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Electrical conductances of dilute aqueous solutions of β-lactam antibiotics of the penicillin group in the 278.15 K to 313.15 K temperature range. Sodium salts of oxacillin, cloxacillin, dicloxacillin and nafcillin
Journal of Molecular Liquids 211 (2015) 417–424
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Electrical conductances of dilute aqueous solutions of β-lactam antibiotics of the penicillin group in the 278.15 K to 313.15 K temperature range. Sodium salts of oxacillin, cloxacillin, dicloxacillin and nafcillin Alexander Apelblat a,⁎, Marija Bešter-Rogač b,⁎ a b
Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana, Slovenia
a r t i c l e
i n f o
Article history: Received 2 May 2015 Received in revised form 28 May 2015 Accepted 30 May 2015 Available online 3 August 2015 Keywords: Electrolyte conductivity Sodium oxacillin Sodium cloxacillin Sodium dicloxacillin Sodium nafcillin Aqueous solutions Limiting ion conductances Dissociation constants
a b s t r a c t Systematic determinations of electrical conductivities of sodium salts of semisynthetic penicillins, oxacillin, cloxacillin, dicloxacillin and nafcillin in the 278.15 K to 313.15 K temperature range are reported. These conductivities are examined by applying the Quint–Viallard conductivity equations and the Debye–Hückel equations for activity coefficients. Determined dissociation constants and the limiting conductances of involved anions are evaluated basing on the assumption that in dilute aqueous solutions these salts, similarly as sodium salts of natural penicillins, behave as acidic salts of dibasic acids which are the final products of degradation reactions in acidic media. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Natural penicillins produced by fermentation and semisynthetic penicillins by chemical synthesis belong to an extremely important group of antibacterial drugs in clinical use. Their chemical, biological, pharmaceutical and medical properties were the subject of extensive studies over many years and they are reviewed in the literature [1–9]. These studies were mainly devoted to the structure, production, chemical stability and the clinical potency of antibiotics and considerably less to their physicochemical properties. Since the instability of penicillin in aqueous solutions has been known from the time of its discovery, many investigations have been dedicated to the transformation, degradation, aging and hydrolysis reactions of penicillins. Considering that degradation reactions are associated with the reduction of antibacterial activity of drugs and with the allergic response after penicillin therapy, numerous kinetic, thermodynamic, structure studies and the analytical identification of degradation products have been reported [10–17]. From these investigations it is evident that penicillins are sensitive to ⁎ Corresponding authors. E-mail addresses: [email protected] (A. Apelblat), [email protected] (M. Bešter-Rogač).
http://dx.doi.org/10.1016/j.molliq.2015.05.066 0167-7322/© 2015 Elsevier B.V. All rights reserved.
chemical additives, electrolytes, oxidizing agents and even water molecules. Their pH dependence of hydrolysis reactions, the influence of buffer species, ionic strength and temperature is well experimentally established but the exact proportion of formed degradation products and details of reaction pathways continue to be uncertain. The basic structure of penicillin molecules consist of a nucleus (the fused β-lactam–thiazolidine ring known as 6-aminopenicillanic acid) and a condensed side-chain group. Many antibiotics are produced semisynthetically by the chemical modification of 6-aminopenicillanic acid and their salts have a strong tendency to form crystalline hydrates. These semisynthetic antibiotics are useful for the treatment of a number of bacterial infections and they are suitable for oral administration in the form of highly soluble sodium or potassium salts. Properties of semisynthetic penicillin solutions were determined by using different experimental techniques [18–25] but our knowledge about them is very limited. Similarly as natural penicillins, the investigated semisynthetic penicillins are fairly strong carboxylic acids. Determined by conventional potentiometric titration methods the apparent pKa values lie in the 2.6–2.8 range and they are very weakly temperature dependent [2,5,19,20]. Determinations of electrical conductivity of natural penicillins started early, close to the time of their discovery (for the complete list
418
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of the literature see [26]). These investigations were associated with the question whether penicillin salts behave as strong, weak or colloidal electrolytes. On contrary, electrical conductances of semisynthetic penicillins in dilute aqueous solutions were never determined and they are for the first time reported and analyzed in this investigation. In more concentrated solutions of semisynthetic penicillins, certain physical properties are consistent with the possibility that their salts are dispersed in water in the form of colloidal solutions [27–32]. As one of experimental techniques, specific conductivity measurements were applied to determine the critical micelle concentrations, but unfortunately these conductances were only presented in graphical form. Continuing our previous investigation of electrical conductances (sodium and potassium penicillin G and potassium penicillin V), in this study sodium salts of oxacillin (3-phenyl-5-methyl-4isoxazototyl-penicillin), cloxacillin (3-(2-chlorophenyl)-5-methyl-4isoxazotyl-penicillin), dicloxacillin (3-(2,6-dichlorophenyl)-5-methyl4-isoxazotyl-penicillin) and nafcillin (6-(2-ethoxy-1-naphtamido)penicillin) were investigated. The structures of their anions are presented in Fig. 1. Electrical conductivities of sodium salts of these semisynthetic penicillins (for briefness denoted as NaHPen) in dilute aqueous solutions, in the 278.15 K to 313.15 K temperature range were measured and interpreted in terms of dissolution and dissociation reactions, in the same way as previously treated natural penicillins [26]. 2. Experimental 2.1. Materials Sodium salts of oxacillin, cloxacillin, dicloxacillin and nafcillin were purchased as monohydrates from Sigma-Aldrich. According to the information of supplier, nafcillin sodium salt contains ~3.5% of trisodium citrate, whereas for other compounds no information about impurities was given by producer. All compounds were stored in the refrigerator (~ 4 °C) and used as received. Demineralized water was distilled two times in a quartz bidistillation apparatus (Destamat Bi 18E, Heraeus). The final product with specific conductance b6·10−7S·cm1 was distilled into a flask permitting storage and transfer of water into the measuring cell under an atmosphere of nitrogen. Stock solutions were prepared by weighing and were stored under nitrogen in the refrigerator. 2.2. Conductivity measurements The conductivities of the solutions were determined with the help of a three-electrode measuring cell, described elsewhere [33]. The cell was calibrated with dilute potassium chloride solutions [34] and immersed in the high precision thermostat described previously [35]. The temperature dependence of the cell constant was taken into account [34]. The water bath can be set to each temperature using a temperature program with a reproducibility of 0.005 K. The temperature in the precision thermostat bath was additionally checked with calibrated Pt100 resistance thermometer (MPMI 1004/300 Merz) in connection with a HP 3458 A. The resistance measurements of the solutions in the cell were performed using a precision LCR Meter Agilent 4284 A.
At the beginning of every measuring cycle, the cell was filled with a known mass of water (~660 g). After measurement of the solvent conductivity at all temperatures of the temperature program, the stepwise concentration was carried out by successive additions, using a gas-tight syringe, of weighed amounts of a stock solution. The measuring procedure, including corrections and extrapolation of the sample conductivity to infinite frequency, has been previously described [35]. Conductivity of sodium dicloxacillin solutions was measured at 298.15 K only, because it turned out as unstable in a longer term period as it is usually demanded for covering whole temperature range. Its stock solution became turbid in about five days namely, what was not the case at other investigated systems. The molar concentrations c were determined from the masses and the corresponding solution densities d. A linear change of d with increasing salt content for diluted solutions was assumed, dðTÞ ¼ d0 ðTÞ þ ~ is the molonity of the elec~ where d0(T) is the density of water and m bm, trolyte (moles of electrolyte per kilogram of solution) and the bcoefficients are assumed as independent of temperature. The densities of the solutions were determined by the method of Kratky et al. [36] using a Paar densimeter (DMA 60, DMA 601 HT) at 298.15 K combined with a precision thermostat. In all sets of the reported conductivityconcentration data (Tables 1–3), the concentrations are given at 298.15 K and they can be converted to other temperatures by use of ~ dðTÞ by help of estimated b-coefficients, the relationship cðTÞ ¼ m given in footnotes of these tables. Considering the sources of error (calibration, measurements, impurities), the specific conductivities are estimated to be accurate within 0.2%. 3. Results and discussion The molar conductivities Λ(c) of oxacillin, cloxacillin, dicloxacillin and nafcillin determined in this work as a function of concentration and temperature are presented in Tables 1, 2 and 3 respectively. Considering difficulty in handle dicloxacillin, its conductances were measured only at 298.15 K. Conductances of nafcillin in Table 3 represent their values after taking into account that solid salt contains ~ 3.5% of trisodium citrate (for conductivities of Na3Cit see [37]) and by assuming that the conductances of both salts are proportional to their mole fractions. The form of Λ(c) versus c1/2 curves in the case of semisynthetic penicillins (Fig. 2) is similar to that natural penicillins (deviation from the straight line appears in very dilute solutions) and can be interpreted by considering hydrolysis (salts of weak acids) and degradation reactions in water. Preliminary calculations based on the simplest version of hydrolysis process Na‐HPen → Naþ þ HPen‐ HPen‐ þ H2 O ⇌ HPen þ OH‐ H2 O ⇌ Hþ þ OH‐
ð1Þ
showed that over large variations of model parameters, this molecular model is unsuitable to represent experimental conductivities Λexp.(c) in dilute aqueous solutions. The contributions coming from the
Fig. 1. Structures of a) oxacillin, b) cloxacillin, c) dicloxacillin and d) nafcillin anion.
