`
`Slayback Exhibit 1101, Page 1 of 39
`Slayback v. Eye Therapies - IPR2022-00142
`
`Slayback Exhibit 1101, Page 1 of 39
`Slayback v. Eye Therapies - IPR2022-00142
`
`

`

`Remington: The
`Science and Practice
`of Pharmacy
`
`Slayback Exhibit 1101, Page 2 of 39
`Slayback v. Eye Therapies - IPR2022-00142
`
`

`

`Dr. Remington (seated right) reading galley proof. Galley proofs of USP monographs hang on the far wall, and USP Circulars are being
`collated on the billiard table.
`
`' · ...
`
`Slayback Exhibit 1101, Page 3 of 39
`Slayback v. Eye Therapies - IPR2022-00142
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`

`

`Editor: Daniel Limmer
`Managing Editor: Matthew J. Hauber
`Marketing Manager: Anne Smith
`
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`
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`
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`otherwise) for any injury resulting from any material contained herein. This
`publication contains information relating to general principles of medical care
`which should not be construed as specific instructions for individual patients.
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`current information, including contraindications, dosages and precautions.
`
`Printed in the United States of America
`
`Entered according to Act of Congress, in the year 1885 by Joseph P Remington,
`in the Office of the Librarian of Congress, at Washington 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 Phila(cid:173)
`delphia College of Pharmacy and Science
`
`Copyright 2000, by the University of the Sciences in Philadelphia
`
`All Rights Reserved
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`ISBN 0-683-3064 72
`
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`the necessary arrangements at the first opportunity.
`
`The use of structural formulas from USAN and the USP Dictionary of Drug
`Names is by permission of The USP Convention. The Convention is not respon(cid:173)
`sible for any inaccuracy contained herein.
`Notice-This text is not intended to rep~ M_r shall it be interpreted to be, the
`equivalent of or a substitute for the off{cf.aJ'tJnfied States Pharmacopeia (USP)
`and/or the National Formulary (NF). In the event of any difference or discrep(cid:173)
`ancy between the current official USP . ..ps-,NF
`1t1;ndards of strength, quality,
`1
`purity, packaging and labeling for dru;.'liJrid!representations of them herein, the
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`Slayback Exhibit 1101, Page 4 of 39
`Slayback v. Eye Therapies - IPR2022-00142
`
`

`

`Remington: Th• Sci•nc• Gnd Proctic• of Pham1Gcy . . . A treot,:,c> on me theory
`and practice of the pharmaceutical sciences, with essential
`information about pharmaceutical and medicinal agents; also, o
`guide to the professional responsibilities of the pharmCicist as the
`drug information specialist of the health team . . . A textbook and
`reference work for pharmacists, physicians, and other practitioners. of
`the pharmaceutical and medical sciences.
`
`EDffORS
`
`Alfonso R Gennaro, Choir
`
`Nicholas G Popovich
`
`Ara H Der Marderosian
`
`Glen R Hanson
`
`Thomas Medwicl~
`
`Roger L Schnaare
`
`Joseph B Schwartz
`
`H Steve White
`
`AUTHORS
`
`The 119 chapters of this edition of Remington were written by the
`
`editors, by members of the Editorial Board, and by the authors
`
`listed on pages viii to x.
`
`MGnGging Editor
`
`John E Hoover, BSc ( Pharm)
`
`EditoriGI AssistGnt
`
`Bo0nie Brigham Packer, RNC, BA
`
`DiNPctor
`
`Philip P Gerbino 1995-2000
`
`Twentieth Edition-2000
`
`Published in the 180th year of the
`PHILADELPHIA COLLEGE OF PHARMACY AND SCIENCE
`
`Slayback Exhibit 1101, Page 5 of 39
`Slayback v. Eye Therapies - IPR2022-00142
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`

