`


`
`

`
`Remington: The
`Science and Practice
`
`
` of Pharmacy
`
`Volume I
`
`

`
`
`
`
`
`
`
`
`
`...,n.7._4.._4.,4q_-3-...4.;p1g..._.._......_.....«.m-..,...,.—~»-"'~---»V~w~--»—».‘.,.-_.,,....%W,,.,..,_.-..-,..,..g,
`
`1 9m
`
`EDITION
`
` Remington:
`Practice of
`
`ALFONSO R GENNARO
`
`Chairman of the Editorial Board
`and Editor
`
`

`
`The Science and
`Pharmacy
`
`1995
`
`MACK PUBLISHING COMPANY
`
`Easton, Pennsylvania 18042
`
`

`
`Entered according to Act of Congress, «in the year 1885 by Joseph P Remington,
`in the Office of the Librarian of Congress, atWashington DC
`
`Copyright 1889, 1894, 1905, 1907,1917, by Joseph P Remington
`
`Copyright 1926, 1936, by the Joseph P Remington Estate
`
`Copyright 1948, 1951, by The Philadelphia College of Pharmacy and Science
`
`Copyright 1956, 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995,by The Philadelphia College of
`Pharmacy and Science
`
`All Rights Reserved
`
`Library of Congress Catalog Card No. 60-53334
`
`ISBN 0-912 734-04-3
`
`The use ofstructuralformulasfrom USAN and the USP Dictionary ofDrug Names is by
`permission of The USP Convention. The Convention is not responsiblefor any inaccuracy
`contained herein.
`
`NoTICE—-This text is not intended to represent, nor shall it be interpreted to be, the equivalent
`ofor a substitutefor the ofiicial United States Pharmacopeia (USP) amt / or the National
`Formulary (NF). In the event ofany difierence or discrepancy between the current oflicial
`USP or NF standards ofstrength, quality, purity, packaging and labelingfor drugs and
`representations ofthem herein, the context and eflect ofthe ofiicial compendia shall prevail.
`
`Printed in the United States ofArnerz'ca by the Mack Printing Company, Easton, Pennsylvania
`
`

`
`224
`
`CHAPTER 17
`
`and the pH of a 0.005 M solution of NaOH would be
`pOH = —log 0.005 = 2.30
`
`pH = pK,,, — pOH = 14.00 — 2.30 = 11.70
`
`Weak Acids or Bases
`
`If a weak acid, HA, is added to water, it will equilibrate with
`its conjugate base, A‘, as
`
`HA + H20 : H3O+ + A‘
`
`Accounting for the ionization of water gives the following PBE
`for this system:
`
`(61)
`[H30“‘] = [0H‘] + [N]
`The concentration of A" as a function of hydronium-ion con-
`centration can be obtained as shown previously to give
`
`[H 0+] — [0H-) + -2 (62)
`3
`[H30+1 + K.
`
`Algebraic simplification yields
`
`(Ca - {H 0*] + {0H‘D
`(H.-.0+1 = K. ———-—3——-——
`([H30+l — l0H‘])
`In most instances for solutions of weak acids,
`[OH‘ ] and the equation simplifies to give
`
`(63)
`
`[H,-30+] >
`
`[H30*]2 + KalH3O+] - Kaca = 0
`This is a quadratic equation* which yields
`
`(64)
`
`in which BH" is the protonated form of the base B, and X‘ is
`the anion of a strong acid. Since X‘ is the anion of a strong
`acid, it is too weak a base to undergo any further reaction with
`water. The protonated base, however, can act as a weak acid
`to give
`
`BH* + H20 : B + 1130*
`
`Thus, Eqs 65 and 66 are valid, with Ca being equal to the
`concentration of the salt in solution.
`IfK,,' for the protonated
`base is not available, it can be obtained by dividing Kb for the
`base B, into Kw.
`E.rample—Ca1culate the pH of a 0.026 M solution of ammonium
`chloli41‘de. AssumethatKb for ammonia is 1.74 X 10‘5 and K,,, is 1.00 x
`10‘
`.
`
`K4 =I& = LT = 5.75 X 10‘“’
`Kb
`1.74 X 10’5
`
`{Ham = @
`
`= x/MWYEM
`= 3.87 X 10“"M
`
`pH = — log (3.87 x 10-6) = 5.41
`
`Since Co is much greater than [H3O+] and [H3O*] is much greater than
`[OH'], the assumptions are valid and the value calculated for pH is
`sufficiently accurate.
