- Email: [email protected]
water mixtures as solvent
Electrochimica Acta 52 (2007) 5773–5780
Electrochemical determination of acidity level and dissociation of formic acid/water mixtures as solvent J.S. Jaime Ferrer, E. Couallier, M. Rakib, G. Durand ∗,1 Laboratoire de G´enie des Proc´ed´es et Mat´eriaux, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chˆatenay-Malabry Cedex, France Received 10 October 2006; received in revised form 23 February 2007; accepted 24 February 2007 Available online 1 March 2007
Abstract The autoprotolysis constant KHS of formic acid/water mixtures as solvent has been calculated from acid–base potentiometric titration curves. A correlation of the acidity scale pKHS of each medium versus pure water has been implemented owing to the Strehlow R0 (H+ ) electrochemical redox function. The results show that formic acid/water mixtures are much more dissociated than pure water; such media are sufficiently dissociated to allow electrochemical measures without addition of an electrolyte. It has also been shown that for a same H+ concentration the activity of protons increases with formic acid concentration. For more than 80 wt.% of formic acid the acidity is sufficiently increased to locate the whole acidity scale pKHS in the super acid medium of the generalized acidity scale pHH2 O . © 2007 Elsevier Ltd. All rights reserved. Keywords: Acidity scale; Autoprotolysis constant; Formic acid; Formic acid/water mixtures; Redox function
1. Introduction Formic acid is an alternative fuel to methanol in direct fuel cells for portable power applications. Many papers have recently been published concerning direct formic acid fuel cells (DFAFCs) [1–13]. In these polymer electrolyte membrane fuel cells (PEMFCs) formic acid is oxidised directly into carbon dioxide and H+ ions, which cross the membrane to the cathodic compartment and produce water from oxygen (air) reduction. Some advantages of formic acid for such devices are its strong dissociation (no need for electrolyte), the high theoretical voltage of the corresponding fuel cell (1.45 V for formic acid/oxygen system) and the possibility of operating with high formic acid concentrations (i.e., high power density with respect to the fuel volume) without strong leakage through the membrane. In fact, formic acid is not used pure but mixed with water. Several authors have shown that an optimum concentration of formic acid is required for best fuel cell performances. Rice et al. [1] empirically showed that an optimum formic acid concentration must be used, around 50/50 wt.% water–formic acid
∗ 1
Corresponding author. Tel.: +33 1 41 13 12 13; fax: +33 1 41 13 11 63. E-mail address: [email protected] (G. Durand). ISE member.
0013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2007.02.058
mixture. Replacing platinum black electrocatalyst with a Pd/C one, Ha et al. [8] recently showed that the optimum could be a 40/60 wt.% mixture. Another limitation of DFAFC pointed out by several authors is formic acid leakage through Nafion® membranes. Rhee et al. [2] observed that more formic acid permeates through the membrane when the formic acid reservoir is filled with 10 mol dm−3 formic acid than with 20 mol dm−3 formic acid. Miesse et al. [13] recently implemented a DFAFC portable power supply for a laptop computer and showed that the optimum formic acid concentration for this device is around 6 mol dm−3 . They also suggested that the decrease in performance over 6 mol dm−3 is due to formic acid leakage through the membrane. Formic acid is also a chemical widely used in many industries, such as textiles, natural rubber, leather processing, agriculture, cosmetics, disinfectants, detergents and pharmaceuticals. In textile manufacturing formic acid is used mainly in cellulose spinning. In this process further fibber washing steps lead to effluents containing diluted sodium formate. Considering this solution as a waste, it might be valuable to split this salt to recycle concentrated formic acid. The more concentrated the recycled formic acid, the more profitable should be the recycling process. Some works have already been done by Luo et al. [14,15] on formic acid concentration by electromembrane processes. But these authors do not really study formic acid
5774
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
