Activity and Activity Coefficient Studies of Aqueous Binary Solutions of

Article pubs.acs.org/jced

Activity and Activity Coefficient Studies of Aqueous Binary Solutions of Procaine, Lidocaine, and Tetracaine Hydrochloride at 298.15 K Vasim R. Shaikh,† Dilip H. Dagade,‡ Santosh S. Terdale,§ Dilip G. Hundiwale,† and Kesharsingh J. Patil*,† †

School of Chemical Sciences, North Maharashtra University, Jalgaon-425001, India Department of Chemistry, Shivaji University, Kolhapur-416004, India § Department of Chemistry, University of Pune, Pune-411007, India ‡

ABSTRACT: Osmotic coefficient and density measurements are reported for the aqueous solutions of three hydrochloride salts of local anesthetical drug compounds, procaine (PC·HCl), lidocaine (LC·HCl), and tetracaine (TC·HCl) at 298.15 K and at ambient pressure. The experimental osmotic coefficient data are used to determine the activity and mean ionic activity coefficients of solute and solvent, respectively. The activity data have been processed to obtain the mixing and excess thermodynamic properties, such as Gibbs free energy (which has been studied as a function of drug concentration), as well as to obtain the osmotic pressure and osmotic virial coefficients of the drug compounds. The mean ionic activity coefficients of the ions decrease with the increase in drug concentration. The results of mixing and excess free energy changes do not show abrupt changes. These results are examined from the point of view of premiceller (associative) equilibria and the occurrence of critical micelle concentration (cmc). A discussion is presented on the basis of aggregation of cations, and the aggregation numbers of 2, 1.56, and 6 are obtained for PC·HCl, LC·HCl, and TC·HCl, respectively, in the solution phase, applying the pseudophase separation model. An application of the McMillan−Mayer theory of solutions to the data is made. It is noted that overall second virial coefficients are small and negative for the drug molecular salt, whereas it is positive for nonelectrolyte contribution. All of these are examined on the basis of structural characteristic of molecules and electrostatic and hydrophobic interactions.

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INTRODUCTION Recently, we have reported the utility of osmotic coefficient measurements by using vapor pressure osmometry to study the critical micelle concentration (cmc) in the case of aqueous surfactant (drug) solutions.1 Also, the studies about activity coefficient variation and excess free energy changes with concentration provide a lot of information to elucidate structural changes in solvent water and about ion−solvent and ion−ion interactions with the help of the application of molecular theories like Kirkwood−Buff and McMillan−Mayer in the solution phase.2,3 The positive deviation of the activity coefficients of aqueous electrolyte solutions from the corresponding Debye−Hückel limiting law has been explained by Bjerrum in terms of ionic hydration, while the negative deviations are indicated for complex-ion formation in solution. Of course, the nature of deviation depends upon the charge, temperature, and the type of anion associated. The variation of osmotic coefficients with the concentration of uni-univalent salts has been discussed by Diamond4 in terms of solvent-enforced ion-pair formation (in the case of salts of long chain fatty acids and tetraalkylammonium salts). He has also explained the occurrence of micelle formation for higher fatty acid anions in terms of minimization of the disturbance to water structure and enhancement of electrostatic attraction for the cations leading to the observed reduction in the value of osmotic and activity coefficients (negative deviation from Debye−Hückel law) and accounted the effect as due to occurrence of solvent enforced ion-pairing. We studied earlier the osmotic coefficient behavior © XXXX American Chemical Society

of some ionic liquids in aqueous solutions and observed that hydrophobic hydration of the cations along with the Coulombic interactions between the ions leads to the formation of the water structure-enforced ion-pairs.5 There is great interest in thermodynamic properties associated with biochemical processes, such as those involved in solvation, association, binding, and conformation changes in aqueous solution. The solution studies for model compounds can be used to derive meaningful information about molecular recognition and self-assembly processes especially for enzymes and proteins.6−8 Attwood et al.9−11 have used amphiphilic drug molecules as models to study association characteristics that are derived from their rigid tricylic hydrophobic groups. According to these authors the micellization of the drug becomes increasingly exothermic with an increase in temperature, while the surface and hydrophobic contributions to the free energy are almost constant. Apparent molar volume, adiabatic compressibilities, and surface tension properties of some antidepressant drugs in aqueous solutions have been studied by Taboada et al.12 The apparent molar volume of two local anesthetical drug compounds in aqueous solutions as a function of temperature are reported and discussed in terms of competitive effects between electrostriction and hydrophobic solvation.13 The calorimetric enthalpies of such a drugs in aqueous solutions at 298.15 K are interpreted in Received: June 26, 2012 Accepted: October 3, 2012

