AlexanderApelblat
`
`SUING aD
`
`al Santos
`
`PFIZER, INC., IPR2017-01357, Ex. 1039, p. 1 of 204
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`

`

`Alexander Apelblat
`
`CITRIC ACID
`
`1 3
`
`PFIZER, INC., IPR2017-01357, Ex. 1039, p. 2 of 204
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`

`

`Alexander Apelblat
`Department of Chemical Engineering
`Ben-Gurion University of the Negev
`Beer Sheva
`Israel
`
`
`
`
`
`ISBN 978-3-319-11232-9
`DOI 10.1007/978-3-319-11233-6
`Springer Cham Heidelberg New York Dordrecht London
`
`ISBN 978-3-319-11233-6 (eBook)
`
`Library of Congress Control Number: 2014955173
`
`© Springer International Publishing Switzerland 2014
`This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part
`of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
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`Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright
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`The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
`does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
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`While the advice and information in this book are believed to be true and accurate at the date of
`publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for
`any errors or omissions that may be made. The publisher makes no warranty, express or implied, with
`respect to the material contained herein.
`
`Printed on acid-free paper
`
`Springer is part of Springer Science+Business Media (www.springer.com)
`
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`

`

`Contents
`
`1 Introduction ..............................................................................................
`References ..................................................................................................
`
` 1
` 6
`
` 13
` 13
`
` 21
` 27
` 32
`
`2 Properties of Citric Acid and Its Solutions ............................................
`2.1
` Physicochemical Properties of Citric Acid in the Solid State ..........
`2.2
` Melting and Freezing Temperatures of Aqueous Solutions
`of Citric Acid ....................................................................................
`2.3 Boiling Points of Aqueous Solutions of Citric Acid ........................
`2.4 Solubility of Citric Acid in Water ....................................................
`2.5
` Vapour Pressures of Water Over Saturated Solutions
` 37
`of Citric Acid ....................................................................................
` 41
` Solubilities of Gases in Aqueous Solutions of Citric Acid ..............
`2.6
` 42
` Volumetric Properties of Aqueous Solutions of Citric Acid ............
`2.7
` 53
` Compressibility Properties of Aqueous Solutions of Citric Acid .....
`2.8
` 67
` Thermodynamic Properties of Aqueous Solutions of Citric Acid ....
`2.9
` 83
`2.10 Viscosities of Aqueous Solutions of Citric Acid ..............................
` 87
`2.11 Diffusion Coefficients of Citric Acid in Aqueous Solutions ............
` 92
`2.12 Thermal Conductivities of Aqueous Solutions of Citric Acid ..........
` 94
`2.13 Electrical Conductance of Citric Acid in Aqueous Solutions ..........
`2.14 Index of Refraction of Aqueous Solutions of Citric Acid ................ 104
`2.15 Surface Tension of Aqueous Solutions of Citric Acid ...................... 107
`2.16 Solubility of Citric Acid in Organic Solvents .................................. 111
`2.17 Two-Phase Citric Acid–Aliphatic Alcohol–Water Systems ............. 116
`2.18 Two-Phase Citric Acid–Tertiary Amine–Water Systems ................. 126
`References ................................................................................................. 130
`
`3 Dissociation Equilibria in Solutions with Citrate Ions ......................... 143
`3.1
` Mathematical Representation of Citric Acid Dissociation ............... 143
`3.2
` Distribution of Citrate Ions in Aqueous Solutions of Acidic
`and Neutral Citrates .......................................................................... 146
` Dissociation Constants of Citric Acid in Pure Water ....................... 148
` Dissociation Constants of Citric Acid in Electrolyte Solutions ....... 161
`
`3.3
`3.4
`
`xi
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`xii
`
`Contents
`
`3.5
`
` Dissociation Constants of Citric Acid in Pure Organic
`Solvents and Organic Solvent-Water Mixtures ................................ 175
` Effect of Pressure on Dissociation Constants .................................. 179
`3.6
` Citrate Buffers .................................................................................. 180
`3.7
` Citric Acid Complexes ..................................................................... 192
`3.8
`References ................................................................................................. 195
`
`4 Citric Acid Chemistry .............................................................................. 213
`4.1
` Chemical Syntheses of Citric Acid .................................................. 213
