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Thermodynamic Parameters for the Interaction of Amoxicillin and Ampicillin with Magnesium in NaCl Aqueous Solution, at Different Ionic Strengths and Temperatures Rosalia Maria Cigala, Francesco Crea,* Concetta De Stefano, Silvio Sammartano, and Giuseppina Vianelli Dipartimento di Scienze Chimiche, Biologiche, Farmaceutiche ed Ambientali, Università di Messina, Viale F. Stagno d’Alcontres, 31, Vill. S. Agata, Messina I-98166, Italy S Supporting Information *

ABSTRACT: In this paper, the sequestering ability of amoxicillin and ampicillin toward Mg2+ in NaCl aqueous solutions at different ionic strengths I = (0 to 1.0) mol·kg−1 and temperatures of T = (288.15 to 318.15) K was investigated by potentiometry (ISE-H+, glass electrode). The complex formation constants determined at different ionic strengths and temperatures were modeled by means of the Debye−Hückel equation and the Specific ion Interaction Theory (SIT). From the results, a weak ability of the two penicillins to bind the metal ion can be observed; in fact, the stability constants of the ML species (M = Mg2+ and L = amoxicillin or ampicillin) are log β = 4.348 and 3.242 at infinite dilution and T = 298.15 K, respectively. The dependence of the formation constants on the temperature was modeled by means of a van’t Hoff equation, which allowed us to calculate the enthalpy and entropy change values of formation of each species. The sequestering ability of amoxicillin and ampicillin toward Mg2+ in the different experimental conditions (pH, ionic strength, temperature) was quantified by means of a sigmoid equation and of the pL0.5 parameter. The pL0.5 values reflect the low stability constant values of the species; as an example at I = 0.15 mol·kg−1, pH = 7.4, and T = 298.15 K, we have pL0.5 = 2.52 and 2.78, for Mg2+/amox2− and Mg2+/amp− systems, respectively.

1. INTRODUCTION Magnesium is naturally present in many foods, added to other food products, available as a dietary supplement, and present in some medicines (such as antacids and laxatives). Magnesium is required for energy production, oxidative phosphorylation, and glycolysis. It contributes to the structural development of bone and for the synthesis of DNA, RNA, and the antioxidant glutathione. It plays a role in the transport of calcium and potassium ions across cell membranes, a process that is important to nerve impulse conduction, muscle contraction, and normal heart rhythm.1−5 Owing to the role of magnesium in the body, it has been extensively investigated with regard to therapeutic use. Magnesium has an efficacy in eclampsia, pre-eclampsia, asthma, migraine and arrhythmia, and possible efficacy for lowering the risk of metabolic syndrome, improving glucose and insulin metabolism, prevention and management of osteoporosis, alleviating leg cramps in pregnant women, and relieving symptoms of dysmenorrhea.6 Many drugs can cause magnesium deficiency, such as diuretics, antibiotics, cortisone, and painkillers; these drugs can deplete magnesium levels in the body by impairing absorption or by increasing excretion by the kidneys, and for this reason, it is important to know the ability of the biologically active molecules to bind/sequester magnesium. © 2017 American Chemical Society

In this paper, our attention was paid to two antibiotics able to reduce the free concentration of magnesium in the body owing to their chemical interactions in different experimental conditions of temperature and ionic strength. The antibiotics we investigated are amoxicillin and ampicillin (see Scheme 1), two important amino-penicillins that have similar mechanisms of action; that is, they do not kill bacteria, but they stop bacteria from multiplying, by preventing bacteria from forming the walls that surround them. This paper can be considered as a further contribution to a series of investigations already undertaken from our research group, for a decade, on the behavior of different biologically Scheme 1. Structural Formula of the Ligands

Received: September 30, 2016 Accepted: January 23, 2017 Published: February 6, 2017 1018

DOI: 10.1021/acs.jced.6b00849 J. Chem. Eng. Data 2017, 62, 1018−1027

Journal of Chemical & Engineering Data

Article

Table 1. Chemicals purity

supplier

[(2S,5R,6R)-6-([(2R)-2-amino-2-phenylacetyl]amino)-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0]heptane-2carboxylic acid], ampicillin anhydrous [(2S,5R,6R)-6-3,3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0]heptane-24-carboxylic acid], amoxicillin trihydrate

