Received Date: September 21, 2017; Accepted Date: October 04, 2017; Published Date:October 07, 2017
Citation:MichaÃ Âowska-Kaczmarczyk AM, Spórna-Kucab A, MichaÃ Âowski T (2017) Dynamic Buffer Capacities in Redox Systems. Biochem Mol Biol J. Vol.3 No. 3:11 DOI: 10.21767/2471-8084.100039
The buffer capacity concept is extended on dynamic redox systems, realized according to titrimetric mode, where changes in pH are accompanied by changes in potential E values; it is the basic novelty of this paper. Two examples of monotonic course of the related curves of potential E vs. and pH vs. Φ relationships were considered. The systems were modeled according to GATES/GEB principles.
Thermodynamics of electrolytic redox systems; Buffer capacity; GATES/GEB.
The buffer capacity concept is usually referred to as a measure of resistance of a solution (D) on pH change, affected by an acid or base, added as a titrant T, i.e., according to titrimetric mode; in this case, D is termed as titrand.
The titration is a dynamic procedure, where V mL of titrant T, containing a reagent B (C mol/L), is added into V0 mL of titrand D, containing a substance A (C0 mol/L). The advance of a titration B(C,V) ⇒ A(C0,V0), denoted for brevity as B ⇒ A is characterized by the fraction titrated [1-4]
That introduces a kind of normalization (independence on V0 value) for titration curves, expressed by pH=pH(Φ), and E=E(Φ) for potential E [V] expressed in SHE scale. The redox systems with one, two or more electron-active elements are modeled according to principles of Generalized Approach to Electrolytic Systems with Generalized Electron Balance involved (GATES/GEB), described in details in [5-16], and in references to other authors' papers cited therein.
According to earlier conviction expressed by Gran , all titration curves: pH=pH(Φ) and E=E(Φ), were perceived as monotonic; that generalizing statement is not true , however. According to contemporary knowledge, full diversity in this regard is stated, namely: (1o) monotonic pH=pH(Φ) and monotonic E=E(Φ) [18- 20]; (2o) monotonic pH=pH(Φ) and non-monotonic E=E(Φ) ; (3o) non-monotonic pH=pH(Φ) and monotonic E=E(Φ) ; (4o) non-monotonic pH=pH(Φ), and non-monotonic E=E(Φ) .
In this paper, we refer to the disproportionating systems: (S1) NaOH ⇒ HIO and (S2) HCl ⇒ NaIO, characterized by monotonic changes of pH and E values during the related titrations (i.e., the case 1o). In both instances, the values: V0=100, C0=0.01, and C=0.1 were assumed. The set of equilibrium data [18-20] applied in calculations, presented in Table 1, is completed by the solubility of solid iodine, I2(s), in water, equal 1.33Ã¢ÂÂ10-3 mol/L. The related algorithms, prepared in MATLAB for S1 (NaOH ⇒ HIO) S2 (HCl ⇒ NaIO) system according to the GATES/GEB principles, are presented in Appendices 1 and 2.