A

dx.doi.org/10.1021/je3006985 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

NaCl of AR grade (Merck) was dried under vacuum at 393 K for 24 h before use. Density Measurements. All of the solutions were prepared on a molality basis using quartz doubly distilled water and were converted to molarity scale whenever required with the help of density data at 298.15 K. A Shimadzu AUW220D balance having a readability of 0.01 mg was used for weighing. The uncertainty in the composition of the solutions is negligibly small and is of the order of ± 5·10−5 mol·kg−1. The density measurements were made using an Anton Paar digital densitometer (model DMA-5000) at 298.15 ± 0.001 K. After applying the humidity and lab pressure (98.258 kPa) corrections, the uncertainty in the density measurements was found to be ± 5·10−3 kg·m−3 at ambient pressure of 101.325 kPa. The details about the density measurements have been reported earlier.15 Osmotic Coefficient Measurements. The osmotic coefficient (ϕ) of aqueous drug solutions were measured using a KNAUR K-7000 vapor pressure osmometer at 298.15 ± 0.001 K. The reproducibility of the temperature changes as monitored by thermister was always better than ± 0.001 K. The instrument was calibrated using aqueous NaCl solutions taking water as a reference. The required osmotic coefficient data of aqueous NaCl solutions were taken from literature17 and the one corrected for Debye−Hückel limiting slope in the limit of infinite dilution.18 The details about the calibration of vapor pressure osmometer for aqueous solution were described earlier.7 We note that excellent agreement with ϕ and mean ionic activity coefficients (γ±) data for NaCl-H2O system at 298.15 K was observed. The uncertainty in ϕ measurements was found to be ±1·10−3 at the lowest concentration studied.

terms of strong solute−solute interactions for dilute salt concentrations in addition to solute−solvent and solvent−solvent interactions.14 Recently, we have reported our measurements of density data for three local anesthetic reagents (PC·HCl, LC·HCl, and TC·HCl) in water at 298.15 K.15 The volume changes due to aggregation were estimated and the existence of micelle-type equilibria found in the case of the TC·HCl−H2O system. In our studies, we found small aggregation numbers in the range of 2 to 8. It was thought that, in such a solution state having limited aggregation, to call the aggregates as micelles is not justified. Probably, the interactions are similar to those appearing in cationic dye molecule aggregation in the form of stacking.16 Therefore, to confirm the aggregation, we extended our experimental work of osmotic vapor pressure studies to aqueous solutions of PC·HCl, LC·HCl, and TC·HCl at 298.15 K. The osmotic coefficients and the mean ionic activity coefficients are determined by using appropriate equations and a proper integration method. The same data are used to obtain mixing and excess free energy changes as a function of drug concentration, while osmotic pressure data are used to calculate overall second virial coefficients of salt molecules. The McMillan−Mayer theory is applied to obtain the contribution to second virial coefficient due to the nonelectrolyte interaction contribution. These results are presented and discussed below.

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EXPERIMENTAL WORK Materials. Procaine hydrochloride, PC·HCl (purity 97 %), lidocaine hydrochloride, LC·HCl (monohydrate), and tetracaine hydrochloride, TC·HCl (purity 99 %) were procured from Sigma-Aldrich and used without further purification. The structures of the drug molecules are shown in Figure 1. The salt

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RESULTS Osmotic and Activity Coefficients. The osmotic coefficient (ϕ) values were determined for aqueous PC·HCl [(∼0.015 to ∼0.51) mol·kg−1], LC·HCl [(∼0.01 to ∼0.49) mol·kg−1], and TC·HCl [(∼0.016 to ∼0.40) mol·kg−1] solutions at 298.15 K. Using the ϕ values obtained for aqueous binary electrolyte solutions, the water activity (aw) values have been calculated using the eq ⎛x ⎞ ln a w = −ϕ⎜ 2 ⎟ ⎝ x1 ⎠

(1)

where x1 and x2 are the mole fractions of water and the drug in the aqueous solutions, respectively. The water activity (aw) data were further utilized to calculate the solvent activity coefficient (γ1) using the eq a γ1 = w x1 The uncertainty in aw and γ1 are of the order of ± 1·10−4. The experimental osmotic coefficient data for 1:1 type electrolyte has been expressed as19 ϕ=1+

