Solution Thermodynamics of Alkyl p -Aminobenzoates
`
`PETER A. SCHWARTZ and ANTHONY N. PARUTA"
`
`Abstract 0 Equilibrium solubilities of the first four homologous
`alkyl p-aminobenzoate esters were determined in methanol, etha-
`nol, and 1-propanol at 25, 33, and 40°; the esters and the alcohols
`comprise separate homologous series. The solution process of a so-
`lute may be considered to be the summation of two sequential
`steps, melting and mixing, and the magnitude of solubility de-
`pends upon temperature and the extent of interactions between
`solute and solvent molecules. Quantitative solute concentrations,
`obtained from spectrophotometric analysis, were converted to
`mole fractions. Statistical analysis of the logarithmic mole fraction
`solubilities of the aminobenzoates, which were linear with respect
`to both reciprocal absolute temperature and the logarithm of abso-
`lute temperature, generated enthalpies and entropies of solution,
`respectively. The heats of fusion and the melting points of these
`aminobenzoates were determined to calculate their ideal solubili-
`ties. Excess free energies and partial molal free energies of each so-
`lution were calculated from the activity Coefficients of the solutes;
`the thermodynamic elements for these systems are discussed.
`Keyphrases p-Aminobenzoates-equilibrium
`solubilities of
`four alkyl esters in alcohols, solution thermodynamics 0 Thermo-
`dynamics, solution-four alkyl p-aminobenzoate esters, equilibri-
`um solubilities in alcohols
`
`Solubility results principally from interactions be-
`tween solute and solvent molecules (1). The extent of
`these interactions, i.e., the magnitude of solubility,
`depends partially upon the polarity and the hydrogen
`bonding characteristics of the solution components
`with respect to each other and to themselves; it de-
`pends also on the temperature of the system.
`Solutes studied included four normal alkyl p-ami-
`nobenzoate esters (methyl, ethyl, propyl, and butyl),
`chosen because these esters comprise a series differ-
`ing in structure from each other by one methylene
`(CHd group. The solvents were methanol, ethanol,
`and 1-propanol; this homologous series was chosen
`because it would provide a range of solvent polarity.
`The equilibrium solubilitjes of each solute in these
`solvents were determined at several temperatures to
`provide enthalpies and entropies of solution with re-
`spect to fundamental thermodynamic relationships.
`
`BACKGROUNP
`
`The solubility of nonelectrolytes has often been interpreted on
`the basis of polarity differences between solutes and solvents (2-
`9). An incremental increase in the length of a hydrocarbon side
`chain effects a polarity difference between consecutive members of
`a homologous series. These structural differences result in altered
`physical properties such as boiling-point elevation, increased par-
`tition coefficient (lipid solubility), decreased aqueous solubility,
`and increased surface tension.
`Since many properties of a homologous series change according
`to a geometric progression (lo), the plot of the logarithm of these
`properties against the carbon number of the nonpolar hydrocarbon
`chain is linear. Solubility studies (11) on the first four homologs of
`the alkyl p-aminobdnzoate esters demonstrated such linearity for
`semilogarithmic plots of solubility in silicone oil and hexane, two
`nonpolar solvents; as well as of their partition coefficients with
`water against alkyl carbon numbers. The solubility increased with
`alkyl carbon number equal to four and decreased thereafter. The
`heats of fusion, melting points, and solubility parameters were
`
`252 /Journal of Pharmaceutical Sciences
`
`used to generate expected values for molar solubility, all of which
`agreed well with the experimental values for hexane. However,
`poor agreement was found with experimental data for water, a
`polar, hydrogen-bonding solvent.
`The similar series of homologous esters, alkyl p-hydroxyben-
`zoates, was studied (3, 4) in several alcohols, i.e., polar, hydrogen-
`bonding solvents. The Hildebrand and Scott (5) solubility parame-
`ter theory was used to predict the points of maximum solubility in
`each solvent. However, the magnitude of solubility depends upon
`specific solute-solvent interactions (6) and is not always predict-
`able.
`Solubility is a colligative property and is related to the tempera-
`ture-dependent thermodynamic equation for freezing-point de-
`pression (12). At any temperature, the concentration of pure solid
`solute is constant and is in equilibrium with the liquid state. The
`solution process is considered to occur in two steps as shown in
`Scheme I:
`
`- -
`
`solute in
`solution (Xp)
`
`solid melting liquid mixing
`solute
`solute
`Scheme I
`where Xp is the solute mole fraction. The enthalpy change for
`melting is the heat of fusion, AHF, and the enthalpy for the second
`step is the heat of mixing, AHM (12). For ideal solutions, the en-
`thalpy of the second step is zero, since, by definition, no heat is
`evolved or absorbed (13).
