Speciation of phytate ion in aqueous solution. Protonation in CsClaq at different ionic strengths and mixing effects in LiClaq + CsClaq

Journal of Molecular Liquids 138 (2008) 76 – 83 www.elsevier.com/locate/molliq

Speciation of phytate ion in aqueous solution. Protonation in CsClaq at different ionic strengths and mixing effects in LiClaq + CsClaq☆ Francesco Crea, Pasquale Crea, Concetta De Stefano, Demetrio Milea, Silvio Sammartano ⁎ Dipartimento di Chimica Inorganica, Chimica Analitica e Chimica Fisica, Università di Messina, Salita Sperone, 31, I-98166 Messina (Vill. S. Agata), Italy Received 4 May 2007; accepted 31 August 2007 Available online 7 September 2007

Abstract This paper reports the results of an investigation (at t = 25 °C by potentiometry, ISE-H+ glass electrode) of phytate acid–base properties both in simple CsClaq solutions at different ionic strengths (0.1 ≤I/mol L− 1 ≤ 1.75) and in LiClaq−CsClaq mixtures at I = 1.28 mol L− 1 and different Li+/Cs+ mole fractions [y = CLi/(CLi + CCs)]. These last measurements allowed us to evaluate the mixing effects on phytate protonation, and the deviation from the ideal mixing (Young rule) has been interpreted by means of a Δ parameter that can be associated to the free energy of mixing (ΔGmix) or, alternatively, in terms of formation of simple and mixed metal complexes. Dependence of protonation constants on ionic strength in simple CsClaq solutions has been taken into account by a Debye–Hückel type equation. Complex formation constants for CsjHiPhy(12 − i − j)− species at different ionic strengths have been calculated too, and comparisons have been made with phytate acid base behavior in other alkali metal chloride aqueous media. © 2007 Elsevier B.V. All rights reserved. Keywords: Protonation constants; Phytate; Alkali metal complexes; Electrolyte mixtures; Dependence on ionic medium; Dependence on ionic strength

1. Introduction Natural waters and biological fluids can be considered as multi-electrolyte aqueous solutions in which many organic and inorganic ions, as well as neutral compounds, are present [1,2]. One important aspect that should be underlined, and that is sometimes neglected, is that the most of them participates in acid–base equilibria, affecting phenomena such as solubility and/or interactions with other ions and ligands, influencing their functionality and activity. Therefore, an accurate knowledge of their acid base properties (as well as stability constants) is essential for a through understanding of their reactions in natural and biological systems. This is particularly important for phytic acid [1,2,3,4,5,6-hexakis(dihydrogen phosphate) myoinositol], which is a bio-ligand, widely present in the environment and in several vegetal species, that shows in its structure twelve displaceable protons with very different acidity (see, e.g., refs. in our last contribution to this topic [3]). As a consequence, its acid–base behavior is quite complex and ☆

Previous contributions to this series are cited in Ref [3]. ⁎ Corresponding author. Tel.: +39 090 393659; fax: +39 090 392827. E-mail address: [email protected] (S. Sammartano).

0167-7322/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2007.08.024

affects many other properties, especially in relation to the fact that the different anionic forms of this ligand may differently interact with several species in aqueous solution. In this light, prior to the study of phytate sequestering ability toward many metal and organometal cations (as well as other organic cations, see, e.g., [3] and our refs. therein), our group paid particular attention to the determination of its acid base properties, by also modeling the effect of medium and ionic strength [3–6]. Phytate protonation constants have been determined in a wide range of ionic strengths (0 b I/mol L− 1 ≤ 5) in various simple ionic media, such as alkali metal chlorides (LiClaq, NaClaq, KClaq) [4,5], sodium nitrate [3] and tetraethylammonium iodide [(C2H5)4NIaq] [4], as well as multielectrolyte solutions (tetraethylammonium iodide/alkali metal chloride mixtures) [5]. As a further contribution to this topic, this paper reports the results of an investigation (at t = 25 °C by potentiometry, ISEH+ glass electrode) on phytate acid–base properties both in simple CsClaq solutions at different ionic strengths (0.1 ≤ I/mol L− 1 ≤ 1.75) and in LiClaq–CsClaq mixtures at I = 1.28 mol L− 1 and different Li+/Cs+ mole fractions [y = CLi/(CLi + CCs)]. These last measurements allowed us to evaluate the mixing effects on phytate protonation, as a further step in the comprehension of its acid–base behavior in real, aqueous multielectrolyte systems.