chemicals

amp

symbol

96.0−100.5%

amox

analytical standard

sodium chloride

NaCl

>99.5%

hydrochloric acid

HCl

sodium hydroxide

NaOH

magnesium chloride hexahydrate

MgCl2

std solution p.a (fixanal) std solution p.a. (fixanal) >99%

ethylenediaminetetraacetic acid sodium salt

EDTA

>99.5%

potassium hydrogen phthalate

KHPHTH

≥99.5%

sodium carbonate

Na2CO3

>99.5%

SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich

Fluka and standardized against potassium hydrogen phthalate and sodium carbonate, respectively. The NaOH aqueous solutions were preserved from atmospheric CO2 by means of soda lime traps. Magnesium chloride stock solutions (Sigma-Aldrich/Fluka, p.a.) were previously standardized against EDTA standard solutions. More details on the chemicals used for this work are reported in Table 1. All solutions were prepared with analytical grade water (ρ = 18 MΩ cm−1) obtained from an ELGA PureLab Ultra system, which was previously boiled and then preserved from atmospheric CO2 by means of soda lime traps. Grade A glassware was used. 2.2. Apparatus and Procedure. Potentiometric measurements were carried out in thermostated cells by means of water circulation, in the outer chamber of the titration cell from a thermocryostat (model D1-G Haake) and in the temperature range T = (288.15 to 318.15) K in NaCl aqueous solutions at different ionic strengths I = (0.1 to 1.0) mol·kg−1. Two different setups were used for the potentiometric titrations; the first setup consisted of a Model 713 Metrohm potentiometer, equipped with a half-cell glass electrode (Ross type 8101, from Thermo-Orion) and a double-junction reference electrode (type 900200, from Thermo-Orion) coupled to a Model 765 Metrohm motorized buret. The apparatus was connected to a PC, and automatic titrations were performed using a suitable homemade computer program to control titrant delivery, data acquisition, and to check for emf stability. The second setup consisted of a Metrohm model 809 Titrando apparatus controlled by Metrohm TiAMO 1.2 software equipped with a combination glass electrode (Ross type 8102, from ThermoOrion). The solutions under study were prepared by addition of different amounts of amoxicillin or ampicillin: camox = (1.0 to 4.6) mmol·dm−3 and camp = (1.0 to 8.0) mmol·dm−3; magnesium chloride cMg = (1.0 to 2.0) mmol·dm−3. Different cL:cM ratios, from 1:1 to 4:1 were used; hydrochloric acid concentration varied in the range cH = (5.0 to 10) mmol·dm−3, while sodium chloride was added at different concentrations in order to obtain the pre-established ionic strength values. The measurements were carried out by titrating 25 cm3 of the titrand solutions with standard solutions of NaOH up to pH ∼ 10. For each measurement, independent titrations of strong acid solutions with standard base were carried out in the same experimental conditions of the Mg2+/L (L = amoxicillin

active molecules in aqueous solutions containing different electrolytes and among them NaCl,7−15 the main inorganic component of the biological fluids. From those studies, the acid−base properties, the solubility (total and intrinsic), the activity coefficients,7−18 and the Setschenow19 parameters were determined, allowing us to model the behavior of those molecules in aqueous solution and physiologic conditions. Because the literature does not report similar investigation and data on the interaction between these kinds of components (i.e., metal ions, biological active molecules) are poor, we decided to study the systems in fairly wide ionic strength and temperature ranges. In fact, the studies were carried out in NaCl aqueous solution at different ionic strengths I = (0.1 to 1.0) mol·kg−1 and in the temperature range T = (288.15 to 318.15) K. Similar speciation schemes were obtained for the complexation of magnesium with the two antibiotics, for both the ionic strengths and temperatures investigated. The dependence of the stability constants on the ionic strength was modeled by means of different approaches (Debye−Hückel and SIT model).20−25 The knowledge of the stability constants at different temperatures allowed us to calculated, by means of the Van’t Hoff equation, the enthalpy change values for each species obtained in the speciation schemes. The ability of antibiotic to bind/sequester Mg2+ and to deplete its free concentration was quantified by means of a sigmoid Boltzman type equation and of an empirical parameters (pL0.5), which defines the amount of ligand necessary to sequester 50% of the total metal concentration. This approach is a very important simple tool to quantity in the different experimental conditions, the ability of a generic ligand to sequester a metal ion, independent of the speciation model.

2. EXPERIMENTAL SECTION 2.1. Chemicals. Amoxicillin and ampicillin were purchased by Sigma-Aldrich and were used without further purification; their purity checked by alkalimetric titration resulted >99%. Sodium chloride solutions were prepared by weighing pure salt (Sigma-Aldrich/Fluka, p.a.) previously dried in an oven at T = 383.15 K. Sodium hydroxide and hydrochloric acid solutions were prepared from concentrated ampules by Sigma-Aldrich/ 1019



Article

A modified version of the SIT equation was proposed in the past,32−34 where the specific interaction coefficient ε is dependent on the ionic strength, following the relationship:

or ampicillin) system investigated, to determine the electrode potential (E0) and the acidic junction potential (Ej = ja [H+]). The pH scale used was the free scale, pH ≡ − log10[H+], where [H+] is the free proton concentration. The estimated precision for the emf and titrant volume readings was ±0.15 mV and ±0.003 cm3, respectively. All the potentiometric titrations were carried out under magnetic stirring and bubbling purified presaturated N2 through the solution, in order to exclude O2 and CO2. 2.3. Working Equations and Computer Programs. The electrode potential (E0), the ionic product of the water (pKw), the liquid junction potential coefficient (ja), the analytical concentration of reagents and all parameters of the potentiometric titrations were calculated by means of the nonlinear least-squares computer program ESAB2M.26 The complex formation constants were calculated by BSTAC computer program,27 that can deal with measurements at different ionic strengths. The LIANA28 computer program was employed to fit different functions, for the dependence of the complex formation constants on ionic strength and on temperature. The ES4ECI29 program was used to draw the speciation diagrams, and to calculate the species formation percentages. The overall complex formation constants (βi) of species are expressed as Mg 2 + + Lz − + i H+ = MgLHi(2 + i − z)

Δε = Δε∞ + (Δε0 − Δε∞)/(I + 1)

where Δε ∞ and Δε 0 are parameters for the dependence on ionic strength for Δε NaCl → ∞ and Δε NaCl → 0, respectively. The dependence of the stability constants on the temperature has been studied by means of a Van’t Hoff equation: log βT = log βθ + ΔH(1/θ − 1/T )/R ln 10

log β = log β − z*AI

1/2

ΔH = ΔH ° − z*A′I1/2(1 + 1.5I1/2)−1 + C(I )

(1 + 1.5I

)

+ CI

where ΔH is the enthalpy change value of formation at infinite dilution, A′ = RT2 ln10 (∂A/∂T) and is equal to A′ = 1.5 + 0.024 (T − 298.15). During the calculation, since a short temperature range was investigated, the ΔCp parameter was considered constants and then neglected. Moreover, in order to model the dependence of the enthalpy change values both on the ionic strength and temperature, a mixed term of dependence on these variables was introduced in eqs 8 and 9.