A. Apelblat, M. Bešter-Rogač / Journal of Molecular Liquids 211 (2015) 417–424 Table 1 Experimental and calculated molar conductivities of sodium oxacillin salt as a function of concentration c and temperature T a. T/K
278.15
103.c⁎
Λexp
Λcalc
0.2566 0.5717 0.9012 1.2215 1.5864 2.0566 2.6327 3.3247 4.2133 5.2621 6.3936 σ(Λ)
45.40 45.15 44.88 44.69 44.25 44.01 43.73 43.44 43.09 42.71
45.55 45.11 44.81 44.54 44.27 43.99 43.71 43.41 43.11 42.84 0.08
293.15 68.94 68.22 67.73 67.15 66.69 66.38 66.00 65.57 64.90 64.44 64.04
0.2566 0.5717 0.9012 1.2215 1.5864 2.0566 2.6327 3.3247 4.2133 5.2621 6.3936 σ(Λ)
308.15 95.23 94.27 93.51 93.00 92.24 91.86 90.96 90.32 89.90 89.19 88.62
0.2566 0.5717 0.9012 1.2215 1.5864 2.0566 2.6327 3.3247 4.2133 5.2621 6.3936 σ(Λ)
283.15
69.53 68.26 67.56 67.08 66.66 66.22 65.79 65.35 64.89 64.43 64.00 0.22
96.54 94.57 93.51 92.80 92.17 91.52 90.89 90.26 89.59 88.93 88.32 0.47
Λexp 53.22 52.55 52.24 51.93 51.47 51.22 50.95 50.54 50.24 49.77 49.46
298.15 77.40 76.56 76.02 75.47 75.02 74.57 74.12 73.46 72.88 72.42 71.98
313.15 104.84 103.61 102.54 102.26 101.59 100.98 100.30 99.58 98.82 98.25 97.79
288.15 Λcalc 53.57 52.66 52.15 51.79 51.48 51.16 50.83 50.51 50.16 49.81 49.49 0.14
78.34 76.85 76.03 75.48 74.99 74.48 73.99 73.49 72.96 72.44 71.95 0.32
419
Table 2 Experimental and calculated molar conductivities of sodium cloxacillin salt as a function of concentration c and temperature T a. T/K
278.15
Λexp
Λcalc
103.c⁎
Λexp
Λcalc
Λexp
Λcalc
Λexp
Λcalc
60.92 60.18 59.77 59.47 59.02 58.62 58.30 57.94 57.40 56.99 56.51
60.71 60.05 59.63 59.32 59.03 58.72 58.40 58.06 57.70 57.33 56.98 0.24
0.3217 0.5985 0.9333 1.2556 1.6943 2.1573 2.7436 3.4327 4.1540 4.9193 5.7513
42.34 42.15 41.85 41.68 41.40 41.24 40.91 40.59 40.32 40.11 39.90
42.79 42.26 41.87 41.60 41.31 41.06 40.80 40.55 40.31 40.10 39.83 0.17
49.01 48.79 48.44 48.26 47.83 47.54 47.37 47.00 46.69 46.45 46.07
49.50 48.89 48.44 48.12 47.78 47.50 47.19 46.90 46.63 46.37 46.13 0.18
56.08 55.81 55.43 55.21 54.74 54.41 54.21 53.81 53.46 53.04 52.77
56.66 55.95 55.43 55.07 54.68 54.35 54.00 53.65 53.34 53.05 52.77 0.22
87.23 85.51 84.57 83.94 83.38 82.81 82.25 81.69 81.09 80.50 79.95 0.38
0.3217 0.5985 0.9333 1.2556 1.6943 2.1573 2.7436 3.4327 4.1540 4.9193 5.7513 σ(Λ)
303.15 86.21 85.25 84.51 83.99 83.38 83.05 82.56 81.85 81.26 80.63 80.25
106.34 104.12 102.93 102.13 101.43 100.72 100.01 99.31 98.56 97.83 97.16 0.60
0.3217 0.5985 0.9333 1.2556 1.6943 2.1573 2.7436 3.4327 4.1540 4.9193 5.7513 σ(Λ)
293.15 63.55 63.24 62.83 62.48 62.03 61.66 61.43 60.97 60.42 60.14 59.80
308.15 88.17 87.74 86.89 86.55 85.94 85.46 84.91 84.29 83.78 83.37 82.94
283.15
64.25 63.43 62.84 62.42 61.98 61.60 61.20 60.81 60.45 60.12 59.80 0.25
89.04 87.88 87.04 86.45 85.82 85.29 84.73 84.17 83.67 83.21 82.76 0.31
298.15 71.49 71.06 70.58 70.17 69.66 69.29 69.01 68.32 67.92 67.58 67.20
313.15 97.21 96.52 95.63 95.20 94.52 94.03 93.37 92.70 92.20 91.71 91.25
288.15
72.46 71.26 70.58 70.10 69.66 69.21 68.75 68.29 67.80 67.30 66.84 0.32
303.15 79.69 79.22 78.67 78.20 77.65 77.24 76.92 76.16 75.72 75.33 74.92
80.46 79.42 78.66 78.14 77.57 77.09 76.59 76.09 75.64 75.22 74.82 0.28
98.02 96.72 95.78 95.13 94.43 93.84 93.21 92.60 92.04 91.53 91.03 0.30
a Units: c, mol dm−3; Λ, σ(Λ), S cm2 mol−1. ⁎ c are molarities at 298.15 K; b — coefficient in the density equation is 0.1463 kg 2 ·dm − 3 ·mol − .
a Units: c, mol dm−3; Λ, σ(Λ), S cm2 mol−1. ⁎ c are molarities at 298.15 K; b — coefficient in the density equation is 0.1687 kg 2 ·dm − 3 ·mol − 1 .
hydrolysis reactions to calculated conductivities Λcalc.(c) are always negligible. From identification studies of degradation products of various penicillins [10–17] it was observed that penicillin has a single carboxylic group as acidic functional group, but that the degradation products are corresponding dibasic acids. In the context of conductivity determinations, the exact composition of degradation products during measurements is not important considering that the main contribution to the conductance comes from the hydrogen and sodium ions and less from the organic anions. Besides, it is expected that differences in contributions from various organic ions to the over-all conductivity will also be small. Because the exact proportion between anions is unknown and varies during the conductivity experiments, we assumed that the system can be treated as containing only one acidic salt of the dibasic penicillinic acid and the measured conductance is the sum of contributions from all the cations and anions present in solution. The molar conductivities, Λ, are the sum of ionic contributions
of the electrolyte. The dissolution of an acidic salt of a dibasic acid in water in terms of the dissociation reactions is governed by the following equations
Λ¼
κ ¼ c
n X z j c jλ j j¼1
c
NaHPen → Naþ þ HPen‐ HPen‐ ⇌ Hþ þ Pen2‐ Hþ þ HPen‐ ⇌ H2 Pen
ð3Þ
where the effect of water dissociation is very small and is neglected. Taking into account the charge balance in the solution cð1 þ α Hþ Þ ¼ cðα 1 þ 2α 2 Þ
ð4Þ
and denoting concentrations of existing species by: ð2Þ
where κ is the measured specific conductance, λj are the ionic conductances, cj and zj are the concentrations and charges of the individual ions present in the solution and c denotes the analytical concentration
þ Naþ ¼ c H ¼ cα Hþ ½hHPen‐i ¼ cα 1 Pen2‐ ¼ cα 2 ½H2 Pen ¼ cβ ¼ ð1−α 1 −α 2 Þc
ð5Þ
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A. Apelblat, M. Bešter-Rogač / Journal of Molecular Liquids 211 (2015) 417–424
Table 3 Experimental and calculated molar conductivities of sodium nafcillin and dicloxacillin salts as a function of concentration c and temperature T a. T/K
278.15
103.c⁎
Λexp
Λcalc
Λexp
Λcalc
Λexp
Λcalc
0.2560 0.5560 0.8770 1.2190 1.5670 1.9670 2.4650 3.1470 3.9300 4.9570 σ(Λ)
38.44 38.02 37.77 37.66 37.42 37.30 37.21 37.06 36.93 36.58
38.53 38.16 37.91 37.71 37.53 37.35 37.15 36.92 36.69 36.43 0.14
44.39 43.99 43.71 43.59 43.29 43.17 43.07 42.89 42.73 42.37
44.59 44.17 43.88 43.63 43.42 43.21 42.98 42.71 42.45 42.14 0.18
50.80 50.39 50.07 49.68 49.58 49.46 49.28 49.14 48.66 48.55
51.04 50.55 50.21 49.92 49.68 49.44 49.17 48.86 48.55 48.20 0.21
0.2560 0.5560 0.8770 1.2190 1.5670 1.9670 2.4650 3.1470 3.9300 4.9570 σ(Λ) 0.2560 0.5560 0.8770 1.2190 1.5670 1.9670 2.4650 3.1470 3.9300 4.9570 σ(Λ)
293.15 57.40 57.03 56.70 56.33 56.26 56.00 55.85 55.36 55.34 55.01
308.15 78.92 78.69 77.98 78.04 77.65 77.51 76.85 76.51 76.40 76.17
283.15
57.84 57.27 56.87 56.54 56.26 55.98 55.68 55.32 54.96 54.56 0.28
298.15 64.44 64.06 63.31 63.28 63.13 62.87 62.69 62.19 61.94 61.78
80.09 79.17 78.56 78.06 77.63 77.22 76.78 76.26 75.75 75.17 0.62
288.15
64.95 64.28 63.82 63.44 63.11 62.79 62.45 62.04 61.63 61.18 0.35
0.3025 0.6347 0.9406 1.2636 1.6004 1.9635 2.3384 2.8222 3.3919 4.1019 4.6833 5.5596 6.6913 σ(Λ)
303.15 71.40 71.27 70.55 70.59 70.26 70.09 69.51 69.20 69.07 68.87 298.15b 77.06 75.76 74.99 74.18 73.72 73.33 72.97 72.59 72.12 71.55 71.25 70.87 70.40
72.35 71.57 71.04 70.61 70.24 69.87 69.48 69.02 68.57 68.05 0.50
77.72 75.85 74.94 74.27 73.73 73.26 72.86 72.42 71.98 71.51 71.18 70.73 70.33 0.21
Units: c, mol dm−3; Λ, σ(Λ), S cm2 mol−1. Conductivities of dicloxacillin sodium salt. ⁎ c are molarities at 298.15 K; b — coefficient in the density equation is 0.1520 kg2·dm−3·mol−1 for nafcillin and 0.1855 kg2·dm−3·mol−1 dicloxacillin solutions. a
b
the dissociation equilibria can be expressed by: þ H ½HPen‐ cðα 1 þ 2α 2 −1Þα 1 F1 ¼ F1 ½H2hPen i 1‐α 1 −α 2 þ 2‐ H Pen cðα 1 þ 2α 2 −1Þα 2 F2 ¼ K2 ðT Þ ¼ F2 ½HPen‐ α1 K1 ðT Þ ¼
ð6Þ
f Hþ f HPen‐ f H2 Pen f Hþ f Pen2‐ F2 ¼ : f HPen‐
ð7Þ
The activity coefficients of the individual ions in dilute solutions, fj, can be approximated by the Debye–Hückel equations pffiffi z2j AðT Þ I pffiffi 1 þ a j BðT Þ I 1:8246 106 ; AðT Þ ¼ ½DðT ÞT 3=2
where D(T) is the dielectric constant of water, aj is the ion size parameter and I denotes the ionic strength of the solution, which is I = c(α1 + 3α2). Values of the size parameters (a(H+) = 9.0 Ǻ, a(Na+) = 4.0 Ǻ, a(HPen−) = 5.0 Ǻ and a(Pen2−) = 5.8 Ǻ) were prescribed and they are assumed to be independent of temperature [38,39]. If the equilibrium constants K1(T) and K2(T) and the activity coefficients are available, the concentration fractions α1 and α2 can be successively evaluated for every concentration c by an iterative solution of two quadratic Eq. (9) 8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 1< K1 K1 2 4K1 ð1−α 2 Þ= 1−2α 2 − α1 ¼ þ 1−2α 2 − þ ; 2: cF1 c F1 c F1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi) ( 1 8K2 α 1 1−α 1 þ ð1−α 1 Þ2 þ : α2 ¼ 4 cF2
ð9Þ
In this work, the ionic conductances λj in Eq. (1) are represented by the Quint–Viallard conductivity equations [40] pffiffi λ j ¼ λ0j ‐S j I þ E j I ln I þ J1 j I‐J2 j I 3=2
ð10Þ
where λ0j is the limiting conductance of the jth ion. The coefficients Sj, Ej, J1j, J2j are rather complex functions of the viscosity η, the dielectric constant of pure water and the average cation–anion distances of closest approach (explicit expressions for these coefficients are given also elsewhere [41]). The molar conductivities of NaHPen are the contributions from the four ion pairs ð1Þ Λ 1 ¼ hλ Hþ þ λð HPen‐ Þ i ð1Þ Λ 2 ¼ λ Hþ þ λ 1=2Pen2‐ ð2Þ Λ 1 ¼ hλ Naþ þ λð HPen‐ Þ i ð2Þ Λ 2 ¼ λ Naþ þ λ 1=2Pen2‐ :
where F1 and F2 denote the quotients of the activity coefficients F1 ¼
Fig. 2. Molar conductivity Λ of sodium salts of semisynthetic penicillins at 298.15 K. — oxacillin; — dicloxacillin; — cloxacillin and — nafcillin.
