PHYSICAL
`PHHHHHHH
`
`ALFRED MARTIN
`
`MYLAN INST. EXHIBIT 1057 PAGE 1
`
`MYLAN INST. EXHIBIT 1057 PAGE 1
`
`

`

`FOURTH EDITION
`
`Physical Pharmacy-
`
`PHYSrCAL CHEMICAL PRINCIPLES
`
` THE PHARMACEUTICAL SCIENCES
`
`Alfred Martin, Ph.D.
`Emeritus CoulterR. Sublett Professor
`Drug Dynamics Institute,
`College of PluLrmacy,
`University of Texas
`
`with the participation of
`PILAR BUSTAMANTE, Ph.D.
`Titular Professor
`Department.of Pharmacy
`and Pharmaceutical Technology,
`University Alcala de Henares,
`Madrid, Spain
`
`and with illustrations by
`A. H. C. CHUN, Ph.D.
`Associate ResearchFellow
`PharmaceuticalProducts Division,
`Abbott Laboratories
`
`B. I. Waverly. Pvt Ltd
`New Delhi
`
`MYLAN INST. EXHIBIT 1057 PAGE 2
`
`MYLAN INST. EXHIBIT 1057 PAGE 2
`
`

`

`B. I. WaverlyPvtLtd
`54 Jan.-til, New Del.. - 110 001
`
`Reprintauthorisedby WaverlyInternational
`
`CopyriabtC 1993WaverlyIntematioul, 428 East PrestonStreet,
`Baltimore,Maryland 2102-3993USA
`
`Indian Reprint 1994
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`Publishedin India by B.I. Waverly Pvt Ltd, 54 Janpatb, New Delhi - 110001 aDd
`prill1ed at United IDdia Press, New Delhi.
`
`MYLAN INST. EXHIBIT 1057 PAGE 3
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`MYLAN INST. EXHIBIT 1057 PAGE 3
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`

`

`6
`Solutions of Electrolytes
`
`I
`
`Properties of Solutions of Electrolytes
`Arrhenius Theory of Electrolytic Dissociation
`Theory of Strong Electrolytes
`
`Coefficients for Expressing Colligative
`Properties
`
`The first satisfactory theory of ionic solutions was
`that proposed by Arrhenius in 1887. The theory was
`based largely on studies of electric conductance by
`Kohlrausch, colligative properties by van't Hoff, and
`chemical properties such as heats of neutralization by
`Thomsen. Arrhenius! was able to bring together the
`results of these diverse investigations into a broad
`generalization known as the theory of electrolytic
`dissociation.
`Although the theory proved quite useful for describ-
`ing weak electrolytes, it was soon found unsatisfactory
`for strong and moderately strong electrolytes. Accord..
`ingly, many attempts were made to modify or replace
`Arrhenius's ideas with better ones, and finally, in 1923,.
`Debye and Huckel put forth a new theory. It is based on
`the principles that strong electrolytes are completely
`dissociated into ions in solutions of moderate concentra-
`tion and that 'any deviation from complete dissociation
`is due to 'interionic attractions. Debye and Hucke!
`expressed the deviations in terms of activities', activity
`coefficients, and ionic strengths of electrolytic solu-
`tions, These quantities, which had been introduced
`earlier by Lewis, are discussed in this chapter together
`with the theory of interionic attraction. Other aspects
`of modem ionic theory and the relationships between
`electricity and chemical phenomena are considered in
`following chapters.
`We begin with a discussion of some of the properties
`of ionic solutions that led to Arrhenius theory of
`electrolytic dissociation.
`
`PROPERnES OF SOLUTIONS OF ELECTROLYTES
`Electrolysis. When, under a potential of several volts,
`a direct electric current (de) flows through an electro-
`lytic cell (Figure 6-1), a chemical reaction occurs. The
`..process is known as electrolysis. Electrons enter the
`
`cell from the battery or generator at the cathode (road
`down); they combine with positive ions or 'cations, in
`the solution, and the cations are accordingly reduced.
`The negative ions, or anions, carry electrons through
`the solution and discharge them at the anode (road up),
`and the anions are accordingly oxidized. Reduction is
`the addition of electrons to a chemical species, and
`oxidation is removal of electrons from a species. The
`CUITent in a solution consists of.a flow of positive and
`negative ions toward the electrodes, whereas the
`current in a metallic conductor consists of a" flow of free
`electrons migrating through a crystal lattice of fixed
`positive ions. Reduction occurs at the cathode, where
`electrons enter from the external circuit and are added
`to a chemical species in solution. Oxidation occurs at the
`anode where the electrons are removed from a chemical
`species in solution and go into the external circuit.
`
`_
`
`E,ectron'll
`
`504 =
`Anions (-)
`Fe+++
`Cations (+)
`
`-Current
`
`
`
`Fil. 6-1. Electrolysis in an electrolytic cell.
`
`12!!\
`
`MYLAN INST. EXHIBIT 1057 PAGE 4
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`MYLAN INST. EXHIBIT 1057 PAGE 4
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`