F. Crea et al. / Journal of Molecular Liquids 138 (2008) 76–83

The choice of lithium and cesium chlorides is justified by the fact that the use of so different alkali metal cations would enhance these effects. Despite literature reports different approaches in treating protonation equilibria in mixed electrolytes solutions, in the present paper we followed a procedure already proposed by our research group for the modeling of acid–base behavior of different polycarboxylic ligands in NaClaq–KClaq mixtures [7]. In this model, the deviation from the ideal mixing (Young rule) [8,9] is interpreted by means of a Δ parameter that can be associated to the free energy of mixing (ΔGmix) or, alternatively, in terms of formation of simple and mixed metal complexes. Dependence of phytate protonation constants on ionic strength in CsClaq has also been modeled, and stability constants for cesium–proton–phytate complexes have been determined too. 2. Experimental section 2.1. Chemicals Hydrochloric acid and sodium hydroxide solutions were prepared by diluting concentrated ampoules (Riedel-deHaën) and were standardized against sodium carbonate and potassium hydrogen phthalate, respectively. LiCl and CsCl solutions were prepared by weighing the puriss. salts (Fluka), dried in an oven at 110 °C. Phytic acid solutions were prepared by weighing Aldrich dipotassium salt (K2H10Phy), and passing it over a strong cationic exchange resin (Dowex 50 W X 8 from Fluka). Concentration was checked potentiometrically by alkalimetric titrations, and the absence of potassium was established by flame emission spectrometry. All solutions were prepared with analytical grade water (R = 18 MΩ cm− 1) using grade A glassware. 2.2. Apparatus Potentiometric titrations were carried out (at 25.0 ± 0.1 °C) using an apparatus consisting of a Crison micropH2002 potentiometer equipped with a half cell glass electrode (Ross type 8101, from Orion) and a calomel reference electrode. The titrant solution was delivered by a model 765 Metrohm motorized burette. Estimated accuracy was ± 0.15 mV and ± 0.003 mL for e.m.f. and titrant volume readings, respectively. The apparatus was connected to a PC and automatic titrations were performed using a suitable computer program to control titrant delivery, data acquisition and to check for e.m.f. stability. 2.3. Procedure Potentiometric titrations were carried out in termostatted cells under magnetic stirring and bubbling purified presaturated N2 through the solution in order to exclude O2 and CO2 inside. The titrand solution consisted of different amounts of phytic acid (2–5 mmol L− 1) and the supporting electrolyte in order to obtain pre-established ionic strength values (0.1 ≤ I mol L− 1 ≤ 1.75 in simple CsClaq; I = 1.28 mol L− 1 for LiClaq– CsClaq mixtures, using different Li+/Cs+ ratios). Potentiometric

77

measurements were carried out (at least in duplicate) by titrating 25 mL of the titrand solution with standard NaOH solutions up to pH = 11.5. For each experiment, independent titrations of strong acid solution with standard base were carried out under the same medium and ionic strength conditions as the systems to be investigated, with the aim of determining electrode potential (E0), acidic junction potential (Ej = ja [H+]), and Kw. In this way, the pH scale used was the total scale, pH ≡ − log [H+], where [H+] is the free proton concentration (not activity). For each titration, 80–100 points were collected, and the equilibrium state during titrations was checked adopting some usual precautions. These included checking the time necessary to reach equilibrium and performing back titrations. For measurements performed at low ionic strengths, the contribution of the ligand has to be considered: in the most critical conditions (i.e. I = 0.1 mol L− 1), this contribution to ionic strength is ∼ 7–8%, which introduces a not dramatic error in calculation. However, this error was taken into account by giving appropriate weights to the results obtained at low ionic strengths in fitting different functions. 2.4. Calculations The BSTAC [10] and STACO [10] computer programs were used in the refinement of all the parameters of an acid–base titration (E0 , Kw, liquid junction potential coefficient ja, analytical concentration of reagents) and in the calculation of complex formation constants. Both programs can deal with measurements at different ionic strengths. The LIANA [10] program was used to test the dependence of log K on ionic strength and to calculate the mixing parameters. The ES2WC [10] computer program was used in the calculation of formation constants of weak phytate – cesium complexes. Protonation constants, KiH, expressed in the molar (mol L− 1) concentration scale, are given according to the equilibrium H þ þ Hi1 Phyð12iþ1Þ ¼ Hi Phyð12iÞ

KiH

ð1Þ

bH i

ð2Þ

or i H þ þ Phy12 ¼ Hi Phyð12iÞ

whilst the complex formation constants refer to the equilibrium jM þ þ i H þ þ Phy12 ¼ Mj Hi Phyð12ijÞ

bji

ð3Þ

The dependence of protonation constants on ionic strength was taken into account using a Debye–Hückel type equation:
 T H 0:5 0:5 ⁎ log bH i ¼ log bi  z 0:51 I = 1 þ 1:5 I
 þ Ci I  log 1 þ 10Ai I

ð4Þ

in which X X z⁎ ¼ ðchargesÞ2reactants  ðchargesÞ2products βiH is the apparent constant at given ionic strength and TβiH is the formation constant at infinite dilution; while Ai and Ci are

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F. Crea et al. / Journal of Molecular Liquids 138 (2008) 76–83

Table 1 Experimental phytate protonation constants in CsClaq at different ionic strengths and at t = 25 °C a) I / mol L− 1 log βH (log KH 1 1)