`

`Ionic Solutions and Electrolytic Equilibria
`
`CHAPTER17
`
`Paul J Niebergall, PhD
`Professor of Pharmaceutical Sciences
`Medical University of South Carolina
`Charleston, SC 29425
`
`ELECTROLYTES
`
`In a preceding chapter, attention was directed to the colligative
`properties of nonelectrolytes, or substances whose aqueous so(cid:173)
`lutions do not C!)nduct electricity. Substances whose aqueous
`solutions conduct electricity are known as electrolytes and are
`typified by inorganic acids, bases, and salts. In addition to the
`property of electrical conductivity, solutions of electrolytes ex(cid:173)
`hibit anomalous colligative properties.
`
`Van't Hoff defined a factor, i, as the ratio ofthe--00lligative
`effect produced by a concentration, m, of electrolyte, divided by
`the effect observed for the same concentration of nonelectro(cid:173)
`lyte, or
`
`t:J>
`!:1T1
`!:1Tb
`1T
`.
`i - - - - - - - - - - -
`(!:1Tb)o
`(!:1T1)0
`(1T)o
`(AP)o
`
`(1)
`
`COLLIGATIVE 'PROPERTIES
`
`In general, for nonelectrolytes, a given colligative property of
`two equimolal solutions will be identical. This generalization,
`however, cannot be made for solutions of electrolytes.
`Van't Hoff pointed out that the osmotic pressure of a solu(cid:173)
`tion of an electrolyte is considerably greater than the osmotic
`pressure of a solution of a nonelectrolyte of the same molal
`concentration. This anomaly remained unexplained until 1887
`when Arrhenius proposed a hypothesis that forms the basis for
`our modern theories of electrolyte solutions.
`This theory postulated that when electrolytes are dissolved
`in water they split up into charged particles known as ions.
`Each of these ions carries one or more electrical charges, with
`the total charge on the positive ions (cations) being equal to the
`total charge on the negative ions (anions). Thus, although a
`solution may contain charged particles, it remains neutral. The
`increased osmotic pressure of such solutions is due to the
`increased number of particles formed in the process of ioniza(cid:173)
`tion. For example, sodium chloride is assumed to dissociate as
`
`It is evident that each molecule of sodium chloride that is
`dissociated produces two ions, and if dissociation is complete,
`there will be twice as many particles as would be the case if it
`were not dissociated at all. Furthermore, if each ion has the
`same effect on osmotic pressure as a molecule, it might be
`expected that the osmotic pressure of the solution would be
`twice that of a solution containing the same molal concentra(cid:173)
`tion of a nonionizing solute.
`Osmotic-pressure data indicate that, in very dilute solutions
`of salts that yield two ions, the pressure is very nearly double
`that of solutions of equimolal concentrations of nonelectrolytes.
`Similar magnification of vapor-pressure lowering, boiling-point
`elevation, and freezing-point depression occurs in dilute solu(cid:173)
`tions of electrolytes.
`
`in which 71', AP, fl.Tb, fl.Tr refer to the osmotic pressure, vapor(cid:173)
`pressure lowering, boiling-point elevation, and freezing-point
`depression, respectively, of the electrolyte. The terms (7r)0 and
`so on refer to the nonelectrolyte of the same concentration. In
`general, with strong electrolytes (those assumed to be 100%
`ionized), the van't Hoff factor is equal to the number of ions
`produced when the electrolyte goes into solution (2 for
`NaCl and MgSO4 ,. 3 for CaC12 and Na2SO4 , 4 for FeC13 and
`Na3PO4 , etc).
`In very dilute solutions the osmotic pressure, vapor-pressure
`lowering, boiling-point elevation, and freezing-point depression
`of solutions of electrolytes approach values two, three, four, or
`more times greater (depending on the type of strong electrolyte)
`than in solutions of the same molality of nonelectrolyte, thus
`confirming the hypothesis that an ion has the same primary
`effect as a molecule on colligative properties. It bears repeat(cid:173)
`ing, however, that two other effects are observed as the con(cid:173)
`centration of electrolyte is increased.
`
`The first effect results in less than 2-, 3-, or 4-fold intensification of a
`colligative property. This reduction is ascribed to interionic attraction
`between the positive and negatively charged ions, in consequence of
`which the ions are not dissociated completely from each other and do
`not exert their full effect on vapor pressure and other colligative prop(cid:173)
`erties. This deviation generally increases with increasing concentration
`of electrolyte.
`The second effect intensifies the colligative properties and is attrib(cid:173)
`uted to the attraction ofions for solvent molecules (called salvation, or,
`if water is the solvent, hydration), which holds the solvent in solution
`and reduces its escaping tendency, with a consequent enhancement of
`the vapor-pressure lowering. Solvation also reduces interionic attrac(cid:173)
`tion and, thereby, further lowers the vapor pressure.
`
`CONDUCTIVITY
`
`The ability of metals to conduct an electric current results from
`the mobility of electrons in the metals. This type of conductivity
`is called metallic conductance. On the other hand, various
`chemical compounds-notably acids, bases, and salts-conduct
`electricity by virtue of ions present or formed, rather than by
`
`227
`
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`

