

I. osmotic pressureII. freezing-point depression

III. vapor pressureIV Raoult's lawV. Henry's law

1. Which of these best explains whya soda bottle fizzes when opened?

(A) I(B) II(C) III(D) IV(E) V

2. Which of these is the method ofchoice to determine the molecularmass of large biomolecules? _

(A) I(B) II(C) III(D) IV(E) V

3. Which two items are most closelyrelated to each other?

(A) I and III(B) II and V(C) III and IV(D) IV and V(E) V and I

4. The extent of ion pairing in asolution of an electrolyte can bebest estimated by using which ofthese?

(A) I and III -(B) II(C) III and V(D) IV(E) V

Solutions 343

Important Concepts

q

Solutions 343

Molecular view of the solution processAttractive forces and randomness in the solution processSolubility related to attractive forcesConcentration units, particularly molarity and molalityColligative propertiesOsmotic pressure

Important EquationsM = moleslliter solutionm = moles/kg solventIlT= -~mIlT= ~mIlV= nRTd = grams/ cm3

3. Which two items are most closelyrelated to each other?

Practice Exercises

For the first four problems below, one or more of the following responses willapply; each response may be used more than once or not at all in these questions.

Multiple-Choice

1. osmotic pressureII. freezing-point depression

III. vapor pressureIV Raoult's lawV Henry's law

1. Which of these best explains whya soda bottle fizzes when opened?

(A) I(B) II(C) III(D) IV(E) V

2. Which of these is the method ofchoice to determine the molecularmass of large biomolecules?

(A) I(B) II(C) III(D) IV(E) V

(A) I and III(B) II and V(C) III and IV(D) IV and V(E) V and I

4. The extent of ion pairing in asolution of an electrolyte can bebest estimated by using which ofthese?

(A) I and III .(B) II(C) III and V(D) IV(E) V

344 AP Chemistry

5. The solubility of cadmiumchloride, CdCl2, is 140 g per100 mL of solution. What is themolar solubility (molarity) of asaturated solution of CdCl2?

(A) 0.765 M(B) 1.31 M(C) 7.65 M(D) 12.61 M(E) 0.131 M

6. The vapor pressure of an idealsolution is 456 mm Hg. If thevapor pressure of the pure solvent

. is 832 mm Hg, what is the molefraction of the nonvolatile solute?

(A) 0.548(B) 0.354(C) 0.645(D) 1.82(E) 0.452

7. All of the following physicalproperties change as solute isadded to the solution. Which isleast likely to be used todetermine the molar mass of acompound?

(A) boiling point(B) surface tension(C) vapor pressure(D) melting point(E) osmotic pressure

8. Which of the following isexpected to be the most solublein hexane, C6H1i(A) KCl(B) C2H50H(C) C6H6(D) H20(E) HC2H302

9. Molarity units are mostappropriate in which of thefollowing experiments?

(A) freezing-point depression(B) vapor pressure(C) boiling-point elevation(D) surface tension(E) osmotic pressure

10. All of the following may be usedto determine molar masses.Which one requires an idealsolution for accurate results?

(A) freezing-point depression(B) boiling-point elevation(C) osmotic pressure(D) vapor pressure(E) gas density .

11. To make a solution, 3.45 mol ofC6H13Cland 1.26 mol of C5Hl2are mixed. Which of thefollowing is needed, but notreadily available, to calculate themolarity of this solution?

(A) the density of the solution(B) the densities of C6H13Cland,

C5Hl2(C) the temperature(D) the molar masses of C6H13Cl

and CSH12(E) the volumes of C6Hl3Cl and

CSH12

12. Which of the following, whenadded to 1.00 kg H20, isexpected to give the greatestincrease in the boiling point ofwater? (kb = 0.052 ~C m-1

)