regeneration from formate salt, only acid concentration. Jaime Ferrer et al. [16] studied a whole process coupling electrodialysis and bipolar membrane electrodialysis for diluted (0.1 mol dm−3 ) sodium formate splitting to produce concentrated formic acid (7 mol dm−3 ). Problems were encountered: leakages through the membranes and consequently limitation of HCOOH concentration reachable, questions about physicochemical behaviour of the concentrated solution when formic acid concentration increased from 1 to 7 mol dm−3 . The present work was stimulated by these studies on formic acid regeneration by electromembrane processes in order to understand limitations of the process. The first question concerns the degree of dissociation of formic acid/water mixtures. This point is important in electrodialysis. As formic acid is a weak acid in water (pKa = 3.7), do we consider that highly concentrated solutions of formic acid remain weakly dissociated [14]? The answer may be obtained by determining the value of the autoprotolysis constant KHS (pKHS = −log KHS ) of each formic acid/water solvent in different proportions. The pKHS values may be obtained from strong acid/strong base potentiometric titrations in each solvent [17–20]. The second question concerns the acidity levels of the formic acid/water mixtures compared to pure water. A correlation of all acidity scales’ zero point versus a generalized pHH2 O scale (referred to pH scale in water) would allow to know the variations of proton activity during formic acid concentration. Such a correlation between acidity scales in various solvents has been widely described [18]. It would also help explain proton leakage and the corrosion power of highly concentrated formic acid solutions. 2. Experimental 2.1. Apparatus Titrations were done with a Metrohm 736 GP Titrino apparatus. Acquisition and processing of data have been done by the TiNet 2.4 software. Acidity was measured with a combined glass/reference electrode Metrohm 6.0299.100 Solvotrode, the reference electrode being Ag/AgCl/LiCl sat. in ethanol. Current–potential curves were recorded with a PARSTAT® 2263 potentiostat/galvanostat from Princeton Applied Research (AMETEK Inc.). The Power PULSE® module from the Power SUITE® software was used to exploit the current–potential curves. The reference electrode was homemade. It was the Ag/AgCl/KClsat. system in each water–formic acid medium. The working electrode was platinum rotating disc electrode EDI 101 (2 mm diameter) connected with a speed control unit, CTV 101 from Radiometer Analytical. For the H+ /H2 electrochemical system the platinum disc was platinized according to the following recipe: H2 PtCl6 3.5% + Pb(CH3 COO)2 0.005% (w/v) in water, 1000 rpm, E = −200 mV/SCE, t = 90 s. The auxiliary electrode was a platinum wire from Radiometer Analytical.
Water traces in pure formic acid were controlled by Karl Fischer titration with a coulometric titrator, aquaprocessor type, from Radiometer Analytical. 2.2. Chemicals Formic acid 97% from Avocado Organics was used for the formic acid/water mixtures. Formic acid 99–100% NORMAPURTM for analysis from VWR Prolabo was used for pure formic acid medium. Perchloric acid 70% for analysis from Fisher Chemicals, pellets of sodium hydroxide 98% and sodium formate 98% from Avocado Organics were used for acid–base titrations. Potassium chloride for analysis used for the reference electrode was from Acros Organics. Ferrocene [bis(cyclopentadienyl)iron] 99% pure was from Avocado Organics. 3. Results and discussion 3.1. Potentiometric determination of autoprotolysis constant 3.1.1. Theory In formic acid/water mixtures the autoprotolysis (or autosolvolysis) reaction is H2 O + HCOOH ⇔ H3 O+ + HCOO−
(1)
with KHS = [H3 O+ ][HCOO− ]
(2)
H3 O+ the solvated proton, also written H+ , is the strong acid; HCOO− is the strong base. So KHS value may be calculated from strong acid/strong base potentiometric titration curves between the pH values for [H3 O+ ] = 1 mol dm−3 (pH 0) and for [HCOO− ] = 1 mol dm−3 (pH = pKHS = −log KHS ). But this computation from two experimental points is imprecise. The best way is to compute the whole titration curve and to fit it with the experimental one. In formic acid/water mixtures, perchloric acid HClO4 is always a strong acid, and sodium hydroxide NaOH always a strong base [18] according to the solvolysis reactions: HCOOH + HClO4 ⇒ HCOOH2 + + ClO4 −
(3)
where HCOOH2 + is the solvated proton, written H+ and HCOOH + NaOH ⇒ HCOO− + Na+ + H2 O
(4)
where HCOO− is the strong base. So NaOH or sodium formate NaHCOO may be used as a strong base in formic acid/water mixtures. In pure water the strong acid/strong base reaction is H+ + (ClO4 − ) + OH− + (Na+ ) ⇔ H2 O + (Na+ ) + (ClO4 − )