`4.2
` Synthesis of Labeled Citric Acid ...................................................... 217
`4.3
` Thermal Decomposition of Citric Acid ............................................ 219
`4.4
` Decomposition of Citric Acid by Irradiation ................................... 223
`4.5
` Oxidation of Citric Acid ................................................................... 225
`4.6
` Qualitative and Quantitative Determination of Citric Acid ............. 232
`4.7
` Formation of Citric Acid Anhydrides ............................................... 234
`4.8
` Esterification and Neutralization Reactions Associated
`with Citric Acid ................................................................................ 236
` Formation of Amides Citrate-Based Siderophores and
`Other Compounds ............................................................................ 237
`References ................................................................................................. 241
`
`4.9
`
`5.4
`
`5.5
`
`5 Physicochemical Properties of Inorganic Citrates ................................ 267
`5.1
` Application of Inorganic Citrates and Their Crystal Structures ....... 267
`5.2
` Solubilities of Inorganic Citrates in Water ....................................... 272
`5.3
` Activities of Alkali Metal Citrates at Freezing Point
`Temperatures .................................................................................... 282
` Vapour Pressures of Water Over Saturated Solutions of
`Alkali Metal Citrates ........................................................................ 287
` Boiling Points, Activities and Vapour Pressure Lowerings
`in Aqueous Solutions of Alkali Metal Citrates ................................. 289
` Volumetric Properties of Aqueous Solutions of Alkali
`Metal Citrates ................................................................................... 307
` Volumetric Properties of Ternary Aqueous Solutions with
`Alkali Metal Citrates ........................................................................ 319
` Compressibility Properties of Aqueous Solutions of Alkali
`Metal Citrates ................................................................................... 325
` Viscosities of Aqueous Solutions of Alkali Metal Citrates .............. 330
`5.9
`5.10 Diffusion Coefficients and Indices of Refraction of Alkali
`Metal Citrates in Aqueous Solutions ................................................ 334
`5.11 Two-Phase Alkali Metal Citrate - Aliphatic
`Alcohol - Water Systems .................................................................. 336
`5.12 Two-Phase Alkali Metal Citrate - Polyethylene Glycol
`(PEG) - Water Systems ..................................................................... 341
`References ................................................................................................. 345
`
`5.6
`
`5.7
`
`5.8
`
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`Chapter 2
`Properties of Citric Acid and Its Solutions
`
`2.1
`
` Physicochemical Properties of Citric Acid
`in the Solid State
`
`Citric acid - 2-hydroxy-1,2,3-tricarboxylic acid, C6H8O7≡H3Cit, molar mass
`192.12 g mol− 1. CAS registry [77-92-9], E 330
`
`Sometimes, also the notation H4Cit is used for it in the literature, when the hy-
`drogen atom from hydroxyl group is involved in complexation reactions. There are
`no asymmetric carbon atoms in citric acid or in its anions, i.e. they are optically in-
`active. However, it is possible to make them asymmetrical by substitution of one of
`the hydrogen atoms in the methylene groups by another atom or group (the central
`carbon atom is prochiral).
`Citric acid is a natural constituent of many plants, animal tissues and physi-
`ological fluids. In trace amounts it appears in a variety of fruits and vegetables, but
`macroscopic quantities are present in citrus fruits notably lemons and limes. Fruits
`having above 1 % (on the dry weight basis) are: lemons 4.0–8.0 %, black currents
`1.5–3.0 %, grapefruits 1.2–2.1 %, oranges, tangerines, red currents, raspberries and
`strawberries contain citric acid in the 0.6–1.3 % range. Some typical values for a hu-
`man body are: blood 10–25 ppm, bones 7500 ppm, semen 2000–4000 ppm, thyroid
`gland 750–900 ppm, mammary gland 3000 ppm, human milk 500–1250 ppm and
`urine 100–750 ppm [1].
`At first, the crystal structure of anhydrous citric acid was established by Bennett
`and Yuill [2] in 1935 and later refined by others [3, 4] with an indication of the
`hydrogen bonding in the crystal. The crystal structure of citric acid monohydrate
`was reported by Burns and Iball [5] and Roelofsen and Kanters [6]. According to
`Nordman et al. [3], anhydrous citric acid is monoclinic, crystallizes in the space
`group P21/a and citric acid monohydrate is orthorhombic and belongs to the space
`13
`© Springer International Publishing Switzerland 2014
`A. Apelblat, Citric Acid, DOI 10.1007/978-3-319-11233-6_2
`
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`