(A) 1.25 mol sucrose(B) 0.25 mol iron(III) nitrate(C) 0.50 mol ammonium

chloride(D) 0.60 mol calcium sulfate(E) 1.00 mol ethanoic acid

13. Ethyl alcohol, C2H50H, andwater become noticeably warmerwhen mixed. This is due to

(A) the decrease in volume whenthey are mixed

(B) smaller attractive forces in themixture than in the pureliquids

(C) the hydrogen bonding of thetwo liquids

(D) the change in vapor pressureobserved

(E) stronger attractive forces inthe mixture than in the pureliquids

14. Which is the most appropriatemethod for determining the molarmass of a newly discoveredenzyme?

(A) freezing-point depression(B) osmotic pressure

measurements(C) boiling-point depression(D) gas density measurements(E) vapor pressure measurements

15. A polluted pond contains 25 ppbof lead ions. What is theconcentration of lead ions inmolarity units?

(A) 1.2 X 108 M(B) 1.2 X 10-7 M(C) 2.5 X 10-8 M '(D) 0.121 M(E) 1.2 X 10-10 M

16. When algae decay in a pond, theprocess uses up the availableoxygen. Which of the followingfactors will also contribute to adecrease in oxygen in a pond?

(A) decreasing salinity (saltconcentration)

(B) increasing acidity due to acidram

(C) increasing temperature(D) increasing surface tension of

the water(E) increasing atmospheric

pressure

17. Liquid A has a vapor pressure of437 mm Hg, and liquid B has avapor pressure of 0.880 atm at85 DC. Which of the followingrepresents a possible solution ofthe two liquids?

(A) a mixture with a vaporpressure of 345 mm Hg

(B) a mixture with a vaporpressure of 0.750 atm

(C) a mixture with a boiling pointof 165 DC

(D) a mixture with a vaporpressure of 1106 mm Hg

(E) a mixture with a boiling pointof 85 DC

18. The freezing-point-depressionconstant for water is 1.86 DC m-I.When 100 g of a compound isdissolved in 500 g H20, thefreezing point is -10.0 DC. Of thefive possibilities below, which isthe most reasonable identity of the

. compound?

(A) Mg(N03)2(B) KCI(C) Na2S04(D) HCOOH(E) HF

Solutions 345

346 AP Chemistry

19. Which of the followingcompounds is incorrectlyclassified?

(A) NaF is an electrolyte.(B) CH30H is a weak electrolyte.(C) Mg(C2H302) is an electrolyte.(D) CH/:::H2COOH is a weak

electrolyte.(E) glucose is a nonelectrolyte.

20. The kf and kb values for water are1.86 and 0.52 DCm-\ respectively.A solution boils at 107.5 DC.Atwhat temperature does thissolution freeze?

(A) 7.5 DC(B) -7.5 DC(C) 0.0 DC(D) -26.8 DC(E) -284.5 DC

21. If equal numbers of moles of eachof the following are dissolved in1 kg of distilled water, the onewith the lowest boiling pointwill be

(A) NaF(B) AlCl3(C) Mg(C2H302)2

(D) CH3CH2COOH(E) glucose

22. The solubility of acetylene,CHCH, in water at 30 DCis0.975 g L-l when the pressure ofacetylene is 1.00 atm. What is thesolubility, at the same temperature,when the pressure of acetyleneabove the water is reduced to0.212 atm?

(A) 4.60 g L-l

(B) 0.207 g L-l

(C) 0.975g L-l

(D) 0.212 g L-l

(E) The answer cannot bedetermined from the datagIven.

I CHALLENGE I23. When KCI dissolves in water, the

solution cools noticeably to thetouch. It may be concluded that

(A) the solvation energy is greaterthan the lattice energy

(B) KCI is relatively insoluble inwater

(C) the entropy decreases whenKCI dissolves

(D) the boiling point of thesolution will be less than100 DC

(E) the entropy increaseovercomes the unfavorableheat of dissolution

24. If 20.0 g of ethanol (molar mass= 46) and 30.0 g of water(molar mass = 18) are mixedtogether, the mole fraction ofethanol in this mixture is

(A) 0.207(B) 0.261(C) 0.739(D) 0.793(E) 4.83

I CHALLENGE I25. A 0.12% solution of a small

protein in water results in anosmotic pressure of 2.25 torr at4 DC.What is the molar mass ofthe protein?