Px = pi ·I ·ΔT

(2)

∑ (charges)2 reactants − ∑ (charges)2 products

(3)

If the Specific ion Interaction Theory (SIT) is used, we have log β = log β 0 − z*AI1/2(1 + 1.5I1/2)−1 + ΔεI

(4)

Table 2. Hydrolytic Constants of Mg2+a (eq 11) in NaCl Aqueous Solution at Different Ionic Strengths and T = 298.15 K

where in this case, the formation constant (β) at different ionic strengths and the formation constant at infinite dilution (β0) are expressed in the molal concentration scale, and Δε is the parameter that account for the dependence of the formation constants in the molal concentration scale on the ionic strength. The Debye−Hückel parameter A can be expressed as a function of the temperature by A = 0.51 + (0.0856(T − 298.15) + 3.8510−3 (T − 298.15)2 )/1000

(10)

3. RESULTS AND DISCUSSION 3.1. Dependence of the Formation Constants on the Ionic Strength. The sequestering ability of the amoxicillin and ampicillin toward Mg2+ was studied in NaCl aqueous solutions at different ionic strengths, I = (0.01 to 1.00) mol·kg−1, and temperatures, T = (288.15 to 318.15) K, by means of potentiometric titrations. For a correct speciation study, the acid−base properties of the two ligands15 as well as those of the metal cation were taken into account (unpublished data from this laboratory). Table 2 reports the hydrolytic constants (βpi)

where C is the parameter that accounts for the dependence of the complex formation constants on the ionic strength, log β is the formation constant at a given ionic strength, log β0 is the formation constant at infinite dilution. z* =

(9)

0

(1)

1/2 −1

(8)

where log βT is the stability constant at a given ionic strength and temperature (in Kelvin), log βθ is the value at the reference temperature (i.e., T = 298.15 K) and R = 8.314472(15) J K−1 mol−1 when ΔH is expressed in kJ mol−1 at a given ionic strength. The dependence of the enthalpy change values, for the complexes formation, on the ionic strength can be modeled by the following equation:

The dependence of the complex formation constants on the ionic strength was studied by means of both a Debye−Hückel type equation22,23,30,31 and the Specific ion Interaction Theory (SIT):20,21,24,25 In the first case, we have 0

(7)

a

(5)

I/mol·kg−1

log β1−1

log β4−4

0 0.1 0.5 1.0

−11.40 −11.58 −11.64 −11.66

−37.0 −36.9 −37.63 −38.15

Unpublished data from our laboratory.

while Δε =

of the magnesium determined in NaCl aqueous solution at different ionic strengths and expressed by means of the equilibrium:

∑ ε(p , q) p

(6)

The ε(p, q) parameters are the SIT interaction coefficients of the species with pth and qth components of opposite charge.

p Mg 2 + + i H 2O = Mgp(OH)i(2p − i) + i H+ 1020

(11)



Article

Table 3. Formation Constants of Mg2+/amox2− Species in NaCl Aqueous Solutions at Different Ionic Strengths and Temperatures (Molal Concentration Scale and Charges Omitted)

The acid−base properties of the two penicillins already published in a previous paper15 are reported in Tables S1−S2 at different ionic strengths and temperatures in the Supporting Information. The potentiometric measurements were carried out by titrating solutions containing the metal ion and the ligand at different concentrations and molar ratios; the ligand concentrations used were camox = (1.0 to 4.6) mmol·dm−3 for amoxicillin and camp = (1.0 to 8.0) mmol·dm−3 for ampicillin. The magnesium chloride concentration varied from cMg2+ = (1.0 to 2.0) mmol·dm−3, and NaCl(aq) was added in order to reach the desired ionic strength values. The experimental data were processed by means of the BSTAC computer program in order to obtain the speciation model that better fit the titration points. The choose of the most reliable speciation model was carried out taking into account different variables, namely, (i) the simplicity of the model; (ii) the significant formation percentages of the species considered in the pH range investigated; (iii) the statistical parameters, namely, standard deviation on stability constants and on the fit of the system; (iv) the differences in variance between the accepted model and other checked ones. The best results were obtained taking into account the speciation model containing the following species: Mg(amox), Mg(amox)H+, and Mg(amox)H22+ for Mg2+/amox2− system and the Mg(amp)+ and Mg(amp)H2+ species for Mg2+/amp− one. Tables 3 and 4 report the formation constants at different ionic strengths and temperatures of the Mg2+/amox2− and Mg2+/amp‑ species, expressed by means of the eq 1. A rough comparison between the data reported in these tables reveals that the stability constants of the Mg2+/amox2− system seems to be slightly higher with respect to those with amp−. Moreover, owing to the particular acid−base properties of the two ligands and of Mg2+, the absence of hydrolytic species in each speciation scheme can be observed, including the Mgp(OH)i(2p−i) ones. In fact, this allowed us to use the hydrolytic constants of magnesium determined at T = 298.15 K, also at the other temperatures. Despite the weakness of the complexes, a significant effect of the ionic strength and temperature on the stability of the species can be observed; the stability constants tend to decrease increasing the ionic strength up to I = 0.25 mol·kg−1 and then increases up to I = 1.0 mol·kg−1. The stability constants decrease regularly with the increase of the temperature. Figures 1 and 2 report the distribution diagrams of the species drawn in NaCl aqueous solution at I = 0.15 mol·kg−1 and T = 298.15 K; cMg = 1.5 mmol·dm−3 and cL = 3.0 mmol· dm −3 for the Mg 2+ /amox 2− and Mg 2+ /amp − species, respectively. The speciation curves of the two studied systems differ significantly. As it can be seen in Figure 1, owing to the weakness of the interaction between Mg2+ and the penicillin derivatives, we observe in the case of amox2− that the free metal ion (Mg2+) is the predominant species in the whole pH range investigated because of the low formation percentages of the species. At pH values higher than 10, the Mg(amox) neutral species becomes the most important one. The other species are present at pH < 7.5 (Mg(amox)H22+), while the Mg(amox)H+ has the maximum formation at pH ∼ 8.2. For the Mg2+-amp− system (Figure 2), the speciation is simple; the two species have the same formation percentage at pH ∼ 7 and reach their maximum value at pH ∼ 5.5 (Mg(amp)H2+) and pH ∼ 8 (Mg(amp)+).