`14
`
`group P212121, both crystals have four molecules in the unit cell. Bennett and Yuill
`also found that the transition from citric acid monohydrate to anhydrous citric acid
`occurs between 36.15 and 36.45 °C with the mean value of 36.3 °C. The Marshall
`results [7] are slightly higher, from 36.35 to 36.6 °C and he proposed the transition
`temperature of 36.5 °C when De Kruif et al. [8] gave the value of 36.0 ± 0.5 °C based
`on the X-ray powder diffraction patterns. Oechler [9] based on solubility and vapour
`pressure measurements reported the value of 36.7 °C. From solubility determina-
`tions Dalman [10] and Slobodin and Novotelnova [11] estimated the transition tem-
`perature as 35.8 and 36.6 °C respectively. Using dynamic vapour sorption (DVS)
`and discontinuous isoperibolic thermal analysis (DITA) techniques Lafontaine et al.
`[12] gave 37.0 ± 1.0 °C result. Lower values about 34.5 °C, were reported by Nývlt
`[13] and Helmdach et al. [14] from solubility, ultrasound and turbidity studies.
`The used by Bennett and Yuill crystals of anhydrous citric acid had density of
`d = 1.665 g cm−3 at 18 °C and the melting point was 156–157 °C. The density of
`citric acid monohydrate as reported by Laguerie et al. [15] was d = 1.542 g cm−3 at
`25 °C. Wilhoit and Shiao [16] measured, from 20 to 80 °C, the specific volumes of
`the solid citric acid by using a glass dilatometer and expressed their results by the
`following quadratic equation
`
`
`
`−
`1
`
`−
`⋅
`⋅
`=
`3
`0.6415 4.770 10
`v/cm g
`
`θ=
`−
`
`(T
`/ K 273.15)
`
`−
`
`5
`
`θ+
`
`⋅
`2.363 10
`
`−
`θ
`6
`2
`
`(2.1)
`
`
`
`The volume expansion and the inner energy coefficients at 25 °C were also determined:
` and
`
`−
`−
`−
`−
`−
`−
`∂
`∂
`=
`∂
`∂
`= −
`3
`1
`1
`4
`1
`1
`3
`(
`/V T
`
`) /cm g K
`0.704·10
`(
`/U P
`
`) /J ·g ·atm
`2.134·10
`P
`T
`with 1 atm = 101.325 kPa. They observed that citric acid decomposes in the 152.9–
`155 °C temperature region. The elastic and thermoelastic properties of anhydrous
`and monohydrate citric acid crystals were studied by Khan and Narasimhamurty
`[17] and Haussuehl and Wang [18].
`Citric acid crystallizes from hot aqueous solutions in the anhydrous form as col-
`orless transparent crystals or white crystalline powders. Citric acid monohydrate
`crystallizes from cold solutions and the crystals lose their hydration water if gently
`heated at 70–75 °C and melt in the range of 135–152 °C. Fast heating leads to dehy-
`dration at about 100 °C, melting at 153 °C and decomposition above 175 °C. Citric
`acid is deliquescent in wet air. Considering the importance of industrial aspects of
`crystallization from aqueous solutions, a number of studies of supersaturated or
`nearly saturated citric acid solutions were performed. It was demonstrated that the
`structure of these solutions and impurities have a great influence on nucleation ki-
`netics and crystal formation and growth of citric acid crystals [19–32].
`Utilization of citric acid in solid dispersions to increase the dissolution and oral
`absorption of sparingly soluble drugs was first suggested by Chiou and Riegelman
`[33] in the case of a water-insoluble antifungal antibiotic griseofulvin. A number
`of other pharmaceutical preparations (e.g. phenobarbital and hexobarbital) in the
`form of glass dispersions mixtures which include citric acid, were also investigated
`by various experimental techniques [34–43]. The melted highly viscous citric acid
`can be drown into threads or sheets and after standing at 37 °C for a few days into a
`
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`2.1 Physicochemical Properties of Citric Acid in the Solid State
`
`15
`
`hard, brittle and transparent glass. This glassy state is transformed into a crystalline
`state after months of standing at room temperature [44]. Thus, a physiologically