`
`Weak Bases
`
`—K + ,/K 2 + 4K C
`[H30-L] = __L1_T‘1;__"'_
`2
`
`(65)
`
`When a weak base, B, is dissolved in water it ionizes to give
`the conjugate acid as
`
`since [H3O* I can never be negative. Furthermore, if [H3O*]
`is less than 5% of Ca, Eq 64 is simplified further to give
`
`B + H20 :2 BH* + OH“
`
`The PBE for this system is
`
`= VKaCa
`
`It generally is preferable to use the simplest equation to calcu-
`late [H;_,0+ ]. However, when [I-l30"] is calculated, it must be
`compared to Ca in order to determine whether the assumption
`Ca >> {H3O+] is valid.
`If the assumption is not valid, the
`quadratic equation should be used.
`ExampLe—Calculate the pH of a 5.00 X 10‘5 M solution of a weak acid
`having aKa = 1.90 X l0‘5.
`
`[H30+1 = VKaCa
`
`= \/1.90 X 10‘5 X 5.00 X 10"5
`= 3.08 X l0‘5M
`
`[BH*] + [H3O*] = [OH‘]
`
`(67)
`
`Substituting [BH*] as a function of hydronium-ion concentra-
`tion and simplifying, in the same manner as shown for a weak
`acid, gives
`
`(Co “ [0H’l + lH30+l)
`_
`[OH'] = K
`(IOH 1 — [H30*l)
`"
`,
`If [OH‘] [H3O*], as is true generally, then
`
`(68)
`
`[OH']2 + K,,[0H‘] — K,,C,, = 0
`
`(69)
`
`which is a quadratic with the following solution:
`
`Since Ca [(5.00 X 1O’5 M)] is not much greater than [H3O*], the quadratic
`equation (Eq 65) should be used.
`
`— K + \/K 2 + 4K C
`[0H—] = __#£
`
`— 1.90 X 10‘5 + \/(1.90 X 10‘5)2 + 4(5.00 X l0‘5)
`2
`
`{Ha0* =
`= 7.06 x 10*?»
`
`If 0,, >> [OH‘], the quadratic equation simplifies to
`
`[OH‘] = \/K,,C,,
`
`(70)
`
`(71)
`
`pH = — log (7.06 x 10*” = 2.15
`Note that the assumption [H3O" ) > [OH‘] is valid. The hydronium-ion
`concentration calculated from Eq 66 has a relative error of about 100%
`when compared to the correct value obtained from Eq 65.
`
`When a salt obtained from a strong acid and a weak base-—
`eg, ammonium chloride, morphine sulfate, pilocarpine hydro-
`chloride, etc——is dissolved in water, it dissociates as
`H20
`BH“X‘ "> BH+ + X‘
`
`* The general solution to a quadratic equation of the form
`
`Once [OH‘] is calculated, it can be converted to pOH, which
`can be subtracted from pKw to give pH.
`E‘:cample—Ca.lcu1ate the pH of a 4.50 X l0‘2M solution of aweak base
`havingK,, = 2.00 X 10*‘. Assume thatlfig = 1.00 X 10”“.
`
`10H’l = VKbCb
`
`= \/ 2.00 x 10*‘ X 4.50 x 10‘2
`
`= \/9.00 X 10”?’ = 3.00 X 10‘3M
`
`Both assumptions are valid.
`
`pOH = — log 3.00 X 10‘3 = 2.52
`
`pH = 14.00 — 2.52 = 11.48
`
`—b...\/b2‘4
`G.X2+bX+C=O1S X=
`
`When salts obtained from strong bases and weak acids (eg,
`sodium acetate, sodium sulfathiazole, sodium benzoate, etc)
`
`

`
`IONIC SOLUTIONS AND ELECTROLYTIC EQUILIBHIA
`
`225
`
`are dissolved in water, they dissociate as
`
`act as a weak base:
`
`Na* A" H10 Na+ + A-
`
`in which A“ is the conjugate base of the weak acid, HA. The
`Na‘‘ undergoes no further reaction with water. The A", how-
`ever, acts as a weak base to give
`
`A‘ + H2O::HA+ OH‘
`
`Thus, Eqs 70 and 7 1 are valid, with 0,, ‘being equal to the
`concentration of the salt in solution. The value for Kb can be
`obtained by dividing Ka for the conjugate acid, HA, into Kw
`
`E'xampLe_—-Calculate the pH of a 0.05 M‘ solution of sodium acetate.
`Assume thatK,, for acetic acid = 1.75 X l0‘5 and K,,, = 1.00 x 10‘”.