(5)
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
in formic acid/water mixtures it is H+ + (ClO4 − ) + HCOO− + (Na+ ) ⇔ HCOOH + (Na+ ) + (ClO4 − )
(6)
All along titration the electroneutrality equation is [H+ ] + [Na+ ] = [HCOO− ] + [ClO4 − ]
(7)
3.1.2. Results Perchloric acid has been titrated by sodium hydroxide or sodium formate in pure water and in formic acid/water mixtures, varying formic acid from 4.6 to 98.3 wt.%. Titration curves have been recorded (E = f(V)). All titration curves have been collected on the same graph (Fig. 1). As foreseen, the curves are gradually translated when the solvent becomes different from water because of the additional junction potential. For each titration, the potential difference between the first part of the curve (acidic media) and the second part (basic media) is correlated to the solvent pKHS (relations
If a volume V0 of HClO4 , the concentration of which is CHClO4 , is titrated by addition of a volume V of a CNaHCOO solution of the strong base, and owing to relations (2) and (6)–(7), the H+ concentration may be calculated from the relation: −(VCNaHCOO − V0 CHClO4 )/(V0 + V ) + [(VCNaHCOO − V0 CHClO4 )/(V0 + V )]2 + 4KHS [H+ ] = 2 Nicolsky [21] and other authors [22,23] have shown that the emf of an electrochemical cell including a glass electrode is E = E0 +
2.3RT log aH + F
(9)
where R is the ideal gas constant (8.314 J K−1 mol−1 ); T the temperature (K); F the Faraday constant (96,485.34 C mol−1 ); aH+ is the activity of protons, linked to concentration and activity coefficient γH+ by the relation: aH+ = γH+ [H+ ]
(10)
Difficulties in computing activity coefficients in water lead to measure E versus H+ concentrations in solutions of constant ionic strength so that γH+ is constant (even = 1). The non-ideality of solutions is then included in E0 , with
E0 = E0 +
2.3RT log γH+ F
(11)
The use of a glass electrode (often with an aqueous inner solution) in non aqueous media introduces other deviations from ideality. But it has been shown [23] that the glass electrode is always usable in such media to measure H+ concentrations, with a linear relation E versus log[H+ ]. So combining relations (9)–(11), the H+ concentration may be measured from glass electrode potential according to E−E0
5775
(8)
(2), (5) and (6)). So at first sight it appears that pKHS strongly decreases from pure water (curve 1) to pure formic acid (curve 15), passing through a minimum. The very small potential variations appearing on Fig. 1 show that only fitting between experimental and calculated curves will allow one to obtain precisely the pKHS value of each solvent. Each theoretical curve is computed from relations (8) and (12), knowing CHClO4 , CNaHCOO , V0 , V, postulating the theoretical value for the glass electrode response (2.3RT/F) and estimating a pKHS value. Calculation is done for a lot of E/V couples of points (with a V increment of 0.01 cm3 and for E0 = 0). Fitting between experimental and calculated curves is achieved with Excel software according to the following steps. The experimental curve is first translated along the E-axis, so that the acidic part of the titration curve is fitted with the calculated one. This translation is justified by the fact that the experimental value of E0 is not known (the glass electrode is not standardized in formic acid mixtures). Then the theoretical curve is computed again, varying pKHS value until the whole experimental and calculated curves are superimposable. An example is given Fig. 2 where only some calculated couples of points E/V are reported for a best visibility of the fitting.
[H+ ] = 10 2.3RT/F
(12)
E − E0 is the sum of all potential differences of the potentiometric chain, including that of the reference electrode. When the combined glass/reference electrode is dipped in different solvents (formic acid/water of various percentages) the junction potential between the reference electrode (in ethanol media) and the solution is not constant. Its variation may be large. Besides, the asymmetry potential of the glass electrode also varies on account of the differences between the inner solution (aqueous) and outer one (formic acid/water mixtures). So E0 values, including junction and asymmetry potentials, are different in each formic acid/water solvent. Thus it is not possible to compare the experimental curves between them. But in a given solvent, E0 value is constant during the whole titration.