`acceptable and easily soluble carrier and poorly water-soluble drug are melted to-
`gether and later solidified by cooling to room temperature. The formed glassy solid
`mixture when exposed to water or gastrointestinal fluids will dissolve rapidly the
`carrier and disperse drug particles. The competition during a rapid cooling between
`crystallization and glass formation determines whether a crystal or glass transition
`occurs. The glass–liquid transition is the reversible transition in amorphous or semi-
`crystalline materials which is accompanied by changes in physical properties (spe-
`cific heat capacity and viscosity).
`The glass transition temperatures Tg and corresponding changes in physical prop-
`erties were determined for investigated solid mixtures but also for pure citric acid.
`Simmer and Enever [35] reported Tg = − 23 °C for citric acid monohydrate, but this
`result was in conflict with the Timko and Lordi [36] findings for anhydrous citric
`acid. The glass transition for bulk-prepared citric acid glass was Tg = 13.2 °C and for
`the in situ conditions Tg = 10.2 °C. Repeated determination by Simmer and Enever
`[37] showed Tg = 7.0 °C and that water present in citric acid monohydrate strongly
`reduces the glass temperature. Thermal citric acid studies of Timko and Lordi also
`indicated that the bulk-prepared melt (an amorphous + crystalline citric acid) exhib-
`its a broad exothermic transition about − 80 °C which is followed by an endothermal
`effect. On contrary, the in situ did not exhibit an exothermic transition. Timko and
`Lordi [38] also investigated the effect of impurities and thermal history on the value
`of Tg and found that the lowering of glass transition temperatures is associated with
`a higher temperature of the melt preparation and with a longer exposure at this tem-
`perature. Decrease in Tg is accompanied by a progressive discoloration of the mol-
`ten citric acid from a clear transparent liquid to a yellowish brown liquid. The effect
`of impurities was simulated by adding acotinic acid, a dehydration decomposition
`product of citric acid, which degrades upon melting. With increasing quantities of
`acotinic acid in the mixture it was observed that the glass transition temperature
`strongly decreases. A more systematic study of the properties of citric acid at its
`glass transition in a dry and hydrated states was performed by Lu and Zografi [39].
`Their values for anhydrous citric acid are: Tg = (10.2 ± 0.2) °C; ΔCp = (0.83 ± 0.04)
`*Hη∆ = 733 kJ mol−1 (the activation energy for viscous flow at Tg) and
`J g−1 K−1 and
`for citric acid monohydrate are: Tg = (10.7 ± 1.0) °C; ΔCp = (0.81 ± 0.05) J g−1 K−1
`*Hη∆ = 410 kJ mol−1. These values are consistent with the Hoppu et al. [42]
`and
`results: Tg = (11.7 ± 0.9) °C; ΔCp = (0.82 ± 0.03) J g−1 K−1; η = 2.6 ⋅ 1010 Pa s and
`*Eη∆ = 156 kJ mol−1 (flow activation energy at Tg). In the case of amorphous citric
`acid which contains 8.6 w/w % of residual water (the equimolar composition) the
`glass transition temperature has the value of Tg = − 25 °C and ΔCp = (0.92 ± 0.02)
`J g−1 K−1 which is similar to the Simmer and Enever value [35]. The glass transition
`of frozen solution of citric acid was estimated to be Tg = − 50 °C [39] which is in an
`agreement with the Kodoya et al. result Tg = − 55.1 °C as determined in the freeze-
`drying process study [40]. Lu and Zografi claimed that the relatively low values
`of Tg are responsible for difficulty to prepare and maintain a large quantity of pure
`citric acid in the amorphous state without significant crystallization. Evidently, be-
`sides drug + citric acid solid dispersions, the values of glass transition temperatures
`
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`