`The equation for the ideal mole fraction solubility of a solute,
`Xp', at a temperature below its melting point, T,, is given in terms
`of the natural logarithm of the solubility, i.e.:
`
`when it is assumed that the heat of fusion is constant with respect
`to temperature, and the gas constant, R, equals 1.987 cal/degree.
`The solubility at any given temperature should be the same for all
`solvents with which it forms an ideal solution. From Eq. 1, it is ap-
`parent that a solute with a low heat of fusion and a low melting
`point will have a high ideal solubility, that the solubility of a solute
`increases as the melting point decreases, and that solubility ap-
`pears to be independent of the nature of the solvent.
`Hildebrand and Scott (14) equated the activity of a solute, a2,
`with X $ for ideal solutions. The activity is a relative quantity and
`represents the deviation from a designated reference state. The
`most useful standard state for solubility is one in which the pure
`liquid solute, extrapolated below the melting point as a super-
`cooled liquid (15), has a value of unity when its mole fraction is
`unity. The ratio of the activity to the mole fraction is the activity
`coefficient, y, i.e.:
`
`(Eq. 2)
`y = a/x
`Because the activity varies with composition, the activity coeffi-
`cients, which remain relatively constant, are more suitable param-
`eters for expressing deviations from ideal solutions.
`Equation 1 is valid only when the heat of fusion is constant with
`respect to temperature. From the heat of fusion at the melting
`poipt, AHmF, and the change in molal heat capacity between liquid
`and solid solute, ACp, also extrapolated below the melting point,
`the heat of fusion a t any temperature can be derived (16):
`AHF zz AHmF - ACp(T, - T)
`(Eq. 3)
`Substitution of this heat expression in Eq. 1 gives the following for
`ideal mole fraction solubility:
`In Xp* = [ M , F / R ( T , - T/T,T)] +
`[ACp/R(T, - T/T)] [ACp/R(In Tm/T)] (Eq. 4)
`For the ideal solution, the plot of the natural logarithm of the
`mole fraction solubility, In X p , uersus the reciprocal of the abso-
`
`Ex. 1117-0001
`
`

`

`Table I-Structure and Thermal Properties of Alkyl phinobenzoate Esters
`Melting Point
`
`Methyl
`Ethyl
`n-Propyl
`n-Butyl
`
`Literature
`112"b, 114°C
`89"d, 90°C, 92"b
`13"d, 13-14"b, 15°C
`51"d. 58"b*C
`
`Capillary Tube
`110.5-111"
`88-90"
`13-14"
`56-58"
`
`Differential
`Scanning
`Calorimetry
`112.5"
`89.7"
`73.0"
`55.8"
`
`Heats
`of Fusion,
`cal /m ole
`
`5180
`5030
`5000
`5290
`
`Entropy
`of Fusion,
`cal/mole
`deg
`
`13.5
`13.9
`14.5
`16.1
`
`aC. 0. Wilson, 0. Gisvold, and R. F. Doerge, "Textbook of Organic, Medicinal and Pharmaceutical Chemistry," 5th ed., Lippincott, PhiL-
`delphia, Pa., 1966, p. 602. b"Dictionary of Organic Compounds," 4th rev., Oxford University Press, New York, N.Y., 1065. C"Handbook of
`Chemistry and Physics," 51st ed., Chemical Rubber Co., Cleveland, Ohio, 1970. dR. Adams, E. K. Rideal, W. B. Burnett, R. L. Jenkins, and
`E. E. Dreger,j. Amer. Chem. SOC., 48, 1758 (1926).
`
`The log yz term for the excess free energy of regular solutions is
`due to the intermolecular forces of the solute and solvent that are
`not present in ideal solutions. These forces can he characterized by
`considering the solubility parameters of the solute and solvent, the
`volume fraction of the solvent, $1, and the molar volume of the so-
`lute, Vp, so that the deviation from the ideal is:
`In yp = (61 - 6 2 ) 2 V ~ $ ~ 2 / R T
`(Eq. 7 )
`Since the solubility parameter is a measure of polarity, the greater
`the differences in polarity between solute and solvent, the greater
`is the deviational term of the activity coefficient.