Fig. 1. Titration curves of ≈0.2 M HClO4 by a 5 M strong base (NaOH or NaHCOO) in formic acid/water mixtures as solvent. Formic acid percentages (by wt.) are: (1) 0%, (2) 4.6%, (3) 9.0%, (4) 17.7%, (5) 26.0%, (6) 34.1%, (7) 41.9%, (8) 49.5%, (9) 56.9%, (10) 64.1%, (11) 71.1%, (12) 77.9%, (13) 84.6%, (14) 96.6% and (15) 98.3%.
5776
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
Fig. 2. Experimental curve for titration of 0.28 M HClO4 by 5 M NaHCOO in formic acid/water 71.1/28.9 wt.%; () calculated curve (the potential scale is shift from experimental one by E0 value).
In order to check that the experimental glass electrode response is always close to the theoretical (and postulated) one, each experimental curve is straightened for the fitted pKHS values. The average 2.3RT/F values obtained (Table 1) are always close to the theoretical one at 20 ◦ C and then justify the former hypothesis. So autoprotolysis constants KHS values are obtained by fitting experimental and calculated titration curves for each formic acid/water mixture. The corresponding values of pKHS are collected in Table 1. Fig. 3 shows the variations of pKHS from pure water to “pure” formic acid (98.3% i.e. ≈1.1 mol dm−3 residual water). The three series of experiments point to a good reproducibility of values. The curve shows a strong and rapid decrease of pKHS when formic acid is added to water. pKHS value is minimum for about 50/50 wt.% water–formic acid mixture and then increases again, the more when formic acid is pure. In fact, a small value of pKHS means a high value of the autoprotolysis constant KHS , and then a great dissociation of the solvent. The graph shows that formic acid/water mixtures are more dissociated than pure water, and then are more conducting media. The maximum of dissociation is obtained for the range 25–65 wt.% HCOOH. In 50/50 wt.% formic acid/water mixture, for example,
Fig. 3. Experimental values of autoprotolysis constant pKHS in formic acid/water mixtures. () First series of measures, () second series, ( ) third series (the point for pure water, pKHS = 14, is omitted).
the pKHS value shows that [H+ ] = [HCOO− ] = 0.07 mol dm−3 . In this case, the conductivity increase may be enough to carry out electrochemical measurements without addition of an electrolyte. 3.2. Correlation of acidity scales 3.2.1. Theory As shown above, the acidity scales, i.e., the number of pH units reachable in formic acid/water mixtures as solvents, strongly vary from pure water (pH = 14) to pure formic acid (pH ≈ 5), passing through a minimum (pH ≈ 2.3) for 50/50 wt.% mixture. But the values, pH 0 in water and in each formic acid/water mixture, are not comparable. What is obtained in each solvent (and water) is [H+ ] = 1 mol dm−3 . But a same concentration of H+ ions do not imply a same activity of proton. In a given solvent the activity of an ion i is linked to its concentration by the relation ai = γi ci . In the same way the activities of an ion i at the same concentration in water and in another solvent are bound by
Table 1 pKHS values of formic acid/water mixtures as solvents (for three series of titration) HCOOH
First series
Second series
Third series
mol dm−3
wt.%
Slope (V)
pKHS
Slope (V)
pKHS
Slope (V)
pKHS
0 1 2 4 6 8 10 12 14 16 18 20 22 25.7 26.2
0.0 4.6 9.0 17.7 26.0 34.1 41.9 49.5 56.9 64.1 71.1 77.9 84.6 96.6 98.3
0.0554 0.0577 0.059 0.0572 0.0586 0.0584 0.0576 0.0579 0.059 0.0574 0.0563 0.0591 0.0564 0.0566 0.059
14 3.45 3.1 2.8 2.46 2.36 2.3 2.26 2.26 2.4 2.56 2.75 3.23 4.4 5
0.0546 0.059 0.0585 0.0578 0.0589 0.0578 0.0584 0.0579 0.0568 0.0589 0.0586 0.058 0.0577 0.0575 0.0572
14 3.45 3.17 2.82 2.57 2.46 2.375 2.3 2.28 2.33 2.62 2.85 3.1 4.27 4.72
0.0599 0.0586 0.0582 0.0587 0.0586
2.5 2.465 2.42 2.45 2.47
0.0583
3.12
Average values (V)
0.0577
0.0578
0.0587
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
5777
the relation: (ai )S = Γt (i)H2 O→S (ai )H2 O
(13)
where Γt (i)H2 O→S is the activity coefficient of solvent transfer from water to S. Relation (13) shows that a same concentration of an ion in two different solvents does not imply a same activity in each of them. In fact there is no reason that the ion i would be solvated in the same manner in water and in another solvent, and then that its activity would be the same. This problem has been widely studied in the past [18,24,25]. The activity coefficient of solvent transfer Γ t allows one to evaluate the differences of solvation of ions from water to non aqueous solvents. If we consider the H+ ion, its activity coefficient of solvent transfer is expressed as log Γt (H+ )H2 O→S = −