`

`126 Physical Pharmacy
`In the electrolysis of a solution of ferric sulfate in a
`cell containing platinum electrodes, a ferric ion mi-
`grates to the cathode where it picks up an electron and
`is reduced:
`Fe3+ + e = Fe2+
`(6-1)
`The sulfate ion carries the current through the solution
`to the anode, but it is. not easily nxidized; therefore,
`hydroxyl ions of the water are converted into molecular
`oxygen, which escapes at the anode, and sulfuric acid is
`found in the solution around the electrode. The oxida-
`tion reaction at the anode is
` + iH20 + e
`OH- =
`(6-2)
`Platinum electrodes are used here since they do not
`pass into solution to any extent. When attackable
`metals, such as copper or zinc, are used as the anode,
`their atoms tend to lose electrons, and the metal passes
`into solution as the positively charged ion.
`In the electrolysis of cupric chloride between plati-
`num .electrodes, the reaction at the cathode is
` + e = !Cu·
`(6-3)
`2
`2
`while at the anode, chloride and hydroxyl ions are
`converted respectively into gaseous molecules of chlo-
`rine and oxygen, which then escape. In each of these
`two examples, the net result is the transfer of one
`electron from the cathode to the anode,
`Transference Numbers. It should be noted that the
`flow of electrons through the solution from right to left
`in Figure 6-1 is accomplished by 'the movement of
`cations to the right as well as anions to the left. The
`fraction
`of total current carried by the cations or by the anions
`is known as the transport or transference number
`t.; or t.:
`
`(6-5)
`
`(6-4)
`
`t _current carried by cations
`+ -
`total current
`t = current carried by anions
`-
`total current
`The sum of the two transference numbers is obviously
`equal to unity:
`t; + t: = 1
`(6-6)
`The transference numbers are related to the veloci-
`ties of the ions, the faster-moving ion carrying the
`greater fraction of current. The velocities of the ions in
`tum depend on hydration' as well as ion size and charge.
`Hence, the speed and the transference numbers are not
`necessarily the same for positive and for negative ions.
`For example, the transference number of the sodium
`ion in a O.lO-M solution of NaCI is 0.385. Because it is
`greatly hydrated, the lithium ion in a 0.10-M solution of
`LiCI moves slower than the sodium ion and hence has a
`lower transference number, viz., 0.317.
`Electrical Units. According to Ohm's law, the strength
`of an electric current 1 in amperes flowing through a
`
`metallic conductor is related to the difference in applied
`potential or voltage E and the resistance R in ohms, as
`follows:
`
`I=E
`(6-7)
`R
`The current strength 1 is the rate of flow of current or
`the quantity Q of electricity (electronic charge) in
`coulombs flowing per unit time:
`1=9-
`t
`
`(6-8)
`
`and
`Quantity of electric charge, Q
`= current, 1 x time, t
`(6-9)
`The quantity of electric charge is expressed in coulombs
`(1 coul = 3 x 109 electrostatic units of charge, or esu),
`the current in amperes, and the electric potential in
`volts.
`Electric energy consists of an intensity factor, elec-
`tromotive force or voltage, and a quantity factor,
`coulombs.
`
`Electric energy ::;: E x Q
`(6-10)
`Faraday'S Laws. In 1833 and 1834, Michael Faraday
`announced his famous laws of electricity, which may be
`summarized in the statement, the passage of 96,500
`coulomb« of electricity through a
` cell
`produces a chemical change of 1
` -equivalen:
`weight of any substance. The quantity 96,500 is known
`as the faraday, F. The best estimate' of the value today
`is 9.648456 x 104 coulombs per gram equivalent.
`A univalent negative ion is an atom to which a
`valence electron has been added; a univalent positive
`ion is an atom from which an electron has been
`removed. Each gram equivalent of ions of any electro-
`.lyte carries Avogadro's number (6.02 x 1ij23) of positive
`or negative charges. Hence, from Faraday's laws, the
`passage of 96,500 coulombs of electricity results in the
`transport of 6.02 x lij23 electrons in the cell. A fa:aday
`is an Avogadro's number of electrons, corresponding to
`the mole, which is an Avogadro's number of molecules.
`The passage of 1 faraday of electricity causes the
`electrolytic deposition of the following number of gram
`atoms or "moles" of various ions: lAg+, 1Cu
`
`!Fe2+, !Fe3+. Thus, the number of positive charges
`kmedty 1 gram equivalent of Fe3+ is 6.02 x lij23, but
`the number of positive charges carried by 1 gram atom
`or 1 mole of ferric ions is 3 x 6.02 X 1023•
`Faraday's laws can be used to compute the charge on
`an electron in the following way, Since 6.02 x 1ij23
`electrons are associated with 96,500 coulombs of elec-
`tricity, each electron has a charge e of
`96,500 coulombs
`e= 6.02 x lij23 electrons
`= 1.6 x 10-19 coulombs/electron
`
`(6-11)
`
`MYLAN INST. EXHIBIT 1057 PAGE 5
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`