1 ln γ 3 ±

(2)

where γ± represents mean molal activity coefficient of solute. According to the Debye−Hückel limiting law, the solute activity coefficient (γ±) is given as: ln γ± = 2.303log γ± = −2.303A γ z+z − m

Figure 1. Molecular structures of the compounds studied. B

(3)



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Substituting eq 3 into eq 2 and considering higher order interaction terms Ai, which will be appreciable at higher concentrations, one can write eq 2 as20 ϕ=1−

2.303 A γ z+z − m + 3

This equation can be processed as: n

ϕ−1=

n

∑ Aimi/2 i=2

(from eq 4b)

i=1

Substituting m1/2 = x

(4a)

n

where Aγ is the Debye−Hückel limiting slope for aqueous solutions, and its value is 0.5115 at 298.15 K. Equation 4a can be written as

ϕ−1=

∑ Ai x i

(6a)

i=1

Solving the right-hand side integral of eq 5 by using eq 6a as given below:

n

ϕ=1+

∑ Aimi/2

∑ Aimi/2

(4b)

i=1

∫0

where A1 is the Debye−Hückel constant for osmotic coefficient, which is equal to −0.3927 for 1:1 electrolyte (z+ = z− = 1) at 298.15 K. The experimentally observed osmotic coefficient values were fitted according to eq 4b, and the corresponding values of Ai coefficients have been determined by least-squares fit method (A1 = −0.3927). The variation of ϕ as a function of square root of solute molality is shown in Figure 2, whereas the data of ϕ

x

⎛ ϕ − 1⎞ ⎜ ⎟d x = ⎝ x ⎠

∫0

x

(A1 + A 2 x + A3x 2 + A4 x 3 + ...)dx (6b)

∫0

x

⎡ ⎤x ⎛ ϕ − 1⎞ x2 x3 x4 ⎜ ⎟d x = ⎢A x + A + + + A A ... ⎥ 1 2 3 4 ⎝ x ⎠ 2 3 4 ⎣ ⎦0 (6c)

By making substitution of eqs 6a and 6c in eq 5, we arrive at ln γ± = (A1x + A 2 x 2 + A3x 3 + A4 x 4 + ...) ⎞ ⎛ x2 x3 x4 + 2⎜A1x + A 2 + A3 + A4 + ...⎟ 2 3 4 ⎠ ⎝

ln γ± =

⎛3 ⎞ 4 5 6 ⎜ A x + A 2 x 2 + A3x 3 + A4 x 4 + ...⎟ ⎝1 1 ⎠ 2 3 4

or ln γ± =

⎛2 + 1 2+2 2+3 ⎜ A1x + A 2x 2 + A3x 3 ⎝ 1 2 3 ⎞ 2+4 A4 x 4 + ...⎟ + ⎠ 4

that is, n

ln γ± =

∑ i=1

and Ai coefficients are collected in Tables 1 and 2, respectively. For further processing ϕ data have also been plotted as a function of reciprocal of molality for the studied systems in Figures 3a, b, and c, respectively. These will be discussed later in the Discussion Section. The mean molal activity coefficient of the drug molecules or solute (γ±) in binary aqueous solutions can be expressed in terms of osmotic coefficient using the eq20 ln γ± = (ϕ − 1) + 2

∫0

(ϕ − 1) d m m

n

∑ i=1

2+i Ai mi /2 i

(6d)

The γ± values are calculated using eq 6d, and the data for all the systems are collected in Table 1. The variation of ln γ± as a function of square root of drug concentration is shown in Figure 4. The calculation details can be obtained from our earlier reported studies.21−23 The overall uncertainty in the calculated activity coefficients of solute is of the order of ± 1·10−3. The activity coefficient data, which have been converted to mole fraction scale, were used to calculate the Gibbs free energy change due to mixing (ΔGm) and excess Gibbs free energy change (ΔGE) of binary aqueous drug solutions at 298.15 K using eqs 7 and 8, respectively.

Figure 2. Variation of experimental osmotic coefficient (ϕ) as a function of square root of molality of drug in aqueous drug solutions at 298.15 K: −●−●−, PC·HCl; −■−■−, LC·HCl; −▲−▲−, TC·HCl; - - -, Debye−Hückel limiting law.

m

2+i i Ai x = i

2

ΔGm = RT ∑ xi ln ai i=1

(7)

2

ΔGE = RT ∑ xi ln γi i=1

(8)

where xi, ai, and γi are the mole fraction, activity, and activity coefficient of ith component.