`300
`
`270
`
`240
`
`210
`
`180
`
`Tg/K
`
`16
`
`0.5
`
`0.6
`
`0.7
`
`0.8
`
`0.9
`
`1.0
`
`w
`
`Fig. 2.1 The glass transition temperature Tg as a function of weight fraction of citric acid w in the
`citric acid + water mixtures.
` - [35–39, 42];
` - [43];
` - [45];
` - [46]; continuous line is calcu-
`lated using Eq. (2.2)
`
`in the citric acid + water system, are also of great interest in meteorological in-
`vestigations. Systematic measurements of Tg as a function of added water to citric
`acid were performed by Lienhard et al. [43], Maltini et al. [45], and Murray [46].
`Moreira [47] determined Tg values in the 0.4 < w < 0.8 concentration range, but un-
`fortunately they are given only in graphical form. All available in the literature Tg
`values are plotted in Fig. 2.1 and they can be correlated by the following equation
`
`
`
`gT
`
`/K =
`
`−
`+
`283.15 419.36w 419.89w
`
`2
`
`
`
`(2.2)
`
`where w is the weight fraction of citric acid in the mixture. This and other fit-
`ting equations were evaluated by using an unweighted multivariate least-squares
`method.
`Aerosols in upper troposphere often contain a substantial and variable fraction
`of organic compounds (ranging from 10 to 70 % of the total dry aerosol mass). They
`are mixed with inorganic material, usually with ammonium sulfate. Water-soluble
`organic components of aerosols effect the hygroscopicity, phase transition, light
`scattering, formation and properties of cloud droplets. Under upper tropospheric
`conditions, droplets containing dissolved organic substances in aqueous solutions
`can become glassy. Thus, the impact of organic compounds on the cloud forming
`and ice cloud nucleation has been widely investigated [46, 48–56]. In this con-
`text, citric acid which was identified in aerosol particles, was frequently used as
`a model substance for atmospheric experiments. Citric acid as well other organic
`acids received much attention because they are able to absorb water and alter the
`radiation balance and finally the climate. It is worthwhile also to note that citric
`acid solutions, as was observed by Corley and Killoy [57], are stable with regards
`
`2 Properties of Citric Acid and Its Solutions
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`2.1 Physicochemical Properties of Citric Acid in the Solid State
`
`17
`
`450
`
`375
`
`300
`
`225
`
`150
`
`75
`
`CP/Jmol-1K-1
`
`0
`
`0
`
`50
`
`100
`
`200
`150
`T/K
`Fig. 2.2 The molar heat capacity of anhydrous and monohydrate citric acid as a function of tem-
`perature. Anhydrous citric acid ■ - [8]; citric acid monohydrate
` - [58];
` - [8]
`
`250
`
`300
`
`350
`
`to time, light and air exposure. The studies of the water-citric acid-electrolyte aero-
`sols in atmosphere are also important because they provide significant information
`about activities, solubilities, surface tension and other properties of aqueous solu-
`tions of citric acid [46, 49–51, 53–56].
`From thermodynamic properties of solid citric acid monohydrate, the heat
`capacities, enthalpies and entropies were determined by Evans et al. [58] in the
`20–300 K temperature range. De Kruif et al. [8] reported the heat capacities, en-
`thalpies, entropies and the Gibbs free energies from 120 to 300 K for monohydrate,
`and the corresponding values of the thermodynamic functions from 90 to 330 K
`for anhydrous citric acid. They observed a slightly superheated large transition at
`312.1 K and above this transition, a very large molar heat capacities with a sig-
`nificant temperature dependence (Fig. 2.2). This temperature is higher than that
`mentioned above from the literature ~ 309.7 K but probably it indicates that the
`formation of the monohydrate from the high-temperature solid phase was not com-
`plete [8]. As can be seen in Fig. 2.2, both sets of molar heat capacities of citric acid
`monohydrate agree well and they can be represented by the polynomial expression
`for 20 K < T < 305 K
`
`−
`−
`=
`−
`+
`1
`2
`C (H Cit· H O)/ Jmol K
`
`
`27.324 2.1259(T
`P
`3
`2
`−
`−
`+
`−
`5
`8
`4
`3
`3.3504·10 (
`/ K)
`3.9008·10 (
`/ K)
`T
`T
`
`/ K) 1.0333·10 (T
`
`−
`1
`
`/ K)
`
`2
`
`(2.3)
`
`
`
`For temperatures below 22 K, Evans et al. [58] obtained the molar heat capacities
`using the Debye function with TD = 150 K. In the case of anhydrous citric acid, in the
`84 K < T < 330 K temperature interval, the molar heat capacities can be expressed by
`
`−
`−
`+
`= −
`3
`
`
`· K
`C (H Cit) / J· mol
`6.7603 1.3632(T
`P
`3
`−
`−
`+
`−
`9
`4
`3
`5
`1.0096·10 (
`/ K)
`9.4236·10 (
`/ K)
`T
`T
`
`−
`1
`
`−
`1
`
`/ K) 4.1314·10 (T
`
`2
`
`/ K)
`
`(2.4)
`
`
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`