`Kw
`1.00 X l0‘”
`Kb = E‘
`= 5.71 x 10-10
`
`my = m =
`= 5.34 x 10“"M
`
`Both assumptions are valid:
`
`pOH = — log (5.34 X l0“6) = 5.27
`
`pH = 14.00 — 5,27 = 8.73
`
`Ampholytes
`
`Substances such as NaHCO3 and NaH2PO4 are termed am-
`pholytes, and are capable of functioning both as acids and
`bases. When an ampholyte of the type NaHA is dissolved in
`water, the following series of reactions can occur:
`
`Na+HA- “:9 Na+ + HA“
`
`HA‘ + H20 : A2“ + H30+
`
`HA‘ + H20 = HZA + OH’
`
`2H2O = H3O* + OH‘
`
`The total PBE for the system is
`
`(72)
`lH30*l + lH2Al = [0H‘l + lA2‘l
`Substituting both IHZA] and [A21 as a function. of [H30+] (see
`Eqs 52 and 54), yields
`
`[H3O*l +
`
`[H3O+]2 Cs
`
`[H3O+l2 4' K1lH30+l + KIKZ
`
`+NH3CH2COO‘ + H20 :2 *NH3CH2COOH + OH‘
`
`This type of substance, which carries both a charged acidic
`and a charged basic moiety on the same molecule is termed a
`zwitterion and, since the two charges balance each other, the
`molecule acts essentially as a neutral molecule. The pH at
`which the zwitteriom concentration is maximum is known as
`the isoelectric point, which can be calculated from Eq 74.
`On the acid side of the isoelectric point, amino acids and
`proteins are cationic and incompatible with anionic materials
`such as the naturally occurring gums used as suspending
`and/ or emulsifying agents. On the alkaline side ofthe isoelec:
`tric point, amino acids and proteins are anionic and incompat-
`ible with cationic materials such as benzalkonium chloride.
`
`Salts ofWeak Acids and Weak Bases
`
`When a salt such as ammonium acetate (which is derived
`from a weak acid and a weak base) is dissolved in water, it
`undergoes the following reactions:
`
`BH"A‘ “:9 311+ + A-
`
`BH+ + H20 : B + H3O+
`
`A‘ + H2O:HA+ OH‘
`
`The total PBE for this system is
`
`[H30*l + {HA} = l0H’l + [B]
`
`(75)
`
`Replacing [HA] and [B] as afunction of [H3O+], gives
`
`{H3O*] + J = [OH‘] +L (76)
`.[H30*l + Ka
`lH30*l + K;
`
`in which C, is the concentration of salt, K,, is the ionization
`constant of the conjugate acid formed from the reaction be-
`tween A“ and water and K,,’ is the ionization constant for the
`protonated base, BH".
`In general, [H30* ], [OH‘ ], Ka and Ka’
`usually are smaller than C, and the equation simplifies to
`
`(77)
`lH30*l = JKIIKI;
`Ezample—-Calculate the pH of a 0.0 1 M solution of ammonium acetate.
`The ammonium ionhas aK,, equal to 5.75 X 10“°, which represents K; in
`Eq 77. Acetic acid has aK,, of 1.75 X 10-5, which represents K,, in Eq 77:
`
`[H30”] = V1.75 X l{)‘5 X 5.75 X 10“°
`= 1.00 X 10‘7
`
`pH = — log (1.00 x 10-7) = 7.00
`
`=
`
`Kw
`
`lH30+l
`
`K,K2c,
`+mm:
`[H30+l2 + K1[H3O+l 4' K1K2
`
`All of the assumptions are valid.
`
`Buffers
`
`This gives a fourth-order equation in [H3O*], which can be
`simplified using certain judicious assumptions to
`
`73
`K‘K2C‘
`H0+ —
`()
`i31—\/Kl+Cs
`In most instances, C, >> K1 and the equation further simplifies
`to
`‘
`
`lH30+l = VK1K2
`
`(74)
`
`and [H3O+] becomes independent of the concentration of the
`salt. A special property of ampholytes is that the concentra-
`tion of the species HA“ is maximum at the pH corresponding
`to Eq 74.
`When the simplest amino acid salt, glycine hydrochloride, is
`dissolved in water, it acts as a diprotic acid and ionizes as
`
`+NH3CH2CO0H + H20 : *NH3CH2COO’ + H3O+
`
`+NH3CH2COO‘ + H20 : NHZCHZCOO“ + H3O+
`The form, +NH3CH2COO‘, is an ampholyte since it also can
`
`The terms bujfer, bufier solution and buflered solution,
`when used with reference to hydrogen-ion concentration or
`pH, refer to the ability of a system, particularly an aqueous
`solution, to resist a change of pH on adding acid or alkali, or
`on dilution with a solvent.
`If an acid or base is added to water, the pH of the latter is
`changed markedly, for water has no ability to resist change of
`pH; it is completely devoid of bufler action. Even a very
`weak acid such as carbon dioxide changes the pH of water,
`decreasing it from 7 to 5.7 when the small concentration of
`carbon dioxide present in air is equilibrated with pure water.