ð11Þ
The corresponding pairs of ions are denoted with the superscripts (1) and (2), and the organic ions are “distributed” between the hydrogen and sodium ions in the following way [42] Λ ðNaHPenÞ ¼
i h i α Hþ h 1 ð1Þ ð1Þ ð2Þ ð2Þ α 1 Λ 1 þ 2α 2 Λ 2 þ α 1 Λ 1 þ 2α 2 Λ 2 : α 1 þ 2α 2 α 1 þ 2α 2
ð12Þ
log f j ðT Þ ¼ ‐
BðT Þ ¼
50:29 108 ½DðT ÞT 1=2
ð8Þ
The representation of NaHPen conductances includes the evaluation of concentrations of all species present in solution and the use of eight Quint–Viallard conductivity equations. Formally, the conductivity-
A. Apelblat, M. Bešter-Rogač / Journal of Molecular Liquids 211 (2015) 417–424
concentration data set (Λ,c) can be expressed in the form: Λ = f [c; K1, K2, λ0(HPen− 1), λ0(1/2Pen−2), aj]. Thus, at a given temperature T, using the physical properties of pure water and the limiting ionic conductances λ0(H+) and λ0(Na+) [43–46] (Table 4) and the distances of closest approach in the Quint–Viallard conductivity equations can be taken as the average value of the ion size parameters in the ion pairs. Dissociation constants K1(T) and K2(T) and the limiting conductances λ0(HPen−1) and λ0(1/2Pen−2) were evaluated in the iterative process, starting with the assumed dissociation constants K1(T) and K2(T) and values of α1 and α2, fj and I for each concentration c. The calculations were repeated with new values of dissociation constants until the satisfactory agreement between the measured and calculated conductivities was reached. The degree of agreement of the obtained fit is expressed by the mean value of standard deviations
σ ðΛÞ ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX 2 u Λ j: exp: ‐Λ j;calc: u t j¼1
ð13Þ
N‐1
where N is the number of experimental points at given T. Determined in such way Λcalc values for investigated here semisynthetic penicillis are compared with Λexp. values in Tables 1, 2 and 3. As can be observed, based on values of the standard deviations σ(Λ), there is a very satisfactory agreement between the experimental and calculated conductivities over the investigated concentration regions and at all temperatures. A detailed analysis of the conductivity data, which is similar to all penicillin, is given only for cloxacillin at 298.15 K (Table 5). Distribution of various ions in solutions shows that the first dissociation step is the most important step, α1 ≫ α2. The contribution to Λcalc. from the ion pairs (Na+ + HPen−) and (H+ + HPen−), which is denoted as is Λ1, is predominant. As expected, the contribution Λ2 coming from the ion pairs (Na+ + Pen2 −) and (H+ + Pen2 −) is very small. Coefficients of the Quint–Viallard conductivity equations together with evaluated K 1 (T) and K 2(T) constants and thermodynamic functions of the dissociation reactions are reported in Tables 6, 7 and 8. The standard thermodynamic functions of the dissociation process are defined by ΔG0j ¼ −RT ln K j
;
j ¼ 1; 2
Table 5 Fractions αj and contributions from dissociation steps to the calculated conductance Λcalc. as a function of sodium cloxacillin salt concentration c at 298.15 Ka. 103.c
α1
α2
αH
β
Λ1
Λ2
0.257 0.572 0.901 1.222 1.587 2.056 2.632 3.325 4.213 5.263 6.394
0.99474 0.99599 0.99640 0.99660 0.99672 0.99682 0.99688 0.99692 0.99694 0.99695 0.99695
0.00482 0.00342 0.00289 0.00261 0.00241 0.00225 0.00212 0.00202 0.00193 0.00187 0.00182
0.00438 0.00283 0.00218 0.00182 0.00155 0.00131 0.00111 0.00095 0.00080 0.00068 0.00059
0.00044 0.00059 0.00071 0.00079 0.00086 0.00094 0.00101 0.00107 0.00113 0.00118 0.00123
71.56 70.64 70.05 69.63 69.23 68.81 68.38 67.94 67.47 66.98 66.53
0.89 0.63 0.52 0.47 0.43 0.40 0.37 0.35 0.33 0.32 0.31
a
Units: c, mol dm−3; Λ, S cm2 mol−1.
expressing the fact that these penicillins are more stable and the degradation process is considerably less important. The first dissociation step is controlled by the entropic term because ΔG01 ≃ | − TΔS01| ≫ ΔH01. The second dissociation constant K2(T) increases with temperature and both, the entropic and enthalpic terms are important, but the behavior of thermodynamic functions is different for each penicillin (Tables 6, 7 and 8). In all cases, the Gibbs free energies can be linearly correlated with temperature. Since the basic β-lactam ring is preserved in all involved molecules, it is expected that the limiting conductances with the lowest charge and the first dissociation constants K1(T) are very similar for penicillins as well as for the degradation products. At 298.15 K, the limiting conductances for anions associated with the first dissociation step are: λ0(HNaf−) = 15.6 S cm2 mol−1 for nafcillin, λ0(HCloxa−) = 21.7 S cm2mol−1for cloxacillin, λ0(HDicloxa−) = 24.9 S cm2 mol−1for dicloxacillin and λ0(HOxa−) = 26.8 S.cm2.mol−1 for cloxacillin. For natural penicillin G, the corresponding value is 26λ0(HPen−) = 20.0 S cm2 mol−1. Temperature dependence of limiting conductances in terms of the Eyring transition states theory [47] can be expressed as h i1 0 2=3 ≠ ∂ ln λ0 ðT Þd0 ðT Þ @ A ¼ ΔHλ 2 ∂T RT
ð15Þ
P
ΔG0j ¼ ΔH0j −TΔS0j ! ∂ΔG0j ΔS0j ¼ − : ∂T
ð14Þ
P
Values of the first dissociation constants coming from conductivity experiments are similar to those reported from potentiometric titration experiments and they are practically independent of temperature. The second dissociation constants of semisynthetic penicillins are lower by two–three orders of magnitude than those of natural penicillins
Table 4 Densities, viscosities, dielectric constants of pure water and limiting ionic conductances in watera. T
d0 [45]
η.103 [44]
D [43]
λ0(Na+) [46]
λ0(H+)[46]
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
0.99997 0.99970 0.99910 0.99821 0.99705 0.99565 0.99404 0.99224
1.5192 1.3069 1.1382 1.0020 0.8903 0.7975 0.7195 0.6531
85.897 83.945 82.039 80.176 78.358 76.581 74.846 73.151
30.30 34.88 39.72 44.81 50.15 55.72 61.53 67.34
250.02 275.55 300.74 325.52 349.85 373.66 396.90 419.15
a
421
Units: T, K; d0, kg dm−3; η, Pa.s; λ0, S cm2 mol−1.
where ΔH≠λ is the partial molar activation enthalpy associated with the ion movement. If ΔH≠λ is independent of temperature, the integral form of Eq. (15) is h i ΔH≠λ 2=3 þ const: ln λ0 ðT Þd0 ðT Þ ¼ − RT
ð16Þ
Using densities of pure water d0 from Table 4 and the limiting conductances from Tables 6, 7 and 8, it was observed that Eq. (16) is valid to represent temperature dependence of limiting conductances h i 2103:5 2=3 ; R2 ¼ 0:9960 ln λ0 ðHOxa‐ ; T Þd0 ðT Þ ¼ 10:327− ðT=KÞ h
i 2077:8 2=3 ; R2 ¼ 0:9985 ln λ0 1=2Oxa2‐ ; T d0 ðT Þ ¼ 10:936− ðT=KÞ h i 2208:2 2=3 ‐ ; R2 ¼ 0:9988 ln λ0 ðHCloxa ; T Þd0 ðT Þ ¼ 10:472− ðT=KÞ h
i 2077:5 2‐ 2=3 ; R2 ¼ 0:9986 ln λ0 1=2Cloxa ; T d0 ðT Þ ¼ 10:726− ðT=KÞ h i 2243:7 2=3 ‐ ; R2 ¼ 0:9957 ln λ0 ðHNaf ; T Þd0 ðT Þ ¼ 10:259− ðT=KÞ h
i 2116:7 2=3 2‐ ; R2 ¼ 0:9988 ln λ0 1=2Naf ; T d0 ðT Þ ¼ 10:531− ðT=KÞ ð17Þ
422
A. Apelblat, M. Bešter-Rogač / Journal of Molecular Liquids 211 (2015) 417–424
Table 6 Coefficients of the Quint–Viallard conductivity equations for ion pairs in aqueous solutions of sodium oxacillin, dissociation constants K1 and K2 and thermodynamic functions at different temperatures T a. T
278.15
283.15
288.15
293.15
298.15
303.15
308.15
313.15
Λ012 S12 E12 J112 J212 Λ014 S14 E14 J114 J214 Λ023 S23 E23 J123 J223 Λ034 S34 E34 J134 J234 K1103 K2108 ΔG01 ΔH01 ΤΔS01 ΔG02 ΔH02 ΤΔS02
45.76 45.42 −0.12 91.20 129.90 61.81 78.02 70.51 31.04 68.39 265.47 94.34 47.50 626 1532 281.52 147.64 120.94 1036 1484 2.60 0.45 13.76 0.63 −13.14 44.44 27.21 −17.24
52.88 52.78 −0.15 106.10 151.23 71.33 90.66 82.03 35.68 78.16 293.56 106.66 52.59 700 1712 312.01 167.28 133.49 1158 1656 2.55 0.55 14.06 0.69 −13.37 44.77 27.22 −17.55
61.07 60.93 −0.02 123.49 176.07 81.58 104.48 94.80 41.32 88.82 322.09 119.85 58.12 780 1906 342.60 188.19 146.84 1287 1839 2.57 0.65 14.29 0.68 −13.61 45.16 27.30 −17.86
68.41 69.32 −0.14 140.33 200.36 92.35 119.23 108.58 47.93 100.13 349.12 133.32 63.66 862 2102 373.06 210.09 160.91 1423 2029 2.60 0.80 14.51 0.66 −13.84 45.44 27.27 −18.17
76.90 78.28 −0.09 159.13 227.34 103.65 134.67 122.98 54.75 111.93 376.60 147.14 69.07 943 2299 403.35 232.35 174.15 1556 2216 2.50 1.00 14.85 0.77 −14.08 45.66 27.18 −18.48
85.45 87.66 −0.05 178.86 255.75 115.41 150.95 138.38 62.72 124.40 403.39 161.41 74.72 1028 2503 433.35 255.49 188.15 1696 2411 2.65 1.20 14.95 0.64 −14.32 45.97 27.18 −18.79
94.41 97.66 −0.01 199.99 286.23 127.78 168.35 154.94 71.40 137.29 429.78 176.21 80.43 1115 2712 463.15 279.62 202.27 1840 2610 2.65 1.40 15.20 0.65 −14.55 46.33 27.23 −19.10
103.87 108.04 0.14 222.58 318.79 140.28 186.29 172.13 80.55 150.03 455.68 191.29 86.26 1204 2925 492.09 304.11 216.46 1986 2810 2.65 1.60 15.45 0.66 −14.79 46.73 27.33 −19.41
a
Units: T, K; K1 and K2, mol dm−3; ΔG0, ΔH0, ΤΔS0, kJ mol−1; Λ0j, S.jc1/2, E.jc, J.1jc, J.2jc3/2, S cm2 mol−1; j = 1–4, 1 — Na+, 2 — HPen−, 3 — H+, 4 — Pen2−.