T/K 288.15

293.15

298.15

308.15

318.15

a

I/mol·kg−1

log βMg(amox)a

log βMg(amox)Ha

log βMg(amox)H2a

0.100 0.150 0.250 0.500 0.750 1.000 0.100 0.150 0.250 0.500 0.750 1.000 0.100 0.150 0.250 0.500 0.750 1.000 0.100 0.150 0.250 0.500 0.750 1.000 0.100 0.150 0.250 0.500 0.750 1.000

3.89 ± 0.02 3.82 ± 0.02 3.76 ± 0.03 3.78 ± 0.03 3.88 ± 0.04 3.96 ± 0.05 3.73 ± 0.01 3.67 ± 0.02 3.62 ± 0.02 3.66 ± 0.02 3.77 ± 0.03 3.87 ± 0.04 3.58 ± 0.01 3.52 ± 0.01 3.48 ± 0.02 3.54 ± 0.02 3.67 ± 0.02 3.79 ± 0.03 3.28 ± 0.01 3.23 ± 0.01 3.21 ± 0.02 3.31 ± 0.02 3.47 ± 0.02 3.63 ± 0.03 3.01 ± 0.02 2.97 ± 0.02 2.96 ± 0.02 3.09 ± 0.03 3.28 ± 0.03 3.48 ± 0.04

12.50 ± 0.04 12.44 ± 0.01 12.42 ± 0.05 12.56 ± 0.07 12.80 ± 0.06 13.09 ± 0.10 12.38 ± 0.03 12.32 ± 0.01 12.29 ± 0.04 12.40 ± 0.06 12.61 ± 0.03 12.86 ± 0.07 12.26 ± 0.02 12.20 ± 0.01 12.16 ± 0.03 12.24 ± 0.05 12.42 ± 0.02 12.64 ± 0.05 12.03 ± 0.02 11.97 ± 0.02 11.91 ± 0.02 11.95 ± 0.05 12.07 ± 0.05 12.22 ± 0.07 11.82 ± 0.04 11.76 ± 0.03 11.68 ± 0.03 11.67 ± 0.07 11.73 ± 0.09 11.82 ± 0.11

19.46 ± 0.06b 19.46 ± 0.06 19.52 ± 0.07 19.59 ± 0.07 20.14 ± 0.09 20.48 ± 0.11 19.29 ± 0.04 19.28 ± 0.05 19.33 ± 0.04 19.59 ± 0.04 19.91 ± 0.06 20.22 ± 0.08 19.13 ± 0.04 19.12 ± 0.04 19.16 ± 0.04 19.39 ± 0.03 19.68 ± 0.04 19.97 ± 0.06 18.82 ± 0.05 18.80 ± 0.06 18.82 ± 0.06 19.01 ± 0.06 19.25 ± 0.07 19.49 ± 0.08 18.53 ± 0.08 18.50 ± 0.09 18.51 ± 0.09 18.65 ± 0.10 18.85 ± 0.12 19.044 ± 0.13

b

b

Refers to eq 1. b95% C.I.

The dependence of the formation constants of the two systems on the ionic strength was modeled by the Debye− Hückel type equation (eq 2) and the Specific ion Interaction Theory (SIT), by using both one- (eq 4) and two-parameter (eq 7) approaches.30−35 In the first case (eq 2), both the ionic strength and stability constants used were in the molar concentration scale. The C parameter (in molar concentration scale) of the eq 2, the specific ion interaction coefficients of the eqs 4 and 7, together with the formation constants at infinite dilution extrapolated by the fit of the experimental data using LIANA computer program are listed in Tables 5 and 6 for the Mg2+/ amox2− and Mg2+/amp− systems, respectively. The data in the molal concentration scale were obtained from the molar ones (see Tables S3 and S4 of the Supporting Information) by using the procedure already reported in other papers.36,37 The knowledge of the formation constants at different ionic strengths allows to draw some diagrams where the distribution of the metal/ligand species can be observed in different conditions; as an example, Figures 3 and 4 report the distribution diagrams of the Mg2+/amox2− and Mg2+/amp− species at two different ionic strengths (a) 0.15 mol·kg−1 and (b) 1.0 mol·kg−1 at T = 298.15 K. In these diagrams, the effect of the ionic strength on the distribution of the species can be resumed as (i) in the case of the Mg2+/amox2− species, the 1021



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Table 4. Formation Constants of Mg2+/amp− Species in NaCl Aqueous Solutions at Different Ionic Strengths and Temperatures (Molal Concentration Scale and Charges Omitted) T/K 288.15

293.15

298.15

308.15

318.15

a

I/mol·kg−1

log βMg(amp)a

log βMg(amp)Ha

0.100 0.150 0.250 0.500 0.750 1.000 0.100 0.150 0.250 0.500 0.750 1.000 0.100 0.150 0.250 0.500 0.750 1.000 0.100 0.150 0.250 0.500 0.750 1.000 0.100 0.150 0.250 0.500 0.750 1.000

3.13 ± 0.05 3.10 ± 0.05 3.09 ± 0.04 3.14 ± 0.03 3.18 ± 0.05 3.19 ± 0.04 3.00 ± 0.04 2.98 ± 0.03 2.97 ± 0.03 3.03 ± 0.03 3.10 ± 0.04 3.15 ± 0.03 2.88 ± 0.04 2.86 ± 0.04 2.85 ± 0.04 2.93 ± 0.04 3.03 ± 0.04 3.20 ± 0.03 2.65 ± 0.07 2.63 ± 0.07 2.63 ± 0.07 2.73 ± 0.06 2.89 ± 0.05 3.31 ± 0.03 2.43 ± 0.11 2.41 ± 0.11 2.42 ± 0.10 2.55 ± 0.09 2.75 ± 0.08 3.41 ± 0.05