`

`'0"
`
`and since 1 coulomb = 3 x 109 esu
`e = 4.8 x 10- 10 electrostatic units
`(6-12)
`of charge/electron
`Electrolytic Conductance. The resistance R in ohms of
`any uniform metallic or electrolytic conductor is di-
`rectly proportional to its length l in cm and inversely
`proportional to its cross-sectional area A in cm'',
`I
`R = p -
`(6-13)
`A
`in which p is the resistance between opposite faces of a
`I-em cube of the conductor and is known as the specific
`resistance.
`The conductance C is the reciprocal of resistance,
`1C=-
`(6-14)
`R
`.and hence can be considered as a measure of the ease
`with which current can pass through the conductor. It
`is expressed in reciprocal ohms or mhos. From equation
`(6-13),
`c =1. =!:4
`(6-15)
`R
`p l
` K is the reciprocal of specific
`The specific
`.resistance and is expressed in mhos/em.
`1 K=-
`(6-16)
`P
`It is the conductance of a solution confined in a cube 1
`em on an edge as seen in Figure 6-2. The relationship
`between specific conductance and conductance or resis-
`tance is obtai
` by combining equations (6-15) and
`(6-16).
`K=ci=1.i
`(6-17)
`A RA
`Measuring the Conductance of Solutions. The Wheat-
`stonebridge assembly for measuring the conductance of
`a solution is shown in Figure 6-3. The. solution of
`unknown resrstance Rx
`is placed in the cell and
`
`Electrodes
`
`+
`
`8
`
`
`
`e
`v = 1 cm3
`Specific conductance (Ie)
`
`Volume containing
`one equivalent
`of solute
`Fil. 6-2. Relationship between specific conductance and equivalent
`conductance.
`
`Chapter 6 • Solutions of Electrolytes 127
`
`Variable condenser
`
`/
`
` Oscillator
`Fig. 6-3. Wheatstone bridge for conductance measurements.
`
`V\
`
`connected in the circuit. The contact point is moved
`along the slide wire beuntil at some point, say d, no cur-
`rent from the source of alternating current (oscillator)
`.flows through the detector (earphones or oscilloscope).
`When the bridge is balanced the potential at a is equal
`to that at d, the sound in the earphones or the
`oscillating pattern on the oscilloscope is at a minimum,
`and the resistances R s' R 1, and R2 are read.. In the
`balanced state, the resistance of the solution
` is
`obtained from the equation
`RI
`s; = R B R2
`(6-18)
`The variable condenser across resistance R 8 is used to
`produce a sharper balance. Some
`
`
`are calibrated in conductance as well as resistance
`values. The electrodes in the cell are platinized with
` so that catal-
`platinum black by electrolytic
`ysis of the reaction will occur at the platmum surfaces,
`and formation of a nonconducting gaseous film will not
`occur on the electrodes.
`Water that is carefully purified by redistillation in the
`presence of a little permanganate is used to prepare the
`solutions. Conductivity water, as it is called, has a
`specific conductance of about 0.05 x 10-6 mho/em at
`18° C whereas ordinary distilled water has a value
` over 1 x 10-6 mho/ern. For most conductiv-
`ity studies, "equilibrium water" containing. CO2 from
`the atmosphere is satisfactory. It 'has a specific conduc-
`tance of about 0.8 x 10-6 mho/em,
`The specific conductance K is computed from
`
`resistance R or conductance C by use of equation
`
`(6-17). The ;uantity lIA, the ratio of distance
`electrodes to the area of the electrode, has a definite
`value for each conductance cell; it is known as the cell
`constant, K. Equation (6-17) thus can be written
`K = KC = K/R
`(6-19)
`(The subscript x is no longer needed on R and is
`therefore dropped.) It would be difficult to measure l
`and A, but it is a simple matter to determine the cell
` ?f
`constant experimentally. The specific
`several standard solutions has been deterrmned In
`carefully calibrated cells. For example, a solution
`
`MYLAN INST. EXHIBIT 1057 PAGE 6
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`MYLAN INST. EXHIBIT 1057 PAGE 6
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`