`Entropy is related to structure (12) and indicates the probability
`of a combination between solute and solvent. An increased entropy
`of solution denotes a more probable state for such a system than
`do the separate pure solute and solvent. As the degree of random-
`ness and disorder for a system increases, the entropy increases, but
`the free energy decreases. For example, at increased temperatures
`there is more randomness, i.e., increased entropy, while the
`amount of useful work or free energy is diminished. For alcohols in
`solution with nonpolar components, there is a decreased entropy
`due to specific interactions, i.e., ordering due to hydrogen bonding,
`and large positive deviations from ideality are expected (26).
`Highly nonideal solubility with such large entropy terms cannot
`be calculated from Eqs. 1-7 and are best calculated in terms of free
`
`p\
`
`-0.5
`
`-1 .o
`>
`b
`-
`-I
`rn
`3 -1.5
`-I $
`2 ; -2.0
`
`a
`0
`lz
`U
`UI -2.5
`J 0
`2
`C -
`-3.0
`
`I
`
`-3.5
`
`I
`
`'
`
`
`
`lute temperature, 1 / T , has a slope proportional to the heat of fu-
`sion at the melting point and an intercept proportional to the en-
`tropy of fusion, i.e., AHmFITm. Data from nonideal solutions plot-
`ted in this manner have slopes and intercepts proportional to the
`differential heats and entropy of solution, respectively (12).
`Hildebrand and Scott (17) showed that the heat capacity is not
`negligible and can be approximated by the entropy of fusion. Sub-
`stitution of ASmF for ACp in Eq. 4 cancels out the first two terms
`on the right side and leaves the ideal mole fraction solubility equa-
`tion as:
`
`In Xzi = (ASmF/R) (In T/Tm)
`(Eq. 5 )
`Accordingly, a plot of In X 2 uersus the natural logarithm of the ab-
`solute temperature, In T, is linear with a slope proportional to the
`entropy of fusion. For nonideal data, the entropy of solution can be
`obtained from the slope of this line (18).
`Since orienting and chemical effects, such as hydrogen bonding,
`solvation, and association, are absent in regular solutions (19) and
`molecules are randomly distributed as in ideal solutions, the two
`types of solutions have equal entropies. The deviation from ideal-
`ity for a regular solution represents the magnitude of the enthalpy
`of mixing, since no heat is evolved in the formation of an ideal so-
`lution.
`The free energy, F, represents the maximum of work that can be
`obtained from a process and applied to useful purposes (20). At
`equilibrium, the total free energy is at a minimum (21) with no
`separation of enthalpic and entropic components (22). Nonideal
`solutions have an excess free energy of mixing, which can be re-
`garded as "the excess of the nonideal free energy of mixing over
`the ideal free energy of mixing" (23); i.e., in terms of free energy:
`pE = R T In yz
`(Eq. 6)
`A partial molal quantity is defined as "the rate of increase in the
`content of the system in that particular quantity while the compo-
`nent is being added to the system" (24). However, Hildebrand and
`Scott (25) warned that the physical property of partial molal quan-
`tities cannot be attributed to molecules of one species alone and
`that it is a property of the solution as a whole-not of the particu-
`lar component.
`
`1
`
`2
`3
`CARBON NUMBER OF ESTER
`Figure 1-Plot of the range of melting points for the alkyl p-ami-
`nobenzoate esters as a function of the alkyl carbon number of the
`ester.
`
`4
`
`I
`I
`I
`I
`looo
`80°
`90°
`70°
`MELTING POINT OF ESTER
`Figure 2-Plot of the In mole fraction solubility in methanol ver-
`sus the melting point of the aminobenzoate ester at the three
`temperatures noted. Key: A, methyl p-aminobenzoate; A, ethyl
`p-aminobenzoate; 0, propyl p-aminobenzoate; and X. butyl p-
`aminobenzoa te.
`
`60°
`
`I
`110°
`
`Vol. 65, No. 2, February 1976 I253
`
`Ex. 1117-0002
`
`

`

`Table 11-Average Mole Fraction Solubilities of Alkyl p-Aminobenzoate Esters in Each Solvent at 25,33, and 40"
`Solvent
`
`Ester
`Methyl
`
`Ethyl
`
`n-Propyl
`
`n-Butyl
`
`Temperature
`2 5"
`33"
`4 0"
`2 5"
`33"
`40"
`~.
`2 5"
`33"
`40"
`25"
`3 3"
`40"
`
`Methanol
`0.0367
`0.0524
`0.0730
`0.0945
`0.1 256
`0.1811
`0.1709
`0.2402
`0.4016
`0.2779
`0.5247
`0.7030
`
`-
`a
`Calculated from Eq. 1. b Calculated from Eq. 5.