`

`T∆S
`
`∆H
`
`∆G
`
`100
`
`50
`
`0
`
`∆G, ∆H, T∆S/kJmol-1
`
`18
`
`-50
`
`0
`
`50
`
`100
`
`200
`
`250
`
`300
`
`150
`T/K
`Fig. 2.3 Thermodynamic functions ΔG, ΔH and T ⋅ ΔS of citric acid monohydrate as a function of
`temperature. ■, ■, ■ - [8]; ■, ■, ■ - [58]
`
`Thermodynamic functions ΔG, ΔH and T ⋅ ΔS of citric acid monohydrate as a func-
`tion of temperature were determined by Evans et al. [58] and De Kruif et al. [8] and
`they are plotted in Fig. 2.3. De Kruif et al. used in calculations of thermodynamic
`functions the absolute entropy and enthalpy reported by Evans et al. at 120 K. The
`functions ΔG, ΔH and T ⋅ ΔS are consistent in both investigations but there is a no-
`ticeable difference between them (Fig. 2.3). As can be observed, the Gibbs free
`energy is negative ΔG < 0 and the enthalpy and entropy are positive and they have
`similar values with ΔH < T ⋅ ΔS. The absolute values of all thermodynamic functions
`increase with increasing of temperature T. Using the Evans et al. [58] results which
`cover a more extended temperature range 0 < T < 300 K, the thermodynamic func-
`tions of citric acid monohydrate are
`
`=
`
`1
`..
`
`−
`2
`
`(T
`
`−
`7
`
`/
`
`K)
`
`
`
`⋅
`−
`.5 1776 10
`3
`K)
`
`/
`
`−
`4
`
`
`
`(T
`
`/
`
`K)
`
`2
`
`(
`
`T T
`
`⋅
`.1 6377 10
`
`+
`⋅
`2185 10
`= −
`⋅
`.2 7307 10
`⋅
`−
`.3 4548 10
`−
`2
`⋅
`−−
`
`−
`⋅
`
`
`
`
`−
`3
`
`(
`
`/
`
`K)
`
`
`
`−
`7
`
`
`
`(T
`
`/
`
`K)
`
`
`5
`
`⋅
`..5329 10
`
`−
`4
`
`
`
`(T
`
`/
`
`K)
`
`2
`
`+
`3
`
`(2.5)
`
`=
`
`1 9108 10.
`
`4 6733 10.
`
`
`−
`7
`
`(T
`
`(
`T
`
`⋅
`
`
`1 0710 10.
`
`−
`3
`
`
`
`(T
`
`/
`
`K)
`
`2
`
`+
`3
`
`/
`
`K)
`
`/
`
`K)
`
`
`
`∆G(H Cit H O) kJmol⋅
`
`
`/
`3
`2
`
`∆
`⋅
`/H(H Cit H O) kJmol
`3
`2
`
`
`
`T
`
`∆
`⋅
`/S(H Cit H O) kJmol
`3
`2
`
`
`
`−
`1
`
`−
`1
`
`−
`1
`
`The enthalpy, entropy and the Gibbs free energy of formation of crystalline monohy-
`drate at 298.15 K, as calculated from the values of constituent elements in their standard
`states are: ΔGf(s, 298.15 K) = − 1472.8 ± 1.3 kJ mol−1, ΔHf (s, 298.15 K) = − 1837.6 ±
`0.8 kJ mol−1 and ΔSf(s, 298.15 K) = − 1223.8 ± 0.8 J mol−1 K−1 [58, 59] when Burton
`
`2 Properties of Citric Acid and Its Solutions
`
`PFIZER, INC., IPR2017-01357, Ex. 1039, p. 11 of 204
`
`