|No.||Reaction||Equilibrium equation||Equilibrium data|
|1||I2 + 2e–1=2I–1 (for dissolved I2 )||[I–1]2=Ke1·[I2][e–1]2||E01=0.621 V|
|2||I3–1 + 2e–1=3I–1||[I–1]3=Ke2·[I3–1][e–1]2||E02=0.545 V|
|3||IO–1 + H2O + 2e–1=I–1 + 2OH–1||[I–1][OH–1]2=Ke3·[IO–1][e–1]2||E03=0.49 V|
|4||IO3–1 + 6H+1 + 6e–1=I–1 + 3H2O||[I–1]=Ke4·[IO3–1][H+1]6[e–1]6||E04=1.08 V|
|5||H5IO6 + 7H+1 + 8e–1=I–1 + 6H2O||[I–1]=Ke5·[H5IO6][H+1]7[e–1]8||E05=1.24 V|
|6||H3IO6–2 + 3H2O + 8e–1=I–1 + 9OH–1||[I–1][OH–1]9=Ke6·[H3IO6–2][e–1]8||E06=0.37 V|
|7||HIO=H+1 + IO–1||[H+1][IO–1]=K11I·[HIO]||pK11I=10.6|
|8||HIO3=H+1 + IO3–1||[H+1][IO3–1]=K51I·[HIO3]||pK51I=0.79|
|9||H4IO6–1=H+1 + H3IO6–2||[H+1][H3IO6–2]=K72·[H4IO6–1]||pK72=3.3|
|10||Cl2 + 2e–1=2Cl–1||[Cl–1]2=Ke7·[Cl2][e–1]2||E07=1.359 V|
|11||ClO–1 + H2O + 2e–1=Cl–1 + 2OH–1||[Cl–1][OH–1]2=Ke8·[ClO–1][e–1]2||E08=0.88 V|
|12||ClO2–1 + 2H2O + 4e–1=Cl–1 + 4OH–1||[Cl–1][OH–1]4=Ke9·[ClO2–1][e–1]4||E09=0.77 V|
|13||HClO=H+1` + ClO–1||[H+1][ClO–1]=K11Cl·[HClO]||pK11Cl=7.3|
|14||HClO2 + 3H+1 + 4e–1=Cl–1 + 2H2O||[Cl–1]=Ke10·[HClO2][H+1]3[e–1]4||E010=1.56 V|
|15||ClO2 + 4H+1 + 5e–1=Cl–1 + 4H2O||[Cl–1]=Ke11·[ClO2][H+1]4[e–1]4||E011=1.50 V|
|16||ClO3–1 + 6H+1 + 6e–1=Cl–1 + 3H2O||[Cl–1]=Ke12·[ClO3–1][H+1]6[e–1]6||E012=1.45 V|
|17||ClO4–1 + 8H+1 + 8e–1=Cl–1 + 4H2O||[Cl–1]=Ke13·[ClO4–1][H+1]8[e–1]8||E013=1.38 V|
|18||2ICl + 2e–1=I2 + 2Cl–1||[I2 ][Cl–1]2=Ke14·[ICl]2[e–1]2||E014=1.105 V|
|19||I2Cl–1=I2 + Cl–1||[I2 ][Cl–1]=K1·[I2Cl–1]||logK1=0.2|
|20||ICl2–1=ICl + Cl–1||[ICl][Cl–1]=K2·[ICl2–1]||logK2=2.2|
|21||H2O=H+1 + OH-1||[H+1][OH-1]=KW||pKW=14.0|
Table 1: Physicochemical data related to the systems S1 and S2.
The titration curves: pH=pH(Φ) and E=E(Φ) presented in Figures 1 and 2 are the basis to formulation of dynamic buffer capacities in the systems S1 and S2.
Dynamic acid-base buffer capacities βV and BV
Dynamic buffer capacity was referred previously only to acid base equilibria in non-redox systems [3,21-23]. However, the dynamic (βV) and windowed (BV) buffer capacities can be also related to acid-base equilibria in redox systems. The βV is formulated as follows [3,21].
It is the current concentration of B in D+T mixture, at any point of the titration. In the simplest case, D is a solution of one substance A (C0 mol/L), and then Equation 3 can be rewritten as follows
where Φ is the fraction titrated (Equation 1). Then we get
is the sharpness index on the titration curve. For comparative purposes, the absolute values,|βV| and |η|, for βV (Equations 1 and 5) and η (Equation 6) are considered. At C0/C << 1 and small Φ value, from Equation 3 we get
The βV value is the point–assessment and then cannot be used in the case of finite pH–changes (ΔpH) corresponding to an addition of a finite volume of titrant (βV is a non–linear function of pH). For this purpose, the ‘windowed’ buffer capacity, BV, defined by the formula [3,21].
has been suggested. From extension in Taylor series we have
From Equations 7 and 9 we see that βV is the first approximation of BV. One should take here into account that finite changes (ΔpH) in pH, e.g. ΔpH=1, are involved with addition of a finite volume of a reagent endowed with acid–base properties, here: base NaOH, of a finite concentration, C.