`
`Ethanol
`0.0419
`0.0545
`0.0740
`0.0895
`0.1276
`0.1843
`0.1634
`0.2177
`0.4018
`0.2212
`0.4319
`0.6220
`
`1-Propanol
`0.0306
`0.0428
`0.0586
`0.0836
`0.0953
`0.1455
`0.1826
`0.2485
`0.3680
`0.2544
`0.3705
`0.6205
`
`Ideal An
`0.1369
`0.1722
`0.2084
`0.2195
`0.2741
`0.3299
`0.3100
`0.3866
`0.4648
`0.4319
`0.5457
`0.6632
`
`Ideal Bb
`0.1752
`0.2096
`0.2442
`0.2539
`0.3054
`0.3576
`0.3376
`0.4093
`0.4825
`0.4507
`0.5586
`0.6709
`
`Table 111-Enthalpies and Entropies of Aikyl p-Aminobenzoates in Alcohols
`Enthalpy, cal/mole
`
`Entropy, cal/mole deg
`
`AH,F
`
`A H M ~
`
` AS,^
`
`AS,F
`
`ASMC
`
`sp
`27.7
`22.9
`26.2
`26.2
`29.2
`22.1
`34.3
`36.0
`28.2
`37.8
`42.1
`35.9
`
`Ssd/Ssb
`
`1.27
`1.34
`1.34
`1.19
`1.16
`1.26
`1.09
`1.09
`1.15
`1.04
`1.01
`1.06
`
`Ester
`Methyl
`
`Ethyl
`
`n-Propyl '
`
`n-Butyl
`
`aHM=H,-H,F.
`
`Solvent
`Methanol
`Ethanol
`1-Propanol
`Methanol
`Ethanol
`1-Propanol
`Methanol
`Ethanol
`1-Propanol
`Methanol
`Ethanol
`1-Propanol
`
`A H ,
`8,470
`7,000
`7,990
`7,990
`8,900
`6,710
`10,460
`10,970
`8,610
`11,570
`12,850
`10,940
`
`3280
`1810
`2800
`2960
`3870
`1680
`5460
`5970
`3610
`6280
`7 560
`5650
`-
`b R timesintercept ofInX,versus l/T.CSM=S,
`S,F.
`
`5180
`5180
`5180
`5030
`5030
`5030
`5000
`5000
`5000
`5290
`5290
`5290
`
`21.9
`17.2
`19.9
`22.1
`25.1
`17.5
`31.5
`33.1
`25.5
`36.3
`40.2
`33.9
`
`13.5
`13.5
`13.5
`13.9
`13.9
`13.9
`14.5
`14.5
`14.5
`16.1
`16.1
`16.1
`
`8.4
`3.7
`6.4
`8.2
`11.2
`3.6
`17.0
`18.6
`11.0
`20.2
`24.1
`17.8
`
`d R times intercept of In X , versus In T
`
`energies. This approach avoids serious errors of oversimplification
`and does not separate enthalpic and entropic effects (22).
`
`EXPERIMENTAL'
`following chemicals were used methyl p-ami-
`Chemicals-The
`nobenzoate2; ethyl p-aminoben~oate~; propyl p-aminoben~oate~;
`butyl p-amin~benzoate~; methanol, anhydrous, spectrophotomet-
`ric grade solvent6; absolute alcohol USP, reagent quality7; l-propa-
`noP; ethanolg 95%, USP grade; stearic acidlo, 99.8% pure; and
`water, distilled and deionized.
`Calorimeter Calibration-The calorimeter cell of a differen-
`tial scanning calorimeter, used to determine heats of fusion, was
`calibrated with stearic acid, 99.8% pure. Three samples of the acid,
`in amounts empirically chosen to produce endothermic fusion
`peaks of maximum area, were accurately weighed (f0.002 mg) on
`an electrobalance into tared aluminum pans. The pans were subse-
`quently sealed to prevent volatilization.
`The samples were heated in a nitrogen atmosphere in the calo-
`
`The following equipment was used: Thomas-Hoover capillary melting-
`point apparatus, No. 6404, A. H. Thomas Co., Philadelphia, Pa.; Cary model
`16 spectrophotometer, Cary Instruments, Monrovia, Calif.; Precision-Porta-
`Temp unit, Precision Scientific Co., Chicago, Ill.; Mettler balance, type
`H6T, Mettler Instrument Corp., Princeton, N.J.; rotating sample holder
`with small motor, Department of Pharmacy, University of Rhode Island;
`Pyrex Corning glass wool, Corning Glass Works, Corning, N.Y.; Cahn gram
`electrobalance, model 18, Cahn Instruments, Paramount, Calif.; and Perkin-
`Elmer differential scanning calorimeter, DSC-18, Perkin-Elmer Corp., In-
`strument Division, Norwalk, Conn.