`This extreme susceptibility of distilled water to a change of pH
`on adding very small amounts of acid or base is often of great
`concern in pharmaceutical operations. Solutions of neutral
`salts, such as sodium chloride, similarly lack ability to resist
`change of pH on adding acid or base; such solutions are called
`unbuffered.
`Characteristic of buffered solutions, which undergo small
`changes of pH on addition of acid or base, is the presence
`either of a weak acid and a salt of the weak acid, or a weak base
`
` 2 l 2
`
`
`
`..,._,........~.w,.....,,.t,..,m-..m.v—,.«.W.,....,,...,.,,.....,,......
`
`

`
`226
`
`CHAPTER 17
`
`and a salt of the weak base. An example of the former system
`is acetic acid and sodium acetate; of the latter, ammonium
`hydroxide and ammonium chloride. From the proton con-
`cept of acids and bases discussed earlier, it is apparent that
`such buffer action involves a conjugate acid—base pair in the
`solution.
`It will be recalled that acetate ion is the conjugate
`base of acetic acid, and that ammonium ion is the conjugate
`acid of ammonia (the principal constituent of what commonly
`is called ammonium hydroxide).
`The mechanism of action of the acetic acid—sodium acetate
`buffer pair is that the acid, which exists largely in molecular
`(nonionized) form, combines with hydroxyl ion that may be
`added to form acetate ion and water, thus
`
`CH3COOH + OH‘ —> CH3COO‘ + H20
`
`while the acetate ion, which is a base, combines with hydrogen
`(more exactly hydronium) ion that may be added to form
`essentially nonionized acetic acid and water, represented as
`
`CH3COO’ + H3o+ —> CH3COOH + H20
`
`As will be illustrated later by an example, the change of pH is
`slight as long as the amount of hydronium or hydroxyl ion
`added does not exceed the capacity of the buffer system to
`neutralize it.
`The ammonia—ammonium chloride pair functions as a buffer
`because the ammonia combines with hydronium ion that may
`be added to form ammonium ion and water, thus
`
`simplifies to
`
`lH30*l =
`
`KGCG
`Cb
`
`or, expressed in terms of pH, as
`
`Cb
`pH = pK,, + log-—
`Ca
`
`(81)
`
`(82)
`
`This equation generally is called the Henderson/—HasselbaLch
`equation.
`It applies to all buffer systems formed from a
`single conjugate acid—base pair, regardless of the nature of
`the salts. For example, it applies equally well to the follow-
`ing buffer systems:
`ammonia—ammonium chloride, monoso-
`dium phosphate—disodium phosphate, phenobarbital—so-
`dium phenobarbital, etc.
`In the ammonia—ammonium
`chloride system, ammonia is obviously the base and the ammo-
`nium ion is the acid (C,, equal to the concentration of the salt).
`In the phosphate system, monosodium phosphate is the acid
`and disodium phosphate is the base. For the phenobarbital
`buffer system, phenobarbital is the acid and the phenobarbital
`anion is the base (Cb equal to the concentration of sodium
`phenobarbital).
`As an example of the application of this equation, the pH of
`a bulfer solution containing acetic acid and sodium acetate,
`each in 0.1 M concentration, may be calculated. The K, of
`acetic acid, as defined above, is 1.8 X lO‘5, at 25°.
`Solution
`
`NH3 + H30+ —> NH,,* + H20
`
`First, the pK,, of acetic acid is calculated
`
`Ammonium ion, which is an acid, combines with added hy-
`droxyl ion to form ammonia and water, as
`
`NH,+ + OH" —> NH3 + H20
`
`Again, the change of pH is slight if the amount of added
`hydronium or hydroxyl ion is not in excess of the capacity of
`the system to neutralize it.
`‘
`Besides these two general types of buffers, a third appears
`to exist. This is the buffer system composed of two salts, as
`monobasic potassium phosphate, KHZPO4, and dibasic potas-
`sium phosphate, KZHPO4. This is not, however, a new type of
`buffer; it is actually aweak-acid/conjugate-base bufier in which
`an ion, HZPO4", serves as the weak acid, and HPO42’ is its
`conjugate base. When hydroxyl ion is added to this buffer
`the following reaction takes place:
`
`HZPO4‘ + OH‘ —> HPO42' + H20
`
`and when hydronium ion is added
`
`H1304?‘ + H,-,0" —> HZPO4’ + H20
`
`It is apparent that the mechanism of action of this type of
`buffer is essentially the same as that of the weak-acid/
`conjugate-base buffer composed of acetic acid and sodium
`acetate.