`

`128 PhysicalPharmacy
`containing 7.45263 g of potassium chloride in 1000 g of
`water has a specific conductance of 0.012856 mho/ernat
`25°C. A solution of this concentration contains 0.1 mole
`of salt per cubic decimeter (100 cm'') of water and is
`known as a 0.1 demal solution. When such a solution is
`placed in a cell and the resistance is measured, the cell
`constant can be determined by use of equation (6-19).
`Ex.mpl, 6- I. A O.I-demal solution of KCI was placed in a cell
`whose constant K was desired. The resistance R was found to be
`34.69ohms at 25° C.
`K = KR = 0.012856 mho/em x 34.69 ohms
`= 0.4460em"!
`Example 6-2. When the cell described in Example 6-1 was filled
` solution, it had a resistance of 397ohms. What
`with a O.OI-N
`'is the specific conductance?
`K = R= 397 = 1.1234 x 10-
`0.4460
`3 mh 1
`K
`0 cm
`Equivalent Conductance. To study the dissociation of
`
`molecules into ions, independent of the
`the electrolyte, it is convenient to use equivalent
`conductance rather than specific conductance. All sol-
`.. utes of equal normality produce the same number of
`ions 'when completely dissociated., and equivalent con-
`ductance measures the current-carrying capacity of this
`given number of ions. Specific conductance, on the
`other hand, measures the current-carrying capacity of
`all ions in a unit volume of solution and accordingly
`varies with concentration.
`Equivalent conductance A is defined as the conduc-
`tance of a solution of sufficient volume to contain 1gram
`equivalent of the solute when measured in a cell in
`which the electrodes are spaced 1 em apart. The
`equivalent conductance Ac at a concentration o( c gram
`equivalents per liter is calculated from the product of
`the specific conductance K and the volume V in cm3 that
`contains 1 gram equivalent of solute. The cell may be
`imagined as having electrodes 1 em apart and to be of
`sufficient area so that it can contain the solution. The
`cell is shown 'in Figure' 6-2.
`
`
`3 ·
`V = 1000 cm./liter = 1000 cm3/E r
`
`,
`c Eqlliter
`c
`The equivalent conductance is obtained when K, the
`s
`conductance per cm of solution (i.e., the specific
`conductance), is multiplied by V, the volume in em3 that
`contains 1 gram equivalent weight of solute. Hence, the
`equivalent conductance Ac' expressed in units of mho
`cm2/Eq, is given by the expression
`Ac = K X V
`= 1000 K mho cm2/Eq
`C
`If the solution is 0.1 N in concentration, then the
`volume containing 1 gram equivalent of the solute will
`be 10,000 em3, and, according to equation
` the
`equivalent conductance will be 10,000 times as great as
`the specific conductance. This is seen in
` 6-9.
`
`(6-20)
`
`\1
`
`
`
`(6-21)
`
`Exampl,6-3. The measured conductance of a O.I-N solution of a
`drug is 0.0563 mho at 25° C. The cell constant at 25°Cis 0.520 em".
`What is the specific conductance and what is the equivalent conduc-
`tance of the solution at this concentration?
`K = 0.0563 x 0.620 = 0.0293 mho/cm
`Ac = 0.0293 x 1000/0.1
`= 293 mho cm2/Eq
`Equivalent Conductance ofStrooland Weak Electrolytes.
`As the solution of a strong electrolyte is diluted, the
`specific conductance K decreases because the number of
`ions per unit volume of solution is reduced. (It some-
`times goes through a maximum before decreasing.)
`Conversely, the equivalent conductance A of a solution
`of a strong electrolyte steadily increases on dilution.
`The increase in A with dilution is explained as follows.
`The quantity of electrolyte remains constant at 1 gram
`equivalent according to the definition of equivalent
`conductance; however, the ions are hindered less by
`their neighbors in the more dilute solution and hence
`can move faster. The equivalent conductance of a weak
`electrolyte also increases on dilution, but not as rapidly
`at first.
`Kohlrausch was one of the first investigators to study
`this phenomenon. He found that the equivalent conduc-
`tance was a linear function of the square root of the
`concentration for strong electrolytes in dilute solutions,
`as illustrated in Figure 6-4. The expression for Ac' the
`equivalent conductance at a concentration c (Eq/L), is
`Ac = Ao - bYe
`(6-22)
`in which Ao is the intercept on the vertical axis and is
`known as the equivalent conductance at infinite dilu-
`tion. The constant b is the slope of the line for the
`strong electrolytes shown in Figure 6-4.
`When the equivalent conductance of a weak electro-
`lyte is plotted against the square root of the concentra-
`
`140
`
`120
`
`100
`
`80
`A
`60
`
`40
`
`20
`
`.... ....
`
`AHc )
`440
`
`420
`
`400
`
`380
`
`360
`
`340
`
`320
`
`00
`
`0.1
`
`0.2
`Vi
`Fli. 8-4. Equivalent conductance of strong and weak electrolytes.
`
`0.3
`
`MYLAN INST. EXHIBIT 1057 PAGE 7
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`MYLAN INST. EXHIBIT 1057 PAGE 7
`
`