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Table 1. Molality (m), Mole Fraction (x2), Osmotic Coefficient (ϕ), Water Activity (aw), Solvent Activity Coefficient (γ1), and Activity Coefficient (γ±) Data for PC·HCl, LC·HCl, and TC·HCl in Aqueous Solutions at 298.15 Ka m/mol·kg−1

x2

0.00000 0.01580 0.01893 0.02475 0.03023 0.03265 0.03891 0.04358 0.04823 0.05787 0.07120 0.09584 0.11650 0.14379 0.17494 0.19725 0.21873 0.24574 0.27908 0.29965 0.32052 0.35234 0.40610 0.46132 0.51695

0.00000 0.00057 0.00068 0.00089 0.00109 0.00117 0.00140 0.00157 0.00173 0.00208 0.00256 0.00344 0.00418 0.00515 0.00626 0.00706 0.00782 0.00878 0.00996 0.01068 0.01142 0.01254 0.01442 0.01635 0.01828

0.00000 0.01004 0.02018 0.02958 0.03474 0.03911 0.04409 0.04809 0.05588 0.07017

0.00000 0.00036 0.00073 0.00106 0.00125 0.00141 0.00159 0.00173 0.00201 0.00252

ϕb

awc

PC·HCl + H2O 1.000 1.0000 0.885 0.9995 0.873 0.9994 0.856 0.9992 0.843 0.9991 0.838 0.9990 0.827 0.9988 0.820 0.9987 0.814 0.9986 0.804 0.9983 0.794 0.9980 0.781 0.9973 0.772 0.9968 0.759 0.9961 0.741 0.9953 0.727 0.9948 0.713 0.9944 0.694 0.9939 0.673 0.9933 0.661 0.9929 0.650 0.9925 0.636 0.9920 0.620 0.9910 0.609 0.9899 0.587 0.9891 LC·HCl + H2O 1.000 1.0000 0.879 0.9997 0.830 0.9994 0.807 0.9991 0.800 0.9990 0.796 0.9989 0.793 0.9987 0.792 0.9986 0.792 0.9984 0.796 0.9980

γ1c

γ±d

m/mol·kg−1

x2

1.0000 1.0001 1.0001 1.0001 1.0002 1.0002 1.0002 1.0003 1.0003 1.0004 1.0005 1.0007 1.0009 1.0013 1.0017 1.0020 1.0023 1.0027 1.0032 1.0036 1.0039 1.0045 1.0055 1.0065 1.0075

1.0000 0.7394 0.7152 0.6777 0.6490 0.6379 0.6126 0.5963 0.5820 0.5566 0.5286 0.4898 0.4646 0.4365 0.4084 0.3901 0.3735 0.3543 0.3330 0.3213 0.3105 0.2961 0.2765 0.2602 0.2433

0.09322 0.11507 0.14098 0.17120 0.18797 0.20816 0.23864 0.26746 0.29064 0.30893 0.33990 0.39192 0.44322 0.49817

0.00335 0.00413 0.00505 0.00613 0.00673 0.00744 0.00852 0.00954 0.01036 0.01101 0.01210 0.01392 0.01572 0.01763

1.0000 1.0000 1.0001 1.0002 1.0002 1.0003 1.0003 1.0004 1.0004 1.0005

1.0000 0.7347 0.6321 0.5763 0.5544 0.5391 0.5245 0.5146 0.4987 0.4776

0.00000 0.01696 0.02050 0.02526 0.03010 0.03454 0.03897 0.04254 0.04793 0.05807 0.06741 0.07521 0.08589 0.09567 0.11611 0.14360 0.17263 0.19243 0.24266 0.30086 0.34788 0.40048

0.00000 0.00061 0.00074 0.00091 0.00108 0.00124 0.00140 0.00153 0.00172 0.00209 0.00242 0.00270 0.00309 0.00344 0.00417 0.00515 0.00618 0.00689 0.00867 0.01072 0.01238 0.01422