`

`2.1 Physicochemical Properties of Citric Acid in the Solid State
`
`19
`
`[60] using the enzymatic equilibrium data, gives a slightly higher value for the Gibbs
`free energy of formation of the crystalline monohydrate ΔGf (s, 298.15 K) = − 1168.8 ±
`6.3 kJ mol−1. The Wilhoit and Shiao value ΔHf(s, 298.15 K) = − 1543.9 kJ mol−1 and
`the Korchergina et al. [61] value ΔHf(s, 298.15 K) = − 1551.7 ± 1.3 kJ mol−1 for the
`enthalpy of formation are lower than these given above because they used in cal-
`culations the heat of formation of the standard substance for CO2(gas) and not for
`C(graphite) as in [58, 59].
`Thermodynamic data which exists for anhydrous citric acid is given in the
`form of relative values. De Kruif et al. [8] reported not absolute values of ther-
`modynamic functions, but changes in the Gibbs free energy, enthalpy and entropy,
`Δ[G( T) − G(90 K)], Δ[H( T) − H(90 K)] and Δ[S( T) − S(90 K)]. They can be repre-
`sented in the 90 K < T < 330 K temperature range by the following polynomials
`
`= −
`⋅
`−
`8.3675 10
`) G(90 K)]/kJmol
`−
`+
`⋅
`θ
`7
`3
`1.7331 10
`−
`=
`−
`⋅
`1
`) H(90 K)]/kJmol
`9.1225 10
`−
`−
`⋅
`θ
`7
`3
`1.3423 10
`−
`−
`=
`−
`⋅
`1
`1
`) S(90 K)]/Jmol K
`9.9208 10
`−
`+
`⋅
`θ
`6
`3
`1.1041 10
`
`−
`1
`
`−
`4
`
`
`
`θ−
`
`⋅
`4.7714 10
`
`−
`4
`
`θ
`2
`
`−
`2
`
`
`
`θ+
`
`⋅
`3.6364 10
`
`−
`4
`
`θ
`2
`
`−
`1
`
`
`
`θ−
`
`⋅
`9.90972 10
`
`−
`4
`
`θ
`2
`
`(2.6)
`
`
`
`∆
`
`
`[G(T
`
`∆
`
`
`[H(T
`
`/
`
`K 90−
`
`∆
`[S(
`
`T T
`
`
`
`
`
`θ=
`
`In order to convert the relative values of entropies of anhydrous citric acid in
`Eq. (2.6) to absolute values, they must be increased by 75 J mol−1 K−1, i.e. S(s,
`90 K) = 75 J mol−1 K−1 and S(s, 298.15 K) = 252.1 J mol−1 K−1 [8]. Thermal effects as-
`sociated with the citric acid monohydrate to anhydrous citric acid transition will be
`discussed later in the context of citric acid dissolution in water.
`The Gibbs free energy of formation of citric acid in a saturated solution is given by
`Evans et al. [58] as ΔGf(sat. soln, 298.15 K) = − 1235.0 ± 1.3 kJ mol−1. They reported
`also the corresponding value for the aqueous citrate ion formation in a solution of
`unit activity, a = 1, as ΔGf(aq. soln, 3 H + + Cit3−, 298.15 K) = − 1161.9 ± 1.4 kJ mol−1
`(the Burton result is ΔGf(aq. soln, Cit3−, 298.15 K) = − 1165.5 ± 0.2 kJ mol−1 [60]).
`Kochergina et al. [61] performed a detailed calorimetric study of formation of citrate
`ions in water and KOH solutions. They presented the following enthalpies of forma-
`tions ΔHf(aq. soln, Cit3−, 298.15 K) = − 1534.6 ± 1.6 kJ mol−1; ΔHf(aq. soln, HCit2−,
`298.15 K) = − 1526.5 ± 1.6 kJ mol−1; ΔHf(aq. soln, H2Cit−, 298.15 K) = − 1530.0 ±
`1.6 kJ mol−1 and ΔHf(aq. soln, undiss. H3Cit, 298.15 K) = − 1528.5 kJ mol−1.
`The equilibrium vapour pressure over crystals of citric acid monohydrate (the
`decomposition pressure of the hydrate) was determined by Marshall [7] using the
`dynamic air current method [62, 63]. His results are in a reasonable agreement
`with those of De Kruif et al. [8]. They used the static method by employing a dia-
`phragm manometer. Oechler [9] applying a direct manometric technique measured
`vapour pressure of water over solutions saturated with both, the monohydrate and
`anhydrous citric acid, and obtained practically the same results. These three sets
`
`PFIZER, INC., IPR2017-01357, Ex. 1039, p. 12 of 204
`
`

`

`20
`
`Table 2.1 Vapour pressures
`of water over solid citric
`acid monohydrate
`
`p/kPa
`t/°C
`0.669a
`10.0 [7]
`0.809
`13.1
`0.895
`13.1
`0.852
`13.1
`0.852
`13.1
`0.964
`15.0
`1.377
`20.0
`1.384
`20.1
`1.367
`20.1
`0.325
`4.95 [8]
`0.521
`9.73
`0.893
`15.96
`1.212
`19.97
`1.213
`20.60
`1.911
`26.10 [9]
`2.836
`31.15
`a 1 kPa = 7.5006 mmHg
`
`t/°C
`20.1
`25.0
`25.0
`25.0
`25.0
`25.1
`25.1
`30.0
`30.1
`24.52
`25.27
`28.84
`30.08
`33.00
`33.88
`37.78
`
`p/kPa
`1.367
`1.961
`1.928
`1.970
`1.845
`1.968
`1.978
`2.770
`2.810
`1.748
`1.760
`2.332
`2.582
`3.240
`3.546
`4.666
`
`t/°C
`30.1
`30.2
`35.0
`35.0
`35.0
`35.0
`35.0
`35.05
`36.50
`33.02
`33.27
`35.81
`35.91
`
`p/kPa
`2.788
`2.898
`3.890
`3.790
`3.834
`3.980
`4.008
`3.913
`4.293
`3.399
`3.373
`3.902
`3.906
`
`6.0
`
`4.0
`
`2.0
`
`p/kPa
`
`0.0
`
`0
`
`10
`
`20
`t / 0C
`
`30
`
`40
`
`Fig. 2.4 Vapour pressure of water over solid citric acid monohydrate and over aqueous saturated
`solutions of citric acid as a function of temperature. Vapour–solid equilibrium ■ - [7]; ■ - [8];
`■ - [9, see text] and liquid–solid equilibrium ■
`
`of experimental data are presented in Table 2.1 and plotted in Fig. 2.4. They are
`presented in the temperature range of citric acid monohydrate existence, together
`with vapour pressures over saturated solutions taken from the literature. As can be
`observed, especially at higher temperatures with approaching the transition point,
`
`2 Properties of Citric Acid and Its Solutions
`
`PFIZER, INC., IPR2017-01357, Ex. 1039, p. 13 of 204
`
`

