y
`
` The Central Science
`
`Eighth Revised Edition
`
` Theodore L. Brown
`University of Iiiinois at Urbana-Champaign
`
`H. Eugene LeMay, Jr.
`
`University of Nevada, Reno
`
`i 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
`
`

`
`Editor: John Challice
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`
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`Upper Saddle River, NJ 07458
`
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`Printed in the United States of America
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`
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`
`Mylan Ex 1057, Page 2
`
`

`
`644
`
`Chapter 17 / Additional Aspects of Aqueous Equilibria
`
`_sm_'alle
`Q11
`
`Sample Exercises 17.1 and 17.2 both involve weak acids. The ionization of a
`weak base is also decreased by the addition of a common ion. For example, the
`addition of NH4+ (as from the strong electrolyte NH4Cl)_ causes the base-diss0-
`ciation equilibrium of NH3 to shift to the left, decreasing the equilibrium con-
`centration of OH" and lowering the pH:
`'
`
`NH3(aq) + H2O(l) t-——-—‘NH4+(aq) + OH‘(aq)
`
`[17.2]
`
`Prepackaged
`V Figure 17.1
`buffer solutions and ingredients
`for forming buffer solutions of
`predetermined pH.
`
`17.2 Buftered Solutions
`
`Solutions like those discussed in Section 17.1, which contain a weak conjugate
`acid—-base pair, resist-drastic changes in pH. Solutions that resist a change in PH
`upon addition of small amounts of acid or base are called buffered solutions (OT
`merely buffers). Human blood is an important example of a complex aqu€0“5
`medium with a pH buffered at about 7.4 (see the "Chemistry and Life” box near
`the end of this section). Much of the chemical behavior of seawater is determined
`by its pH, buffered at about 8.1 to 8.3 near the surface." Buffered solutions find
`many important applications in the laboratory and in medicine (Figure 17.1 4)-
`
`Composition and Action of Buffered Solutions
`
`Buffers resist changes in pH because they contain both an acidic species to 1151'
`tralize OH‘ ions and a basic one to neutralize H+ ions. It is necessary 1113”-he
`acidic and basic species of the buffer do not consume each other through 3 new
`tralization reaction. These requirements are fulfilled by a weak acid—base C01”
`jugate pair such as HC2H3O2—C2H3O2“ or NH4+—NH3. Thus, buffers are Often
`prepared by mixing a weak acid or a weak base with a salt of that acid or base‘
`
`Mylan Ex 1057, Page 3
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`

`
`17.2 / Buffered Solutions
`
`645
`
`l_For example, the HC2H3O2—C2H3O2‘ buffer can be prepared by adding NaC2H3O2
`to a solution of HC2H3O2; the NH4+—NH3 buffer can be prepared by adding
`ENH4Cl to a solution of NH3. By choosing appropriate components and adjusting
`ifcheir relative concentrations, we can buffer a solution at Virtually any pH.
`To understand better how a buffer works, let's consider a buffer composed
`got a weak acid (I-D() and one of its salts (MX, where M+ could be Na+, K“, or
`lather cations). The acid-dissociation equilibrium in this buffered solution in-
`Evolves both the acid and its conjugate base:
`"
`
`HX(aq) <———"—‘ H+(aq) + X‘(aq)
`P
`fflxe corresponding acid-dissociation-constant expression is
`[H+l[X‘l
`K ___ ___j
`n
`solving this expression for [H"], we have
`
`[17.3]
`
`[17.4]
`
`[HX]
`‘-‘T
`[H+ =
`[175]
`K4 [X 1
`]
`see from this expression that [H’'], and thus the pH, is determined by two fac-
`;tors: the value of K, for the weak—acid component of the buffer, and the ratio of
`Eihe concentrations of the conjugate acid—base pair, [I*D(]/[X‘].
`, V
`If OH" ions are added to the buffered solution, they react with the acid com-
`Eionent of the buffer:
`[17.6]
`OH'(aq) + I-[X(uq) —--> H2O(l) + X_(uq)
`reaction causes [HX] to decrease and [X’] to increase. However, as long as
`the amounts of HX and X’ in the buffer are large compared to the amount of
`added, the ratio [I-D(]/[X‘] doesn't change much, and thus the change in
`is small (Figure 17.2 V).
`If H+ ions are added, they react with the base component of the buffer:
`H*(uq) + X‘(aq) --9 HX(mi)
`[177]
`"s reaction can also be represented using I-130+:
`
`Hs0+(!1ti) + X‘(aq) ‘——> HX(fl¢Ii + H200)
`
`Buffer after
`Q
`addition of OH‘
`
`Buffer with equal
`concentrations of
`weak acid and its
`con‘u ate base
`
`Buffer after
`addition of Hi‘
`
`1 Figure 17.2 A buffer
`consists of a mixture of a weak
`conjugate acid—base pair, here
`represented as HX and X‘.
`When a 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 [X‘] and increasing
`[HX] in the buffer.
`
`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 E
`[HX] to increase. As long as the change in the ratio [HX]/[X‘] is small, the change
`in pH will be small (Figure 17.2).
`=i
`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 we see
`that when [HX] equals [X7], [H+] equals K,,. For this reason, we usually try to se.
`lect a buffer whose acid 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. Buffer ca-
`pacity is the amount of acid or base the buffer can neutralize before the pH be;
`gins to change to an appreciable degree. This capacity depends on the amount of
`acid and base from which the buffer is made. The pH of the buffer depends on
`the K, for the acid and on the relative concentrations of the acid and base that
`comprise the buffer. For example, we can see from Equation 17.5 that [H+] fora
`1—L solution that is 1 M in HC2H3O2 and 1 M in NaC2H3O2 will be the same as for
`a 1~L solution that is 0.1 M in HC2H3O2 and 0.1 M in NaC2H3O2. However, the
`first solution has a greater buffering capacity because it contains more HC2H3Q2
`and C2H3O2‘. The greater the amounts of the conjugate acid—base pair, the more
`resistant the ratio of their concentrations, and hence the pH, is to change.
`of
`Because conjugate acid—base pairs share a common ion, 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. Taking the
`negative log of both sides of Equation 17.5, we have
`
`—log [H+] = —log (K,
`
`[HX]
`
`= —log K, — log [HX]
`
`[X"l
`
`Because ~log [H‘”] = pH and —-log K, = pK,, we have
`
`"
`
`‘ Calculating pH
`. Using the
`' Henderson—Hasse|balch
`Equation activity
`
`In general,
`
`[1'7‘s9]:
`
`where [acid] and [base] refer to the equilibrium concentrations of the conjugate
`acid—base pair. Note that when [base] = [acid], pH = pI(,.
`V
`Equation 17.9 is known as the Henderson—Hasselba1ch equation. Biolo-n
`gists, biochemists, and others who work frequently with buffers often use this.
`equation to calculate the pH of buffers. In doing equilibrium calculations,nW.€
`have seen that we can normally neglect the amounts of the acid and base of the
`buffer that ionize. Therefore, we can usually use the starting concentrations of-the
`acid and base components of the buffer directly in Equation 17.9.
`
`Mylan Ex 1057, Page 5
`
`