0.223

9.92 ± 0.04

0.357

9.84 ± 0.04

0.586

9.83 ± 0.02

0.810

9.81 ± 0.02

1.040

9.81 ± 0.02

1.275

9.79 ± 0.02

1.491

9.77 ± 0.02

1.734

9.73 ± 0.02

a) b)

b)

a) log βH (log KH 2 2)

b)

19.80 ± 0.04 (9.88) 19.49 ± 0.02 (9.65) 19.30 ± 0.02 (9.47) 19.23 ± 0.02 (9.42) 19.18 ± 0.02 (9.37) 19.14 ± 0.02 (9.35) 19.11 ± 0.02 (9.34) 19.07 ± 0.04 (9.34)

a) log βH (log KH 3 3)

29.56 ± 0.04 (9.76) 29.09 ± 0.02 (9.60) 28.78 ± 0.02 (9.48) 28.66 ± 0.02 (9.43) 28.60 ± 0.02 (9.42) 28.53 ± 0.02 (9.39) 28.48 ± 0.02 (9.37) 28.42 ± 0.04 (9.35)

b)

a) log βH (log KH 4 4)

37.79 ± 0.04 (8.23) 37.14 ± 0.02 (8.05) 36.65 ± 0.02 (7.87) 36.45 ± 0.02 (7.79) 36.40 ± 0.02 (7.80) 36.27 ± 0.02 (7.74) 36.18 ± 0.02 (7.70) 36.13 ± 0.04 (7.71)

b)

a) log βH (log KH 5 5)

43.93 ± 0.04 (6.14) 43.06 ± 0.02 (5.92) 42.36 ± 0.02 (5.71) 42.05 ± 0.02 (5.60) 41.99 ± 0.02 (5.59) 41.81 ± 0.02 (5.54) 41.70 ± 0.02 (5.52) 41.64 ± 0.04 (5.51)

b)

a) log βH (log KH 6 6)

48.75 ± 0.04 (4.82) 47.69 ± 0.02 (4.63) 46.80 ± 0.04 (4.44) 46.41 ± 0.04 (4.36) 46.37 ± 0.04 (4.38) 46.13 ± 0.02 (4.32) 45.99 ± 0.02 (4.29) 45.94 ± 0.02 (4.30)

b)

a) log βH (log KH 7 7)

b)

51.57 ± 0.04 (2.82) 50.35 ± 0.04 (2.66) 49.21 ± 0.04 (2.41) 48.76 ± 0.04 (2.35) 48.72 ± 0.02 (2.35) 48.44 ± 0.02 (2.31) 48.31 ± 0.02 (2.32) 48.31 ± 0.04 (2.37)

+ 12− log βH = HiPhy(12 − i)−; ± standard deviation. i refers to equilibrium: i H + Phy H log Ki in parenthesis refers to equilibrium: H+ + Hi − 1Phy(12 − i + 1)− = HiPhy(12 − i)−.

empirical parameters. Ci parameters can be, in turn, dependent on ionic strength [11]: Ci ¼ cil þ ðci0  cil Þ=ð I þ 1Þ ð5Þ where ci∞ and ci0 represent Ci values for I → ∞ and I → 0, respectively. In previous works [4,5], the dependence of protonation constants on ionic strength in alkali metal chloride aqueous solutions has been modeled by a similar relationship
 logKiH ¼ logT KiH þ Ci I  log 1 þ 10DiM I

ð6Þ

in which, in analogy with Eq. (4), Ci and DiM are empirical parameters. From previous studies Ci has the same value in all alkali metal chloride media, whilst DiM parameters can be considered as a measure of the interaction between M + (M = alkali metal cation) and HiPhy(12 − i)−. Main differences among Eqs. (4) and (6) are due to the presence, in the first equation, of a Debye–Hückel term. Preliminary calculations showed that this term was needed to improve the quality of fits in CsClaq in respect to the modeling of phytate protonation constants in other alkali metal chlorides aqueous media. This is probably due to the fact that Cs+ interacts with phytate more

weakly than other investigated alkali metal cations: in fact, the use of a term dependent on the square root of ionic strength (as the Debye–Hückel term) is coherent with the modeling of phytate protonation constants in ionic media scarcely interacting with this ligand [e.g., (C2H5)4NIaq] [4]. However, as well as Eq. (4), dependence of phytate protonation constants on ionic strength has also been taken into account by Eq. (6), for a faster comparison with its acid base behavior in other alkali metal chloride media. Formation constants, species concentrations and ionic strengths are expressed in the molar (mol L− 1) concentration scale; errors are always expressed as ± standard deviation. 3. Models for the interpretation of mixing effects Young rule, first formulated for densities in the mixing of solutions of strong electrolytes [8,9], if applied to protonation constants in MX + M′X (M and M′ are generic cations,

Table 2 Phytate protonation constants in different ionic media at I = 1.0 mol L− 1 and t = 25 °C Medium a)

LiClaq NaClaq b) KClaq a) CsClaq c) Et4NIaq b) a) b) c) d)

d) d) d) d) d) d) d) log KH log KH log KH log KH log KH log KH log KH 1 2 3 4 5 6 7

8.83 8.69 9.35 9.82 13.60

8.57 8.95 8.61 9.38 12.48

7.69 8.56 8.99 9.41 11.06

6.67 7.21 7.45 7.77 9.71

5.40 5.65 5.77 5.57 7.50

4.15 4.42 4.54 4.34 6.16

1.92 2.22 2.28 2.32 3.72

Ref. [5]. Ref. [4]. This work. log KiH refers to equilibrium: H+ + Hi − 1Phy(12 − i + 1)− = HiPhy(12 − i)−.