G0t (H+ )H2 O→S 2.3RT
(14)
where G0t (H+ )H2 O→S is the molar free energy variation for H+ ion transferred from water to solvent S (variation of solvation energy by changing the solvent). A value of Γ t (H+ ) higher than unity (log Γ t (H+ ) > 0) means an H+ solvation more energetic in the solvent S than in water (the contrary if Γ t (H+ ) < 1). The more solvated the H+ , the less reactive it is. A potentiometric evaluation of activity coefficients of solvent transfer has been proposed by Strehlow [26,27] through the use of the ferrocene/ferricinium redox couple (ferrocene is dicyclopentadienyl-iron(II)). Strehlow postulated that solvation of ferrocene and its oxidised form ferricinium (complex dicyclopentadienyl-iron(III)) are similar in all solvents. This electrochemical couple may thus be considered as a “universal” potential reference electrode in all solvents. (Its redox power is not influenced by change of solvents because oxidant and reducer are solvated in the same manner.) Consequently, Strehlow defined an experimental parameter, designated by R0 (redox function), allowing one to determine the ion activity coefficients of solvent transfer. The redox function corresponds to the difference of potential measured between two electrochemical couples, one of them being ferrocene/ferricinium, in water on the one hand and in a solvent S on the other hand. If the second electrochemical couple is H+ /H2 (hydrogen electrode), we have R0 (H+ )H2 O→S =
0 )H −(ENHE/Fec
2.3RT/F
2 O→S
= log Γt (H+ )H2 O→S (15)
where NHE is normal hydrogen electrode and Fec is ferrocene/ferricinium couple. So the activity coefficient of solvent transfer for H+ ion can be potentiometrically measured. This allows one to correlate acidity scales of solvents with that of water. In water, the standard potential E0 for hydrogen electrode is 0 −0.40 V versus Fec (Fec/Fec+ couple). Measures of ENHE in a + 0 solvent S allow one to calculate the value of R (H ) according
Fig. 4. Current–potential curves of the H+ /H2 electrochemical system for several concentrations of formic acid in water: (1) 6 M, (2) 8 M, (3) 10 M, (4) 14 M, (5) 16 M, (6) 22 M, (7) 25.7 M and (8) 26.2 M. The working electrode is a rotating platinized platinum one (3.14 mm2 area, 1000 rpm). All scans are recorded at 1 mV s−1 . Potentials are given vs. Ag/AgCl/KClsat. in corresponding media. The solution is hydrogen saturated and contains HClO4 1 M.
to Koepp et al. [27]. This value gives the shift between pH 0 in water and pH 0 in S. This is the difference of acidity level for pH 0 in the two solvents. To compare the acidity levels of all solvents (and solvent mixtures), a generalized acidity scale pHH2 O called R(H+ ) was defined. In water, the acidity scale stretches from pHH2 O = 0 to 14. Some works have been done to correlate the acidity scales of water and anhydrous formic acid [28–30]. A R0 (H+ )H2 O→HCOOH value equal to −7.4 has been estimated by Br´eant et al. [28]. So the acidity scale origin in anhydrous formic acid would be pHH2 O = −7.4. Consequently, the activity of a proton is strongly increased in formic acid, owing to its least solvation, from that in water. Apart from this determination for anhydrous formic acid, nothing is known about formic acid/water mixtures. It is why a correlation between the acidity scales has been achieved in order to know the acidity level variations of formic acid/water mixtures. 3.2.2. Results 3.2.2.1. Hydrogen electrode potential. Current–potential curves have been recorded for a hydrogen system corresponding to the reaction: 2H+ + 2e− ⇔ H2 on platinized platinum in formic acid/water mixtures of several percentages. For each medium, HClO4 concentration was 1 mol dm−3 and hydrogen gas saturated the solution. The curves are represented on Fig. 4. Their shapes are similar. It only appears that hydrogen solubility increases slightly with formic acid concentration. More important is the potential shift (≈+300 mV) from formic acid 6 mol dm−3 (26 wt.%) to 26.2 mol dm−3 (98.3 wt.%). The H+ /H2 potential is negative versus the reference electrode when formic acid percentage is low and becomes positive with high formic acid percentage. This shows that it is easier to reduce H+ ions when formic
5778
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780 Table 2 Determination of standard potential E0 of H+ /H2 system in water–formic acid mixtures HCOOH
Fig. 5. Experimental and calculated current–potential curves for H+ /H2 electrochemical system. Continuous lines: experimental curves. Calculated points for HCOOH: () 6 M, (♦) 16 M and ( ) 25.7 M.