`Lot 3403, Eastman Chemical Co., Rochester, N.Y.
`Lot EX 305, Matheson, Coleman and Bell, Norwood, Ohio.
`Lot 3, City Chemical Co., supplied through the courtesy of Astra Phar-
`maceutical Products, Worcester, Mass.
`Lot 7, Matheson. Coleman and Bell, Norwood, Ohio.
`6 Lot VNM, Mallinckrodt Chemical Works, St. Louis, Mo.
`U.S. Industrial Chemicals Co., New York, N.Y.
`* Analyzed reagent, Lot 39420, J.T. Baker Chemical Co., Phillipsburg,
`N.J.
`Lot TM 288671. Industrial Chemicals Co., Littleton, Mass.
`lo Applied Sciences, State College, Pa.
`
`254 / Journal of Pharmaceutical Sciences
`
`rimeter cell over a temperature range of 60-75' a t a heating rate of
`5O/min and at a chart recording speed of 304.8 cm (120 in.)/min.
`Each sample was melted twice, and calibration constants were cal-
`culated from only those curves having essentially straight baselines
`for both pre- and postfusion.
`The value of HmF, the heat absorbed by a sample during fusion,
`is proportional to the area under the curve defined by the endo-
`thermic peak and by a line drawn between the point of departure
`from the baseline (onset of fusion) to the point of baseline return
`after fusion (27). The thermograms generated by the samples were
`reproduced on paper of a uniform thickness, and each area was
`carefully cut out and weighed (28). The stearic acid calibration
`coefficient, 0.0641969 (0.0642). is the average of the determina-
`tions from each sample calculated according to the following equa-
`tion:
`
`(Eq. 8)
`
`where:
`
`K = calibration coefficient, millicalories per milligram of paper
`HsaF = heat of fusion for stearic acid, -47.54 mcal/mg
`M = weight of stearic acid sample, milligrams
`W = weight of stearic acid sample, milligrams of paper
`r = power coefficient of the instrument
`
`Because the instrument does not provide readings in Celsius de-
`grees, the fusion endotherms of stearic acid were used to determine
`a calibration constant for temperature correction. The melting
`point for a solid is best represented by the extrapolation to the
`prefusion baseline of its endotherm (28). The known melting point
`of 68.82O was subtracted from the average value of the instrument
`readings for the onset of fusion for stearic acid to produce a correc-
`tion constant of 378.4'.
`average of the two calo-
`Melting-Point Determinations-The
`rimeter melting points for each aminobenzoate ester was converted
`to Celsius melting points by subtracting the temperature correc-
`tion constant. Since there was a close agreement in melting points
`
`Ex. 1117-0003
`
`

`

`Table IV-Ideal, Actual, and Excess Free Energy of Alkyl
`p-Aminobenzoates in Alcohols
`
`-1 0 L
`
`Ester
`
`Methyl
`
`Ethyl
`
`n-Propyl
`
`n-Butyl
`
`Free Energy, cal/mole
`
`Solvent
`
`Methanol
`Ethanol
`1-Propanol
`Methanol
`Ethanol
`1-Propanol
`Methanol
`Ethanol
`1-Propanol
`Methanol
`Ethanol
`1-Propanol
`
`A F A
`
`1 7 9 0
`1754
`1 9 2 0
`1250
`1244
`1 3 7 2
`852
`874
`832
`498
`587
`600
`
`AFI
`
`A FE
`
`1 0 6 3 ~ .
`1 0 6 3
`1 0 6 3
`790
`790
`790
`577
`577
`577
`379
`379
`379
`
`+727
`. ~
`+691
`+863
`+460
`+454
`+582
`+275
`+297
`+255
`+119
`+210
`+221
`
`> -1.5
`k
`-
`1
`3 -2.0
`~ m
`
`0
`w
`2
`
`-2.5
`0 a
`a:
`U
`w -3.0
`1
`0
`
`5 = -3.5
`
`between experimental and literature values for the esters, these
`compounds were used directly and without further purification.
`The purity of the solutes was accepted from the label claiming
`greater than 99.8% in all cases, since the melting point of these ma-
`terials did not differ from ethanolic recrystallized samples of these
`solutes.
`Heats of Fusion-Samples
`of the four aminobenzoate esters
`were carefully weighed into aluminum volatile sample pans, and
`thermograms of a 10" prefusion baseline and a fusion endotherm
`were recorded. Because direct remelts of the same sample indicat-
`ed an apparent formation of liquid crystals after fusion, each fused
`sample was cooled to Oo for 30 min prior to remelting. Recordings
`were analyzed for melting points and endothermic areas in the
`same manner as for stearic acid.
