Chemistry
`
`The Central Science
`Eighth Revised Edition
`
`TheodoreL. Brown
`University of Illinoisat Urbana-Champaign
`
`H. Eugene LeMay, Jr.
`
`University of Nevada, Reno
`
`Bruce E. Bursten
`: . The Ohio State University
`
`With contributions by Julia R. Burdge, University of Akron
`
`PRENTICE HALL
`Upper Saddle River, New Jersey 07458
`
`Mylan Ex 1057, Page 1
`
`Mylan Ex 1057, Page 1
`
`

`

`Editor: John Challice
`Development Editor/Editor in Chief, Development: Carol Trueheart
`Associate Editor: Mary Hornby
`Editorial Assistants: AmandaK.Griffith, Gillian Buonanno
`Media Editor: Paul Draper
`Editorial/Production Supervision: Bob Walters
`Art Director: Joseph Sengotta
`Assistant Art Director: John Christiana
`Page layout: Richard Foster, Karen Noferi, Karen Stephens, AmyPeltier, Jeff Henn,
`Joanne Del Ben, Donna Marie Paukovits
`Art Studios: Academy Artworks/Michael Goodman/BioGrafx/Wellington
`Editor in Chief: Paul F. Corey
`Director of Marketing: John Tweeddale
`Assistant Vice President ESM Production and Manufacturing: David W.Riccardi
`Executive Managing Editor: Kathleen Schiaparelli
`Art Manager: Gus Vibal
`Art Editor: Karen Branson
`Assistant Art Editor: Adam Velthaus
`Senior Marketing Manager: Steve Sartori
`Marketing Assistant: Dorothy Marrero
`Director, Creative Services: Paul Bélfanti
`. Associate Creative Director: Amy Rosen
`Interior Design: Judith A. Matz-Coniglio
`Manufacturing Manager: Trudy Pisciotti
`Photo Editor: Melinda Reo
`Photo Researcher: Yvonne Gerin
`CoverIllustration: © Kenneth Eward/BioGrafx, 1999
`Copy Editor: Fay Ahuja
`
`-
`
`’
`
`© 2002, 2000, 1997, 1994, 1991, 1988, 1985, 1981, 1977 by Prentice-Hall, Inc.
`Upper Saddle River, NJ 07458
`
`All rights reserved. No part of this book may be
`reproduced, in any form or by any means,
`without permission in writing from the publisher.
`Printed in the United States of America
`100987654321
`
`ISBN O-13-06114e-5
`
`Prentice-Hall International (UK) Limited, London
`Prentice-Hall of Australia Pty. Limited, Sydney
`Prentice-Hall Canada Inc., Toronto
`Prentice-Hall Hispanoamericana, $.A., Mexico
`Prentice-Hall of India Private Limited, New Delhi
`Prentice-Hall of Japan, Inc., Tokyo
`Prentice-Hall (Singapore) Pte. Ltd., Singapore
`Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro
`
`Mylan Ex 1057, Page 2
`
`Mylan Ex 1057, Page 2
`
`

`

`Fe“concentration iis substantially:smallé
`
`
`
`
` @A0)(@).
`
`
`
`644=Chapter 17 / Additional Aspects of Aqueous Equilibria
`joaassumé‘thatxis.smallrelativeto0.10.or0.20:M,
`thisexpressionsimplifies to-give
`
`
`
`
`on; Htyh
`
`Sample Exercises 17.1 and 17.2 both involve weakacids. The ionization ofa
`weakbase is also decreased by the addition of a commonion. For example,the
`addition of NH," (as from the strong electrolyte NH,Cl) causes the base-disso-
`ciation equilibrium of NH,to shift to the left, decreasing the equilibrium con-
`centration of OH” and lowering the pH:
`NH,(@q) + H,O(1) == NHy* (aq) + OH" (aq)
`
`[17.2]
`
`
`
`17.2 Buffered Solutions
`
`Solutions like those discussed in Section 17.1, which contain a weak conjugate
`acid~basepair, resist.drastic changes in pH.Solutions thatresist a change in pH
`upon addition of small amounts ofacid or baseare called buffered solutions(of
`merely buffers). Human blood is an important example of a complex aqueous
`medium with a pH buffered at about7.4 (see the “Chemistry and Life” box neat
`the endof this section). Much ofthe chemical behavior of seawater is determined
`by its pH, buffered at about8.1 to 8.3 near the surface. Buffered solutions find
`many important applications in the laboratory and in medicine (Figure 17.1 4).
`
`Prepackaged
`Vv Figure 17.1
`buffer solutions and ingredients
`for forming buffer solutions of
`predetermined pH.
`
`
`
`Composition and Action of Buffered Solutions
`Buffers resist changes in pH becausethey contain both an acidic species to neu”
`tralize OH™ ions and a basic one to neutralize H*ions.It is necessary that the
`acidic andbasic species of the buffer do not consumeeachother through a neu"
`tralization reaction. These requirements are fulfilled by a weak acid-base co%
`jugate pair such as HC,H,0,-C,H,0,- or NH,*-NH. Thus, buffers are often
`prepared by mixing a weak acid or a weak base withasalt of that acid or bas¢
`
`Mylan Ex 1057, Page 3
`
`Mylan Ex 1057, Page 3
`
`