`
`Calculations—-—A buffer system composed of a conjugate
`acid—base pair, NaA — HA (such as sodium acetate and acetic
`acid), would have a PBE of
`
`lH3O+] + [HA] = [0H”l + IA‘!
`
`(78)
`
`pK,, = — log K“ = V log 1.8 X l0'5
`
`= — log 1.8 — log 10‘5
`= — 0.26 — (- 5) = +4.74
`
`Substituting this value into Eq 82
`0.1
`pH = log-(E + 4.74 = +4.74
`
`The Henderson—Hasselbalch equation predicts that any so-
`lutions containing the same molar concentration of acetic acid
`as of sodium acetate will have the same pH. Thus, a solution
`of 0.01 M concentration of each will have the same pH, 4.74,
`as one of 0.1 M concentration of each component. Actually,
`there will be some difference in the pH of the solutions, for the
`activity coeflicient of the components varies with con-
`centration. For most practical purposes, however, the ap-
`proximate values of pH calculated by the equation are
`satisfactory.
`It should be pointed out, however, that the
`buffer of higher concentration of each component will have a
`much greater capacity for neutralizing added acid or base and
`this point will be discussed further under Buffer Capacity.
`The Henderson—Hasselbalch equation is useful also for cal-
`culating the ratio of molar concentrations of a buffer system
`required to produce a solution of specific pH. As an ex-
`ample, suppose that an acetic acid-sodium acetate buffer of
`pH 4.5 is to be prepared. What ratio of the buffer compo-
`nents should be used‘?
`Solution
`
`Replacing [HA] and [A‘] as a function of hydronium-ion con-
`centration gives
`
`Rearranging Eq 82, which is used to calculate the pH of weak acid- salt
`type bufiers, gives
`
`[H3O+] +
`
`[H,,o+10,,
`
`lH30*l + Ka
`
`= [OH‘] +
`
`K,,C,,
`
`IH30*l + K.
`
`(79)
`
`where Cb is the concentration of the salt, NaA, and 0,, is the
`concentration of the weak acid, HA. This equation can be
`rearranged to give
`
`C — H 0* + OH‘
`“[30,, _Ka( .
`I
`3 +1
`I
`_1)
`(Cb + [H30 1 - [OH 1)
`
`(80)
`
`In general, both Ca and 0,, are much greater than [H3O+],
`which is in turn much greater than [OH‘], and the equation
`
`1
`
`[base] _ H
`“g [acid] ‘ P ’ “K”
`= 4.5 — 4.76 = -0.24 = (9.76 -— 10)
`
`[base]
`[acid]
`
`: antilog of (9.76 — 10) = 0.575
`
`The interpretation of this result is that the proportion of
`sodium acetate to acetic acid should be 0.575 mol of the
`former to 1 mol of the latter to produce a pH of 4.5. A
`solution containing 0.0575 mol of sodium acetate and 0.1 mol
`of acetic acid per liter would meet this requirement, as would
`
`

`
`also one containing 0.00575 mol of sodium acetate and 0.01
`mol of acetic acid per liter; The actual concentration se-
`lected would depend chiefly on thedesired buffer capacity.
`Buffer Capacity—The ability of a bufier solution to resist
`changes in pH upon addition of acid or alkali may be measured
`in terms of bufier capacity.
`In the preceding discussion of
`buffers, it has been seen that, in a general way, the concentra-
`tion of acid in a weak-acid/conjugate-base buffer determines
`the capacity to “neutralize” added base, while the concentra-
`tion of salt of the weak acid determines the capacity to" neutral-
`ize added acid. Similarly,
`in a weak-base/conjugate-acid
`buffer the concentration of the weak base establishes the
`buffer capacity toward added acid, while the concentrationof
`the conjugate acid of the weak base determines the capacity
`toward added base. When the buffer is equimolar in the
`concentrations of weak acid and conjugate base, or of weak
`base and conjugate acid, it has equal buffer capacity toward
`added strong acid or strong base.
`_,
`Van Slyke, the biochemist, introduced a quantitative expres-
`sion for evaluating buffer capacity. This may be defined as
`the amount, in gram-equivalents (g-eq) per liter, of strong acid
`or strong base, required to be added to a solution to change its
`pH by 1 unit; a solution has a buffer capacity of 1 when 1 L
`requires 1 g-eq of strong base or acid to change the pH 1 unit
`(in practice, considerably smaller increments are measured,
`expressed as the ratio of acid or base added to the change of
`pH produced). From this definition it is apparent that the
`smaller the pH change in a solution caused by the addition of a
`specified quantity of acid or alkali, the greater the buffer
`capacity of the solution.
`.
`The following numerical examples illustrate certain basic
`principles and calculations concerning buffer action and buffer
`capacity.