`228
`
`CHAPTER 17
`
`electrons. This is called electrolytic conductance, and the con(cid:173)
`ducting compounds are electrolytes. Although the fact that
`certain electrolytes conduct electricity in the molten state is
`important, their behavior when dissolved in a solvent, partic(cid:173)
`ularly in water, is of greater concern in pharmaceutical science.
`The electrical conductivity (or conductance) of a solution of
`an electrolyte is merely the reciprocal of the resistance of the
`solution. Therefore, to measure conductivity is actually to mea(cid:173)
`sure electrical resistance, commonly with a Wheatstone bridge
`apparatus, and then to calculate the conductivity. Figure 17-1
`is a representation of the component parts of the apparatus.
`The solution to be measured is placed in a glass or quartz
`cell having two inert electrodes, commonly made of platinum or
`gold and coated with spongy platinum to absorb gases, across
`which passes an alternating current generated by an oscillator
`at a frequency of about 1000 Hz. The reason for using alter(cid:173)
`nating current is to reverse the electrolysis that occurs during
`flow of current that would cause polarization of the electrodes
`and lead to abnormal results. The size of the electrodes and
`their distance apart may be varied to reduce very high resis(cid:173)
`tance or increase very low resistance to increase the accuracy
`and precision of measurement. Thus, solutions of high conduc(cid:173)
`tance (low resistance) are measured in cells having small elec(cid:173)
`trodes relatively far apart, whereas solutions of low conduc(cid:173)
`tance (high resistance) are measured in cells with large
`electrodes placed close to each other.
`Electrolytic resistance, like metallic resistance, varies di(cid:173)
`rectly with the length of the conducting medium and inversely
`with its cross-sectional area. The known resistance required for
`the circuit is provided by a resistance box containing calibrated
`coils. Balancing of the bridge may be achieved by sliding a
`contact over a wire of uniform resistance until no (or minimum)
`current flows through the circuit, as detected either visually
`with a cathode-ray oscilloscope or audibly with earphones.
`The resistance, in ohms, is calculated by the simple proce(cid:173)
`dure used in the Wheatstone bridge method. The reciprocal of
`the resistance is the conductivity, the units of which are recip(cid:173)
`rocal ohms (also called mho). As the numerical value of the
`conductivity will vary with the dimensions of the conductance
`cell, the value must be calculated as specific conductance, L,
`which is the conductance in a cell having electrodes of 1-cm2
`cross-sectional area and 1 cm apart. If the dimensions of the
`cell used in the experiment were known, calculating the specific
`conductance would be possible. Nevertheless, this information
`actually is not required, because calibrating a cell by measur(cid:173)
`ing in it the conductivity of a standard solution of known
`specific conductance is possible-and much more convenient(cid:173)
`and then calculating a cell constant. Because this constant is a
`function only of the dimensions of the cell, it can be used to
`
`Oscillator
`
`Sli de Wir e
`
`R1
`
`R2
`
`Conductivity
`Cell
`
`Figure 17-1. Alternating current Wheatstone bridge for measuring
`conductivity.
`
`convert all measurements in that cell to specific conductivity.
`Solutions of known concentration of pure potassium chloride
`are used as standard solutions for this purpose.
`EQUIVALENT CONDUCTANCE-In studying the varia(cid:173)