where values of ΔH≠λ in each step are similar for all penicillins, the average value for the first step is ΔH≠λ = 18.0 kJ mol−1 and for the second step ΔH≠λ = 17.4 kJ mol−1. Temperature dependence of limiting conductances can also be represented in terms of Walden products of individual ions and their values for corresponding anions are presented in Table 9.
Using the Nerst–Hartley equation for the limiting value of the diffusion coefficient for pair of ions [46] D0 ðT Þ ¼
RT ðjzþ j þ jz− jÞ λ0þ ðT Þλ0− ðT Þ h i F 2 jz þ j jz − j λ0 ðT Þ þ λ0 ðT Þ þ
ð18Þ
−
Table 7 Coefficients of the Quint–Viallard conductivity equations for ion pairs in aqueous solutions of sodium cloxacillin, dissociation constants K1 and K2 and thermodynamic functions at different temperatures T a. T
278.15
283.15
288.15
293.15
298.15
303.15
308.15
313.15
Λ012 S12 E12 J112 J212 Λ014 S14 E14 J114 J214 Λ023 S23 E23 J123 J223 Λ034 S34 E34 J134 J234 K1103 K2108 ΔG01 ΔH01 ΤΔS01 ΔG02 ΔH02 ΤΔS02
42.65 44.73 −0.80 86.48 123.60 55.87 74.98 66.71 5.48 46.95 262.36 93.65 46.83 619 1515 275.58 144.88 115.82 1002 1433 2.60 0.32 13.76 0.86 −12.90 45.23 15.34 −29.89
49.35 51.99 −0.92 100.70 144.01 64.43 87.11 77.59 5.72 53.07 290.03 105.87 51.82 692 1693 305.11 164.06 127.49 1118 1597 2.50 0.36 14.10 0.93 −13.13 45.77 15.34 −30.42
56.47 59.89 −1.05 116.36 166.57 73.66 100.37 89.64 6.38 59.61 317.49 118.81 57.09 770 1881 334.68 184.46 139.83 1240 1770 2.55 0.40 14.31 0.89 −13.36 46.32 15.36 −30.96
64.01 68.32 −1.13 133.39 191.13 83.35 114.51 102.65 7.49 66.40 344.72 132.32 62.66 851 2077 364.06 205.80 152.79 1369 1949 2.60 0.45 14.51 0.91 −13.60 46.84 15.34 −31.50
71.84 77.12 −1.25 151.04 216.60 93.53 129.31 116.25 8.58 73.49 371.54 145.98 67.91 931 2270 393.23 227.47 164.87 1495 2125 2.60 0.50 14.75 0.93 −13.83 47.38 15.34 −32.04
80.13 86.43 −1.30 170.22 244.29 104.12 144.93 130.78 10.28 80.83 398.07 160.17 73.47 1016 2472 422.06 249.99 177.60 1627 2308 2.65 0.55 14.95 0.89 −14.06 47.93 15.36 −32.57
88.66 96.31 −1.39 190.50 273.67 115.25 161.60 146.40 12.12 88.14 424.03 174.87 79.05 1101 2678 450.62 273.45 190.33 1762 2494 2.65 0.60 15.20 0.91 −14.29 48.50 15.39 −33.11
97.54 106.54 −1.41 211.97 304.77 126.48 178.77 162.60 14.00 94.97 449.35 189.80 84.71 1189 2887 478.29 297.24 203.03 1898 2680 2.70 0.68 15.40 0.87 −14.52 48.96 15.31 −33.65
a
Units: T, K; K1 and K2, mol dm−3; ΔG0, ΔH0, ΤΔS0, kJ mol−1; Λ0j, S.jc1/2, E.jc, J.1jc, J.2jc3/2, S cm2 mol−1; j = 1–4, 1 — Na+, 2 — HPen−, 3 — H+, 4 — Pen2−.
A. Apelblat, M. Bešter-Rogač / Journal of Molecular Liquids 211 (2015) 417–424
423
Table 8 Coefficients of the Quint–Viallard conductivity equations for ion pairs in aqueous solutions of sodium nafcillin and dicloxacillin, dissociation constants K1 and K2 and thermodynamic functions at different temperatures T a. T
278.15
283.15
288.15
293.15
298.15
303.15
308.15
298.15b
Λ012 S12 E12 J112 J212 Λ014 S14 E14 J114 J214 Λ023 S23 E23 J123 J223 Λ034 S34 E34 J134 J234 K1103 K2109 ΔG01 ΔH01 ΤΔS01 ΔG02 ΔH02 ΤΔS02
39.11 43.94 −1.57 81.10 116.42 48.71 71.38 62.04 −24.10 22.44 258.82 92.86 46.06 611 1496 268.42 141.57 109.71 962 1373 2.60 0.010 13.76 1.22 −12.54 58.57 100.25 41.68
45.26 51.07 −1.82 94.43 135.66 56.13 82.91 72.14 −28.94 24.40 285.94 104.96 50.92 683 1670 296.81 160.20 120.33 1070 1526 2.50 0.020 14.10 1.34 −12.77 57.99 100.42 42.43
51.78 58.83 −2.09 109.06 156.85 64.13 95.50 83.31 −34.05 26.24 312.80 117.75 56.05 759 1855 325.15 179.99 131.48 1185 1687 2.60 0.047 14.26 1.27 −12.99 56.97 100.15 43.18
58.62 67.09 −2.36 124.88 179.82 76.89 111.16 98.32 −20.71 43.10 339.33 131.09 61.43 839 2047 357.60 202.73 147.00 1331 1893 2.65 0.10 14.46 1.24 −13.22 56.12 100.04 43.93
65.75 75.72 −2.66 141.31 203.67 81.35 122.98 107.97 −44.85 29.57 365.45 144.58 66.50 917 2235 381.05 221.64 153.82 1422 2017 2.70 0.20 14.66 1.22 −13.44 55.36 100.03 44.68
73.15 84.81 −2.94 158.88 229.26 90.53 137.79 121.43 −50.38 31.06 391.09 158.55 71.83 999 2431 408.47 243.42 165.04 1544 2185 2.70 0.35 14.91 1.24 −13.67 54.87 100.30 45.43
80.81 94.47 −3.27 177.56 256.53 100.16 153.59 135.89 −56.46 32.00 416.18 173.03 77.16 1083 2631 435.53 266.08 176.11 1668 2355 2.65 0.65 15.20 1.30 −13.90 54.19 100.37 46.17
75.01 77.85 −0.52 156.11 223.33 99.87 132.66 120.48 37.32 97.37 374.71 146.71 68.64 939 2288 399.57 230.52 170.67 1533 2182 2.70 28.0 14.66
a b
43.11
Units: T, K; K1 and K2, mol dm−3; ΔG0, ΔH0, ΤΔS0, kJ mol−1; Λ0j, S.jc1/2, E.jc, J.1jc, J.2jc3/2, S cm2 mol−1; j = 1–4, 1 — Na+, 2 — HPen−, 3 — H+, 4 — Pen2−. Corresponding values for dicloxacillin sodium salt.
in the range of observed limiting conductances of semisynthetic penicillins λ0(HPen−) at 298.15 K, the limiting diffusion coefficients of the ion pairs (Na+ + HPen−) lie in 0.6–0.9.10− 5 cm2 s− 1 range and the ion pairs (H+ + HPen−) in 0.9–1.3.10−5 cm2 s−1 range.