`Example 1—-What is the change of pH on adding 0.0 1 mol of NaOH to 1
`L of 0. 10 M acetic acid?
`(a) Calculate the pH of a 0. 10 molar solution of acetic acid
`
`[H3O+] = ,/K,,c, = ,/1.75 x 10-4 x 1.0 x 104 = 4.18 x 10-3
`
`§
`
`pH = — mg 4.13 x 1043 = 2.33
`(b) On adding 0.01 mol of NaOH to a liter of this solution, 0.01 mol of
`acetic acid is converted to 0.01 mol of sodium acetate, thereby decreasing
`Cu to 0.09M, and Cb = 1.0 X 102M. Using the Henderson- Hasselbach
`equation gives
`
`IONIC SOLUTIONS AND ELECTROLYTIC EQUILIBRIA
`
`227
`
`Thus, the buffer capacity of the acetic acid—sodium acetate buffer solution
`is approximately 10 times that of the acetic acid solution.
`
`As is in part evident from these examples, and may be
`further evidenced by calculations of pH changes in other
`systems, the degree of buffer action and, therefore, the buffer
`capacity, depend on the kind and concentration of the buffer
`components, the pH region involved and the kind of acid or
`alkali added.
`Strong Acidsand Bases as “Bufl'ers”—In the foregoing
`discussion, buffer action was attributed to systems of (1) weak
`acids and their conjugate bases, (2) weak bases and their
`conjugate acids and (3) certain acid-base pairs which can
`function in the manner either of System 1 or 2.
`The ability to resist change in pH on adding acid or alkali is
`possessed also by relatively concentrated solutions of strong
`acids and strong bases.
`If to 1 L of pure water having a pH of
`7.0 is added 1 mL of 0.01 M hydrochloric acid, the pH is
`reduced to about 5.0.
`If the same volume of the acid is added
`to 1 L of 0.00 1 M hydrochloric acid, which has a pH of about 3,
`the hydronium-ion concentration is increased only about 1°/o
`and the pH is reduced hardly at all. The nature of this buffer
`action is quite different from that of the true buffer solutions.
`The very simple explanation is that when 1 mL of 0.01 M HCl,
`which represents 0.00001 g-eq of hydronium ions, is added to
`the 0.000000 1 g-eq of hydronium ions in 1 L of pure water, the
`hydronium-ion concentration is increased 100-fold (equiva-
`lent to two pH units), but when the same amount is added to
`the 0.001 g-eq of hydronium ions in 1 L of 0.001 M HCl, the
`increase is only 1/ 100 the concentration already present.
`Similarly, if 1 mL of 0.01 M NaOH is added to 1 L of pure
`water, the pH is increased to 9, while if the same volume is
`added to 1 L of 0.001 molar Na0H, the pH is increased almost
`immeasurably.
`In general, solutions of strong acids of pH 3 or less, and
`solutions of strong bases of pH 1 1 or more, exhibit this kind of
`buffer action by virtue of the relatively high concentration of
`hydronium or hydroxyl ions present. The USP includes
`among its Standard Bufier Solutions a series of hydrochloric
`acid buffers, covering the pH range 1.2 to 2.2, which also
`contain potassium chloride. The salt does not participate in
`the buffering mechanism, as is the case with salts of weak
`acids; instead, it serves as a nonreactive constituent required
`to maintain the proper electrolyte environment of the solu-
`tions.
`
`
`
`
`
`.........t.,...m».«—W«,....,-...-w..¢~..,.,—«...,Wrh‘(wve-4.,.....,..
`
`0.01
`
`pH = 4.76 + logo 09 = 4.76 — 0.95 =_ 3,81
`
`Determination of pH
`
`The pH change is, therefore, 0.93 unit. The buffer capacity as defined
`above is calculated t0_be
`mols of NaOH added
`
`change in pH
`
`= 0.0.11
`
`Example 2-What is the change of pH on adding 0.1 mol of NaOH to 1 L
`of buffer solution 0. 1 M in acetic acid and 0. I M in sodium acetate?
`
`(a) The pH of the buffer solution before adding NaOl-I is
`
`(b) On adding 0.01 mol of NaOH per liter to this buffer solution, 0.01
`mol of acetic acid is converted to 0.01 mol of sodium acetate, thereby
`decreasing the concentration of acid to 0.09 M and increasing the concen-
`tration of base to 0.1 1 M. The pH is calculated as
`‘
`0.11
`
`pH = log W + 4.76
`= 0.087 + 4.76 = 4.85
`
`The change of pH in this case is only 0.09 unit, about I/.0 the change in the
`preceding example. The buffer capacity is calculated as
`mols of NaOH added
`0.01
`
`change of pH
`
`:7
`
`= 0'11
`
`Calorimetry
`
`A relatively simple and inexpensive method for determining
`the approximate pH of a solution depends on the fact that
`some conjugate acid base pairs (indicators) possess one color
`in the acid form and another color in the base form. Assume
`that the acid form of a particular indicator is red, while the
`base form is yellow. The color of a solution of this indicator
`will range from red, when it is sufliciently acid, to yellow, when
`it is sufficiently alkaline.