`tion of conductance of electrolytes with dilution it is essential to
`make allowance for dilution so that the comparison of conduc(cid:173)
`tances may be made for identical amounts of solute. This may
`be achieved by expressing conductance measurements in terms
`of equivalent conductance, A, which is obtained by multiplying
`the specific conductance, L, by the volume in milliliters, v., of
`a solution containing 1 g-eq of solute. Thus,
`
`lOOOL
`11.=LV,.= - c -
`
`(2)
`
`where C is the concentration of electrolyte in the solution in
`g-eq/L, that is, the normality of the solution. For example, the
`equivalent conductance of 0.01 N potassium chloride solution,
`which has a specific conductance of 0.001413 mho/cm, may be
`calculated in either of the following ways:
`A = 0.001413 x 100,000 = 141.3 mho cm'/eq
`
`or
`
`1000 X 0.001413
`0.01
`
`A =
`
`= 141.3
`
`STRONG AND WEAK ELECTROLYTES-Electrolytes
`are classified broadly as strong electrolytes and weak electro(cid:173)
`lytes. The former category includes solutions of strong acids,
`strong bases, and most salts; the latter includes weak acids and
`bases, primarily organic acids, amines, and a few salts. The
`usual criterion for distinguishing between strong and weak
`electrolytes is the extent of ionization. An electrolyte existing
`entirely or very largely as ions is considered a strong electro(cid:173)
`lyte, while one that is a mixture of some molecular species
`along with ions derived from it is a weak electrolyte. For the
`purposes of this discussion, classification of electrolytes as
`strong or weak will be based on certain conductance character(cid:173)
`istics exhibited in aqueous solution.
`The equivalent conductances of some electrolytes, at differ(cid:173)
`ent concentrations, are given in Table 17-1 and for certain of
`these electrolytes again in Figure 17-2, where the equivalent
`conductance is plotted against the square root of concentration.
`By plotting the data in this manner a linear relationship is
`observed for strong electrolytes, while a steeply rising curve is
`noted for weak electrolytes; this difference is a characteristic
`that distinguishes strong and weak electrolytes. The interpre(cid:173)
`tation of the steep rise in the equivalent conductance of weak
`electrolytes is that the degree of ionization increases with di(cid:173)
`lution, becoming complete at infinite dilution.
`Interionic interference effects generally have a minor role in
`the conductivity of weak electrolytes. With strong electrolytes,
`which are usually completely ionized, the increase in equiva(cid:173)
`lent conductance results not from increased ionization but from
`diminished ionic interference as the solution is diluted, in
`
`Table 17-1. Equivalent Conductances• at 25°
`Nal
`NaCl
`g-Eq/l
`HCI
`HOAc
`KCI
`Inf dil
`390.6·
`126.5
`149.9
`126.9
`426.1
`147.8
`125.4
`422.7
`67.7
`124.5
`0.0005
`146.9
`124.3
`421 .4
`49.2
`123.7
`0.0010
`120.6
`143.5
`121 .3
`415.8
`22.9
`0.0050
`118.5
`141 .3
`119.2
`0.0100
`412.0
`16.3
`11.6
`115.8
`138.3
`116.7
`0.0200
`407.2
`133.4
`7.4
`111.1
`112.8
`0.0500
`399.1
`106.7
`129.0
`108.8
`391 .3
`5.2
`0.1000
`• The equivalent conductance at infinite dilution for acetic acid, a weak
`electrolyte, is obtained by adding the equivalent conductances of hydrochlo-
`ric acid and sodium acetate and subtracting that of sodium chloride.
`
`NaOAc
`91.0
`89.2
`88.5
`85.7
`83.8
`81.2
`76.9
`72.8
`
`Kl
`150.3
`
`144.4
`142.2
`139.5
`135.0
`131.1
`
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`