`

`tion, as shown for acetic acid in Figure 6-4, the curve
`cannot be extrapolated to a limiting value, and Ao must
`be obtained by a method such as is described in the
`following paragraph. The steeply rising curve for acetic
`acid results from the fact that the dissociation of weak
`electrolytes increases on dilution, with a large increase
`in the number of ions capable of carrying the current.
`Kohlrausch concluded that the ions of all electrolytes
`begin to migrate independently as the solution is
`diluted; the ions in dilute solutions are so far apart that
`they do not interact in any. way. Under these condi-
`tions, Ao is the sum of the equivalent conductances of
`the cations leo and the anions lao at infinite dilution
`(6-23)
`Based on this law, the known Ao values for certain
`electrolytes can be added and subtracted to yield Ao for
`the desired weak electrolyte. The method is illustrated
`in the following example.
`Example 6-4. What is the equivalent conductance at infinite
`dilution of the weak acid phenobarbital? The Ao of the strong
`electrolytes, HCI, sodium phenobarbital (NaP), and NaCI are ob-
`tained from the experimental results shown in Figure
` The
`values are AoHC1 = 426.2, AoNaP = 73.5, and
` = 126.5 mho
`cm2/Eq.
`Now, by Kohlrausch's law of the independent migration of ions,
`AoHP = lff+ +
`
`
`and
` +
`+
`AoHC1 + AoNaP - AoNaCI = lil+ +
` -
` -
`which, on simplifying the right-hand side of the equation, becomes
`AoHCl + AoNaP - AoNaCI = lYi+ +
`
`
`Therefore,
`
`AoHP = AoHC1 + A oNaP - AoNaCI
`
`and
`
`A oHP = 426.2 + 73.5 - 126.5
`= 373.2 mho cm
`2IEq
`Collilative Properties of Electrolytic Solutions and Con-
`centrated Solutions of Nonelectrolytes. As stated in the
`previous chapter, van't Hoff observed that the osmotic
`pressure of dilute solutions of nonelectrolytes, such as
`sucrose and urea, could be expressed satisfactorily by
`the equation, 'IT = RTc, equation (5-34), page 118, in
`which R is the gas constant, T is the absolute temper-
`ature, and c is the concentration in moles per liter.
`Van't Hoff found, however, that solutions of electro-
`lytes gave osmotic pressures approximately two, three,
`and more times larger than expected from this equa-
`tion, depending on the electrolyte investigated. By
`introducing a correction factor i to account for the
`irrational behavior of ionic solutions, he wrote
`(6-24)
`11" = iRTc
`By the use of this equation, van't Hoff was able to
`obtain calculated values that compared favorably with
` results of osmotic pressure. Van't
`the
`Hoff'recognized that i approached' the number of ions
`intowhich the molecule dissociated as the solution was
`made increasingly dilute.
`
`Chapter6 • Solutions of Electrolytes 129
`The factor i may also be considered to express the
`departure of concentrated solutions of nonelectrolytes
`from the laws of ideal solutions. The deviations of
`concentrated solutions of nonelectrolytes can be ex-
`plained on the same basis as deviations of real solutions
`from Raoult's law, considered in the preceding chapter.
`They included differences of internal pressures of the
`solute and solvent, polarity, compound formation or
`complexation, and association of either the solute or
`solvent. The departure of electrolytic solutions from the
`colligative effects in ideal solutions of nonelectrolytes
`may be attributed-in addition to the factors just
`enumerated-
`to dissociation of weak electrolytes and
`to interaction of the ions of strong electrolytes. Hence,
`the van't Hoff factor i accounts for the deviations of real
`solutions of nonelectrolytes and electrolytes, regardless
`of the reason for the discrepancies.
`The i factor is plotted against the molal concentration
`of both electrolytes and nonelectrolytes in Figure 6...;..5.
`For nonelectrolytes, it is seen to approach unity, and
`for strong electrolytes, it tends toward a value equal to
`the number of ions formed upon dissociation. For
`example, i approaches the value of 2 for solutes such as
` and CaCI2, and 4 for
`NaCI and CaS04' 3 for
`K3Fe(C)6 and. FeCI3•
`The van't Hoff factor can also be expressed as the
`ratio of any colligative property of a real solution to that
`of an ideal solution of a nonelectrolyte, since i repre-
`sents the number of times greater that the colligative
`effect is for a real solution (electrolyte 'or nonelectro-
`lyte) than .for an ideal nonelectrolyte.
`The colligative properties in dilute solutions of elec-
`trolytes- are expressed on the molal scale by the
`equations
`ap = O.Ol8ip1om
`11' = iRTm
`aTf = iKfm
`aTb = iKbm
`
`(6-25)
`(6-26)
`(6-27)
`(6-28)
`
`5
`
`4
`
`3
`
`2
`
`1
`
`NaCI
`
`Sucrose
`
`°0
`
`1
`
`2
`Molality
`FII.8-5. Van't Hoffi factor of representative compounds.
`
`3
`
`MYLAN INST. EXHIBIT 1057 PAGE 8
`
`MYLAN INST. EXHIBIT 1057 PAGE 8
`
`