`
`’ neither acidic nor basic; I-1'20 is a_much weaker acid than HC3I-I503 and a weakerib
`‘than C3H5O3“. Therefore; the VpH.wi1ib_e.\contr:'o1led»by'the acid’-dissociation equi1i__
`‘um oflactic acidshowrffielow. The inii_:ia1 and equilibrium concentrafions of the sped
`, involved equilibrium are
`L‘
`
`_ Hc3H5—o3(aq):H+(aq). + c3H5o3-;(aq)
`
`17.2 / Buffered Solutions
`
`647
`
`the‘ 1-'feseti‘c__e" .ion,:wé expect 3: to.
`K“
`H:.13eo.‘cf‘tu;s:e‘;o‘1“~’_ti'.ie’
`j mall re1atiy‘e"to’0:12_or'Q;10 M.fI‘h1V1s,”'o"ur qiiafion'Cai‘1
`'
`'
`'
`"
`'
`‘
`togivev J
`
`NH3 to fogm a;buifeif
`'4Q1 n1us:t:be'Aad,ded- to 2,§)_iL of V
`> “‘e thatthe"ac1ditior_1 of doesiiot chaitige the Vo1ume..of___
`
`,
`
`l\‘Ol_'I‘ The, inajot‘ si)eCies"in the solution Willbe NH,;*, Cl’, NH;;, and H2‘O._Of ‘
`§e; the C1""ion is 'a'spectator (it is theconjugate base ’of'a strong a'cid),and H‘2O.,i‘;‘s?a:_ .
`fv “Weak acid—ojr.base.:‘Thu§-,':the NI-I4‘+—NH3 conjugate'jacid—base'will deteiirrfiiié *
`PH of thje.buffer,so1utio‘n. The eq '
`'briuI_n relationship between NH[-~ai1d‘NH3'-is__
`en‘ the baéegciisggoeietionvconstant_for NH3:
`
`;NH3(aq> + H200)-e=NH:<aq> + OHWIIJ)
`
`"
`
`Kb
`
`=’_ INH;?i[bfi*1 ;
`LNH31
`
`fifi ause Ki, isjsmall aha thezommon ion NH; isjpreéentj.the equilibriurii cenaenfrgié ‘
`fN113,WflI»:es§§fifiaHY'eqi4a1V'its~initieil ck3ri_c_‘é'ritra“{i,or’_"'1:_?‘
`[NH3] .= 0.a1oM'
`V
`.
`
`Mylan Ex 1057, Page 6
`
`

`
`650
`
`Chapter 17 / Additional Aspects of Aqueous Equilibria
`
`Let's compare the buffer action of a mixture of a weak acid and its c0njU'
`gate base with that of a solution that is not buffered. We saw in Sample Exercise
`17.5 that 1.00 L of a solution that is 0.300 M in acetic acid and 0.300 M in sodium
`acetate undergoes a pH change of 0.06 pH units when 0.020 mol of HC1 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 up_0n
`addition of 0.020 mol of NaOH. As this comparison shows, a buffered solution
`exhibits a much smaller change in pH than does an unbuffered one.
`
`17.3 Acid-Base Titrations
`
`_,.......%
`
`In Section 4.6 we briefly described titnztions. In an acid—base titration, a solufifff‘
`containing a known concentration of base is slowly added to an acid (or the add
`is added to the base). Acid-base indicators can be used to signal the equivaleflfe
`
`Mylan Ex 1057, Page 7