`

`consequence of which ions have greater freedom of mobility (ie,
`increased conductance).
`The value of the equivalent conductance extrapolated to
`infinite dilution (zero concentration), designated by the symbol
`A0 , has special significance. It represents the equivalent con(cid:173)
`ductance of the completely ionized electrolyte when the ions are
`so far apart that there is no interference with their migration
`due to interionic interactions. It has been shown, by Kohl(cid:173)
`rausch, that the equivalent conductance of an electrolyte at
`infinite dilution is the sum of the equivalent conductances of its
`component ions at infinite dilution, expressed symbolically as
`A0 = lo(cation) + lo(anion)
`
`(3)
`
`The significance 9fKohlrausch's law is that each ion, at infinite
`dilution, has a characteristic value of conductance that is in(cid:173)
`dependent of the conductance of the oppositely charged ion
`with which it is associated. Thus, if the equivalent conduc(cid:173)
`tances of various ions are known, the conductance of any elec(cid:173)
`trolyte may be calculated simply by adding the appropriate
`ionic conductances.
`As the fraction of current carried by cations (transference
`number of the cations) and by anions (transference number of
`anions) in an electrolyte may be determined readily by exper(cid:173)
`iment, ionic conductances are known. Table 17-2 gives the
`
`400
`
`Cl) 300
`u
`C:
`2 u
`
`::,
`"O
`C:
`0
`(.)
`
`c
`
`Cl)
`
`C
`>
`::, 200
`C"
`w
`
`I
`I
`I
`I
`I
`
`100
`
`NaCl
`
`______ 0.3
`,JC on centrat ion
`Figure 17-2. Variation of equivalent conductance with square root
`of concentration.
`
`IONIC SOLUTIONS AND ELECTROLYTIC EQUILIBRIA
`
`229
`
`Table 17-2. Equivalent Ionic Condudivities
`at Infinite Dilution, at 25°
`CATIONS
`H+
`u +
`Na+
`K+
`NH4 +
`½Ca 2 +
`½Mg2+
`
`ANIONS
`ow
`c1 -
`Br-
`1-
`Aco -
`½So/-
`
`lo
`349.8
`38.7
`50.1
`73 .5
`61.9
`59.5
`53.0
`
`lo
`198.0
`76.3
`78.4
`76.8
`40.9
`79.8
`
`equivalent ionic conductances at infinite dilution of some cat(cid:173)
`ions and anions. It is not necessary to have this information to
`calculate the equivalent conductance of an electrolyte, for Kohl(cid:173)
`rausch's law permits the latter to be calculated by adding and
`subtracting values of A0 for appropriate electrolytes. For exam(cid:173)
`ple, the value of A0 for acetic acid may be calculated as
`A0(CH 3COOH) = A0(HC1) + A0(CH3COONa) - A0(NaCI)
`which is equivalent to
`l 0(H • ) + lo(CH3COO·) = l 0(H•) + lo(Cl·)
`+ (lO(Na•) + l 0(CH3COO·) - lo(Na•) - l 0(Cl- )
`
`This method is especially useful for calculating for weak
`electrolytes such as acetic acid. As evident from Figure 17-2,
`the Ao value for acetic acid cannot be determined accurately by
`extrapolation because of the steep rise of conductance in dilute
`solutions. For strong electrolytes, on the other hapd, the ex(cid:173)
`trapolation can be made very accurately. Thus, in the example
`above, the values of for HCl, CH3C00Na, and NaCl are deter(cid:173)
`mined easily by extrapolation as the substances are strong
`electrolytes. Substitution of these extrapolated values, as given
`in Table 17-2, yields a value of 390.6 for the value of A0 for
`CH3COOH.
`IONIZATION OF WEAK ELECTROLYTES-When Ar(cid:173)
`rhenius introduced his theory of ionization he proposed that
`the degree of ionization, a , of an electrolyte is measured by the
`ratio
`
`a = A/A 0
`
`(4)
`
`where A is the equivalent conductance of the electrolyte at any
`specified concentration of solution and A0 is the equivalent
`conductance at infinite dilution. As strong electrolytes were
`then not recognized as being 100% ionized, and interionic in(cid:173)
`terference effects had not been evaluated, he believed the equa(cid:173)
`tion to be applicable to both strong and weak electrolytes. It
`now is known that the apparent variation of ionization of
`strong electrolytes arises from a change in the mobility of ions
`at different concentrations, rather than from varying ioniza(cid:173)
`tion, so the equation is not applicable to strong electrolytes. It
`does provide, however, a generally acceptable approximation of
`the degree of ionization of weak electrolytes, for which devia(cid:173)
`tions resulting from neglect of activity coefficients and of some
`change of ionic mobilities with concentration are, for most
`purposes, negligible. The following example illustrates the use
`of the equation to calculate the degree of ionization of a typical
`weak electrolyte.
`Example-Calculate the degree of ionization of 1 X 10-3 N acetic
`acid, the equivalent conductance of which is 48.15 mho cm2/eq. The
`equivalent conductance at infinite dilution is 390.6 mho cm2/eq.
`
`48.15
`a= 390.6 = 0.12
`
`% ionization= 100a = 12%
`
`The degree of dissotjation also can be calculated using the van't Hoff
`factor, i, and
`
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`