Fig. 1. First phytate protonation constants, as log KH 1 , in various ionic media at different ionic strengths and at t = 25 °C. △ = LiClaq; ◯ = NaClaq; ▽ = KClaq; = CsClaq.

◇

F. Crea et al. / Journal of Molecular Liquids 138 (2008) 76–83

79

Fig. 2. Second phytate protonation constants, as log KH 2 , in various ionic media at different ionic strengths and at t = 25 °C. △ = LiClaq; ◯ = NaClaq; ▽ = KClaq; = CsClaq.

Fig. 3. Third phytate protonation constants, as log KH 3 , in various ionic media at different ionic strengths and at t = 25 °C. □ = (C2H5)4NIaq; △ = LiClaq; ◯ = NaClaq; ▽ = KClaq; = CsClaq.

respectively) aqueous mixtures can be written as a function of the mole fraction (y)

H protonation constants on y The dependence of mixed log βiM,M′ (mole fraction) and the deviation from linear mixing can be given by the free energy of mixing, which can be expressed as

◇

H H log bH iM;M V ¼ y log biM þ ð1  yÞlog biM V

or, for y = 0.5
 H H log bH iM;M V ¼ log biM þ log biM V =2

ð7Þ

DGimix ¼ 2:303 RT Di ð8Þ

H H H where log βiM,M′ , log βiM and log βiM′ are the protonation constants in the MX + M'X mixture and in pure MX and M'X salt solutions, respectively. Eqs. (7) and (8) are valid for linear (ideal) mixing. The Guggenheim zeroth approximation [12], applied to the protonation constants in mixtures of MX and M'X, leads to a three parameter equation

2 H H 2 log bH iM;M V ¼ y log biM þ ð1  yÞ log biM V þ 2yð1  yÞlog bH im

ð9Þ

H where log βim is an intermediate value that accounts for the non linearity of the function log βiH = f (y). Note that Eq. (9) reduces H H H to (7) when log βim = (log βiM + log βiM′ )/2. This equation, also called Högfeldt three parameter equation [13–15], was applied to a variety of problems (formation of mixed micelles, protonation equilibria of chelating resins, ion exchange reactions, protonation of polyelectrolytes). After simple rearrangement, Eq. (9) can be written as

H 2 log bH ð1  yÞ2 log bH iM;M V ¼ y log biM þ iM V
 H þ yð1  yÞ log bH iM þ log biM V þ 4Di

◇

ð13Þ

Positive ΔGimix values (negative Δi values) indicate that the formation of simple or ternary weak complexes is preferred with respect to the protonation reactions. 4. Results and discussion 4.1. Phytate protonation constants in CsClaq and alkali metalproton-phytate complexes In our previous contributions, phytate protonation constants were determined in different ionic media [3–5]. Potentiometric measurements performed in CsClaq in the experimental conditions previously mentioned allowed us to determine the first seven protonation constants at different ionic strength

ð10Þ

or H H log bH iM;M V ¼ ylog biM þ ð1  yÞlog biM V þ 4Di yð1  yÞ

ð11Þ

where Δi is a measure of the deviation from linearity:
 H H Di ¼ log bH iM þ log biM V =2  log biM;M V

ð12Þ

for y = 0.5. Negative Δi values mean lowering of protonation constants with respect to the ones calculated by (8) at y = 0.5.

Fig. 4. Fourth phytate protonation constants, as log KH 4 , in various ionic media at different ionic strengths and at t = 25 °C. □ = (C2H5)4NIaq; △ = LiClaq; ◯ = NaClaq; ▽ = KClaq; = CsClaq.