ϕb

awc

LC·HCl + H2O 0.805 0.9973 0.812 0.9966 0.813 0.9959 0.805 0.9950 0.797 0.9946 0.785 0.9941 0.765 0.9934 0.748 0.9928 0.736 0.9923 0.728 0.9919 0.720 0.9912 0.718 0.9899 0.720 0.9886 0.696 0.9876 TC·HCl + H2O 1.000 1.0000 0.896 0.9995 0.884 0.9993 0.871 0.9992 0.858 0.9991 0.848 0.9989 0.839 0.9988 0.832 0.9987 0.822 0.9986 0.805 0.9983 0.790 0.9981 0.778 0.9979 0.762 0.9976 0.747 0.9974 0.716 0.9970 0.672 0.9965 0.622 0.9961 0.587 0.9959 0.498 0.9957 0.411 0.9956 0.367 0.9954 0.363 0.9948

γ1c

γ±d

1.0006 1.0008 1.0009 1.0012 1.0014 1.0016 1.0020 1.0024 1.0027 1.0030 1.0034 1.0039 1.0044 1.0053

0.4556 0.4404 0.4245 0.4058 0.3952 0.3823 0.3636 0.3473 0.3359 0.3279 0.3169 0.3038 0.2939 0.2774

1.0000 1.0001 1.0001 1.0001 1.0002 1.0002 1.0002 1.0003 1.0003 1.0004 1.0005 1.0006 1.0007 1.0009 1.0012 1.0017 1.0023 1.0028 1.0044 1.0063 1.0079 1.0091

1.0000 0.7587 0.7346 0.7063 0.6814 0.6610 0.6427 0.6290 0.6101 0.5785 0.5531 0.5338 0.5095 0.4890 0.4500 0.4034 0.3597 0.3327 0.2740 0.2232 0.1955 0.1780

The uncertainty in molality m is of the order of ± 5·10−5 mol·kg−1. bThe uncertainty in ϕ values at the lowest concentration is of the order ± 1·10−3. All measurements of ϕ were made at 298.15 K. The reproducibility of the changes as monitored by thermister were always better than ± 0.001 K. cThe uncertainty in the water activity (aw) and solvent activity coefficient (γ1) are of the order of ± 1·10−4. dThe mean ionic activity coefficient of the electrolyte (γ±) at the lowest concentration studied are accurate up to ± 1·10−3. a

The values for ΔGm and ΔGE are collected in Table 3. It is observed that ΔGm and ΔGE are negative, the variations of which as a function of square root of drug concentration are shown in Figures 5 and 6, respectively. The corrections to ln γ±, ΔGm, and ΔGE data due to hydrolysis in the low concentration region are assumed to be negligible. The errors in ΔGm and ΔGE are estimated to be of the order of ± 0.05 J·mol−1. The molal osmotic coefficient is related to the osmotic pressure (π) by following equation

Table 2. Coefficients Ai in eq 4b A1 A2 A3 A4 A5 A6 A7 A8

PC·HCl + H2O

LC·HCl + H2O

TC·HCl + H2O

−0.3927a −9.0383 49.2853 −86.9178 18.8584 58.6538 15.9089 −53.9901b

−0.3927a −17.0290 110.3808 −232.3868 110.9356 148.2003 −79.8972 −56.2647b

−0.3927a −6.6430 36.3691 −82.1249 60.6712b

π=

a

The coefficient A1 represents the term [(−2.303Aγz+z−)/3], assuming the hydrochlorides studied as 1:1 electrolytes (i.e., z+ = z− = 1), the value of A1 is −0.3927 since Aγ = 0.5115 at 298.15 K. bWe stopped up to the coefficient A5 (for TC·HCl) and coefficient A8 (for PC·HCl and LC·HCl), since the experimental data gets well-fitted within the experimental uncertainties and requires no higher order terms.

νRTW1 ϕm 1000V1̅

(9)

where W1 is the molecular weight of the solvent and V̅ 1 is the partial molal volume of the solvent. The estimated osmotic pressure value accuracy is of the order of ± 0.5 kPa. We made these calculations, and the parameter π/cRT values (where c is concentration of solute in grams per unit volume) at D



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various concentrations are obtained. In Figure 7, π/cRT values are plotted as a function of concentration for the salts studied. This enabled us to calculate molecular weights of the compounds studied and the van’t Hoff factor at the studied concentration confirming the reliability about the extent of ionization. Further since osmotic coefficient data gives information about pairwise and higher order interaction coefficients (see eq 11 below), we used Figure 7 to obtain overall second virial coefficients for the studied salts. Application of the McMillan-Mayer Theory. In dilute solutions of up to 0.1 mol·kg−1, if the Debye−Hückel electrostatic contribution is subtracted from a thermodynamic parameter, that is, from ln γ±, then the remainder is linear in the molality, as it is for a nonelectrolyte.18 The mean molal activity coefficient of the solute (γ±) in dilute concentration range can be represented as ln γ± = −αm1/2(1 + bm1/2)−1 + ωm