(k0 /(kD )R )IR 10β(E−E
0 )/(2.3RT/2F )
1 + (k0 /(kD )R )10β(E−E
+ (k0 /(kD )Ox )10−α(E−E
where k0 is the standard rate constant (cm s−1 ); kD the diffusion rate constant (cm s−1 ); α and β the charge transfer coefficients for reduction of H+ and oxidation of H2 ; IR and IOx the limiting currents for reduction and oxidation; E0 is the standard potential of the H+ /H2 system. The theoretical current–potential curves have been calculated assuming that α = β = 0.5, IOx » IR (IOx /IR ≈ 1000) and 2.3RT/F = 0.06 V for postulated k0 /kD and E0 values. The IR values are measured from experimental I–E curves subtracted from residual current. The theoretical equation of Iresidual –E curves, considered as straight lines, is calculated by fitting from the experimental corresponding curves. Then the (I + Iresidual )–E theoretical curves are calculated and compared to experimental recorded ones. Fitting is achieved by variation of E0 values until good superposition of curves is found. If necessary, k0 /kD values are then adjusted for a better fit. Fitting between experimental and calculated curves is very good for each medium, as shown on Fig. 5 for three of them (only some calculated I–E couples of points are reported). The standard potentials thus obtained are collected in Table 2. 3.2.2.2. Ferrocene/ferricinium potential. Correlation of acidity scales through relation (15) needs knowledge of the standard potential of the ferrocene/ferricinium couple. According to Strehlow, this one may be considered as a reference potential system valid in all solvents (independent of solvation). The standard potential E0 of the reaction: Fec − e− ⇔ Fec+
6 8 10 14 16 22 25.7 26.2
26.0 34.1 41.9 56.9 64.1 84.6 96.6 98.3
0.4 0.7 0.7 0.7 0.6 0.1 0.55 0.4
−0.223 −0.211 −0.194 −0.146 −0.117 −0.008 0.112 0.098
where Fec is dicyclopentadienyl-iron(II) is obtained by fitting experimental and calculated current–potential curves of ferrocene oxidation. The theoretical curve is calculated from the Nernst relation applied to equilibrium at electrode interface: E = E0 +
+ (k0 /(kD )Ox )IOx 10−α(E−E
0 )/(2.3RT/2F )
wt.%
E0 vs. Ag/AgCl, KClsat. (V)
Potentials are referred to Ag/AgCl/KClsat. in each media, computations have been done for α = β = 0.5, IOx » IR , 2.3RT/2F = 0.03.