`

`17.2 / Buffered Solutions
`
`645
`
`[17.3]
`
`17.4
`N74
`
`&E
`
`For example, the HC,H,O,-C,H,0,~ buffer can be prepared by adding NaC,H,0,
`to a solution of HC,H3O,; the NH,*—NH,buffer can be prepared by adding
`NH,Cl to a solution of NH. By choosing appropriate components andadjusting
`their relative concentrations, we can buffer a solution at virtually any pH.
`:
`To understand better how a buffer works,let’s consider a buffer composed
`of a weak acid (HX) and oneofits salts (MX, where M* could be Na‘, K*, or
`other cations). The acid-dissociation equilibrium in this buffered solutionjin-
`volves both the acid andits conjugate base:
`HX(aq) —= H* (aq) + X° (a9)
`the correspondingacid-dissociation-constantexpressionis
`[H*X7]
`}
`R=
`:
`|
`[Od
`&f
`Solving this expression for [H*], we have
`|
`.
`[HX]
`[17.5]
`{[H*] = K, DC]
`L.
`Wesee fromthis expression that [H*], and thus the pH,is determinedby twofac-
`fors: the value of K, for the weak-acid component of the buffer, andtheratio of
`the concentrations of the conjugate acid-base pair, [HX]/[X7].
`_.
`If OOHions are added to the buffered solution, they react with the acid com-
`Ponentofthebuffer:
`OH (aq) + HX(aq) —> H,O(1) + X7 (aq)
`[17.6]
`This reaction causes [HX] to decrease and [X] to increase. However, as lorig as
`the amounts of HX and X7 in the buffer are large compared to the amountof
`OH” added, the ratio [HX]/[X7] doesn’t change much, and thusthe changein
`pHiis small (Figure 17.2 W).
`ib
`If H* ions are added, they react with the base componentof the buffer:
`f
`H* (aq) + X~ (aq) —> HX(aq)
`[17.7]
`t is reaction can also be represented using H,O+:
`H,O* (aq) + X~(aq) —> HX(aq) + H,O()
`
`Figure 17.2 A buffer
`consists of a mixture of a weak
`conjugate acid—basepair, here
`represented as HX and X~.
`Whena small portion of OH™ is
`added to the buffer (left), it
`—
`reacts with HX, decreasing [HX]
`and increasing [X~] in the
`buffer. When a small portion of
`H* is added to the buffer
`(right), it reacts with X-,
`decreasing [X7] and increasing
`[HX] in the buffer.
`
`Mylan Ex 1057, Page 4
`
`
`
`
`addition of OH™
`
`Buffer with equal
`concentrations of
`weakacid andits
`conjugate base
`
`Buffer after
`addition of H+
`
` Buffer after
`
`Mylan Ex 1057, Page 4
`
`

`

`646=Chapter 17 / Additional Aspects of Aqueous Equilibria
`
`Using either equation, we see that the reaction causes [X”] to decrease and
`[HX] toincrease.Aslongas thechangeintheratio [HX]/[X7] is small,thechange
`in pH will be small (Figure 17.2).
`Buffers most effectively resist a change in pH in either direction when the
`concentrations of HX and X~ are about the same. From Equation 17.5 wesee
`that when [HX] equals [X], [H*] equals K,. For this reason, we usually try to se-
`lect a buffer whoseacid form has a pK, close to the desired pH.
`
`Buffer Capacity and pH
`
`Two important characteristics of a buffer are its capacity and its pH. Bufferca-
`pacity iis the amountofacid or base the buffer can neutralize before the pH be;
`gins to changeto an appreciable degree. This capacity depends on the amount of
`acid and base from which the buffer is made. The pH ofthe buffer depends on
`the K, for the acid and on therelative concentrationsof the acid and basethat
`comprise the buffer. For example, we can see from Equation 17.5 that [H*] fora
`1-L solution that is 1 M in HC,H,O,and 1 M in NaC,H,0,will be the sameasfor
`a 1-L solution that is 0.1. M in HC,H,O, and 0.1 M in NaC,H,O,. However, the
`first solution has a greater buffering capacity because it contains more HC,H,Q,
`and C,H,O,. The greater the amountsof the conjugate acid-basepair, the more
`resistant the ratio of their concentrations, and hencethe pH,is to change.
`=:
`Because conjugate acid-basepairs share a commonion, we can use the same
`procedures to calculate the pH of a buffer that we used in treating the common-
`ion effect (see Sample Exercise 17.1). However, an alternate approach is some-
`times taken that is based on an equation derived from Equation 17.5. Takingthe
`negative log of both sides of Equation 17.5, we have
`
`—log [H*] = 10g (K,oy = —logK, — log
`
`
`[HX]
`[X7]
`
`Because —log [H*] = pH and ~log K, = pK,, we have
`
`
`pH = pK, — log Bel = pK, + log ay
`
`[17.8]
`
`In general,
`
`79)
`
`pH = pK, + log lPasel
`*
`[acid]
`where[acid] and[base] refer to the equilibrium concentrationsof the conjugate
`acid-basepair. Note that when [base] = [acid], pH = pK,,.
`Equation 17.9 is known as the Henderson-Hasselbalch equation. Biolo-
`gists, biochemists, and others who work frequently with buffers often usethis,
`equation to calculate the pH of buffers. In doing equilibrium calculations, we
`have seen that we can normally neglect the amounts of the acid and baseofthe
`buffer that ionize. Therefore, we can usually use the starting concentrations ofthe
`acid and base componentsof the buffer directly in Equation 17.9.
`
`
`
`Mylan Ex 1057, Page 5
`
`- Calculating pH
`
`sii
`Using the
`=”
`- Henderson-Hasselbalch
`
`Equation activity
`
`Mylan Ex 1057, Page 5
`
`