◇

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F. Crea et al. / Journal of Molecular Liquids 138 (2008) 76–83

Table 3 Alkali metal-proton-phytate complexes at t = 25 °C, at different ionic strengths Reaction

I/mol L− 1

log βji Li+

Phy + 6M = M6Phy a)

Phy + 5M + H = M5HPhy

Phy + 4M + 2 H = M4H2Phy

Phy + 3M + 3 H = M3H3Phy

Phy + 2M + 4 H = M2H4Phy

Phy + M + 5 H = MH5Phy

Phy + M + 6 H = MH6Phy

Phy + 2 M + 5 H = M2H5Phy

Phy + 3 M + 4 H = M3H4Phy

Phy + 4 M + 3 H = M4H3Phy

Phy + 5 M + 2 H = M5H2Phy

Phy + 6 M + H = M6HPhy

Phy + 7 M = M7Phy

0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1 0 0.1 0.5 1

b)

37.4 28.1 22.6 20.7 46.1 36.8 31.3 29.4 54.5 45.2 39.7 37.8 60.2 52.5 47.4 45.4 64.5 58.6 54.1 52.1 67.8 63.3 59.4 57.2 72.8 68.5 65.0 62.9 70.0 64.5 60.6 59.1 66.5 59.4 55.1 53.7 62.1 53.3 48.2 46.9 56.2 45.9 40.4 39.3 47.7 37.3 31.9 30.7 38.8 28.5 23.0 21.7

Na+ 35.1 25.9 20.3 18.4 43.3 34.0 28.5 26.6 52.6 43.3 37.8 35.9 59.0 51.3 46.2 44.1 63.9 57.9 53.5 51.4 67.4 62.9 59.0 56.8 72.4 68.2 64.6 62.6 69.4 63.9 60.0 58.5 65.6 58.6 54.2 52.9 60.7 51.9 46.9 45.5 53.8 43.5 38.0 36.9 45.1 34.8 29.3 28.1 36.2 25.9 20.4 19.3

b)

K+

b)

33.8 24.5 19.0 17.1 43.0 33.7 28.2 26.3 51.5 42.2 37.7 34.8 58.5 50.8 45.7 43.7 63.6 57.6 53.2 51.1 67.3 62.8 58.9 56.6 72.4 68.1 64.5 62.6 69.3 63.7 59.8 58.3 65.3 58.3 53.9 52.5 60.1 51.3 46.3 45.0 53.0 42.6 37.1 36.0 44.4 34.0 28.6 27.4 35.0 24.7 19.2 18.0

Cs+

c)

33.4 24.0 18.8 16.7 42.9 33.4 28.3 26.1 52.1 42.7 37.8 35.4 59.1 51.3 46.5 44.2 64.5 58.4 54.3 52.0 68.6 63.9 60.4 57.9 74.0 69.6 66.2 64.1 70.4 64.7 61.0 59.4 66.0 58.9 54.7 53.3 60.6 51.6 46.8 45.4 53.2 42.7 37.5 36.3 44.1 33.6 28.4 27.2 34.4 24.0 18.7 17.4

a)

M = Li+, Na+, K+ or Cs+, charges omitted for simplicity; b) Ref. [5]; c) this work, ±0.1–0.2 standard deviation.

values, as shown in Table 1. Worth of mention is that, as observed in other alkali metal cation ionic media, at I N 0.5 mol L− 1 the inversion in the stability of first three protonated species is observed in CsClaq too, i.e. logK1H N log K3H ≥ log K2H (the same trend is observed in KClaq, while we observed logK1H Nlog K2H N log K3H in LiClaq and logK2H N log K1H N log K3H in NaClaq).

This trend was already explained by other authors [16,17] for NaClaq. Slight differences with other alkaline cations may be “macroscopically” ascribed to the fact that first three phytate protonation steps are very similar in strength, and the different interacting ability of these cations may yield to slight variations in the stability of its various protonated species. This is better evidenced in Table 2, where log KiH values are reported at I = 1.0 mol L− 1, in order to compare protonation constants obtained in other simple ionic media. By analyzing these protonation data, it can be also noted that values obtained using alkali metal chlorides as supporting electrolytes are markedly lower than those found in (C2H5)4NIaq. In particular, the trend shown in Table 2 is ðC2 H5 Þ4 NI NN CsCl ≥ KCl ≥ NaCl N LiCl evidencing again [4,5] that strong interactions occur between phytate and alkali metal cations, with a trend that is the opposite of that shown by protonation constants (i.e., Li+ N Na+ ≥ K+ N Cs+), and the same of that reported by other authors [18]. The above reported trend for protonation constants can be better observed in Figs. 1–4, where the first four phytate protonation constants are reported, as log K1H, vs. ionic strength in various ionic media. The different interactions have already been explained in terms of complex formation between the various protonated phytate species and the alkali metal cations, being (C2H5)4NIaq considered as not interacting with this ligand [5]. According to the procedure already reported [5], cesium–proton–phytate stability constants have also been determined (Table 3), and the best speciation model obtained resulted in perfect agreement with that in LiClaq, NaClaq and KClaq: CsjHiPhy(12 − i − j)− species are all those where complex charge is 6− and 5−. Other authors also reported a net phytate charge of z = 5− in sodium aqueous media [16,17]. The analysis of Table 3, where complex formation constants for MjHiPhy(12 − i − j)− species (M+ = Li+, Na+, K+, Cs+) are reported at different ionic strengths, confirms that Li+ interacts with phytate more than the other alkali metal cations, whilst Cs+ shows the lower interacting ability (higher protonation constants). 4.2. Dependence of protonation constants on ionic strength We previously stated that phytate protonation constants in Table 1 proved to be fairly dependent on ionic strength (and on Table 4 Empirical parameters of Eq. (4) for the dependence of phytate protonation constants on ionic strength in CsClaq, at t = 25 °C i

a)