4. Conclusions
Acknowledgment Financial support by the Slovenian Research Agency through Grant No. P1-0201 is gratefully acknowledged. MB-R is grateful Mr. Anton Kelbl for performing density measurements. References
Systematic determinations of the conductivities of sodium salts of semisynthetic penicillins: oxacillin, cloxacillin, dicloxacillin and nafcillin in dilute aqueous solutions over the 278.15 to 308.15 K temperature range are reported for the first time. Similarly as with natural penicillins, the dissociation of the final products of penicillin degradation in acidic media is responsible for the measured conductance and not the hydrolysis of neutral sodium salts. The observed excellent agreement between the Λexp. and Λcalc. values strongly supports the proposed molecular model. Determined dissociation constants K1(T) agree well with those reported in the literature. The second dissociation constants K2(T) are considerably lower than those of natural penicillins indicating their higher stability. As for all penicillins, the limiting mobility of anions lie in rather narrow range because the effect of various side-chain groups in penicillin molecules is rather small. Table 9 Walden products of one and two charged anions of oxacillin, cloxacillin, nafcillin and dicloxacillin. Walden products
S cm2 equiv−1 Pa s
η(T).λ0(HOxa−, T) η(T).λ0(1/2HOxa2−, T) η(T).λ0(HCloxa−, T) η(T).λ0(1/2HCloxa2−, T) η(T).λ0(HNaf−, T) η(T).λ0(1/2HNaf2−, T) η(T).λ0(HDicloxa−, T) η(T).λ0(1/2HDicloxa2−, T)
0.238 ± 0.003 0.477 ± 0.001 0.293 ± 0.004 0.387 ± 0.001 0.137 ± 0.002 0.278 ± 0.001 0.221 0.443
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Electrical conductances of dilute aqueous solutions of β-lactam antibiotics of the penicillin group in the 278.15 K to 313.15 K temperature range. Sodium salts of oxacillin, cloxacillin, dicloxacillin and nafcillin Alexander Apelblat a,⁎, Marija Bešter-Rogač b,⁎ a b
Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ljubljana, Slovenia
a r t i c l e
i n f o
Article history: Received 2 May 2015 Received in revised form 28 May 2015 Accepted 30 May 2015 Available online 3 August 2015 Keywords: Electrolyte conductivity Sodium oxacillin Sodium cloxacillin Sodium dicloxacillin Sodium nafcillin Aqueous solutions Limiting ion conductances Dissociation constants
a b s t r a c t Systematic determinations of electrical conductivities of sodium salts of semisynthetic penicillins, oxacillin, cloxacillin, dicloxacillin and nafcillin in the 278.15 K to 313.15 K temperature range are reported. These conductivities are examined by applying the Quint–Viallard conductivity equations and the Debye–Hückel equations for activity coefficients. Determined dissociation constants and the limiting conductances of involved anions are evaluated basing on the assumption that in dilute aqueous solutions these salts, similarly as sodium salts of natural penicillins, behave as acidic salts of dibasic acids which are the final products of degradation reactions in acidic media. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Natural penicillins produced by fermentation and semisynthetic penicillins by chemical synthesis belong to an extremely important group of antibacterial drugs in clinical use. Their chemical, biological, pharmaceutical and medical properties were the subject of extensive studies over many years and they are reviewed in the literature [1–9]. These studies were mainly devoted to the structure, production, chemical stability and the clinical potency of antibiotics and considerably less to their physicochemical properties. Since the instability of penicillin in aqueous solutions has been known from the time of its discovery, many investigations have been dedicated to the transformation, degradation, aging and hydrolysis reactions of penicillins. Considering that degradation reactions are associated with the reduction of antibacterial activity of drugs and with the allergic response after penicillin therapy, numerous kinetic, thermodynamic, structure studies and the analytical identification of degradation products have been reported [10–17]. From these investigations it is evident that penicillins are sensitive to ⁎ Corresponding authors. E-mail addresses: [email protected] (A. Apelblat), [email protected] (M. Bešter-Rogač).
http://dx.doi.org/10.1016/j.molliq.2015.05.066 0167-7322/© 2015 Elsevier B.V. All rights reserved.
chemical additives, electrolytes, oxidizing agents and even water molecules. Their pH dependence of hydrolysis reactions, the influence of buffer species, ionic strength and temperature is well experimentally established but the exact proportion of formed degradation products and details of reaction pathways continue to be uncertain. The basic structure of penicillin molecules consist of a nucleus (the fused β-lactam–thiazolidine ring known as 6-aminopenicillanic acid) and a condensed side-chain group. Many antibiotics are produced semisynthetically by the chemical modification of 6-aminopenicillanic acid and their salts have a strong tendency to form crystalline hydrates. These semisynthetic antibiotics are useful for the treatment of a number of bacterial infections and they are suitable for oral administration in the form of highly soluble sodium or potassium salts. Properties of semisynthetic penicillin solutions were determined by using different experimental techniques [18–25] but our knowledge about them is very limited. Similarly as natural penicillins, the investigated semisynthetic penicillins are fairly strong carboxylic acids. Determined by conventional potentiometric titration methods the apparent pKa values lie in the 2.6–2.8 range and they are very weakly temperature dependent [2,5,19,20]. Determinations of electrical conductivity of natural penicillins started early, close to the time of their discovery (for the complete list
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of the literature see [26]). These investigations were associated with the question whether penicillin salts behave as strong, weak or colloidal electrolytes. On contrary, electrical conductances of semisynthetic penicillins in dilute aqueous solutions were never determined and they are for the first time reported and analyzed in this investigation. In more concentrated solutions of semisynthetic penicillins, certain physical properties are consistent with the possibility that their salts are dispersed in water in the form of colloidal solutions [27–32]. As one of experimental techniques, specific conductivity measurements were applied to determine the critical micelle concentrations, but unfortunately these conductances were only presented in graphical form. Continuing our previous investigation of electrical conductances (sodium and potassium penicillin G and potassium penicillin V), in this study sodium salts of oxacillin (3-phenyl-5-methyl-4isoxazototyl-penicillin), cloxacillin (3-(2-chlorophenyl)-5-methyl-4isoxazotyl-penicillin), dicloxacillin (3-(2,6-dichlorophenyl)-5-methyl4-isoxazotyl-penicillin) and nafcillin (6-(2-ethoxy-1-naphtamido)penicillin) were investigated. The structures of their anions are presented in Fig. 1. Electrical conductivities of sodium salts of these semisynthetic penicillins (for briefness denoted as NaHPen) in dilute aqueous solutions, in the 278.15 K to 313.15 K temperature range were measured and interpreted in terms of dissolution and dissociation reactions, in the same way as previously treated natural penicillins [26]. 2. Experimental 2.1. Materials Sodium salts of oxacillin, cloxacillin, dicloxacillin and nafcillin were purchased as monohydrates from Sigma-Aldrich. According to the information of supplier, nafcillin sodium salt contains ~3.5% of trisodium citrate, whereas for other compounds no information about impurities was given by producer. All compounds were stored in the refrigerator (~ 4 °C) and used as received. Demineralized water was distilled two times in a quartz bidistillation apparatus (Destamat Bi 18E, Heraeus). The final product with specific conductance b6·10−7S·cm1 was distilled into a flask permitting storage and transfer of water into the measuring cell under an atmosphere of nitrogen. Stock solutions were prepared by weighing and were stored under nitrogen in the refrigerator. 2.2. Conductivity measurements The conductivities of the solutions were determined with the help of a three-electrode measuring cell, described elsewhere [33]. The cell was calibrated with dilute potassium chloride solutions [34] and immersed in the high precision thermostat described previously [35]. The temperature dependence of the cell constant was taken into account [34]. The water bath can be set to each temperature using a temperature program with a reproducibility of 0.005 K. The temperature in the precision thermostat bath was additionally checked with calibrated Pt100 resistance thermometer (MPMI 1004/300 Merz) in connection with a HP 3458 A. The resistance measurements of the solutions in the cell were performed using a precision LCR Meter Agilent 4284 A.
At the beginning of every measuring cycle, the cell was filled with a known mass of water (~660 g). After measurement of the solvent conductivity at all temperatures of the temperature program, the stepwise concentration was carried out by successive additions, using a gas-tight syringe, of weighed amounts of a stock solution. The measuring procedure, including corrections and extrapolation of the sample conductivity to infinite frequency, has been previously described [35]. Conductivity of sodium dicloxacillin solutions was measured at 298.15 K only, because it turned out as unstable in a longer term period as it is usually demanded for covering whole temperature range. Its stock solution became turbid in about five days namely, what was not the case at other investigated systems. The molar concentrations c were determined from the masses and the corresponding solution densities d. A linear change of d with increasing salt content for diluted solutions was assumed, dðTÞ ¼ d0 ðTÞ þ ~ is the molonity of the elec~ where d0(T) is the density of water and m bm, trolyte (moles of electrolyte per kilogram of solution) and the bcoefficients are assumed as independent of temperature. The densities of the solutions were determined by the method of Kratky et al. [36] using a Paar densimeter (DMA 60, DMA 601 HT) at 298.15 K combined with a precision thermostat. In all sets of the reported conductivityconcentration data (Tables 1–3), the concentrations are given at 298.15 K and they can be converted to other temperatures by use of ~ dðTÞ by help of estimated b-coefficients, the relationship cðTÞ ¼ m given in footnotes of these tables. Considering the sources of error (calibration, measurements, impurities), the specific conductivities are estimated to be accurate within 0.2%. 3. Results and discussion The molar conductivities Λ(c) of oxacillin, cloxacillin, dicloxacillin and nafcillin determined in this work as a function of concentration and temperature are presented in Tables 1, 2 and 3 respectively. Considering difficulty in handle dicloxacillin, its conductances were measured only at 298.15 K. Conductances of nafcillin in Table 3 represent their values after taking into account that solid salt contains ~ 3.5% of trisodium citrate (for conductivities of Na3Cit see [37]) and by assuming that the conductances of both salts are proportional to their mole fractions. The form of Λ(c) versus c1/2 curves in the case of semisynthetic penicillins (Fig. 2) is similar to that natural penicillins (deviation from the straight line appears in very dilute solutions) and can be interpreted by considering hydrolysis (salts of weak acids) and degradation reactions in water. Preliminary calculations based on the simplest version of hydrolysis process Na‐HPen → Naþ þ HPen‐ HPen‐ þ H2 O ⇌ HPen þ OH‐ H2 O ⇌ Hþ þ OH‐
ð1Þ
showed that over large variations of model parameters, this molecular model is unsuitable to represent experimental conductivities Λexp.(c) in dilute aqueous solutions. The contributions coming from the
Fig. 1. Structures of a) oxacillin, b) cloxacillin, c) dicloxacillin and d) nafcillin anion.