10.10 ± 0.16b 10.13 ± 0.15 10.13 ± 0.14 10.45 ± 0.16 10.60 ± 0.15 10.74 ± 0.12 9.82 ± 0.0.12 9.85 ± 0.10 9.93 ± 0.09 10.22 ± 0.13 10.42 ± 0.12 10.61 ± 0.10 9.54 ± 0.10 9.59 ± 0.09 9.73 ± 0.06 10.01 ± 0.12 10.25 ± 0.12 10.48 ± 0.12 9.02 ± 0.15 9.07 ± 0.14 9.36 ± 0.12 9.59 ± 0.17 9.92 ± 0.18 10.23 ± 0.19 8.53 ± 0.24 8.60 ± 0.23 9.00 ± 0.21 9.20 ± 0.25 9.61 ± 0.27 10.01 ± 0.28

b

Figure 2. Distribution diagram of Mg2+/amp‑system, in NaCl aqueous solution at I = 0.15 mol·kg−1 and T = 298.15 K; cMg = 1.5 mmol·dm−3 and camp = 3.0 mmol·dm−3. Species: 1. Mg2+, 2. Mg(amp)H2+, and 3. Mg(amp)+.

those at I = 1.0 mol·kg−1. This observation is also valid for the other ionic strength values investigated. 3.2. Dependence of the Formation Constants on the Temperature. The knowledge of the formation constants of the Mg2+/amox2− and Mg2+/amp− species at different temperatures, allows us to draw some distribution diagrams at the same component concentration, ionic strength but different temperatures (T/K). As an example, Figures 5 and 6 report the distribution of the species at I = 0.15 mol·kg−1 (cM = 1.5 mmol·dm−3; cL = 3.0 mmol·dm−3) and T = 288.15, 298.15, and 318.15 K, for the Mg2+/amox2− and Mg2+/amp− systems, respectively. We can observe the different distribution of the different species as a function of the pH; for the Mg2+/amox2− system at I = 0.15 mol·kg−1, we have an overlapping of the curves, independently of the temperature. Moreover, the molar fraction of all the species in solution, except for Mg(amox)H22+ species, decreases and leads to an increase in the temperature. For the Mg2+/amp2−system, see Figure 6, the complexation of ampicillin toward magnesium increases, when the temperature increases. The fraction of free metal is never less than 0.6 up to pH ∼ 8. The dependence of the stability constants on the temperature and the enthalpy change values of formation of the different metal−ligand species was modeled by the van’t Hoff eq 8. In our calculation, owing to the short temperature range investigated, the ΔCp0 term of the eq 10 was neglected. A mixed term of dependence on ionic strength and temperature was tested (eq 12). The use of this mixed term (Px) allowed us to obtain a significant improvement of the statistical parameters (i.e., error associated with the ΔH/kJ mol−1 and standard deviation in the fit of the equations). Table 7 report the enthalpy, free Gibbs energy, and entropy change values of formation for the Mg2+/amox2− and Mg2+/ amp−species and the parameter pi of the mixed term of eq 12. The low standard deviation values confirm the goodness of the used model. 3.3. Sequestering Ability. In the industrial, environmental, and biological fields, where binding equilibria are involved in crucial processes, many aspects must be taken into account in the choice of the “best” chelant or to quantify its ability to bind the metal(s).


Figure 1. Distribution diagram of Mg2+/amox2−system, in NaCl aqueous solution at I = 0.15 mol·kg−1 and T = 298.15 K; cMg = 1.5 mmol·dm−3 and camox = 3.0 mmol·dm−3. Species: 1. Mg2+, 2. Mg(amox)H22+, 3. Mg(amox)H+, and 4. Mg(amox)0.

molar fraction of the free Mg2+ decreases in favor of the increase of the molar fractions of the complexes with increasing the ionic strength; (ii) an opposite trend has been observed for Mg2+/amp‑ species; in fact, in this case, the molar fraction of the complexes species at I = 0.15 mol·kg−1 are higher than 1022



Article

Table 5. Debye−Hückel and SIT Parameters of Mg2+/amox2− Species at Different Temperatures and log βpqr Values at Infinite Dilution T/K 288.15

293.15

298.15

308.15

318.15

a

species 0

Mg(amox) Mg(amox)H+ Mg(amox)H22+ Mg(amox)0 Mg(amox)H+ Mg(amox)H22+ Mg(amox)0 Mg(amox)H+ Mg(amox)H22+ Mg(amox)0 Mg(amox)H+ Mg(amox)H22+ Mg(amox)0 Mg(amox)H+ Mg(amox)H22+

log βpqr0a 4.674 13.218 19.936 4.508 13.112 19.779 4.348 13.007 19.627 4.043 12.811 19.338 3.758 12.626 19.066

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.014b 0.012 0.010 0.010 0.004 0.008 0.008 0.004 0.018 0.012 0.010 0.010 0.014 0.016 0.008

Δε

C 0.97 1.50 1.77 1.04 1.38 1.69 1.12 1.27 1.59 1.27 1.05 1.41 1.40 0.85 1.23

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.03 0.01 0.03 0.02 0.01 0.01 0.02 0.01 0.01 0.02 0.01 0.02 0.02 0.02 0.02

0.9667 1.498 1.772 1.046 1.380 1.693 1.121 1.267 1.595 1.267 1.052 1.408 1.401 0.850 1.233

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

σfit 0.056 0.026 0.060 0.036 0.008 0.028 0.036 0.010 0.030 0.040 0.024 0.034 0.042 0.034 0.036