1 2 3 4 5 6 7 a) b) c)

log TβiH b)

ci∞

18.17 33.49 46.25 56.30 63.89 70.05 73.57

− 0.485 ± 0.006 − 0.359 ± 0.009 − 0.388 ± 0.008 − 0.276 ± 0.009 0.000 ± 0.005 0.217 ± 0.001 0.703 ± 0.007

ci0 c)

7.109 ± 0.010 9.728 ± 0.011 12.675 ± 0.009 14.633 ± 0.009 15.643 ± 0.007 16.620 ± 0.008 16.721 ± 0.002

Ai c)

6.767 ± 0.005 9.593 ± 0.006 10.320 ± 0.006 9.963 ± 0.004 9.360 ± 0.004 8.920 ± 0.005 7.961 ± 0.001

i index refers to phytate protonation step. + 12− Refs. [4,5], log βH = HiPhy(12 − i)−. i refers to equilibrium: i H + Phy ±standard deviation.

c)

F. Crea et al. / Journal of Molecular Liquids 138 (2008) 76–83

81

Table 5 Phytate protonation constants in CsClaq at different ionic strengths and at t = 25 °C, calculated by Eq. (4) a) I / mol L− 1 log βH (log KH 1 1)

0.10

10.42 ± 0.04

0.25

9.91 ± 0.02

0.50

9.79 ± 0.01

0.75

9.81 ± 0.01

1.00

9.82 ± 0.01

1.25

9.81 ± 0.01

1.50

9.77 ± 0.01

1.75

9.72 ± 0.01

a) b)

b)

a) log βH (log KH 2 2)

20.75 ± 0.03 (10.33) 19.72 ± 0.02 (9.81) 19.33 ± 0.01 (9.54) 19.24 ± 0.01 (9.43) 19.20 ± 0.01 (9.38) 19.16 ± 0.01 (9.35) 19.11 ± 0.01 (9.34) 19.05 ± 0.02 (9.33)

b)

a) log βH (log KH 3 3)

30.86 ± 0.03 (10.11) 29.43 ± 0.02 (9.71) 28.84 ± 0.01 (9.51) 28.68 ± 0.01 (9.44) 28.61 ± 0.01 (9.41) 28.55 ± 0.01 (9.39) 28.48 ± 0.01 (9.37) 28.40 ± 0.02 (9.35)

b)

a) log βH (log KH 4 4)

39.48 ± 0.03 (8.62) 37.61 ± 0.02 (8.18) 36.77 ± 0.01 (7.93) 36.51 ± 0.01 (7.83) 36.38 ± 0.01 (7.77) 36.29 ± 0.01 (7.74) 36.20 ± 0.01 (7.72) 36.11 ± 0.02 (7.71)

Table 6 Empirical parameters of Eq. (6) for the dependence of phytate protonation constants on ionic strength in alkali metal chloride aqueous solutions, at t = 25 °C

1 2 3 4 5 6 7 a)

a) log βH (log KH 5 5)

46.01 ± 0.03 (6.53) 43.69 ± 0.02 (6.08) 42.55 ± 0.01 (5.78) 42.15 ± 0.01 (5.64) 41.95 ± 0.01 (5.57) 41.82 ± 0.01 (5.53) 41.72 ± 0.01 (5.52) 41.64 ± 0.02 (5.53)

b)

a) log βH (log KH 6 6)

51.17 ± 0.03 (5.16) 48.46 ± 0.01 (4.77) 47.06 ± 0.02 (4.51) 46.55 ± 0.02 (4.40) 46.29 ± 0.02 (4.34) 46.14 ± 0.01 (4.32) 46.02 ± 0.01 (4.30) 45.93 ± 0.01 (4.29)

b)

a) log βH (log KH 7 7)

b)

54.35 ± 0.03 (3.18) 51.23 ± 0.02 (2.77) 49.55 ± 0.02 (2.49) 48.92 ± 0.02 (2.37) 48.62 ± 0.01 (2.33) 48.45 ± 0.01 (2.31) 48.36 ± 0.01 (2.34) 48.31 ± 0.02 (2.38)

+ 12− log βH = HiPhy(12 − i)−; ± standard deviation. i refers to equilibrium: i H + Phy H log Ki in parenthesis refers to equilibrium: H+ + Hi − 1Phy(12 − i)− = HiPhy(12 − i)−.