`230
`
`CHAPTER 17
`
`i - 1
`a= - -
`v - 1
`
`(5)
`
`where v is the number of ions into which the electrolyte dissociates.
`
`Example-A 1.0 x 10-• N solution of acetic acid has a van't Hoff
`factor equal to 1.12. Calculate the degree of dissociation of the acid at
`this concentration.
`
`1.12 - 1
`i - 1
`a= V - 1 = ~ = 0.12
`
`This result agrees with that obtained using equivalent conductance and
`Equation 4.
`
`MODERN THEORIES
`
`The Arrhenius theory explains why solutions of electrolytes
`conduct electricity, and why they exhibit enhanced colligative
`properties. The theory is satisfactory for solutions of weak
`electrolytes. Several deficiencies, however, do exist when it is
`applied to solutions of strong electrolytes. It does not explain
`the failure of strong electrolytes to follow the law of mass action
`as applied to ionization; discrepancies exist between the degree
`of ionization calculated from the van't Hoff factor and the
`conductivity ratio for strong electrolyte solutions having con(cid:173)
`centrations greater than about 0.5 M.
`These deficiencies can be explained by the following obser(cid:173)
`vations
`1.
`In the molten state, strong electrolytes are excellent conductors of
`electricity. This suggests that these materials are already ionized in
`the crystalline state. Further support for this is given by x-ray
`studies of crystals, which indicate that the units comprising the
`basic lattice structure of strong electrolytes are ions.
`2. Arrhenius neglected the fact that ions in solution, being oppositely
`charged, tend to associate through electrostatic attraction. In solu(cid:173)
`tions of weak electrolytes, the number of ions is not large and it is
`not surprising that electrostatic attractions do not cause apprecia(cid:173)
`ble deviations from theory. In dilute solutions, in which strong
`electrolytes are assumed to be 100% ionized, the number of ions is
`large, and interionic attractions become major factors in determin(cid:173)
`ing the chemical properties of these solutions. These effects should,
`and do, become more pronounced as the concentration of electrolyte
`or the valence of the ions is increased.
`It is not surprising, therefore, that the Arrhenius theory of
`partial ionization involving the law of mass action and neglect(cid:173)
`ing ionic charge does not hold for solutions of strong electro(cid:173)
`lytes. Neutral molecules of strong electrolytes, if they do exist
`in solution, must arise from interionic attraction rather than
`from incomplete ionization.
`ACTMTY AND ACTIVITY COEFFICIENTS-Due to
`increased electrostatic attractions as a solution becomes more
`concentrated, the concentration of an ion becomes less efficient
`as a measure of its net effectiveness. A more efficient measure
`of the physical or chemical effectiveness of an ion is known as
`its activity, which is a measure of the concentration of an ion
`related to its concentration at a universally adopted reference(cid:173)
`standard state. The relationship between the activity and the
`concentration of an ion can be expressed as
`
`a = m-y
`
`(6)
`
`where m is the molal concentration, 'Y is the activity coefficient,
`and a is the activity. The activity also can be expressed in terms
`of molar concentration, c, as
`
`(7)
`a = fc
`where f is the activity coefficient on a molar scale. In dilute
`solutions (below 0.01 M ) the two activity coefficients are iden(cid:173)
`tical, for all practical purposes.