`In the intermediate pH range (the transition interval) the
`color will be a blend of red and yellow depending upon the
`ratio of the base to the acid form.
`In general, although there
`are slight differences between indicators, color changes appar-
`ent to the eye cannot be discerned when the ratio of base to
`acid form, or acid to base form exceeds 10:1. The use of Eq
`82 indicates that the transition range of most indicators is
`equal to the pK,, of the indicator :1 pH unit, or a useful range
`of approximately two pH units. Standard indicator solutions
`can be made at known pH values within the transition range of
`the indicator, and the pH of an unknown solution determined
`by adding the indicator to it and comparing the resulting color
`with the standard solutions. Details of this procedure can be
`found in RPS-14. Another method for using these indicators
`is to apply them to thin strips of filter paper. A drop of the
`unknown solution is placed on a piece of the indicator paper
`
`

`
`228
`
`CHAPTER 17 ‘
`
`and the resulting color compared to a color chart supplied
`with the indicator paper. These papers are available in a
`wide variety of pH ranges.
`
`Potentiometry
`
`Electrometric methods for the determination of pH are
`based on the fact that the difference of electrical potential
`between two suitable electrodes dipping into a solution con-
`taining hydronium ions depends on the concentration (or
`activity) of the latter. The development of a potential differ-
`ence is not a specific property of hydronium ions. A solution
`of any ion will develop a potential proportional to the concen-
`tration of tlmt ion if a suitable pair of electrodes is placed in
`the solution.
`The relationship between the potential difference and con-
`centration of an ion in equilibrium with the electrodes may be
`derived as follows. When a metal is immersed into a solution
`of one of its salts, there is a tendency for the metal to go into
`solution in the form of ions. This tendency is known as the
`solution pressure of the metal and is comparable to the
`tendency of sugar molecules, eg, to dissolve in water. The
`metallic ions in solution tend, on the other hand, to become
`discharged by forming atoms, this effect being proportional to
`the osmotic pressure of the ions.
`In order for an atom of a metal to go into solution as a
`positive ion, electrons, equal in number to the charge on the
`ion, must be left behind on the metal electrode with the result
`that the latter becomes negatively charged. The positively
`charged ions in solution, however, may become discharged as
`atoms by taking up electrons from the metal electrode.
`Depending on which effect predominates, the electrical charge
`on the electrode will be either positive or negative and may be
`expressed quantitatively by the following equation proposed
`by Nernst in 1 889:
`
`For the determination of hydronium-ion concentration or
`pH, an electrode at which an equilibrium between hydrogen
`gas and hydronium ion can be established must be used, in
`place of metallic electrodes. Such an electrode may be made
`by electrolytically coating a strip of platinum, or other noble
`metal, with platinum black and saturating the latter with pure
`hydrogen gas. This device functions as a hydrogen
`electrode. Two such es ectrodes may be assembled as shown
`in Fig 3.
`In this diagram one electrode dips into Solution A, contain-
`ing a known hydronium-ion concentration, and the other elec-
`trode dips into SolutionB, containing an unknown hydronium-
`ion concentration. The two electrodes and solutions,
`sometimes called half—cells, then are connected by a bridge of
`neutral salt solution, which :33 no significant effect on the
`solutions it connects. The zotential difference across the
`two electrodes is measured by means of a potentiometer, P.
`If the concentration, C 1, of hydronium ion in So1utionA is l N,
`Eq 86 simplifies to
`
`E‘ = 1-zvln L
`nF (:2
`
`or in terms of Briggsian logarithms
`
`E = 2.303 1:1-“log”, -1-
`rzF
`C2
`
`(87)
`
`(88)
`
`If for log“) 1/C2 there 9 substituted its equivalent pH, the
`equation becomes
`
`E 2 30 3 RT H
`_ _
`. nF p
`
`(89)
`
`and finally by substituting numerical values for R, n, T and F,
`and assuming the tempera tune to be 20°, the following simple
`relationship is derived:
`
`= E 1" 13
`
`(83)
`
`E = 0.0581 pH or pH =
`
`E
`
`0.0581
`
`(90)
`
`where E is the potential difference or electromotive force, R is
`the gas constant (8.3 1 6 joules), T is the absolute temperature,
`72. is the valence of the ion, F is the Faraday of electricity
`(96,500 coulombs), p is the osmotic pressure of the ions andP
`is the solution pressure of the metal.