`

`2.2 Melting and Freezing Temperatures of Aqueous Solutions of Citric Acid
`
`21
`
`the scattering of the experimental points is large and the results are less certain.
`Melia [64, 65] erroneously claimed that he measured vapour pressures over citric
`acid monohydrate (above T > 313 K) but these vapour pressures are probably over
`the saturated solutions of citric acid.
`The enthalpy change associated with dehydration process is determined from the
`Clausius–Clapeyron equation
`
`
`
`
`∂
`
`ln ( )p T
`
`∂
`(1/
`)
`T
`
`
`
`
`
`s
`
`→
`
`g
`
`= −
`
`H( )T
`
`∆
`
`R
`
`
`
`(2.7)
`
`and by assuming that ΔH ( T) linearly depends on temperature T, the integral form
`of Eq. (2.7) gives the temperature dependence of vapour pressures
`
`/K)
`
`
`
`(2.8)
`
`
`
`∆
`
`
`H ( )/kJ molT
`
`1
`
`=
`
`135.22 0.2724 (T
`
`/K)
`
`16262.7
`
`(T
`/K)
`−
`
`
`ln[
`
`
`
`( )/kPa]p T
`
`241.82
`
`−
`
`−
`
`
`
`32.757 ln (T
`
`−=
`
`It follows from Eq. (2.8) that ΔH (298.15 K) = 54.0 kJ mol−1 when the De Kruif
`et al. [8] values are ΔH (298.15 K) = 56.8 ± 1.0 kJ mol−1 and ΔH (309.5 K) = 55.8 ±
`1.0 kJ mol−1. Marshall [7] gives in the 288.15–308.15 K temperature range, the aver-
`age enthalpy of hydration reaction as ΔH ( T) = 51.6 kJ mol−1.
`
`2.2
`
` Melting and Freezing Temperatures of Aqueous
`Solutions of Citric Acid
`
`The complete phase diagram of the citric acid–water system in the 273–373 K tem-
`perature range which includes the liquid and solid phases is plotted in Fig. 2.5. The
`solid–liquid equilibrium is considered here and the vapour–liquid equilibrium will
`be discussed later. The temperature–composition curves (in Fig. 2.5, the composi-
`tion of phases is expressed in the mass fractions of citric acid w) were constructed
`using experimental data available from the literature. They come from determina-
`tions of melting, freezing points, glass transitions and solubilities. The homogenous
`ice freezing temperatures and the glass transition temperatures were already dis-
`cussed when other phase relations will be considered in a more detail below. The
`melting temperatures Tm (Fig. 2.6) and the homogenous ice freezing temperatures
`Tf are presented in Table 2.2.
`Related to determinations of Tm temperatures are cryoscopic measure-
`ments where the freezing-point depressions of aqueous solutions of citric acid,
`θ( m) = Tf.p (H2O) − Tf.p ( m), are very accurately measured. This colligative prop-
`erty depends only on the solvent and not on the nature of the solute present in
`
`PFIZER, INC., IPR2017-01357, Ex. 1039, p. 14 of 204
`
`

`

`22
`
`t / 0C
`
`100
`
`50
`
`0
`
`-50
`
`Tsat
`
`SOLID
`
`Tm
`
`LIQUID
`
`Tg
`
`METASTABLE LIQUID
`
`Tf
`
`ICE
`
`GLASS
`
`-100
`0.0
`
`0.2
`
`0.4
`
`0.6
`
`0.8
`
`1.0
`
`w
`Fig. 2.5 Phase diagram of the citric acid–water system. ■ - liquid–solid equilibrium (the solubil-
`ity curve); ■ - equilibrium melting curve; ■ - homogenous ice freezing temperature curve; ■ - the
`glass transition curve
`
`0
`
`-5
`
`-10
`
`-15
`
`-20
`
`t / 0C
`
`-25
`0.00
`
`0.15
`
`0.30
`w
`Fig. 2.6 The equilibrium melting-point curve of the citric acid–water system. ■ - [43]; ■ - [45