`

`130 Physical Pharmacy
`Equation (6-25) applies only to aqueous solutions,
`whereas (6-26), (6-27), and (6-28) are independent of
`the solvent used.
`Example 6-5. What is the osmotic pressure of a 2.0-m solution of
`sodium chloride at 20° C?
`The i factor for a 2.0-m solution of sodium chloride as observed in
`Figure 6-5 is about 1.9.
`1T = 1.9 x 0.082 x 293 x 2.0 = 91.3 atm
`
`ARRHENIUS THEORY OF ELECTROLYTIC D"ISSOCIATION
`During the period in which van't Hoff was developing
`the solution laws, the Swedish chemist Svante Arrhe-
`nius was preparing his doctoral thesis on the properties
`of electrolytes at the University of Uppsala in Sweden.
`In 1887, he published the results of his investigations
`and proposed the now classic theory of dissociation. 1
`The new
`theory resolved many of the anomalies
`encountered in the earlier interpretations of electrolytic
`solutions. Although the theory was viewed with disfa-
`vor by some influential scientists of the nineteenth
`century, Arrhenius's basic principles of electrolytic
`dissociation were gradually accepted and are still
`considered valid today. The theory of the existence of
`ions in solutions of electrolytes even at ordinary
`temperatures remains intact, aside from some modifi-
`cations and elaborations that have been made through
`the years to bring it into line with certain stubborn
`experimental facts.
`The original Arrhenius theory, together with the
`alterations that have come about as a result of the
`intensive research on electrolytes, is summarized as
`follows. When electrolytes are dissolved "in water, the
`solute exists in the form of ions in the solution, as seen
`in the following equations
`Na" + CI- + H20
`H20 + Na+CI-
`
`[Ionic compound]
`.[Strong electrolyte]
`HgO+ + CI-
`
`
`(6-29)
`
`H20 + HCI
`[Covalent
`compound]
`
`[Strong electrolyte]
` HgO+ + CHgCQO-
`
`(6-30)
`
`H20 + CHgCOOH
`[Covalent
`compound]
`
`(6-31)
`[Weak electrolyte]
`The solid form of sodium chloride is.marked with +
`and - signs in reaction (6-29) to indicate that sodium
`chloride exists as ions even in the crystalline state. If
`electrodes are connected to a source of current ana are
`placed in a mass of fused sodium chloride, the molten
`compound will conduct the electric current, since the
`crystal lattice of the pure salt consists of ions. The
`addition of water to the solid dissolves the crystal and
`separates the ions in solution.
`
`I
`
`Hydrogen chloride exists essentially as neutral mol-
`ecules rather than as ions in the pure form, and does not
`conduct electricity. When it reacts with water, how-
`ever, it ionizes according to reaction (6-30). HgO+ is
`the modern representation of the hydrogen ion in water
`and is known as the hydronium or oxonium ion. In