(10)

−1/2

where α = 1.173 kg ·mol at 25 °C and b = 1.0 kg1/2·mol−1/2 and ω is nonelectrolyte solute−solute interaction parameter. According to McMillan−Mayer,24 1/2

π * n2 + B222 * n3 + ... = n + B22 kT

(11)

where n is number density of the solute and B22 * and B222 * are the osmotic second and third virial coefficients for solute−solute interaction. Hill25,26 has shown that the coefficient A22, and so forth, in the free energy expression, may be related to the coefficient B22 *, and so forth. For example,

Figure 3. Variation of experimental osmotic coefficient (ϕ) of a drug as a function of reciprocal of molality (1/m) of drug in aqueous drug solutions at 298.15 K: (a) −●−●−, PC·HCl; (b) −■−■−, LC·HCl; (c) −▲−▲−, TC·HCl. The arrow denotes the critical concentration.

0 *0 − v2̅ 0 + b11 A 22 v10 = 2B22

(12)

where ν01 and ν−0 2 are the molecular volume of the pure solvent and partial molecular volume of the solute at infinite dilution, respectively, and b011(= −B*110) is the solute−solvent cluster integral. The solute−solvent cluster integral b011 is related to the partial molecular volume of the solute at infinite dilution by27 0 b11 = − v2̅ 0 + kTκT

(13)

where k is the Boltzmann constant, T is the absolute temperature, and κT is the isothermal compressibility coefficient for the pure solvent. For a 1:1 electrolyte,18 2 ln γ2* = A 22 m̅ + B222 m̅ 2

(14)

where γ*2 is the nonelectrolyte contribution to the solute activity coefficient, and m̅ is the mole ratio of solute to solvent (N2/N1). From eqs 10 and 14, ω = (A22M1)/2 (where M1 is the molar mass of solvent in kg·mol−1). Thus from eqs 12 and 13 *0 = NB22

A 22 V10 RTk T + V2̅ 0 − 2 2

(15)

(B*220)

The values for the solute−solute virial coefficient have been calculated from the values of ω. The values of ω, A22, NB11 *0, and NB22 *0 at 298.15 K for PC·HCl, LC·HCl, and TC·HCl are collected in Table 4.

Figure 4. Variation of the mean activity coefficient of a drug (ln γ±) as a function of square root of molality of drug in aqueous drug solutions at 298.15 K: −●−●−, PC·HCl; −■−■−, LC·HCl; −▲−▲−, TC·HCl; - - -, Debye−Hückel limiting law. E



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Table 3. Molality (m), Density (d), Concentration (c), Gibbs Free Energy Change due to Mixing (ΔGm), Excess Gibbs Free Energy Change (ΔGE), and Osmotic Pressure (π) Data for PC·HCl, LC·HCl, and TC·HCl in Aqueous Solutions at 298.15 Ka db

m mol·kg

−1

kg·m

ΔGm

c −3

0.00000 0.01580 0.01893 0.02475 0.03023 0.03265 0.03891 0.04358 0.04823 0.05787 0.07120 0.09584 0.11650 0.14379 0.17494 0.19725 0.21873 0.24574 0.27908 0.29965 0.32052 0.35234 0.40610 0.46132 0.51695

997.043 997.809 997.979 998.219 998.477 998.609 998.872 999.105 999.338 999.774 1000.37 1001.52 1002.46 1003.64 1005.05 1005.94 1007.01 1008.14 1009.54 1010.41 1011.32 1012.67 1014.95 1016.97 1019.21

0.00000 0.01004 0.02018 0.02958 0.03474 0.03911 0.04409 0.04809 0.05588 0.07017

997.043 997.370 997.713 998.034 998.184 998.350 998.510 998.641 998.887 999.384

mol·dm

−3

−1

J·mol

PC·HCl + H2O 0.00000 0.00 0.00428 −12.21 0.00513 −14.36 0.00669 −18.26 0.00817 −21.84 0.00882 −23.40 0.01049 −27.37 0.01174 −30.29 0.01298 −33.16 0.01554 −39.01 0.01906 −46.92 0.02551 −61.10 0.03087 −72.65 0.03788 −87.52 0.04577 −104.08 0.05136 −115.72 0.05670 −126.78 0.06333 −140.51 0.07141 −157.24 0.07635 −167.45 0.08131 −177.73 0.08879 −193.26 0.10088 −219.14 0.11367 −245.27 0.12596 −271.21 LC·HCl + H2O 0.00000 0.00 0.00270 −8.17 0.00542 −15.34 0.00793 −21.65 0.00930 −25.02 0.01046 −27.83 0.01178 −30.99 0.01284 −33.51 0.01489 −38.33 0.01864 −46.98