`Inasmuch as it is impossible to measure the potential differ-
`ence between one electrode and a solution with any degree of
`certainty, it is customary to use two electrodes and to measure
`the potential dilference between them.
`If two electrodes,
`both of the same metal, are immersed in separate solutions
`containing ions of that metal, at osmotic pressure p, and p2,
`respectively, and connected by means of a tube containing a
`nonreacting salt solution (a so-called salt bridge), the poten-
`tial developed across the two electrodes will be equal to the
`difference between the potential differences of the individual
`electrodes; thus
`
`E :
`
`-—
`
`(84)
`
`p2
`RT pl
`‘Z "”'
`““‘ — T T
`nFlnP1
`nF'lnP2
`E2
`E‘
`Since both electrodes are of the same metal, P1 = P2 and the
`equation may be simplified to
`
`The hydrogen electrons flipping into a solution of known
`hydronium-ion concenz El 2' -n.
`lled the reference eLectrode,
`may be replaced by a c
`ectrode, one type of which is
`shown in Fig 4. The
`LS of a calomel electrode are
`mercury and calomel .
`ir- aqueous solution of potassium
`chloride. The potentia:
`is electrode is constant, regard-
`less of the hydronium-ion
`ncentration of the solution into
`which it dips. The potentnr depends onthe equilibrium which
`is set up between mercury and mercurous ions from the calo-
`mel, but the concentration of the latter is governed, according
`to the solubility-product principle, by the concentration of
`chloride ions, which are derived mainly from the potassium
`chloride in the solution. Therefore, the potential of this elec-
`trode varies with the concentration of potassium chloride in
`the electrolyte.
`Because the calomel electrode always indicates voltages
`which are higher, by a constant value, than those obtained
`
`can be measured.
`
`RT pl
`RT
`RT
`- —lnp1 — —ln.p2 = ——-ln-
`_ nF
`nF
`11F
`p2
`In place of osmotic pressures it is permissible, for dilute
`solutions, to substitute the concern rations c, and C2 which
`were found (see Chapter 16), to be proportional to p1 and p2.
`The equation then becomes
`
`(85)
`
`If either cl or C2 is known, it is obvious that the value of the
`other may be found if the potential difference, E, of this cell
`
`(86)
`
`Hydrogen-ion conce
`
`.tion chain.
`
`

`
`IONIC SOLUTIONS AND ELECTROLYTIC EQU|LlBRlA
`
`229
`
`consists of a piece of gold or platinum wire or foil dipping into
`the solution to be tested, in which has been dissolved at small
`quantity of quinhydrone. A calomel electrode may be used
`for reference, just as in determinations with the hydrogen
`electrode.
`Quinhydrone consists of an equimolecular mixture of qui-
`none and hydroquinone; the relationship between these sub-
`stances and hydrogen-ion concentration is
`
`Quinone + 2 hydrogen ions + 2 electrons = hydroquinone
`
`In a solution containing hydrogen iorrs the potential of the
`quinhydrone electrode is related logarithmically to hydronium-
`ion concentration if the ratio of the hydroquinone concentra-
`tion to that of quinone is constant and practically equal to one.
`This ratio is maintained in an acid solution containing an
`excess of quinhydrone, and measurements may be made
`quickly and accurately; however, quinhydrone cannot be used
`in solutions more alkaline than pH 8.
`An electrode which, because of its simplicity of operation
`and. freedom from contamination or change of the solution
`being tested, has replaced both the hydrogen and quinhy-
`drone electrodes is the glass electrode.
`It functions by. vir-
`tue of the fact that when a thin membrane of a special compo-
`sition of glass separates two solutions of different pH, there is
`developed across the membrane a potential difference which
`depends on the pH of both solutions.
`If the pH of one of the
`solutions is known, the other may be calculated from the
`potential difference.
`In practice, the glass electrode usually
`consists of a bulb of the special glass fused to the end of a tube
`of ordinary glass.
`Inside the bulb is placed a solution of
`known pH, in contact with an internal silver- silver chloride or
`other electrode. This glass electrode and another reference
`electrode are immersed in the solution to be tested and the
`potential difference is measured. A potentiometer providing
`electronic amplification of the small current produced is
`employed. The modern instruments available permit read-
`ing the pH directly and provide also for compensation of
`variations due to temperature in the range of 0-50’ and to the
`small but variable asymmetry potential inherent in the glass
`electrode.
`
`Pharmaceutical Significance
`
`In the broad realm of knowledge concerning the prepara-
`tion and action of drugs few, if any, variables are so important
`as pH. For the purpose of this presentation, four principal
`types of pH-dependence of drug systems will be discussed:
`solubility,