`The activity coefficient may be determined in various ways,
`such as measuring colligative properties, electromotive force,
`
`solubility,_ or _dist~b~tion coe~cients. For a strong electrolyte,
`the mean i~ru~ activity coefficient, 'Y;: or{;:, provides a measure
`of the deviation of the electrolyte from ideal behavior. The
`mean ionic activity coefficients on a molal basis for several
`strong electrolytes are given in Table 17-2. It is characteristic
`of the electrolytes that the coefficients at first decrease with
`~creasing _con~entrat~on, pass through a minimum and finally
`increase with mcreasmg concentration of electrolyte.
`IONIC STRENGTH-Ionic strength is a measure of the
`intensity of the electrical field in a solution and may be ex(cid:173)
`pressed as
`
`(8)
`
`µ. = ½ I c,z~
`where z; is the valence of ion i. The mean ionic activity coeffi(cid:173)
`cient is a function of ionic strength as are such diverse phe(cid:173)
`nomena as solubilities of sparingly soluble substances, rates of
`ionic reactions, effects of salts on pH of buffers, electrophoresis
`of proteins, and so on.
`The greater effectiveness of ions of higher charge on a spe(cid:173)
`cific property, compared with the effectiveness of the same
`number of singly charged ions, generally coincides with the
`ionic strength calculated by Equation 8. The variation of ionic
`strength with the valence (charge) of the ions comprising a
`strong electrolyte should be noted.
`For univalent cations and univalent anions (called uniuni(cid:173)
`valent or 1-1) electrolytes, the ionic strength is identical with
`molarity. For bivalent cation and univalent anion (biunivalent
`or 2-1) electrolytes, or univalent cation and bivalent anion
`(unibivalent or 1-2) electrolytes, the ionic strength is three
`times the molarity. For bivalent cation and bivalent anion
`(bibivalent or 2-2) electrolytes, the ionic strength is four times
`the molarity. These relationships are evident from the follow(cid:173)
`ing example.
`
`Example-Calculate the ionic strength of 0.1 M solutions of NaCl,
`Na2SO4 , MgCl2 , and MgSO4 , respectively, for
`½ (0.1 X 12 + 0.1 X 12)
`
`NaClµ.
`
`0.1
`
`½ (0 .2 X 12 + 0.1 X 22)
`
`½ (0.1 X 22 + 0.2 X 12)
`
`½ (0.1 X 22 + 0.1 X 22)
`
`0.3
`
`0.3
`
`0.4
`
`MgC1 2 µ.
`
`MgSO4 µ.
`
`The ionic strength of a solution containing mor""E: than one
`electrolyte is the sum of the ionic strengths of the individual
`salts comprising the solution. For example, the ionic strength
`of a solution containing NaCl, Na2SO4 , MgC12 , and MgSO4 ,
`each at a concentration of 0.1 M, is 1.1.
`DEBYE-HUCKEL THEORY-The Debye-Huckel equa(cid:173)
`tions, which are applicable only to very dilute solutions (about
`0.02 µ.), may be extended to somewhat more concentrated so(cid:173)
`lutions (about 0.1 µ.) in the simplified form
`
`logf; =
`
`-0.51 z~ /;.
`,
`1 + yµ
`
`(9 )
`
`The mean ionic activity coefficient for aqueous solutions of
`electrolytes at 25° can be expressed as
`
`logf,. =
`
`-0.51 Z+Z - Vµ
`,
`1 + yµ
`
`is the valence of the cation and z is the valence of
`in which z
`the anion. When the ionic strength of the solution becomes high
`(approximately 0.3 to 0.5), these equations become inadequate
`and a linear term in µ. is added. This is illustrated for the mean
`ionic activity coefficient,
`
`logf,, =
`
`-0.51 Z+Z- Vµ
`,
`1 + yµ
`
`+ K,µ
`
`( 11)
`
`Slayback Exhibit 1101, Page 9 of 39
`Slayback v. Eye Therapies - IPR2022-00142
`
`