ionic medium). This dependence was modeled by Eq. (4) that, as explained above, shows both analogies and slight differences with respect to Eq. (6), already used for the modeling of ionic strength dependence of phytate protonation constants in other alkali metal chloride aqueous media [4,5]. Table 4 reports refined parameters of Eq. (4) and protonation constants at infinite dilution taken from refs. [4,5], while corresponding values calculated by these parameters in CsClaq in the ionic strength range 0.1 ≤ I/mol L− 1 ≤ 1.75 are shown in Table 5. The quality of fits obtained by this equation is significantly better than those achieved by Eq. (6), as expressed by mean deviations on the whole fits: m.d. = 0.02 for Eq. (4) vs. m.d. = 0.08 for Eq. (6). In fact, for comparison we also fitted protonation constants in Table 1 to Eq. (6), by means of log TKiH and Ci parameters previously obtained for other alkali metal chloride aqueous media [5] and refining DiM parameters for cesium cation, and we obtained that mean deviation value. These parameters are reported in Table 6 together with corresponding DiM values calculated for other alkali metal cations (i.e., Li+, Na+, K+). A regular trend in the DiM (generally, DiLi N DiNa N DiK N DiCs) values, strictly linked

i

b)

a)

logTKiH 18.17 15.32 12.76 10.05 7.59 6.13 3.52

b)

b)

DiLi

0.13 0.12 0.06 0.08 0.13 0.14 0.27

9.47 6.88 5.14 3.46 2.32 2.10 1.87

Ci

b)

DiNa 9.59 6.50 4.27 2.91 2.06 1.83 1.56

b)

DiK 8.94 6.83 3.84 2.68 1.94 1.71 1.50

b)

DiCs

c)

8.57 ± 0.03 6.07 ± 0.02 3.45 ± 0.03 2.37 ± 0.03 2.12 ± 0.02 1.92 ± 0.02 1.41 ± 0.01

i index refers to phytate protonation step; b) Refs. [4,5]; c) this work; ±standard deviation.

to the different interacting nature of investigated alkali metal cations toward phytate, can be also observed [5]. 4.3. Protonation constants in LiClaq–CsClaq mixtures Experimental details for the composition of background salt solutions for measurements in LiClaq–CsClaq mixtures are given in Table 7. The corresponding phytate protonation constants are reported in Table 8 for different mole fractions. As described in Section 3, these constants do not follow an ideal behavior, i.e. they are not linear function of the mole fraction y. This is better evidenced in Fig. 5 where, for example, log β1H determined in LiClaq–CsClaq mixtures at ITOT = 1.28 mol L− 1 are plotted vs. y. In this figure a dotted straight line, representing the ideal behavior, is drawn between log β1H at y = 0 (log β1H in pure CsClaq solution) and at y = 1 (log β1H in pure LiClaq solution). Curve in the same Figure corresponds to fit of Eq. (11), which has been used to model the dependence of phytate protonation constants on y, allowing us to calculate the Δi values reported in Table 9 together with corresponding ΔGimix [by Eq. (13)]. We already stated in Section 3 that positive

Table 7 Experimental details for potentiometric measurements in LiClaq–CsClaq mixtures, at t = 25 °C CLi

a)

1.249 0.994 0.752 0.497 0.255 0.000 a) c)

CCs

a)

0.000 0.253 0.505 0.743 0.996 1.248

y

b)

1.000 0.797 0.598 0.401 0.204 0.000

ITOT a) 1.279 1.275 1.284 1.267 1.276 1.275 1.278 ± 0.006 c)

In mol L− 1; b) y = CLi/(CLi + CCs). Mean total ionic strength value for all titrations, ±standard deviation.

82

F. Crea et al. / Journal of Molecular Liquids 138 (2008) 76–83

Table 8 Phytate protonation constants in LiClaq–CsClaq mixtures, at ITOT = 1.28 mol L− 1 and t = 25 °C y

a)

b) log βH (log KH 1 1)

1.000

8.55 ± 0.04

0.797

8.49 ± 0.02

0.598

8.53 ± 0.02

0.401

8.69 ± 0.02

0.204

9.06 ± 0.02

0.000

9.71 ± 0.04

c)

b) log βH (log KH 2 2)

17.00 ± 0.04 (8.45) 17.00 ± 0.03 (8.51) 17.13 ± 0.02 (8.60) 17.46 ± 0.02 (8.77) 18.00 ± 0.03 (8.94) 19.06 ± 0.04 (9.35)

c)

b) log βH (log KH 3 3)

24.33 ± 0.05 (7.33) 24.62 ± 0.03 (7.62) 25.03 ± 0.03 (7.90) 25.70 ± 0.03 (8.24) 26.68 ± 0.03 (8.68) 28.33 ± 0.06 (9.27)

c)

b) log βH (log KH 4 4)

c)

30.55 ± 0.06 (6.22) 31.14 ± 0.04 (6.52) 31.77 ± 0.04 (6.74) 32.70 ± 0.04 (7.00) 33.99 ± 0.04 (7.31) 36.03 ± 0.06 (7.70)

b) log βH (log KH 5 5)

c)

35.60 ± 0.07 (5.05) 36.31 ± 0.04 (5.17) 37.03 ± 0.04 (5.26) 38.04 ± 0.04 (5.34) 39.46 ± 0.04 (5.47) 41.62 ± 0.06 (5.59)