0.085

0.096

0.105

0.088

0.110

Δε∞ 0.766 1.537 1.865 0.840 1.393 1.587 0.916 1.253 1.477 1.056 0.985 1.277 1.185 0.734 1.086

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.200 0.088 0.360 0.132 0.030 0.096 0.128 0.040 0.098 0.0132 0.084 0.108 0.124 0.124 0.108

1.105 1.469 1.678 1.188 1.370 1.766 1.265 1.278 1.677 1.416 1.100 1.500 1.556 0.934 1.336

Δε0

σfit

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.044

0.166 0.096 0.304 0.0110 0.034 0.078 0.106 0.038 0.082 0.118 0.090 0.090 0.110 0.132 0.088

0.054

0.073

0.032

0.059


Table 6. Debye−Hückel and SIT Parameters of Mg2+/amp− Species at Different Temperatures and log βpqr Values at Infinite Dilution T/K 288.15 293.15 298.15 308.15 318.15 a

species +

Mg(amp) Mg(amp)H2+ Mg(amp)+ Mg(amp)H2+ Mg(amp)+ Mg(amp)H2+ Mg(amp)+ Mg(amp)H2+ Mg(amp)+ Mg(amp)H2+

log βpqr0a 3.527 10.013 3.392 9.717 3.242 9.434 2.926 8.900 2.728 8.388

± ± ± ± ± ± ± ± ± ±

0.024b 0.042 0.024 0.012 0.006 0.014 0.120 0.088 0.042 0.086

Δε

C 0.49 0.76 0.62 0.92 0.77 1.08 1.33 1.36 1.24 1.62

± ± ± ± ± ± ± ± ± ±

0.06 0.04 0.03 0.02 0.01 0.02 0.12 0.06 0.11 0.06

0.496 0.761 0.617 0.923 0.769 1.078 1.331 1.356 1.240 1.626

± ± ± ± ± ± ± ± ± ±

σfit 0.118 0.084 0.062 0.050 0.022 0.032 0.434 0.128 0.234 0.136

Δε∞

0.077 0.066 0.088 0.074 0.098

0.643 0.403 0.758 0.776 0.829 1.303 1.171 2.220 1.480

± ± ± ± ± ± ± ± ±

0.380 0.228 0.254 0.082 0.132 0.765 0.246 0.423 0.331

Δε0

σfit

± ± ± ± ± ± ± ± ± ±

0.049

0.840 0.848 0.768 1.050 0.767 1.271 1.384 1.498 0.577 1.751

0.360 0.392 0.222 0.220 0.066 0.124 0.652 0.280 0.317 0.343

0.033 0.066 0.053 0.081


Figure 3. Distribution diagram of Mg2+/amox2− system at two different ionic strengths, (a) 0.15 mol·kg−1 and (b) 1.00 mol·kg−1. Experimental conditions: cMg = 1.5 mmol·dm−3 and camox = 3.0 mmol· dm−3, at T = 298.15 K. Species: 1. Mg2+, 2. Mg(amox)H22+, 3. Mg(amox)H+, and 4. Mg(amox)0.

Figure 4. Distribution diagram of Mg2+/amp− system at two different ionic strengths, (a) 0.15 mol·kg−1 and (b) 1.00 mol·kg−1. Experimental conditions: cMg = 1.5 mmol·dm−3 and camox = 3.0 mmol·dm−3, at T = 298.15 K. Species: 1. Mg2+, 2. Mg(amp)H2+, and 3. Mg(amp)+.

The formation of the different metal−ligand systems depends on some factors, such as concentration of the components, their molar concentration ratios, pH, the acid− base properties of the metal (hydrolysis) and of the ligand (protonation). In fact, both the hydrolysis and the protonation reaction are competitive with respect to the metal complex

formation reactions. Owing to different acid−base properties, two metal−ligand systems may show the same formation percentages (at a given pH value), even with different formation constants, or vice versa. Moreover, weak interactions with the supporting electrolyte may also occur; the anion of the 1023



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cations taking simultaneously into account the factors above cited.38−42 x=

1 1 + 10(pL − pL0.5)

(12)

where x is the fraction of the metal M complexed by the ligand. The parameter pL0.5, calculated by least-squares analysis, gives the conditions for which 50% of metal is complexed by the ligand ([L]tot = 10−pL0.5). The sequestering ability of penicillin toward magnesium was studied at different temperatures, ionic strengths (NaCl aqueous solution), and pHs. As it can be seen from the pL0.5 values reported in the Tables 8 and 9, independent of the conditions, the different penicillin derivatives are able to sequester weakly the metal ion.

Figure 5. Distribution diagram of Mg2+/amox2− system at I = 0.15 mol·kg−1. Legend: (a) T = 288.15 K, (b) T = 298.15 K, and (c) T = 318.15 K. cM = 1.5 mmol·dm−3 and cL = 3.0 mmol·dm−3. Species: 1. Mg2+, 2. Mg(amox)H22+, 3. Mg(amox)H+, and 4. Mg(amox)0.