`addition to HgO+, other hydrated species of the proton
`probably exist in solution, but they need not be
`considered here. 2
`Sodium chloride and hydrochloric acid are strong
`electrolytes because they exist almost completely in the
`ionic form in moderately concentrated aqueous solu-
`tions. Inorganic acids such as HCI, HN03, H2S04, and
`HI; inorganic bases as NaOH and KOH of the alkali
`metal family and Ba(OH)2 and Ca(OH)2 of the alkaline
`earth group; and most inorganic and organic salts are
`highly
`ionized and belong to the class of strong
`electrolytes.
`Acetic acid is a weak electrolyte, the oppositely
`directed arrows in equation (6-31) indicating that an
`equilibrium between the molecules and ions is estab-
`lished. Most organic acids and bases and some inorganic
`compounds, such as HgBOg, H2COg, and NH 40H,
`belong to the class of weak electrolytes. Even some
`salts (lead acetate, HgCI2, HgI, and HgBr) and the
`complex ions Hg(NHg)2+ Cu(NHa)42+, and Fe(CN)63-
`are weak electrolytes.
`Faraday applied the term ion (Greek: wanderer) to
`these species of electrolytes and recognized that the
`cations (positively charged ions) and anions (negatively
`charged ions) were responsible for conducting the
`electric current. Before thetime of Arrhenius's publi-
`cations, it was believed that a solute was not spontane-
`ously decomposed in water, but rather dissociated
`appreciably into ions only when an electric current was
`passed through the solution.
`Drugs and Ionization. Some drugs, such as anionic and
`cationic antibacterial and antiprotozoal agents, are
`more active when in the ionic state. Other compounds,
`such as the hydroxybenzoate esters (parabens) and
`many general anesthetics, bring about their biologic
`effects as nonelectrolytes. Still other compounds, such
`as the sulfonamides, are thought to exert their drug
`action both as ions and as neutral molecules. 3
`Degree of Dissociation. Arrhenius did not originally
`consider strong electrolytes to be ionized completely
`except in extremely dilute solutions. He differentiated
`between strong and weak electrolytes by the fraction of I
`the molecules ionized: the degree of dissociation Q. A!
`strong electrolyte was one that dissociated into ions to !
`a high degree and a weak electrolyte one that dissoci-!
`ated into ions to a low degree.
`Arrhenius determined the degree of dissociation!
`directly from conductance measurements. He 'recog-.
` that the
` conductance at.infin.ite. dilu-!
`tion Ao was a measure of the complete dISSOCIatIon of
`the solute into its ions and that Ac represented the!
`number of solute particles present as ions at a concen-
`tration c. Hence, the fraction of solute molecules!
`
`I
`
`I
`
`MYLAN INST. EXHIBIT 1057 PAGE 9
`
`MYLAN INST. EXHIBIT 1057 PAGE 9
`
`