Dynamic redox buffer capacities and
In similar manner, one can formulate dynamic buffer capacities and , involved with infinitesimal and finite changes of potential E values:
Where c is defined by Equation 2, and then we have
Graphical presentation of dynamic buffer capacities in redox systems
Referring to dynamic redox systems represented by titration curves presented in Figures 1 and 2, we plot the relationships: βV vs. Φ, βV vs. pH, βV vs. E, and βEV vs. Φ, βEV vs. pH, βEV vs. E for the systems: (S1) NaOH ⇒ HIO; (S2) HCl ⇒ NaIO. The relations: (A) βV vs. Φ, (B) βV vs. pH, (C) βV vs. E and (D) βEV vs. Φ, (E) βEV vs. pH, (F) βEV vs. E are plotted in Figures 3 and 4.
Disproportionation of the solutes considered (HIO or NaIO) in D occurs directly after introducing them into pure water. The disproportionation is intensified, by greater pH changes, after addition of the respective titrants: NaOH (in S1) or HCl (in S2), and the monotonic changes of E=E(Φ) and pH=pH(Φ) occur in all instances.
All attainable equilibrium data related to these systems are included in the algorithms implemented in the MATLAB computer program (see Appendices 1 and 2). In all instances, the system of equations was composed of: generalized electron balance (GEB), charge balance (ChB) and concentration balances for particular elements ≠ H, O.
In the system S1, the precipitate of solid iodine, I2(s), is formed, see Figure 5. In the (relatively simple) redox system S2, we have all four basic kinds of reactions; except redox and acid-base reactions, the solid iodine (I2(s)) is precipitated and soluble complexes: I2Cl-1, ICl and ICl2-1 are formed, see Figure 6A. Note that I2(s) + I-1=I3-1 is also the complexation reaction.
In the system S2, all oxidized forms of Cl-1 were involved, i.e. the oxidation of Cl-1 ions was thus pre-assumed. This way, full “democracy” was assumed, with no simplifications [18-20]. However, from the calculations we see that HCl acts primarily as a disproportionating, and not as reducing agent. The oxidation of Cl-1 occurred here only in an insignificant degree (Figure 6B); the main product of the oxidation was Cl2, whose concentration was on the level ca. 10-16-10-17 mol/L.
The redox buffer capacity concepts: βV and βEV can be principally related to monotonic functions. This concept looks awkwardly for non-monotonic functions pH=pH(Φ) and/or E=E(Φ) specified above (2o–4o) and exemplified in Figures 7-9 presented in Appendix 3. For comparison, in isohydric (acid-base) systems, the buffer capacity strives for infinity. In particular, it occurs in the titration HB (C,V) ⇒ HL (C0,V0), where HB is a strong monoprotic acid HB and HL is a weak monoprotic acid characterized by the dissociation constant K1=[H+1][L-1]/[HL]; at 4KW/C2<<1, the isohydricity condition is expressed here by the MichaÃ Âowski formula [24-26].
The formula for the buffer capacity, suggested by Bard et al.  after Levie , is not correct. Moreover, it involves formal potential value, perceived as a kind of conditional equilibrium constant idea, put in (apparent) analogy with the simplest static acid-base buffer capacity, see criticizing remarks in the study by MichaÃ Âowska-Kaczmarczyk et al. ; it is not adaptable for real redox systems.
Buffered solutions are commonly applied in different procedures involved with classical (titrimetric, gravimetric) and instrumental analyses [30-33]. There are in close relevance to isohydric solutions [24-26] and pH-static titration [4,34], and titration in binary-solvent systems [12,35]. Buffering property is usually referred to an action of an external agent (mainly: strong acid, HB, or strong base, MOH) inducing pH change, ΔpH, of the solution. Redox buffer capacity is also involved with the problem of interfacing in CE-MS analysis, and bubbles formation in reaction 2 H2O=O2(g) + 4H+1 + 4e-1 at the outlet electrode in CE [36-39].
In the paper, a nice proposal of “slyke”, as the name for (acid- base, pH) buffer capacity unit, has been raised .
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