+ 12− y = CLi/(CLi + CCs);b) log βH = HiPhy(12 − i)−; ± standard deviation; i refers to equilibrium: i H + Phy (12 − i + 1)− (12 − i)− = HiPhy . H + Hi − 1Phy

a)

b) log βH (log KH 6 6)

38.87 ± 0.07 (3.27) 40.05 ± 0.04 (3.74) 40.98 ± 0.04 (3.95) 42.17 ± 0.04 (4.13) 43.74 ± 0.04 (4.28) 45.98 ± 0.07 (4.36) c)

c)

b) log βH (log KH 7 7)

c)

40.85 ± 0.07 (1.98) 42.06 ± 0.04 (2.01) 43.02 ± 0.04 (2.04) 44.27 ± 0.04 (2.10) 45.90 ± 0.04 (2.16) 48.27 ± 0.07 (2.29)

log KH i in parenthesis refers to equilibrium:

+

ΔGimix values indicate that the formation of simple or ternary weak complexes is preferred with respect to the protonation reactions. Therefore, as an alternative procedure to the calculations of ΔGimix values, the deviation from linearity of phytate protonation constants in LiClaq–CsClaq mixtures can interpreted in terms of formation of simple and mixed metal complexes:
 q q H ð14Þ log bH iLi;Cs ¼ log biCs  log 1 þ bLi CLi þ bLi;Cs CLi CCs Phytate protonation constants in LiClaq–CsClaq mixtures are given by the values of corresponding constants in the “less interacting” pure electrolyte (CsClaq in this case) lowered by a term that takes simultaneously into account the formation of both simple phytate metal complexes with the most interacting cation (i.e., βLi) and mixed metal complexes (i.e., βLi,Cs). Both βLi and βLi,Cs can be considered as a combination of formation constants of different simple [LijHiPhy(12 − i − j)−] and mixed [LijCsj'HiPhy(12 − i − j)−] species, respectively. Exponent q of lithium total concentrations accounts for this possibility. In the case of first phytate protonation constants, we calculated (± standard deviation): log βLi = 1.03 ± 0.01, log βLi,Cs = 1.62 ±

0.02, and q = 1.72 ± 0.04, with a standard deviation on the whole fit of σ = 0.10. 5. Conclusions Our main conclusions on the study of phytate acid–base properties both in simple CsClaq solutions at different ionic strengths and in LiClaq–CsClaq mixtures can be summarized as follows: a) dependence of phytate protonation constants on ionic strength in CsClaq media has been modeled by a Debye– Hückel type equation; b) interactions among different phytate protonated species and Cs+ ions proved to be weaker (but of the same order of magnitude) than those involving other investigated alkali metal cations (Li+, Na+, K+); c) in analogy with previously investigated systems, these interactions have been expressed in terms of formation of thirteen weak CsjHiPhy(12 − i − j)− complexes (i.e., all those where the complex charge is 6− and 5−); d) corresponding formation constants at different ionic strengths have been calculated and compared with those of analogue MjHiPhy(12 − i − j)− complexes (M+ = Li+, Na+, K+); e) phytate protonation constants in LiClaq–CsClaq mixtures at I = 1.28 mol L− 1 and different Li+/Cs+ mole fractions have been determined here for the first time and showed a nonTable 9 Parameters of Eqs. (9) and (10) for phytate protonation in LiClaq–CsClaq mixtures at ITOT = 1.28 mol L− 1 and t = 25 °C log βH i

Fig. 5. First phytate protonation constants, as log βH 1 , vs. y [y = CLi / (CLi + CCs)] in LiClaq–CsClaq mixtures, at ITOT = 1.28 mol L− 1 and t = 25 °C.

log log log log log log log a)

βH 1 βH 2 βH 3 H β4 βH 5 βH 6 βH 7

Δi

a)

− 0.54 ± 0.07 − 0.78 ± 0.08 − 1.01 ± 0.10 − 1.10 ± 0.12 − 1.12 ± 0.12 − 0.87 ± 0.13 − 0.94 ± 0.14

a) log βH iLi

a) log βH iCs

ΔGimix

8.57 ± 0.07 17.04 ± 0.08 24.39 ± 0.10 30.62 ± 0.11 35.68 ± 0.13 38.98 ± 0.14 40.97 ± 0.14

9.68 ± 0.07 19.01 ± 0.09 28.27 ± 0.11 35.95 ± 0.12 41.54 ± 0.12 45.88 ± 0.13 48.17 ± 0.13

3.1 ± 0.4 4.4 ± 0.5 5.8 ± 0.6 6.3 ± 0.7 6.4 ± 0.7 5.0 ± 0.8 5.4 ± 0.8

±standard deviation; b) in kJ mol− 1.

a, b)

σ(fit) 0.033 0.057 0.084 0.104 0.111 0.139 0.147

F. Crea et al. / Journal of Molecular Liquids 138 (2008) 76–83

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