`solubility of the four amino-
`Solubility Determinations-The
`benzoate esters in several alcohols and water was determined by
`the following procedure. Each solute, in an amount in excess of its
`solubility, was placed in screw-capped glass vials" with each sol-
`vent. The vials were sealed with adhesive tape. Vials were rotated
`at 28 rpm in a large constant-temperature (f0.2") water bath
`maintained successively at 25,33, and 40".
`After an equilibrium solubility was attained by at least 24 hr of
`continuous rotation12, each of sixI3 sample vials was removed in
`succession for assay. The exterior of the vial was quickly dried, the
`sealing tape was removed, and the cap was carefully unscrewed to
`prevent water contamination. A filtered aliquot of the saturated
`solution was pipetted into tared containers, weighed, and appro-
`priately diluted for spectrophotometric assay with 95% ethanol to
`give a final concentration of solute in the range of 1-5 pglml. All
`pipets were prewarmed to prevent thermal precipitation, and each
`had a pledget of fiber glass wrapped around its tip to act as a filter.
`The variation in solubility values was about 5% for the methyl de-
`rivatives and fell to about 3% for the butyl derivative.
`Spectrophotometric Determination-The
`spectrophotometer
`was calibrated for each aminobenzoate ester at its wavelength of
`maximum absorbance, at concentrations up to 15 rg/ml in 95%
`ethanol, in matched silica cells. A least-squares method was used
`to determine the statistical significance (a = 0.OOOl) of the linear
`relationship between absorbance and concentration, i.e., the Beer's
`law equation.
`The molar absorptivities for the esters were very close in value,
`varying from 2.05 for the methyl, ethyl, and propyl esters to 2.07
`for the butyl ester.
`
`RESULTS AND DISCUSSION
`
`The chemical structures of the alkyl p-aminobenzoate esters
`and their thermal properties are shown in Table I. Experimentally
`determined differential scanning calorimetric and capillary tube
`melting points in Table I agree well with literature values shown
`there and are the same as those recently reported (11). The heats
`
`" Lined with Teflon.
`l2 Previous studies showed that this time was sufficient to obtain saturat-
`ed solutions at 25O.
`l3 Only three samples of propyl p-aminobenzoate were used because of its
`scarcity.
`
`~
`
`3.20 3.24
`
`3.32 3.36
`3.28
`I I T X lo3
`Figure 3-Plot of the In mole fraction solubility in 1-propanol
`versus the reciprocal temperature, "K. The ideal curues are from
`heat of fusion data, and the actual curues are from experimental
`data. Key: 0, ethyl p-aminobenzoate, ideal; 0 , ethyl p-aminoben-
`zoate. actual; A, methyl p-aminobenzoate, ideal; and A, methyl
`p-aminobenzoate, actual.
`
`of fusion show the same trend as do the Yalkowsky et al. (11) data;
`i.e., enthalpies for the methyl and butyl esters are higher than for
`the ethyl and propyl esters.
`The average mole fraction solubilities of these esters in metha-
`nol, ethanol, and 1-propanol and the ideal solubilities predicted by
`both Eqs. 3 and 7 at 25, 33, and 40' are summarized in Table I1
`and show an expected direct relationship between the magnitude
`of solubility and the temperature for each solvent.
`In Fig. 1, the melting-point range for the alkyl p-aminoben-
`is plotted uersus the alkyl carbon number. This relationship
`zo&s
`is approximately linear and reflects a regularity on the structural
`differences between homologs.
`Figure 2 shows a plot of the log, mole fraction solubility in
`methanol at the three temperatures studied uersus the melting
`points of the solutes. The decrease in solubility at any temperature
`is linear with increasing melting point for carbon numbers less
`than or equal to four. The parallelism observed for the three tem-
`peratures indicates similar solute-solvent interactions and a con-
`stant dissolution mechanism for these solutes.
`In Fig. 3, the In X Z in 1-propanol for each solute is plotted uer-
`sus the In T at the temperatures studied. The heats of fusion,
`heats of solution, and heats of mixing were obtained from the
`slopes of the lines generated from observed and calculated data as
`shown in Fig. 3. The entropy of fusion, entropy of solution, and en-
`tropy of mixing were obtained as intercepts of Figs. 3 and 4.