acid concentration increases, in connection with its higher activity. To correlate the acidity scales of water and formic acid/water mixtures, the standard potential of the H+ /H2 system must be known. This one has been calculated by fitting theoretical and experimental curves in each medium. Theoretical current–potential curves are calculated from the Butler–Volmer relation applied to the hydrogen system [31,32]: I=
mol dm−3
k0 /kD
2.3RT [Fec+ ]el log F [Fec]el
0 )/(2.3RT/2F )
0 )/(2.3RT/2F )
(16)
where [Fec+ ]el = I/dFec+ , [Fec]el = (IFec − I)/dFec ; dFec and dFec+ the diffusion coefficients of ferrocene and ferricinium species; IFec is the limiting diffusion current for ferrocene. Then I=
IFec 10(E−E1/2 )/(2.3RT/F ) 1 + 10(E−E1/2 )/(2.3RT/F )
(17)
with E1/2 = E0 + 2.3(RT/F )log((kD )Fec /(kD )Fec+ ) ≈ E0 . Experimental current–potential curves for ferrocene oxidation have been recorded in several formic acid/water mixtures (Fig. 6). Values of IFec are firstly deduced from recorded I–E curves for ferrocene oxidation and corresponding residual currents. Theoretical current–potential curves are then calculated according to relation (17), postulating the theoretical value for 2.3RT/F and estimating an E1/2 value. The equation of Iresidual –E curves, considered as straight line, is deduced from experimental recorded curves. I + Iresidual versus E curves are then calculated. For each formic acid/water mixture, experimental and calculated current–potential curves are fitted. E1/2 is varied until a good superposition is obtained. If necessary, the 2.3RT/F value is slightly modified to obtain a best fit (2.3RT/F values deduced from experimental curves remain in a narrow gap (0.056 to 0.064 V)). The half-wave potentials E1/2 for each medium are collected in Table 3. From these values and those of H+ /H2 standard potentials (Table 2), the H+ redox function of transfer from water to formic acid/water mixtures, R0 (H+ ), is calculated according to (15) (Table 4).
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
Fig. 6. Current–potential curves for oxidation of ferrocene in H2 O/HCOOH mixtures. HCOOH: (1) 6 M, (2) 8 M, (3) 10 M, (4) 14 M, (5) 16 M, (6) 22 M, (7) 25.2 M and (8) 26.2 M. Potentials are vs. Ag/AgCl/KClsat. reference electrode. Ferrocene 0.0043 mol dm−3 is introduced in each solution containing HClO4 0.25 M (only a part is soluble). Table 3 Values of the half-wave potentials E1/2 for ferrocene oxidation in formic acid/water mixtures HCOOH mol dm−3
wt.%
6 8 10 14 16 22 25.7 26.2
26.0 34.1 41.9 56.9 64.1 84.6 96.6 98.3
IFec (A)
E1/2 (V)
2.8 4.6 5.8 8.5 19.8 43 36 56
0.193 0.197 0.202 0.202 0.202 0.193 0.185 0.153
Potentials are referred to Ag/AgCl/KClsat. .
3.2.2.3. R(H+ ) scales. Owing to these R0 (H+ ) values and to the pKHS values determined by titration, the water–formic acid mixing diagram is drawn (Fig. 7). This diagram shows the variation of the acidity limit from pure water, R0 (H+ ) = 0, to pure (98.3 wt.%) formic acid, R0 (H+ ) = −5.95. This means that in 98.3 wt.% formic acid the activity of a concentration equal to 1 mol dm−3 of H+ is largely increased versus in pure water (Γt (H+ )H2 O→HCOOH = 10−5.95 ). The diagram also shows that until about 50 wt.% formic acid, the basicity of water molecules limits the acidity scale (R0 (H+ ) ≈ 0). For HCOOH 98.3 wt.%, the whole acidity scale is in the super acid medium
5779
Fig. 7. Water–formic acid mixing diagram showing variations of the acidity level and pKHS values vs. the generalized acidity scale R(H+ ). (), ( ), (♦) and () are experimental values. Continuous lines are calculated by polynomial regression from experimental values. Dotted line is the acidity neutrality.
(R(H+ ) = pKHS < 0). So even 1 mol dm−3 of the strong base (formate) gives an acidity level higher than 1 mol dm−3 of H+ in pure water. This diagram also shows that from formic acid percentage over 9% (≈2 mol dm−3 ), the medium is much more dissociated than pure water ([H+ ] = [HCOO− ] ≥ 0.03 mol dm−3 ). The maximum of dissociation is for a 50/50 wt.% mixture (0.07 mol dm−3 ). 4. Conclusions The autoprotolysis constants of formic acid/water mixtures have been determined by potentiometric titrations of a strong acid by a strong base in a series of mixtures. Fitting of experimental curves with calculated ones allowed an accurate determination of pKHS values, giving the extent of acidity scales. The obtained values show that the addition of formic acid in water leads to more dissociated media than pure water. The pKHS value varies from 3.45 to 5 (HCOOH 4.6–98.3 wt.%) with a minimum value of 2.3 around 50 wt.%. In the range HCOOH 4 mol dm−3 (17.7 wt.%) to 22 mol dm−3 (84.6 wt.%), the ionic strength is above 0.03. A correlation between acidity scales of formic acid/water mixtures and the acidity scale of pure water has also been achieved by determination of the redox function of Strehlow in each medium. This correlation shows that the acidity level in acidic media is limited by the basicity of water molecules from
Table 4 Values of the redox function R0 (H+ ) in formic acid/water mixtures (computation with 2.3RT/F = 0.058 V) HCOOH
Potential (V) vs. Ag/AgCl/KClsat.