A. Apelblat, M. Bešter-Rogač / Journal of Molecular Liquids 211 (2015) 417–424 Table 1 Experimental and calculated molar conductivities of sodium oxacillin salt as a function of concentration c and temperature T a. T/K
278.15
103.c⁎
Λexp
Λcalc
0.2566 0.5717 0.9012 1.2215 1.5864 2.0566 2.6327 3.3247 4.2133 5.2621 6.3936 σ(Λ)
45.40 45.15 44.88 44.69 44.25 44.01 43.73 43.44 43.09 42.71
45.55 45.11 44.81 44.54 44.27 43.99 43.71 43.41 43.11 42.84 0.08
293.15 68.94 68.22 67.73 67.15 66.69 66.38 66.00 65.57 64.90 64.44 64.04
0.2566 0.5717 0.9012 1.2215 1.5864 2.0566 2.6327 3.3247 4.2133 5.2621 6.3936 σ(Λ)
308.15 95.23 94.27 93.51 93.00 92.24 91.86 90.96 90.32 89.90 89.19 88.62
0.2566 0.5717 0.9012 1.2215 1.5864 2.0566 2.6327 3.3247 4.2133 5.2621 6.3936 σ(Λ)
283.15
69.53 68.26 67.56 67.08 66.66 66.22 65.79 65.35 64.89 64.43 64.00 0.22
96.54 94.57 93.51 92.80 92.17 91.52 90.89 90.26 89.59 88.93 88.32 0.47
Λexp 53.22 52.55 52.24 51.93 51.47 51.22 50.95 50.54 50.24 49.77 49.46
298.15 77.40 76.56 76.02 75.47 75.02 74.57 74.12 73.46 72.88 72.42 71.98
313.15 104.84 103.61 102.54 102.26 101.59 100.98 100.30 99.58 98.82 98.25 97.79
288.15 Λcalc 53.57 52.66 52.15 51.79 51.48 51.16 50.83 50.51 50.16 49.81 49.49 0.14
78.34 76.85 76.03 75.48 74.99 74.48 73.99 73.49 72.96 72.44 71.95 0.32
419
Table 2 Experimental and calculated molar conductivities of sodium cloxacillin salt as a function of concentration c and temperature T a. T/K
278.15
Λexp
Λcalc
103.c⁎
Λexp
Λcalc
Λexp
Λcalc
Λexp
Λcalc
60.92 60.18 59.77 59.47 59.02 58.62 58.30 57.94 57.40 56.99 56.51
60.71 60.05 59.63 59.32 59.03 58.72 58.40 58.06 57.70 57.33 56.98 0.24
0.3217 0.5985 0.9333 1.2556 1.6943 2.1573 2.7436 3.4327 4.1540 4.9193 5.7513
42.34 42.15 41.85 41.68 41.40 41.24 40.91 40.59 40.32 40.11 39.90
42.79 42.26 41.87 41.60 41.31 41.06 40.80 40.55 40.31 40.10 39.83 0.17
49.01 48.79 48.44 48.26 47.83 47.54 47.37 47.00 46.69 46.45 46.07
49.50 48.89 48.44 48.12 47.78 47.50 47.19 46.90 46.63 46.37 46.13 0.18
56.08 55.81 55.43 55.21 54.74 54.41 54.21 53.81 53.46 53.04 52.77
56.66 55.95 55.43 55.07 54.68 54.35 54.00 53.65 53.34 53.05 52.77 0.22
87.23 85.51 84.57 83.94 83.38 82.81 82.25 81.69 81.09 80.50 79.95 0.38
0.3217 0.5985 0.9333 1.2556 1.6943 2.1573 2.7436 3.4327 4.1540 4.9193 5.7513 σ(Λ)
303.15 86.21 85.25 84.51 83.99 83.38 83.05 82.56 81.85 81.26 80.63 80.25
106.34 104.12 102.93 102.13 101.43 100.72 100.01 99.31 98.56 97.83 97.16 0.60
0.3217 0.5985 0.9333 1.2556 1.6943 2.1573 2.7436 3.4327 4.1540 4.9193 5.7513 σ(Λ)
293.15 63.55 63.24 62.83 62.48 62.03 61.66 61.43 60.97 60.42 60.14 59.80
308.15 88.17 87.74 86.89 86.55 85.94 85.46 84.91 84.29 83.78 83.37 82.94
283.15
64.25 63.43 62.84 62.42 61.98 61.60 61.20 60.81 60.45 60.12 59.80 0.25
89.04 87.88 87.04 86.45 85.82 85.29 84.73 84.17 83.67 83.21 82.76 0.31
298.15 71.49 71.06 70.58 70.17 69.66 69.29 69.01 68.32 67.92 67.58 67.20
313.15 97.21 96.52 95.63 95.20 94.52 94.03 93.37 92.70 92.20 91.71 91.25
288.15
72.46 71.26 70.58 70.10 69.66 69.21 68.75 68.29 67.80 67.30 66.84 0.32
303.15 79.69 79.22 78.67 78.20 77.65 77.24 76.92 76.16 75.72 75.33 74.92
80.46 79.42 78.66 78.14 77.57 77.09 76.59 76.09 75.64 75.22 74.82 0.28
98.02 96.72 95.78 95.13 94.43 93.84 93.21 92.60 92.04 91.53 91.03 0.30
a Units: c, mol dm−3; Λ, σ(Λ), S cm2 mol−1. ⁎ c are molarities at 298.15 K; b — coefficient in the density equation is 0.1463 kg 2 ·dm − 3 ·mol − .
a Units: c, mol dm−3; Λ, σ(Λ), S cm2 mol−1. ⁎ c are molarities at 298.15 K; b — coefficient in the density equation is 0.1687 kg 2 ·dm − 3 ·mol − 1 .
hydrolysis reactions to calculated conductivities Λcalc.(c) are always negligible. From identification studies of degradation products of various penicillins [10–17] it was observed that penicillin has a single carboxylic group as acidic functional group, but that the degradation products are corresponding dibasic acids. In the context of conductivity determinations, the exact composition of degradation products during measurements is not important considering that the main contribution to the conductance comes from the hydrogen and sodium ions and less from the organic anions. Besides, it is expected that differences in contributions from various organic ions to the over-all conductivity will also be small. Because the exact proportion between anions is unknown and varies during the conductivity experiments, we assumed that the system can be treated as containing only one acidic salt of the dibasic penicillinic acid and the measured conductance is the sum of contributions from all the cations and anions present in solution. The molar conductivities, Λ, are the sum of ionic contributions
of the electrolyte. The dissolution of an acidic salt of a dibasic acid in water in terms of the dissociation reactions is governed by the following equations
Λ¼
κ ¼ c
n X z j c jλ j j¼1
c
NaHPen → Naþ þ HPen‐ HPen‐ ⇌ Hþ þ Pen2‐ Hþ þ HPen‐ ⇌ H2 Pen
ð3Þ
where the effect of water dissociation is very small and is neglected. Taking into account the charge balance in the solution cð1 þ α Hþ Þ ¼ cðα 1 þ 2α 2 Þ
ð4Þ
and denoting concentrations of existing species by: ð2Þ
where κ is the measured specific conductance, λj are the ionic conductances, cj and zj are the concentrations and charges of the individual ions present in the solution and c denotes the analytical concentration
þ Naþ ¼ c H ¼ cα Hþ ½hHPen‐i ¼ cα 1 Pen2‐ ¼ cα 2 ½H2 Pen ¼ cβ ¼ ð1−α 1 −α 2 Þc
ð5Þ
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A. Apelblat, M. Bešter-Rogač / Journal of Molecular Liquids 211 (2015) 417–424
Table 3 Experimental and calculated molar conductivities of sodium nafcillin and dicloxacillin salts as a function of concentration c and temperature T a. T/K
278.15
103.c⁎
Λexp
Λcalc
Λexp
Λcalc
Λexp
Λcalc
0.2560 0.5560 0.8770 1.2190 1.5670 1.9670 2.4650 3.1470 3.9300 4.9570 σ(Λ)
38.44 38.02 37.77 37.66 37.42 37.30 37.21 37.06 36.93 36.58
38.53 38.16 37.91 37.71 37.53 37.35 37.15 36.92 36.69 36.43 0.14
44.39 43.99 43.71 43.59 43.29 43.17 43.07 42.89 42.73 42.37
44.59 44.17 43.88 43.63 43.42 43.21 42.98 42.71 42.45 42.14 0.18
50.80 50.39 50.07 49.68 49.58 49.46 49.28 49.14 48.66 48.55
51.04 50.55 50.21 49.92 49.68 49.44 49.17 48.86 48.55 48.20 0.21
0.2560 0.5560 0.8770 1.2190 1.5670 1.9670 2.4650 3.1470 3.9300 4.9570 σ(Λ) 0.2560 0.5560 0.8770 1.2190 1.5670 1.9670 2.4650 3.1470 3.9300 4.9570 σ(Λ)
293.15 57.40 57.03 56.70 56.33 56.26 56.00 55.85 55.36 55.34 55.01
308.15 78.92 78.69 77.98 78.04 77.65 77.51 76.85 76.51 76.40 76.17
283.15
57.84 57.27 56.87 56.54 56.26 55.98 55.68 55.32 54.96 54.56 0.28
298.15 64.44 64.06 63.31 63.28 63.13 62.87 62.69 62.19 61.94 61.78
80.09 79.17 78.56 78.06 77.63 77.22 76.78 76.26 75.75 75.17 0.62
288.15
64.95 64.28 63.82 63.44 63.11 62.79 62.45 62.04 61.63 61.18 0.35
0.3025 0.6347 0.9406 1.2636 1.6004 1.9635 2.3384 2.8222 3.3919 4.1019 4.6833 5.5596 6.6913 σ(Λ)
303.15 71.40 71.27 70.55 70.59 70.26 70.09 69.51 69.20 69.07 68.87 298.15b 77.06 75.76 74.99 74.18 73.72 73.33 72.97 72.59 72.12 71.55 71.25 70.87 70.40
72.35 71.57 71.04 70.61 70.24 69.87 69.48 69.02 68.57 68.05 0.50
77.72 75.85 74.94 74.27 73.73 73.26 72.86 72.42 71.98 71.51 71.18 70.73 70.33 0.21
Units: c, mol dm−3; Λ, σ(Λ), S cm2 mol−1. Conductivities of dicloxacillin sodium salt. ⁎ c are molarities at 298.15 K; b — coefficient in the density equation is 0.1520 kg2·dm−3·mol−1 for nafcillin and 0.1855 kg2·dm−3·mol−1 dicloxacillin solutions. a
b
the dissociation equilibria can be expressed by: þ H ½HPen‐ cðα 1 þ 2α 2 −1Þα 1 F1 ¼ F1 ½H2hPen i 1‐α 1 −α 2 þ 2‐ H Pen cðα 1 þ 2α 2 −1Þα 2 F2 ¼ K2 ðT Þ ¼ F2 ½HPen‐ α1 K1 ðT Þ ¼
ð6Þ
f Hþ f HPen‐ f H2 Pen f Hþ f Pen2‐ F2 ¼ : f HPen‐
ð7Þ
The activity coefficients of the individual ions in dilute solutions, fj, can be approximated by the Debye–Hückel equations pffiffi z2j AðT Þ I pffiffi 1 þ a j BðT Þ I 1:8246 106 ; AðT Þ ¼ ½DðT ÞT 3=2
where D(T) is the dielectric constant of water, aj is the ion size parameter and I denotes the ionic strength of the solution, which is I = c(α1 + 3α2). Values of the size parameters (a(H+) = 9.0 Ǻ, a(Na+) = 4.0 Ǻ, a(HPen−) = 5.0 Ǻ and a(Pen2−) = 5.8 Ǻ) were prescribed and they are assumed to be independent of temperature [38,39]. If the equilibrium constants K1(T) and K2(T) and the activity coefficients are available, the concentration fractions α1 and α2 can be successively evaluated for every concentration c by an iterative solution of two quadratic Eq. (9) 8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 1< K1 K1 2 4K1 ð1−α 2 Þ= 1−2α 2 − α1 ¼ þ 1−2α 2 − þ ; 2: cF1 c F1 c F1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi) ( 1 8K2 α 1 1−α 1 þ ð1−α 1 Þ2 þ : α2 ¼ 4 cF2
ð9Þ
In this work, the ionic conductances λj in Eq. (1) are represented by the Quint–Viallard conductivity equations [40] pffiffi λ j ¼ λ0j ‐S j I þ E j I ln I þ J1 j I‐J2 j I 3=2
ð10Þ
where λ0j is the limiting conductance of the jth ion. The coefficients Sj, Ej, J1j, J2j are rather complex functions of the viscosity η, the dielectric constant of pure water and the average cation–anion distances of closest approach (explicit expressions for these coefficients are given also elsewhere [41]). The molar conductivities of NaHPen are the contributions from the four ion pairs ð1Þ Λ 1 ¼ hλ Hþ þ λð HPen‐ Þ i ð1Þ Λ 2 ¼ λ Hþ þ λ 1=2Pen2‐ ð2Þ Λ 1 ¼ hλ Naþ þ λð HPen‐ Þ i ð2Þ Λ 2 ¼ λ Naþ þ λ 1=2Pen2‐ :
where F1 and F2 denote the quotients of the activity coefficients F1 ¼
Fig. 2. Molar conductivity Λ of sodium salts of semisynthetic penicillins at 298.15 K. — oxacillin; — dicloxacillin; — cloxacillin and — nafcillin.