Table 8. Values of pL0.5 Calculated in Different Experimental Conditions for Mg2+/amox2− System T/K

I/mol·kg−1

pH

pL0.5

308.15

0.15

5.0 7.4 8.2 9.5 7.4

2.35 2.51 2.62 3.04 2.63 2.89 2.50 2.52 2.51 2.48

288.15 298.15 308.15 318.15

0.50 1.00 0.15

7.4

Table 9. Values of pL0.5 Calculated in Different Experimental Conditions for Mg2+/amp− System −

2+

Figure 6. Distribution diagram of Mg /amp system at I = 0.15 mol· kg−1. Legend: (a) T = 288.15 K, (b) T = 298.15 K, and (c) T = 318.15 K. cM = 1.5 mmol·dm−3 and cL = 3.0 mmol·dm−3. Species: 1. Mg2+, 2. Mg(amp)H2+, and 3. Mg(amp)+.

supporting electrolyte may form weak species with the metal cation, and the ligands can interact with the cation. This means that the comparison of the selectivity and of the sequestering ability of one or more ligands toward cation(s) cannot be easily estimated by the simple analysis of single sets of stability constants, especially if different speciation models are formed. This problem can be overcome by using a sigmoid Boltzmann-type equation already proposed in many works and tested on many systems; it give a quantitative evaluation of the sequestering ability of a given ligand toward different

T/K

I/mol·kg−1

pH

pL0.5

308.15

0.15

5.0 7.4 8.2 9.5 7.4

2.28 2.58 2.62 2.62 2.74 3.30 3.00 2.78 2.58 2.38

288.15 298.15 308.15 318.15

0.50 1.00 0.15

7.4

Figures 7 and 8 show that the pL0.5 values are fairly independent of pH up to 9.5; over this value, a significant increase of sequestering ability of amox2− toward Mg2+ is observed. In the case of amp−, the pL0.5 is fairly constant.

Table 7. Enthalpy Changes Values of Formationa at Infinite Dilution for the Mg2+/amp− and Mg2+/amox2− Species, at T = 298.15 K and pi Parameter of the Mixed Term [eq 10] ΔH0b

species +

Mg(amp) Mg(amp)H2+ Mg(amox)0 Mg(amox)H+ Mg(amox)H22+ a

−31.1 −77.9 −36.1 −38.2 −53.5

± ± ± ± ±

1.0 2.7 1.3 1.5 1.1

−ΔG0b c

18.50 53.84 24.81 74.23 112.01

± ± ± ± ±

0.03 0.08 0.05 0.02 0.10

TΔS0b −12.6 −24.1 −11.3 36.0 58.5

± ± ± ± ±

1.0 2.5 2.1 3.1 2.8

pi 1.3 2.2 0.38 −0.98 −0.97

± ± ± ± ±

0.4c 0.3 0.18 0.16 0.12

Refers to eq 8. bkJ mol−1. c± Std Dev. 1024



Article

Figure 7. Sequestering ability of Mg2+/amox2− system at T = 308.15 K, I = 0.15 mol·kg−1, and different pH values. Legend: 1 pH = 5 pL0.5 = 2.35; 2. pH = 7.4 pL0.5 = 2.51; 3. pH = 8.2 pL0.5 = 2.62; and 4. pH = 9.5 pL0.5 = 3.04.

Figure 9. Sequestering ability of Mg2+/amox2− system at pH = 7.4, I = 0.15 mol·kg−1, and different T/K values. Legend: 1 T = 288.15 K pL0.5 = 2.50; 2. T = 298.15 K pL0.5 = 2.52; 3.T = 308.15 K pL0.5 = 2.51; and 4. T = 318.15 K pL0.5 = 2.48.

Figure 8. Sequestering ability of Mg2+/amp− system at T = 308.15 K, I = 0.15 mol·kg−1, and different pH values. Legend: 1 pH = 5 pL0.5 = 2.28; 2. pH = 7.4 pL0.5 = 2.58; 3. pH = 8.2 pL0.5 = 2.62; and 4. pH = 9.5 pL0.5 = 2.64.

Figure 10. Sequestering ability of Mg2+/amp− system at pH = 7.4, I = 0.15 mol·kg−1, and different T/K values. Legend: 1 T = 288.15 K pL0.5 = 3.00; 2. T = 298.15 K.

At the same pH value (pH = 7.4) and ionic strength (I = 0.15 mol·kg−1), as it can be seen in Figures 9 and 10, the sequestering ability of amox2− can be considered constants at the different temperatures, whereas for the amp− it decreases significantly. The dependence of the pL0.5 on the ionic strength for the two penicillins is reported in Figures 11 and 12; at pH = 7.4 and T = 308.15 K, we observe an increasing trend, increasing the ionic strength, especially for the Mg2+/amp−.

4. CONCLUSIONS From the speciation studies carried out by potentiometry in NaCl aqueous solution at different ionic strengths and temperatures, it has been possible to propose the speciation models for the Mg2+/amox2− and Mg2+/amp− systems. The best results were obtained taking into account the following speciation schemes: Mg(amox), Mg(amox)H+, and Mg(amox)H22+ for Mg2+/amox2− system and the Mg(amp)+ and Mg(amp)H2+ species for Mg2+/amp‑ one, where it is possible to observe the absence of hydrolytic species due to the acid−base properties of the metal ion. From the low stability of the Mg2+-penicillin species and observing the distribution diagrams drawn at different ionic

Figure 11. Sequestering ability of Mg2+/amox2− system at T = 308.15 K, pH = 7.4, and different pH values. Legend: 1 I = 0.15 mol·kg−1 pL0.5 = 2.51; 2. I = 0.50 mol·kg−1 pL0.5 = 2.63; 3. I = 1.00 mol·kg−1 pL0.5 = 2.89.

strengths and temperatures, it is possible to see as the free metal ion is the main component of the system for wide pH 1025



Article

Notes

The authors declare no competing financial interest.