`

`ionized, or the degree of dissociation, was expressed by
`the equation'
`
`Ac
`0.=-
`(6-32)
`Ao
`in which Ac/Ao is known as the conductance ratio.
`Example 6-6. The equivalent conductance of acetic acid at 25° C
`and at infinite dilution is 390.7 mho cm2/Eq. The equivalent conduc-
`tance of a 5.9 x 10-3 M solution of acetic acid is 14.4 mho cm2/Eq.
`What is the degree of dissociation of acetic acid at this concentration?
`14.4
`a = 390.7 = 0.037 or 3.7%
`The van't Hoff factor i can be connected with the
`degree of dissociation a in the following way. The i
`factor equals unity for an ideal solution of a nonelectro-
`lyte; however, a term must be added to account for the
`particles produced when a molecule of an electrolyte
`dissociates. For 1 mole of calcium chloride, which yields
`3 ions per molecule, the van't Hoff factor is given by
`i = 1 + 0.(3 - 1)
`(6-33)
`or, in general, for an electrolyte yielding v ions,
`i = 1 + o.(v - 1)
`(6-34)
`from which is obtained an expression for the degree of
`dissociation,
`
`i-I
`(6-35)
`o.=v-1
`The cryoscopic method is used to determine' i from the
`expression
`
`or
`
`(6-36)
`
`(6-37)
`
`Example 6-7. The freezing point of a 0.10-m solution of acetic acid
`is -0.188° C. Calculate the degree of ionization of acetic acid at this
`concentration. Acetic acid dissociates into two ions, that is, v = 2.
`.
`0.188
`t = 1.86 x 0.10 = 1.011
`a = i-I = 1.011 - 1 = 0.011
`v-I
`2-1
`In other words, according to the result of Example
`6-7 the fraction of acetic acid present as free ions in a
`O.10-m solution is 0.011. Stated in percentage terms,
`acetic acid in 0.1 m concentration is ionized to the
`extent of about 10/0.
`
`THEORY OF STRONG, ELECTROLYTES
`Arrhenius used a to express the degree of dissocia-
`tion of both strong and weak electrolytes, and van't
`Hoffintroduced the factor i to account for the deviation
`of strong and weak electrolytes and nonelectrolytes
`
`Chapter 6 • Solutions of Electrolytes 131
`from the ideal laws of the colligative properties,
`regardless of the nature of these discrepancies. Accord-
`ing to the early ionic theory, the degree' of dissociation
`of ammonium chloride, a strong electrolyte, was calcu-
`lated in the same manner as that of a weak electrolyte.
`Example 6-8. The freezing point depression for a O.Ol-msolution of
`ammonium chloride is 0.0367° C. Calculate the "degree of dissocia-
`tion" of this electrolyte.
`0.0367° = 1.97
` =
`i =
`1.86 x 0.010
`Kfm
`a = 1.97 - 1 = 0.97
`2 - 1
`The Arrhenius theory is now accepted for describing
`the behavior only of weak electrolytes. The degree of
`dissociation of a weak electrolyte can be calculated
`satisfactorily from the conductance ratio AdAo or
`obtained from the van't Hoff i factor.
`Many inconsistencies arise, however, when an at-
`tempt is made to apply the theory to solutions of strong
`electrolytes. In dilute and moderately concentrated
`solutions, they dissociate almost completely into ions,
`and it is not satisfactory to write an equilibrium
`expression relating the concentration of the ions and
`the minute amount of undissociated molecules, as is
`done lor weak electrolytes (Chapter 7). Moreover, a
`discrepancy exists between a calculated from the i
`value and a calculated from the conductivity ratio for
`strong electrolytes in aqueous solutions having concen-
`trations greater than about 0.5 M.
`For these reasons, one "does not account for the
`deviation of a strong electrolyte from ideal nonelectro-
`lyte behavior by calculating a degree of dissociation. It
`is more convenient to cbnsider a strong electrolyte 'as
`completely ionized and to introduce a factor that
`expresses the deviation of the solute from 10.0% ioniza-
`tion. The activity and osmotic coefficient, discussed in
`subsequent paragraphs, are used for this purpose,
`Activity and Activity Coefficients. An approach that
`conforms well to the facts and that has evolved from a
`large number of studies on solutions of strong electro-
`lytes ascribes the behavior .of strong electrolytes to an
`electrostatic attraction between the ions.
`The large number of oppositely charged ions in
`solutions of electrolytes influence one another through
`interionic attractive forces. Although this interference
`is negligible in dilute solutions, it becomes appreciable
`at moderate concentrati