ð11Þ
The corresponding pairs of ions are denoted with the superscripts (1) and (2), and the organic ions are “distributed” between the hydrogen and sodium ions in the following way [42] Λ ðNaHPenÞ ¼
i h i α Hþ h 1 ð1Þ ð1Þ ð2Þ ð2Þ α 1 Λ 1 þ 2α 2 Λ 2 þ α 1 Λ 1 þ 2α 2 Λ 2 : α 1 þ 2α 2 α 1 þ 2α 2
ð12Þ
log f j ðT Þ ¼ ‐
BðT Þ ¼
50:29 108 ½DðT ÞT 1=2
ð8Þ
The representation of NaHPen conductances includes the evaluation of concentrations of all species present in solution and the use of eight Quint–Viallard conductivity equations. Formally, the conductivity-
A. Apelblat, M. Bešter-Rogač / Journal of Molecular Liquids 211 (2015) 417–424
concentration data set (Λ,c) can be expressed in the form: Λ = f [c; K1, K2, λ0(HPen− 1), λ0(1/2Pen−2), aj]. Thus, at a given temperature T, using the physical properties of pure water and the limiting ionic conductances λ0(H+) and λ0(Na+) [43–46] (Table 4) and the distances of closest approach in the Quint–Viallard conductivity equations can be taken as the average value of the ion size parameters in the ion pairs. Dissociation constants K1(T) and K2(T) and the limiting conductances λ0(HPen−1) and λ0(1/2Pen−2) were evaluated in the iterative process, starting with the assumed dissociation constants K1(T) and K2(T) and values of α1 and α2, fj and I for each concentration c. The calculations were repeated with new values of dissociation constants until the satisfactory agreement between the measured and calculated conductivities was reached. The degree of agreement of the obtained fit is expressed by the mean value of standard deviations
σ ðΛÞ ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX 2 u Λ j: exp: ‐Λ j;calc: u t j¼1
ð13Þ
N‐1
where N is the number of experimental points at given T. Determined in such way Λcalc values for investigated here semisynthetic penicillis are compared with Λexp. values in Tables 1, 2 and 3. As can be observed, based on values of the standard deviations σ(Λ), there is a very satisfactory agreement between the experimental and calculated conductivities over the investigated concentration regions and at all temperatures. A detailed analysis of the conductivity data, which is similar to all penicillin, is given only for cloxacillin at 298.15 K (Table 5). Distribution of various ions in solutions shows that the first dissociation step is the most important step, α1 ≫ α2. The contribution to Λcalc. from the ion pairs (Na+ + HPen−) and (H+ + HPen−), which is denoted as is Λ1, is predominant. As expected, the contribution Λ2 coming from the ion pairs (Na+ + Pen2 −) and (H+ + Pen2 −) is very small. Coefficients of the Quint–Viallard conductivity equations together with evaluated K 1 (T) and K 2(T) constants and thermodynamic functions of the dissociation reactions are reported in Tables 6, 7 and 8. The standard thermodynamic functions of the dissociation process are defined by ΔG0j ¼ −RT ln K j
;
j ¼ 1; 2
Table 5 Fractions αj and contributions from dissociation steps to the calculated conductance Λcalc. as a function of sodium cloxacillin salt concentration c at 298.15 Ka. 103.c
α1
α2
αH
β
Λ1
Λ2
0.257 0.572 0.901 1.222 1.587 2.056 2.632 3.325 4.213 5.263 6.394
0.99474 0.99599 0.99640 0.99660 0.99672 0.99682 0.99688 0.99692 0.99694 0.99695 0.99695
0.00482 0.00342 0.00289 0.00261 0.00241 0.00225 0.00212 0.00202 0.00193 0.00187 0.00182
0.00438 0.00283 0.00218 0.00182 0.00155 0.00131 0.00111 0.00095 0.00080 0.00068 0.00059
0.00044 0.00059 0.00071 0.00079 0.00086 0.00094 0.00101 0.00107 0.00113 0.00118 0.00123
71.56 70.64 70.05 69.63 69.23 68.81 68.38 67.94 67.47 66.98 66.53
0.89 0.63 0.52 0.47 0.43 0.40 0.37 0.35 0.33 0.32 0.31
a
Units: c, mol dm−3; Λ, S cm2 mol−1.
expressing the fact that these penicillins are more stable and the degradation process is considerably less important. The first dissociation step is controlled by the entropic term because ΔG01 ≃ | − TΔS01| ≫ ΔH01. The second dissociation constant K2(T) increases with temperature and both, the entropic and enthalpic terms are important, but the behavior of thermodynamic functions is different for each penicillin (Tables 6, 7 and 8). In all cases, the Gibbs free energies can be linearly correlated with temperature. Since the basic β-lactam ring is preserved in all involved molecules, it is expected that the limiting conductances with the lowest charge and the first dissociation constants K1(T) are very similar for penicillins as well as for the degradation products. At 298.15 K, the limiting conductances for anions associated with the first dissociation step are: λ0(HNaf−) = 15.6 S cm2 mol−1 for nafcillin, λ0(HCloxa−) = 21.7 S cm2mol−1for cloxacillin, λ0(HDicloxa−) = 24.9 S cm2 mol−1for dicloxacillin and λ0(HOxa−) = 26.8 S.cm2.mol−1 for cloxacillin. For natural penicillin G, the corresponding value is 26λ0(HPen−) = 20.0 S cm2 mol−1. Temperature dependence of limiting conductances in terms of the Eyring transition states theory [47] can be expressed as h i1 0 2=3 ≠ ∂ ln λ0 ðT Þd0 ðT Þ @ A ¼ ΔHλ 2 ∂T RT
ð15Þ
P
ΔG0j ¼ ΔH0j −TΔS0j ! ∂ΔG0j ΔS0j ¼ − : ∂T
ð14Þ
P
Values of the first dissociation constants coming from conductivity experiments are similar to those reported from potentiometric titration experiments and they are practically independent of temperature. The second dissociation constants of semisynthetic penicillins are lower by two–three orders of magnitude than those of natural penicillins
Table 4 Densities, viscosities, dielectric constants of pure water and limiting ionic conductances in watera. T
d0 [45]
η.103 [44]
D [43]
λ0(Na+) [46]
λ0(H+)[46]
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
0.99997 0.99970 0.99910 0.99821 0.99705 0.99565 0.99404 0.99224
1.5192 1.3069 1.1382 1.0020 0.8903 0.7975 0.7195 0.6531
85.897 83.945 82.039 80.176 78.358 76.581 74.846 73.151
30.30 34.88 39.72 44.81 50.15 55.72 61.53 67.34
250.02 275.55 300.74 325.52 349.85 373.66 396.90 419.15
a
421
Units: T, K; d0, kg dm−3; η, Pa.s; λ0, S cm2 mol−1.
where ΔH≠λ is the partial molar activation enthalpy associated with the ion movement. If ΔH≠λ is independent of temperature, the integral form of Eq. (15) is h i ΔH≠λ 2=3 þ const: ln λ0 ðT Þd0 ðT Þ ¼ − RT
ð16Þ
Using densities of pure water d0 from Table 4 and the limiting conductances from Tables 6, 7 and 8, it was observed that Eq. (16) is valid to represent temperature dependence of limiting conductances h i 2103:5 2=3 ; R2 ¼ 0:9960 ln λ0 ðHOxa‐ ; T Þd0 ðT Þ ¼ 10:327− ðT=KÞ h
i 2077:8 2=3 ; R2 ¼ 0:9985 ln λ0 1=2Oxa2‐ ; T d0 ðT Þ ¼ 10:936− ðT=KÞ h i 2208:2 2=3 ‐ ; R2 ¼ 0:9988 ln λ0 ðHCloxa ; T Þd0 ðT Þ ¼ 10:472− ðT=KÞ h
i 2077:5 2‐ 2=3 ; R2 ¼ 0:9986 ln λ0 1=2Cloxa ; T d0 ðT Þ ¼ 10:726− ðT=KÞ h i 2243:7 2=3 ‐ ; R2 ¼ 0:9957 ln λ0 ðHNaf ; T Þd0 ðT Þ ¼ 10:259− ðT=KÞ h
i 2116:7 2=3 2‐ ; R2 ¼ 0:9988 ln λ0 1=2Naf ; T d0 ðT Þ ¼ 10:531− ðT=KÞ ð17Þ
422
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Table 6 Coefficients of the Quint–Viallard conductivity equations for ion pairs in aqueous solutions of sodium oxacillin, dissociation constants K1 and K2 and thermodynamic functions at different temperatures T a. T
278.15
283.15
288.15
293.15
298.15
303.15
308.15
313.15
Λ012 S12 E12 J112 J212 Λ014 S14 E14 J114 J214 Λ023 S23 E23 J123 J223 Λ034 S34 E34 J134 J234 K1103 K2108 ΔG01 ΔH01 ΤΔS01 ΔG02 ΔH02 ΤΔS02
45.76 45.42 −0.12 91.20 129.90 61.81 78.02 70.51 31.04 68.39 265.47 94.34 47.50 626 1532 281.52 147.64 120.94 1036 1484 2.60 0.45 13.76 0.63 −13.14 44.44 27.21 −17.24
52.88 52.78 −0.15 106.10 151.23 71.33 90.66 82.03 35.68 78.16 293.56 106.66 52.59 700 1712 312.01 167.28 133.49 1158 1656 2.55 0.55 14.06 0.69 −13.37 44.77 27.22 −17.55
61.07 60.93 −0.02 123.49 176.07 81.58 104.48 94.80 41.32 88.82 322.09 119.85 58.12 780 1906 342.60 188.19 146.84 1287 1839 2.57 0.65 14.29 0.68 −13.61 45.16 27.30 −17.86
68.41 69.32 −0.14 140.33 200.36 92.35 119.23 108.58 47.93 100.13 349.12 133.32 63.66 862 2102 373.06 210.09 160.91 1423 2029 2.60 0.80 14.51 0.66 −13.84 45.44 27.27 −18.17
76.90 78.28 −0.09 159.13 227.34 103.65 134.67 122.98 54.75 111.93 376.60 147.14 69.07 943 2299 403.35 232.35 174.15 1556 2216 2.50 1.00 14.85 0.77 −14.08 45.66 27.18 −18.48
85.45 87.66 −0.05 178.86 255.75 115.41 150.95 138.38 62.72 124.40 403.39 161.41 74.72 1028 2503 433.35 255.49 188.15 1696 2411 2.65 1.20 14.95 0.64 −14.32 45.97 27.18 −18.79
94.41 97.66 −0.01 199.99 286.23 127.78 168.35 154.94 71.40 137.29 429.78 176.21 80.43 1115 2712 463.15 279.62 202.27 1840 2610 2.65 1.40 15.20 0.65 −14.55 46.33 27.23 −19.10
103.87 108.04 0.14 222.58 318.79 140.28 186.29 172.13 80.55 150.03 455.68 191.29 86.26 1204 2925 492.09 304.11 216.46 1986 2810 2.65 1.60 15.45 0.66 −14.79 46.73 27.33 −19.41
a
Units: T, K; K1 and K2, mol dm−3; ΔG0, ΔH0, ΤΔS0, kJ mol−1; Λ0j, S.jc1/2, E.jc, J.1jc, J.2jc3/2, S cm2 mol−1; j = 1–4, 1 — Na+, 2 — HPen−, 3 — H+, 4 — Pen2−.