`

`17.2 / Buffered Solutions
`
`647
`
`042M -
`010M
`
`
`
`
`
`“neither acidic nor basic; H,O.is a much weaker acid than HC3HO; and a weaker.
`‘than C;H;O;". Therefore;the pHwillbe:controlled:bythe acid-dissociation equilil
`umoflactic acidshownbelow. Theinitial and equilibrium concentrations of the speci
`
`
`
`involvedinthisequilibrium are
`“4
`
`_ HC3H503(aq) == H"(aq). + CsH,O57(aq)
`
`
`[Equilibrium | (Q12-2M.. |
`
`The equilibrium concentrations are governed by the eq
`
`a HIGH:O:~
`Ka t4x10"= LHAUC505");
`
`
`
`“Becauseofthe smallK, arid the presence fthécommo
`1
`
`
`"sniall relativeto0.12or 0:10:M.Thus,our equation’canbe
`
`
`
`
`
`
` a
`
`
`
`‘ 5 arenead200+
`
`
`
`
`
`oe PH = slog (7 x10~4)'=3.77
`
`
`Alternatively,wecouldhave used'theHenderson-Hasselbalch equation.to C
`
`: a 18 (=dy}, 1ae is
`
`
`
`
`
`
`
`Cl must be. added. to 2.0L of ¢ 10 M NH, to-form abuffer :
`imé thattheaddition ofNH,Cl-doesnot change the volumeof...
`
`
`
`ion’ Themajor species‘in the solution will’be NH,*, Cl", NH, and’H;0:Of
`Se, the CI“ionis aspectator(it is theconjugate baseof'a strong acid),and H,0.is.a:
`'yWeak acidorbase.Thus,the NH,*-NH; conjugateacid-basepairwill determine -
`PHofthebuffersolution. The equilibriumtelationshipbetween NH,":and:NH,is-
`
`enby the base-dissociationconstantfor NH:
`oe PN
`
`__INH,*OH-]
`|
`_NHy(aq) + 1,00) ==NH,*(aq) + OH™(q)—K
`INH]
`
`eng
`os
`(Because. K, is‘small and thecommon ion NH,"ispresent,the equilibrium concentra*
`if NHwilléssentiallyequal itsinitial concentration: Te
`[NH] = 010M
`
`»
`-
`
`
`
`Mylan Ex 1057, Page 6
`
`Mylan Ex 1057, Page 6
`
`

`

`650=Chapter 17 / Additional Aspects of Aqueous Equilibria
`
`
`
`
`
`Let’s comparethe buffer action of a mixture of a weak acid and its conju-
`gate base with thatofa solution thatis not buffered. We saw in Sample Exercise
`17.5 that 1.00 L ofa solution thatis 0.300 M in acetic acid and 0.300 M in sodium
`acetate undergoes a pH changeof0.06 pH units when 0.020 mol of HCl or NaOH
`is added.In contrast, 1.00 L of pure water would change from pH = 7.00 to pH
`= 1.70 upon addition of 0.020 mol HCl and from pH = 7.00 to pH = 12.30 upon
`addition of 0.020 mol of NaOH.Asthis comparison shows,a buffered solution
`exhibits a much smaller change in pH than does an unbuffered one.
`
`17.3 Acid-BaseTitrations
`eee
`In Section 4.6 we briefly described titrations. In an acid-base titration, a solution
`containing a known concentration of base is slowly addedto an acid (or the acid
`is added to the base). Acid-base indicators can be used to signal the equivalence
`
`Mylan Ex 1057, Page 7
`
`Mylan Ex 1057, Page 7
`
`