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(1) Institute of Medicine. Dietary Reference Intakes for Calcium, Phosphorus, Magnesium, Vitamin D, and Fluoride; The National Academies Press: Washington, DC, 1997; p 448. (2) Dean, C. The Magnesium Miracle; Ballantine Books: New York, 2007. (3) Fox, C.; Ramsoomair, D.; Carter, C. Magnesium: Its Proven and Potential Clinical Significance. South. Med. J. 2001, 94, 1195−1201. (4) Rude, R. K. Magnesium. In Encyclopedia of Dietary Supplements, 2nd ed.; Coates, P. M., Betz, J. M., Blackman, M. R., Cragg, G. M., Levin, M., Moss, J., White, J. D., Eds.; Informa Healthcare: New York, 2010; pp 527−537. (5) Rude, R. K. Magnesium. In Modern Nutrition in Health and Disease, 11th ed.; Ross, A. C., Caballero, B., Cousins, R. J., Tucker, K. L., Ziegler, T. R., Eds.; Lippincott Williams & Wilkins: Baltimore, 2012; pp 159−175. (6) Alexander, R. T.; Hoenderop, J. G.; Bindels, R. J. Molecular determinants of magnesium homeostasis: insights from human disease. J. Am. Soc. Nephrol. 2008, 19, 1451−1458. (7) Battaglia, G.; Cigala, R. M.; Crea, F.; Sammartano, S. Solubility and Acid-Base Properties of Ethylenediaminetetraacetic Acid in Aqueous NaCl Solution at 0 < I < 6 mol kg−1 and T = 298.15 K. J. Chem. Eng. Data 2008, 53, 363−367. (8) Bretti, C.; Cigala, R. M.; Crea, F.; De Stefano, C.; Vianelli, G. Solubility and modeling acid-base properties of adrenaline in NaCl aqueous solutions at different ionic strengths and temperatures. Eur. J. Pharm. Sci. 2015, 78, 37−46. (9) Bretti, C.; Crea, F.; De Stefano, C.; Foti, C.; Materazzi, S.; Vianelli, G. Thermodynamic Properties of Dopamine in Aqueous Solution. Acid-Base Properties, Distribution, and Activity Coefficients in NaCl Aqueous Solutions at Different Ionic Strengths and Temperatures. J. Chem. Eng. Data 2013, 58, 2835−2847. (10) Bretti, C.; Crea, F.; De Stefano, C.; Sammartano, S.; Vianelli, G. Some thermodynamic properties of DL-Tyrosine and DL-Tryptophan. Effect of the ionic medium, ionic strength and temperature on the solubility and acid-base properties. Fluid Phase Equilib. 2012, 314, 185−197. (11) Bretti, C.; Crea, F.; Foti, C.; Sammartano, S. Solubility and Activity Coefficients of Acidic and Basic Nonelectrolytes in Aqueous Salt Solutions. 1. Solubility and Activity Coefficients of o-Phthalic Acid and L-Cystine in NaCl(aq), (CH3)4NCl(aq), and (C2H5)4NI(aq) at Different Ionic Strengths and at t = 25 °C. J. Chem. Eng. Data 2005, 50, 1761−1767. (12) Cataldo, S.; Crea, F.; Gianguzza, A.; Pettignano, A.; Piazzese, D. Solubility and acid-base properties and activity coefficients of chitosan in different ionic media and at different ionic strengths, at T = 25 °C. J. Mol. Liq. 2009, 148, 120−126. (13) Cigala, R.; Crea, F.; De Stefano, C.; Lando, G.; Milea, D.; Sammartano, S. Modeling the acid−base properties of glutathione in different ionic media, with particular reference to natural waters and biological fluids. Amino Acids 2012, 43, 629−648. (14) Cigala, R. M.; Crea, F.; Lando, G.; Milea, D.; Sammartano, S. Solubility and acid-base properties of concentrated phytate in selfmedium and in NaClaq at T = 298.15 K. J. Chem. Thermodyn. 2010, 42, 1393−1399. (15) Crea, F.; Cucinotta, D.; De Stefano, C.; Milea, D.; Sammartano, S.; Vianelli, G. Modelling solubility, acid−base properties and activity coefficients of amoxicillin, ampicillin and (+)6-aminopenicillanic acid, in NaCl(aq) at different ionic strengths and temperatures. Eur. J. Pharm. Sci. 2012, 47, 661−677. (16) Bretti, C.; Cigala, R. M.; Crea, F.; Foti, C.; Sammartano, S. Solubility and activity coefficients of acidic and basic nonelectrolytes in aqueous salt solutions. 3. Solubility and acitivity coefficients of adipic and pimelic acids in NaCl(aq), (CH4)4NCl(aq) and (C2H5)4NI(aq) at different ionci strengths and at t = 25 °C. Fluid Phase Equilib. 2008, 263, 43−54.

Figure 12. Sequestering ability of Mg2+/amp− system at T = 308.15 K, pH = 7.4, and different pH values. Legend: 1 I = 0.15 mol·kg−1 pL0.5 = 2.58; 2. I = 0.50 mol·kg−1 pL0.5 = 2.74; 3. I = 1.00 mol·kg−1 pL0.5 = 3.30.

values, while the Mg2+-penicillin species become significant over pH 6.5−7. The knowledge of the stability constants at different temperatures allowed us to calculate the enthalpy and entropy change values of formation of each species reported in the speciation schemes. The formation constants at different temperatures and ionic strengths were fitted with the van’t Hoff equation; the enthalpy and entropy change values of formation were calculated at the reference temperature of T = 298.15 K and infinite dilution. By means of the pL0.5 parameter, the sequestering ability of amoxicillin and ampicillin toward Mg2+ was quantified as a function of pH, ionic strength, and temperature. The obtained values highlight that the penicillins here studied tend to bind/ sequester weakly the metal ion (Mg2+) with pL0.5 values of about ∼2.5−3.3 in dependence on the experimental conditions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00849. Calculated protonation constants in the molal concentration scale of ampicillin in NaCl aqueous solution at different ionic strengths and temperatures; calculated protonation constants in the molal concentration scale of amoxicillin in NaCl aqueous solution at different ionic strengths and temperatures; experimental formation constants of Mg2+/amp− species in NaCl aqueous solutions at different ionic strengths and temperatures; experimental formation constants of Mg2+/amox2− species in NaCl aqueous solutions at different ionic strengths and temperatures (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Tel: +39-090-6765761. ORCID

Francesco Crea: 0000-0002-9143-9582 Funding

We thank the University of Messina for the partial financial support. 1026



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