`The entropies of solution in Table 111 were determined from a
`least-squares analysis of the mole fraction data in Table 11. The
`value of Ssb was obtained from the intercepts of In X Z uersus the
`reciprocal absolute temperature shown graphically in Fig. 3 for 1-
`propanol solutions. The Hildebrand entropy of solution, Ssd, was
`obtained from the slopes of In X2 uersus the natural logarithm of
`the absolute temperature, shown graphically in Fig. 4 for l-propa-
`no1 solutions. These graphs are similar to the graphs of the other
`alcohol solutions and were chosen as representative examples of
`the solute behavior.
`Hildebrand's entropy of solution for the solid solutes, Sad, which
`includes the heat of fusion of the solute, has values several entropy
`units (calories per mole degree) higher than the corresponding
`values of entropy of solutions, Ssb (Table 111). However, Hilde-
`brand applied a correction factor to his experimental data from so-
`lutions with mole fractions greater than 0.1, i.e., good solvents
`(29). The "Henry's law" factor (the change in solute activity per
`change in solute mole fraction) could not be calculated for the ami-
`nobenzoates because the solutions were not considered dilute sys-
`tems. Thus, the Hildebrand entropy of solution values are uncor-
`
`Vol. 65, No. 2, February 1976 j 255
`
`Ex. 1117-0004
`
`

`

`Table V-Activity Coefficients for Alkyl p - Aminobenzoates
`Based upon the Ideal Solubilities from Eq. 3
`
`Table VI-Partial Molal Excess Free Energies Calculated
`from the Activity Coefficients of Alkyl p-Aminobenzoates
`
`Ester
`
`Methyl
`
`Ethyl
`
`Tem-
`perature Methanol
`
`Solvent
`
`Ethanol 1-Propanol
`
`2 5"
`3 3"
`4 0"
`2 5"
`33"
`4 0"
`
`3.7
`3.3
`2.8
`2.3
`2.2
`1.8
`
`3.3
`~~ 3.2
`2.8
`2.5
`2.2
`1.8
`
`4.5
`4.0
`~~ 3.6
`2.6
`2.9
`2.3
`
`rected, and actual values of the entropy of solution, Ssd, would be
`less than those given in Table 111.
`The diminishing difference between the two values for entropy
`of solution as the alkyl chain length increases is shown by the de-
`crease in the ratio Ssd/Ssb in Table 111. Since the two values of the
`ideal solubilities from Eqs. 1 and 5 in Table I1 are reasonably close,
`the ideal values from Eq. 1 were chosen as a basis for comparison
`in the activity coefficient determinations. The choice of the entro-
`py of solution obtained from plots of Eq. 1, In Xp uersus 1/T, was
`due to its conventional and generally accepted use.
`The maximum entropy of solution within a group of solvents de-
`notes the best solvent for that solute, and comparison between
`groups illustrates the effect of the alcohols upon the solubility of
`each ester. As the solute alkyl chain length increases, the molecules
`become less polar and the entropy of solution increases. Although
`the methyl ester, the most polar of these solutes ( l l ) , has a maxi-
`mum entropy in methanol, the most polar alcohol, all other esters
`have their entropic maxima in ethanol, a less polar solvent.
`The heats of solution in Table I11 can be compared with the
`heats of fusion in Table I to show that a positive heat of mixing,
`AHmix, was generated for all solutions in the alcohols and that the
`magnitudes of these heats increased as the alkyl chain length in-
`creased. This excess heat above ideal also showed the most in-
`crease in methanol for the methyl ester and in ethanol for all other
`esters, i.e., the same result observed for the entropy of solution
`data.
`Since values for the entropy and heat of solution are determined
`
`-0.5
`
`-2.5
`
`-3.0
`
`6
`a
`n
`-I 8 -4.5
`w
`
`-3.5
`
`-4.0
`
`5 -5.0
`
`-5.5
`
`5.70
`
`5.71
`
`5.72
`In T
`Figure 4-Plot of the In mole fraction solubility in 1-propanol for
`each solute as a function of the ln temperature, OK. Key: X, butyl
`p-aminobenzoate; A, propyl p-aminobenzoate; @, ethyl p-amino-
`benzoate; and 0, methyl p-aminobenzoate.