ΔGE J·mol

−1

πb kPa

0.00 −0.26 −0.35 −0.54 −0.74 −0.84 −1.10 −1.31 −1.52 −2.01 −2.73 −4.21 −5.56 −7.48 −9.84 −11.63 −13.44 −15.83 −18.93 −20.93 −23.02 −26.31 −32.12 −38.37 −44.93

0.00 69.4 82.0 105.1 126.4 135.7 159.6 177.3 194.8 230.9 280.6 371.5 446.2 541.4 643.4 711.7 773.6 846.8 931.6 982.3 1033.3 1111.8 1250.1 1393.5 1505.7

0.00 −0.17 −0.52 −0.94 −1.21 −1.44 −1.72 −1.95 −2.42 −3.33

0.00 43.8 83.1 118.5 137.9 154.5 173.5 189.0 219.6 277.1

db

m mol·kg

−1

kg·m

ΔGm

c −3

0.09322 0.11507 0.14098 0.17120 0.18797 0.20816 0.23864 0.26746 0.29064 0.30893 0.33990 0.39192 0.44322 0.49817

1000.14 1000.85 1001.69 1002.65 1003.15 1003.81 1004.84 1005.71 1006.37 1006.95 1007.94 1009.45 1011.03 1012.71

0.00000 0.01696 0.02050 0.02526 0.03010 0.03454 0.03897 0.04254 0.04793 0.05807 0.06741 0.07521 0.08589 0.09567 0.11611 0.14360 0.17263 0.19243 0.24266 0.30086 0.34788 0.40048

997.043 997.722 997.869 998.076 998.265 998.444 998.614 998.764 998.980 999.405 999.767 1000.07 1000.49 1000.88 1001.66 1002.67 1003.78 1004.46 1006.27 1008.22 1009.67 1011.44

mol·dm

−3

−1

J·mol

LC·HCl + H2O 0.02463 −60.47 0.03024 −72.84 0.03683 −87.09 0.04442 −103.26 0.04859 −112.06 0.05356 −122.52 0.06099 −138.06 0.06792 −152.54 0.07343 −164.04 0.07773 −173.03 0.08495 −188.09 0.09685 −212.95 0.10834 −236.94 0.12038 −262.17 TC·HCl + H2O 0.00000 0.00 0.00506 −12.98 0.00612 −15.37 0.00753 −18.53 0.00896 −21.67 0.01027 −24.50 0.01157 −27.28 0.01262 −29.50 0.01420 −32.81 0.01716 −38.93 0.01987 −44.46 0.02212 −49.01 0.02520 −55.17 0.02800 −60.74 0.03380 −72.20 0.04152 −87.32 0.04955 −103.03 0.05496 −113.65 0.06845 −140.35 0.08367 −171.05 0.09565 −195.73 0.10874 −223.11

ΔGE −1

J·mol

−4.89 −6.44 −8.36 −10.69 −12.04 −13.71 −16.34 −18.93 −21.10 −22.85 −25.89 −31.15 −36.48 −42.36 0.00 −0.26 −0.35 −0.49 −0.65 −0.81 −0.97 −1.12 −1.35 −1.82 −2.29 −2.71 −3.32 −3.93 −5.29 −7.36 −9.82 −11.67 −16.94 −24.06 −30.48 −38.16

πb kPa 372.5 463.5 568.6 683.6 743.2 811.0 906.4 992.2 1060.8 1116.1 1214.5 1397.0 1582.8 1719.8 0.00 75.4 89.9 109.1 128.2 145.4 162.2 175.6 195.5 231.9 264.2 290.3 324.7 354.8 412.5 478.6 532.7 560.2 600.0 613.4 633.6 721.8

The temperature of the densitometer was maintained at 298.15 ± 0.001 K. bThe error involved in density determination at lowest concentration is of the order of ± 5·10−3 kg·m−3, while the calculated osmotic pressure is reproducible within ± 0.5 kPa.

a

■

DISCUSSION

extrapolation in the high concentration region) and critical micelle concentration cmc according to eq28,29