(A) 922 g morl

(B) 12 g marl(C) 9.2 X 103 g marl(D) 135 g morl

(E) 9.3 x 105 g mol-l

382 AP Chemistry

4. A chemical system in equilibriumwill

Practice Exercises

Multiple-Choice

For the first three problems below, oneor more of the following responses willapply; each response may be used morethan once or not at all in thesequestions.

I.~II. 1\p

III. QIV 1(V Le Chatelier's principle

1. The effect of temperature on achemical system is best describedusmg

(A) I and III(B) II(C) III and V(D) IV(E) V

2. This is the correct term(s) to useto determine if a system has cometo equilibrium.

(A) I and III(B) II(C) III(D) IV(E) V

3. The term(s) most useful indetermining the solubility of asubstance is (are)

(A) I and III(B) II(C) III and V(D) IV(E) V

(A) have the same concentrationsof all products and reactants

(B) form more products if thetemperature is increased

(C) have a specific ratio of productto reactant concentrations

(D) not have any precipitates(E) represent a spontaneous

chemical process

5. Chemical equilibrium may be usedto describe

(A) gas phase chemical reactions(B) acid and base ionization(C) solubility(D) A and C(E) A, B, and C

6. For the following reaction:

which change will not be effectivein increasing the amount ofN204(g)?

(A) decreasing the volume of thereaction vessel

(B) increasing the temperature(C) adding N 2 to increase the

pressure(D) adsorbing the N204(g) with a

solid adsorbant(E) adding more N02(g) to the

reaction vessel

Chemical Equilibrium 383

8. The correct form of the solubilityproduct for silver chromate,Ag2Cr04, is

(A) [Ag+]2[CrOr](B) [Ag+][CrOt](C) [Ag+][CrOr]2(D) [Ag+]2[Cr02-]4(E) [Ag]2[Cr04]

7. The reaction

has an equilibrium constant of4.5 X 103 at a certain temperature.What is the equilibrium constantof

2N204(g) ~ 4N02(g)?

(A) 4.5 X 103

(B) 9.0 X 106

(C) 2.2 X 10-4

(D) 2.0 X 107

(E) 4.9 X 10-8

9. For which of the following will ~ = 1<?

(A) MgC03(s) + 2HCl(g) ~ MgCl2(s) + CO2 (g) + H20(l)(B) C(s) + 02(g) ~ CO2 (g)(C) CH4(g) + 302(g) ~ CO2(g) + 2H20(g)(D) Zn(s) + 2HCl(aq) ~ H2(g) + ZnCl2(aq)(E) 2N02(g) + 02(g) ~ N205(g)

10. Which is an appropriate formulation of the equilibrium expression for thereaction

MgC03 (s)+ 2HCl(g) ~ MgCl2 (s) + CO2 (g) + H20(l)?

(A) [C02]

[HCl]

(B) [MgCl2] [C02] [H20][HClf[MgC03]

(C) [HClf[MgC03]

[MgCl2] [C02] [H20]

(D) [C02]

[HCl]2

(E) [C02] [H20][HClf

384 AP Chemistry

11. In the reaction

2HI(g) ~ Hz (g) + Iz(g)

the equilibrium constant is 0.020.If 0.200 mol of HI is placed in a10.0-L flask, how many moles ofIz(g) will be in the flask whenequilibrium is reached?

(A) 0.022(B) 0.025(C) 0.0022(D) 2.2(E) 0.0025

12. For the reaction

~ = 8.8 when pressures aremeasured in atmospheres. Underwhich of the following conditionswill the reaction proceed in theforward direction?

13. The solubility product of Pbl, is7.9 X 10-9• What is the molarsolubility of PbI2 in distilled water?

(A) 2.0 X 10-3

(B) 1.25 X 10-3

(C) 5.0 X 10-4

(D) 8.9 X 10-5

(E) 7.9 X 10-3

14. The solubility of gold(II!) chlorideis 1.00 X 10-4 g L-I. What is thesolubility product of AuCl3 (molarmass = 303)?

(A) 1.00 X 10-16

(B) 2.7 X 10-15

(C) 1.2 X 10-26

(D) 3.2 X 10-25

(E) 9.6 X 10-25

(A) 0.200 atm(B) 250 mm Hg(C) 0.00255 atm(D) 46.5 mm Hg(E) 0.138 atm

0.352 atm400mmHg0.000134 atm82.3 mm Hg0.764 atm

15. If units were used with the equilibrium constant, 1(, for the followingreaction:

they would be

(A) lvi2(B) M2

(C) M• (D) lvil

(E) M3

16. Which of the following CANNOTaffect the extent of reaction?

(A) changing the temperature(B) adding a catalyst(C) increasing the amounts of

reactants(D) removing some product(E) changing the volume

17. In which of the following cases isthe reaction expected to beexothermic?

(A) Increasing the pressureincreases the amount ofproduct formed.