`
`5.73
`
`5.74
`
`256 /Journal of Pharmaceutical Sciences
`
`Ester
`
`Methyl
`
`Ethyl
`
`n-Propyl
`
`n-Butyl
`
`Tem-
`perature Methanol
`
`Solvent
`
`Ethanol
`
`1-Propanol
`
`2 5"
`33"
`40"
`2 5"
`33"
`40"
`2 5"
`3 3"
`40"
`25"
`33"
`40"
`
`-34
`-4 0
`-4 4
`-3 3
`-3 9
`-3 5
`-3 0
`-29
`-5
`-3 0
`-1
`-2
`
`-3 0
`-38
`-4 3
`-36
`-38
`-3 3
`-34
`-3 9
`-5
`-58
`-1 6
`-2
`
`-4 0
`-4 8
`-55
`-4 0
`-60
`-55
`-25
`-26
`-1 2
`-4 1
`-38
`-3
`
`as averages over a narrow temperature range, they do not reflect
`the temperature change upon the solubility parameters or the di-
`electric constant of the solutes. This objection limits the usefulness
`of separate entropic or enthalpic interpretations of solubility (22).
`From the values presented in Table 111, various free energy
`values can be calculated. Table IV presents the ideal, actual, and
`excess free energies for each solute in each solvent. As expected
`from the solubility data, the excess free energies decrease with in-
`creasing size. The closer the ideal and actual free energies, the
`smaller are the excess free energy terms and the actual mole frac-
`tion solubility approaches the ideal mole fraction solubility.
`The activity coefficients in Table V are based upon the ideal
`mole fraction solubilities of Eq. 1 and were used to calculate the
`partial molal excess free energy of the solutes (Table VI). Since the
`activity coefficients are high for the methyl ester (2.824.47) and
`decrease progressively to near unity for the tiutyl ester (1.96-0.95),
`the excess free energies also decrease proportionally. Although free
`energies near zero were obtained for several butyl solutions at high
`temperatures, the high entropy of solution values indicate in-
`creased molecular disorder and prevent these from being classed as
`regular solutions.
`
`SUMMARY
`
`The magnitudes of the solubility of these esters dissolved in the
`normal alcohols increased with increased temperatures, indicative
`of an endothermic dissolution process. The conventional relation-
`ship between the natural log mole fraction data and the reciprocal
`temperature was linear for all solutions and produced values for
`the enthalpy and entropy of solution. The Hildebrand entropy of
`solution values were obtained from the linear relationship between
`the natural log mole fraction solubility and the log of the absolute
`temperature. The Hildebrand entropy values include the heat ca-
`pacity of the solute.
`Thermodynamic data for the aminobenzoates dissolved in the
`normal alcohols indicate increased entropy of solution as the alkyl
`chain length increases. There was no significant difference be-
`tween the conventional entropy of solution values and the Hilde-
`brand entropy of solution values.
`The butyl ester was highly soluble in the alcohols.
`From the
`heat of fusion and the melting-point data determined for these so-
`lutes, their ideal mole fraction solubilities were calculated. Activity
`coefficients of the solutes compare ideal to actual solubilities and
`were used to calculate partial molal excess free energies. These free
`energies were near zero in some cases, but the high entropy of solu-
`tion values for these solutions do not indicate regular solutions.
`
`REFERENCES
`(1) T. Higuchi, in "Pharmaceutical Compounding and Dis-
`pensing," R. Layman, Ed., Lippincott, Philadelphia, Pa., 1949,
`chap. 7.
`(2) M. Sax and J. Pletcher, Science, 166,1546(1969).
`(3) F. A. Restaino and A. N. Martin, J . Pharm. Sci., 53,
`636( 1964).
`(4) A. N. Paruta, ibid., 58.216(1969).
`
`Ex. 1117-0005
`
`

`

`(5) J. H. Hildebrand and R. L. Scott, “The Solubility of Non-
`electrolytes,” 3rd ed., Reinhold, New York, N.Y., 1949.
`(6) A. N. Paruta, B. J. Sciarrone, and N. G. Lordi, J. Pharrn.
`Sci., 53,1349(1964).
`(7) M. J. Chortkoff and A. N. Martin, J. Arner. Pharm. Ass.,
`Sci. Ed., 49,444(1960).
`( 8 ) W. G. Gorman and G. D. Hall, J. Pharrn. Sci., 53,
`1017(1964).
`(9) J. H. Hildebrand, J. M. Prausnitz, and R. L. Scott, “Regu-
`lar and Related Solutions,” Van Nostrand Reinhold, New York,
`N.Y., 1970.
`(10) J. Ferguson, J . Proc. Roy. SOC. (Ser. B ) , 127,397(1939).
`(11) S. H. Yalkowsky, G. L. Flynn, and T. G. Slunick, J. Pharm.
`Sci., 61,853(1972).
`(12) B. H. Mahan, “Elementary Chemical Thermodynamics,”
`W. A. Benjamin, New York, N.Y., 1963, chap. 4.
`(13) J. H. Hildebrand and R. L. Scott, “The Solubility