It is observed from Figure 2 that the osmotic coefficient (ϕ) for aqueous PC·HCl, LC·HCl, and TC·HCl solutions decreases as a function of the square root of drug concentration. The ϕ values are lower than the Debye−Hückel limiting law values and show nonlinear variation. In electrolytic solutions, the negative deviations from the limiting law have been accounted or explained in terms of ionic hydration or complex formation interactions.17 A distinct inflection or a break is observed at a certain concentration of the drug electrolytes. In the TC·HCl system, this break is quite distinct and can be attributed to existence of aggregation or miceller type of equilibria. As suggested by Desnoyers et al.28 and also by Attwood et al.,11 we applied the pseudophase separation model to ϕ data. When ϕ values are plotted against 1/m (Figures 3a, b, and c) lead to simultaneous determination of aggregation number n (by linear

ϕ=

⎛ 1 1 ⎞ cmc + ⎜1 − ⎟ ⎝ n n⎠ m

(16)

Using eq 16 and the data shown in Figure 3a, b, and c, we calculated the values of n as 2, 1.56, and 6 and cmc values are (0.16, 0.16, and 0.12) mol·kg−1 for PC·HCl, LC·HCl, and TC·HCl in aqueous solutions at 298.15 K, respectively. An examination of Figure 3 reveals that ϕ varies linearly in the lower concentration region and after a certain concentration showing a break or change in slope value with increase in concentration for PC·HCl and TC·HCl, respectively (Figure 3a and c). The case of LC·HCl seems to be unusual (Figure 3b). The ϕ values decreases, reaching a minimum, and thereafter goes through a maximum with an increase in the concentration of LC·HCl. The minimum in the ϕ value occurs in a concentration F



Article

Figure 7. Variation of (π/cRT) of a drug as a function of concentration (gm·cc−1) of drug in aqueous drug solutions at 298.15 K: −●−●−, PC·HCl; −■−■−, LC·HCl; −▲−▲−, TC·HCl.

Figure 5. Variation of Gibbs free energy change due to mixing (ΔGm) of a drug as a function of square root of molality of drug in aqueous drug solutions at 298.15 K: −●−●−, PC·HCl; −■−■−, LC·HCl; −▲−▲−, TC·HCl.

Table 4. Apparent Molar Volumes (V̅ 02), Nonelectrolyte Solute−Solute Interaction Parameter (ω), Coefficient A22, Solute−Solvent (NB11 *0), and Solute−Solute (NB22 *0) Virial Coefficients of Drug Molecules in Aqueous Solutions at 298.15 K ω

V̅ 02 cm ·mol 3

PC·HCl + H2O LC·HCl + H2O TC·HCl + H2O

−1

15

225.0 237.115 259.815

kg·mol

NB*110 −1

8.96 14.13 6.89

A22 994.73 1568.69 764.92

NB*220 −1

cm ·mol 3

223.9 236.0 258.7

cm3·mol−1 9211 14408 7170

the corresponding concentrations. The ln γ± values decrease with increasing concentration and show inflection at the respective cmc concentration. The negative deviation from the Debye−Hückel limiting law in premicellar region is in the order LC·HCl > PC·HCl ≥TC·HCl, meaning that the hydrophobic hydration of TC·HCl cation is minimum. However, at higher concentrations (postmicellar region) ln γ± shows a reversal in trend being the greatest for TC·HCl. This can be attributed to ion-pair and hydrophobic interaction between TC·HCl cations. Figure 4 nicely illustrates the importance of structural characteristic and the linkages present in the solute molecule. The PC·HCl contains a polar amino (−NH2) group and an ester group linkage, getting hydrophobically hydrated least while LC·HCl contains amide linkage and therefore hydrated most in the premicellar region. The presence of hydrophobic groups in TC·HCl makes it exhibit hydrophobic interaction (solute− solute, cation−cation attraction) more subtly than the other two solutes studied. The variation of ΔGm and ΔGE as a function of concentration of drug molecules (Figures 5 and 6, respectively) also reveal important differences in the mode of interaction of these electrolyte molecules (ions) with solvent water. The ΔGm is almost similar for all the salts in the studied concentration region (Figure 5). The ΔGE values decrease with concentration but show more negative values for TC·HCl at higher concentration (Figure 6). The solution enthalpies for PC·HCl and LC·HCl in a very low concentration region (

Activity and Activity Coefficient Studies of Aqueous Binary Solutions of

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