where values of ΔH≠λ in each step are similar for all penicillins, the average value for the first step is ΔH≠λ = 18.0 kJ mol−1 and for the second step ΔH≠λ = 17.4 kJ mol−1. Temperature dependence of limiting conductances can also be represented in terms of Walden products of individual ions and their values for corresponding anions are presented in Table 9.
Using the Nerst–Hartley equation for the limiting value of the diffusion coefficient for pair of ions [46] D0 ðT Þ ¼
RT ðjzþ j þ jz− jÞ λ0þ ðT Þλ0− ðT Þ h i F 2 jz þ j jz − j λ0 ðT Þ þ λ0 ðT Þ þ
ð18Þ
−
Table 7 Coefficients of the Quint–Viallard conductivity equations for ion pairs in aqueous solutions of sodium cloxacillin, dissociation constants K1 and K2 and thermodynamic functions at different temperatures T a. T
278.15
283.15
288.15
293.15
298.15
303.15
308.15
313.15
Λ012 S12 E12 J112 J212 Λ014 S14 E14 J114 J214 Λ023 S23 E23 J123 J223 Λ034 S34 E34 J134 J234 K1103 K2108 ΔG01 ΔH01 ΤΔS01 ΔG02 ΔH02 ΤΔS02
42.65 44.73 −0.80 86.48 123.60 55.87 74.98 66.71 5.48 46.95 262.36 93.65 46.83 619 1515 275.58 144.88 115.82 1002 1433 2.60 0.32 13.76 0.86 −12.90 45.23 15.34 −29.89
49.35 51.99 −0.92 100.70 144.01 64.43 87.11 77.59 5.72 53.07 290.03 105.87 51.82 692 1693 305.11 164.06 127.49 1118 1597 2.50 0.36 14.10 0.93 −13.13 45.77 15.34 −30.42
56.47 59.89 −1.05 116.36 166.57 73.66 100.37 89.64 6.38 59.61 317.49 118.81 57.09 770 1881 334.68 184.46 139.83 1240 1770 2.55 0.40 14.31 0.89 −13.36 46.32 15.36 −30.96
64.01 68.32 −1.13 133.39 191.13 83.35 114.51 102.65 7.49 66.40 344.72 132.32 62.66 851 2077 364.06 205.80 152.79 1369 1949 2.60 0.45 14.51 0.91 −13.60 46.84 15.34 −31.50
71.84 77.12 −1.25 151.04 216.60 93.53 129.31 116.25 8.58 73.49 371.54 145.98 67.91 931 2270 393.23 227.47 164.87 1495 2125 2.60 0.50 14.75 0.93 −13.83 47.38 15.34 −32.04
80.13 86.43 −1.30 170.22 244.29 104.12 144.93 130.78 10.28 80.83 398.07 160.17 73.47 1016 2472 422.06 249.99 177.60 1627 2308 2.65 0.55 14.95 0.89 −14.06 47.93 15.36 −32.57
88.66 96.31 −1.39 190.50 273.67 115.25 161.60 146.40 12.12 88.14 424.03 174.87 79.05 1101 2678 450.62 273.45 190.33 1762 2494 2.65 0.60 15.20 0.91 −14.29 48.50 15.39 −33.11
97.54 106.54 −1.41 211.97 304.77 126.48 178.77 162.60 14.00 94.97 449.35 189.80 84.71 1189 2887 478.29 297.24 203.03 1898 2680 2.70 0.68 15.40 0.87 −14.52 48.96 15.31 −33.65
a
Units: T, K; K1 and K2, mol dm−3; ΔG0, ΔH0, ΤΔS0, kJ mol−1; Λ0j, S.jc1/2, E.jc, J.1jc, J.2jc3/2, S cm2 mol−1; j = 1–4, 1 — Na+, 2 — HPen−, 3 — H+, 4 — Pen2−.
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423
Table 8 Coefficients of the Quint–Viallard conductivity equations for ion pairs in aqueous solutions of sodium nafcillin and dicloxacillin, dissociation constants K1 and K2 and thermodynamic functions at different temperatures T a. T
278.15
283.15
288.15
293.15
298.15
303.15
308.15
298.15b
Λ012 S12 E12 J112 J212 Λ014 S14 E14 J114 J214 Λ023 S23 E23 J123 J223 Λ034 S34 E34 J134 J234 K1103 K2109 ΔG01 ΔH01 ΤΔS01 ΔG02 ΔH02 ΤΔS02
39.11 43.94 −1.57 81.10 116.42 48.71 71.38 62.04 −24.10 22.44 258.82 92.86 46.06 611 1496 268.42 141.57 109.71 962 1373 2.60 0.010 13.76 1.22 −12.54 58.57 100.25 41.68
45.26 51.07 −1.82 94.43 135.66 56.13 82.91 72.14 −28.94 24.40 285.94 104.96 50.92 683 1670 296.81 160.20 120.33 1070 1526 2.50 0.020 14.10 1.34 −12.77 57.99 100.42 42.43
51.78 58.83 −2.09 109.06 156.85 64.13 95.50 83.31 −34.05 26.24 312.80 117.75 56.05 759 1855 325.15 179.99 131.48 1185 1687 2.60 0.047 14.26 1.27 −12.99 56.97 100.15 43.18
58.62 67.09 −2.36 124.88 179.82 76.89 111.16 98.32 −20.71 43.10 339.33 131.09 61.43 839 2047 357.60 202.73 147.00 1331 1893 2.65 0.10 14.46 1.24 −13.22 56.12 100.04 43.93
65.75 75.72 −2.66 141.31 203.67 81.35 122.98 107.97 −44.85 29.57 365.45 144.58 66.50 917 2235 381.05 221.64 153.82 1422 2017 2.70 0.20 14.66 1.22 −13.44 55.36 100.03 44.68
73.15 84.81 −2.94 158.88 229.26 90.53 137.79 121.43 −50.38 31.06 391.09 158.55 71.83 999 2431 408.47 243.42 165.04 1544 2185 2.70 0.35 14.91 1.24 −13.67 54.87 100.30 45.43
80.81 94.47 −3.27 177.56 256.53 100.16 153.59 135.89 −56.46 32.00 416.18 173.03 77.16 1083 2631 435.53 266.08 176.11 1668 2355 2.65 0.65 15.20 1.30 −13.90 54.19 100.37 46.17
75.01 77.85 −0.52 156.11 223.33 99.87 132.66 120.48 37.32 97.37 374.71 146.71 68.64 939 2288 399.57 230.52 170.67 1533 2182 2.70 28.0 14.66
a b
43.11
Units: T, K; K1 and K2, mol dm−3; ΔG0, ΔH0, ΤΔS0, kJ mol−1; Λ0j, S.jc1/2, E.jc, J.1jc, J.2jc3/2, S cm2 mol−1; j = 1–4, 1 — Na+, 2 — HPen−, 3 — H+, 4 — Pen2−. Corresponding values for dicloxacillin sodium salt.
in the range of observed limiting conductances of semisynthetic penicillins λ0(HPen−) at 298.15 K, the limiting diffusion coefficients of the ion pairs (Na+ + HPen−) lie in 0.6–0.9.10− 5 cm2 s− 1 range and the ion pairs (H+ + HPen−) in 0.9–1.3.10−5 cm2 s−1 range.
4. Conclusions
Acknowledgment Financial support by the Slovenian Research Agency through Grant No. P1-0201 is gratefully acknowledged. MB-R is grateful Mr. Anton Kelbl for performing density measurements. References
Systematic determinations of the conductivities of sodium salts of semisynthetic penicillins: oxacillin, cloxacillin, dicloxacillin and nafcillin in dilute aqueous solutions over the 278.15 to 308.15 K temperature range are reported for the first time. Similarly as with natural penicillins, the dissociation of the final products of penicillin degradation in acidic media is responsible for the measured conductance and not the hydrolysis of neutral sodium salts. The observed excellent agreement between the Λexp. and Λcalc. values strongly supports the proposed molecular model. Determined dissociation constants K1(T) agree well with those reported in the literature. The second dissociation constants K2(T) are considerably lower than those of natural penicillins indicating their higher stability. As for all penicillins, the limiting mobility of anions lie in rather narrow range because the effect of various side-chain groups in penicillin molecules is rather small. Table 9 Walden products of one and two charged anions of oxacillin, cloxacillin, nafcillin and dicloxacillin. Walden products
S cm2 equiv−1 Pa s
η(T).λ0(HOxa−, T) η(T).λ0(1/2HOxa2−, T) η(T).λ0(HCloxa−, T) η(T).λ0(1/2HCloxa2−, T) η(T).λ0(HNaf−, T) η(T).λ0(1/2HNaf2−, T) η(T).λ0(HDicloxa−, T) η(T).λ0(1/2HDicloxa2−, T)
0.238 ± 0.003 0.477 ± 0.001 0.293 ± 0.004 0.387 ± 0.001 0.137 ± 0.002 0.278 ± 0.001 0.221 0.443
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