`

`Table 17-3. Values of Some Salting-Out Constants
`for Various Barbiturates at 25°
`BARB ITU RA TE
`KBr
`KCI
`Amobarbital
`0.168
`0.095
`Aprobarbital
`0.136
`0.062
`Barbital
`0.092
`0.042
`Phenobarbital
`0.092
`0.034
`Vin barbital
`0.125
`0.036
`
`NaCl
`0.212
`0.184
`0.136
`0.132
`0.143
`
`NaBr
`0.143
`0.120
`0.088
`0.078
`0.096
`
`in which K. is a salting-out constant chosen empirically for
`each salt. This equation is valid for solutions with ionic
`strength up to approximately ~-
`SAL TING-OUT EFFECT-The aqueous solubility of a
`slightly soluble organic substance generally is affected mark(cid:173)
`edly by the addition of an electrolyte. This effect is particularly
`noticeable when the electrolyte concentration reaches 0.5 Mor
`higher. If the aqueous solution of the organic substance has a
`dielectric constant lower than that of pure water, its solubility
`is decreased and the substance is salted-out. The use of high
`concentrations of electrolytes, such as ammonium sulfate or
`sodium sulfate, for the separation of proteins by differential
`precipitation is perhaps the most striking example of this
`effect. The aqueous solu.t_ions of a few substances such as hy(cid:173)
`drocyanic acid, glycine, and cystine have a higher dielectric
`constant than that of pure water, and these substances are
`salted-in. These phenomena can be expressed empirically as
`log S = log S 0 :!: K,m
`in which S0 represents the solubility of the organic substance in
`pure water and S is the solubility in the electrolyte solution.
`The slope of the straight line obtained by plotting log S versus
`m is positive for salting-in and negative for salting-out. In
`terms of ionic strength this equation becomes
`
`(12)
`
`log S = log S 0 ± K; µ,
`(13)
`where K; = K. for univalent salts, K; = K/3 for unibivalent
`salts, and K; = K/4 for bivalent salts. The s~ting-out constant
`depends on the temperature as well as the nature of both the
`organic substance and the electrolyte. The effect of the electro(cid:173)
`lyte and the organic substance can be seen in Table 17-3. In all
`instances, if the anion is constant, the sodium cation has a
`greater salting-out effect than the potassium cation, probably
`due to the higher charge density of the former. Although the
`reasoning is less clear, it appears that, for a constant cation,
`chloride anion has a greater effect than bromide anion upon the
`salting-out phenomenon.
`
`ACIDS AND BASES
`
`Arrhenius defined an acid as a substance that yields hydrogen
`ions in aqueous solution and a base as a substance that yields
`hydroxyl ions in aqueous solution. Except for the fact that
`hydrogen ions neutralize hydroxyl ions to form water, no com(cid:173)
`plementary relationship between acids and bases (eg, that be(cid:173)
`tween oxidants and reductants) is evident in Arrhenius' defi(cid:173)
`nitions for these substances; rather, their oppositeness of
`character is emphasized. Moreover, no account is taken of the
`behavior of acids and bases in nonaqueous solvents. Also, al(cid:173)
`though acidity is associated with so elementary a particle as
`the proton (hydrogen ion), basicity is attributed to so relatively
`complex an association of atoms as the hydroxyl ion. It would
`seem that a simpler concept of a base could be devised.
`PROTON CONCEPT-In pondering the objections to Ar(cid:173)
`rhenius' definitions, Br~nsted and Bjerrum in Denmark and
`Lowry in England developed, and in 1923 announced, a more
`satisfactory, and more general, theory of acids and bases. Ac(cid:173)
`cording to this theory, an acid is a substance capable of yielding
`
`IONIC SOLUTIONS AND ELECTROLYTIC EQUILIBRIA
`
`231
`
`a proton (hydrogen ion), whereas a base is a substance capable
`of accepting a proton. This complementary relationship may be
`expressed by
`
`A
`acid
`
`;:: ff++ B
`base
`
`The pair of substances thus related through mutual ability to
`gain or lose a proton is called a conjugate acid-base pair.
`Specific examples of such pairs are
`
`Base
`Acid
`HCl;::ff+ + Cl·
`Cff