(B) Increasing the amount ofreactants increases the amountof product formed.

(C) Increasing the temperatureincreases the amount ofproduct formed.

(D) Increasing the volumedecreases the amount ofproduct formed.

(E) Increasing the temperaturedecreases the amount ofproduct formed.

18. A reaction has a very largeequilibrium constant of 3.3 X 1013.

Which statement is NOT trueabout this reaction?

(A) The reaction is very fast.(B) The reaction is essentially

complete.(C) The reaction is spontaneous.(D) The equilibrium constant will

change if the temperature ischanged.

(E) The products will react toyield very little reactant.

Chemical Equilibrium 385

19. The f\p of AgCl is 1.8 X 10-10, and

the f\p of AgI is 8.3 X 10-17• Asolution is 0.100 M in 1- and Cl.What is the molarity of iodide ionswhen AgCl just starts toprecipitate?

(A) 1.0 X 10-5

(B) 9.1 X 10-9

(C) 8.3 X 10-7

(D) 4.6 x 10-8

(E) 1.2 x 104

20. One liter of solution contains2.4 X 10-3 mol of sulfate ions.What is the molar solubilityof BaSO4 in this solution?(f\p = 1.1 x 10-10 for BaS04.)

(A) 1.05 X 10-5

(B) 1.1 X 10-9

(C) 2.6 X 10-13

(D) 2.2 X 107

(E) 4.6 X 10-8

I CHALLENGE I21. The equilibrium constant for the

reaction

H2 (g) + 12 (g) ~ 2HI(g)

must be determined. If 1.00 g ofHI is placed in a 2.00-L flask,which of the following is LEASTimportant in determining theequilibrium constant?

(A) The temperature must remainconstant at the desired value.

(B) Several measurements must bemade to assure that thereactionis at equilibrium.

(C) Only one of the threeconcentrations needs to beaccurately determined.

(D) All three concentrations mustbe accurately measured.

(E) The original mass and volumeof the flask must be accuratelymeasured.

386 AP Chemistry

I CHALLENGE I22. In an experiment 0.0300 mol each of S03(g), S02(g), and 02(g) were placed

in a 1O.0-Lflask at a certain temperature. When the reaction came toequilibrium, the concentration of S02(g) in the flask was 3.50 X 10-5 M.What is I( for the reaction

(A) 3.5·x 10-5(B) 1.9 x 107

(C) 5.2 X 10-8

(D) 1.2 x 10-9

(E) 8.2 x 108

23. The weak acid H~ ionizes in two steps with these equilibrium constants:

H2A ----'" H+ + HA-~l = 2.3 xfO-4~

HA-2 ----'" H+ + A2- ~2 = 4.5 X 10-7~

What is the equilibrium constant for the reaction:

H2A ~ 2H+ +A2-

(A) 6.8 x 10-11

(B) 1.0 x 10-10

(C) 2.3045 X 10-4

(D) 2.0 x 10-3

(E) 5.1 x 102

ANSWER KEY

1. E 6. C 11. A 16. B 21. D2. C 7. E 12. B 17. E 22. B3. B 8. A 13. B 18. A 23. B4. C 9. B 14. D 19. D5. E 10. D 15. D 20. E

See Appendix 1 for explanations of answers.

Free-ResponseUse the principles and techniques of chemical equilibrium to answer the followingquestions.

(a) The solubility product of HgI2 is 1.1 X 10-28.(i) What is the molar solubility of HgI2?(ii) What is the molar solubility if HgI2 is dissolved in 0.00025 molar NaI

solution?