Potential (V) vs. Fec/Fec+
mol dm−3
wt.%
E0 [H+ /H2 ]
E0 [ferrocene]
E0 [H+ /H2 ]
6 8 10 14 16 22 25.7 26.2
26.0 34.1 41.9 56.9 64.1 84.6 96.6 98.3
−0.223 −0.211 −0.194 −0.146 −0.117 −0.008 0.112 0.098
0.193 0.197 0.202 0.202 0.202 0.193 0.185 0.153
−0.416 −0.408 −0.396 −0.348 −0.319 −0.201 −0.073 −0.055
R0 (H+ )
0.28 0.14 −0.07 −0.90 −1.40 −3.43 −5.64 −5.95
5780
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
0 to 50 wt.% formic acid. For high concentrations of formic acid (>80% by weight), the whole acidity scale is in the super acid part of the generalized acidity scale pHH2 O . The diagram also shows that formic acid/water mixtures are relatively dissociated media. This would explain problems encountered in formic acid regeneration from formate by electromembrane process [16]. On the contrary, this dissociation is favourable for implementation of electrochemical devices such as direct formic acid fuel cells. References [1] C. Rice, S. Ha, R.I. Masel, P. Waszczuk, A. Wieckowski, T. Barnard, J. Power Sources 111 (2002) 83. [2] Y.W. Rhee, S.Y. Ha, R.I. Masel, J. Power Sources 117 (2003) 35. [3] S. Ha, B. Adams, R.I. Masel, J. Power Sources 128 (2004) 119. [4] X. Wang, J.M. Hu, I.M. Hsing, J. Electroanal. Chem. 562 (2004) 73. [5] Y. Zhu, S.Y. Ha, R.I. Masel, J. Power Sources 130 (2004) 8. [6] Y. Zhu, Z. Khan, R.I. Masel, J. Power Sources 139 (2005) 15. [7] R.S. Jayashree, J.S. Spendelow, J. Yeom, C. Rastogi, M.A. Shannon, P.J.A. Kenis, Electrochim. Acta 50 (2005) 4674. [8] S. Ha, R. Larsen, R.I. Masel, J. Power Sources 144 (2005) 28. [9] X. Li, I.M. Hsing, Electrochim. Acta 51 (2006) 3477. [10] R. Larsen, S. Ha, J. Zakzeski, R.I. Masel, J. Power Sources 157 (2006) 78. [11] S. Ha, Z. Dunbar, R.I. Masel, J. Power Sources 158 (2006) 129. [12] J. Yeom, R.S. Jayashree, C. Rastogi, M.A. Shannon, P.J.A. Kenis, J. Power Sources 160 (2006) 1058. [13] C.M. Miesse, W.S. Jung, K.J. Jeong, J.K. Lee, J. Lee, J. Han, S.P. Yoon, S.W. Nam, T.H. Lim, S.A. Hong, J. Power Sources 162 (2006) 532.
[14] G.S. Luo, F.Y. Wu, Sep. Sci. Technol. 35 (2000) 2485. [15] G.S. Luo, S. Pan, J.G. Liu, Desalination 150 (2002) 227. [16] J.S. Jaime Ferrer, S. Laborie, G. Durand, M. Rakib, J. Membr. Sci. 280 (2006) 509. [17] J.J. Lagowski, The Chemistry of Non-Aqueous Solvents, vol.1. Principles and Techniques, Academic Press, New York, 1966. [18] B. Tr´emillon, Electrochimie analytique et r´eactions en solution, tome 1: R´eactions en Solution, Chapitre 6: Solvants Mol´eculaires, Masson, Paris, 1993 (translated: Reactions in Solution, An Applied Analytical Approach, John Wiley, Chichester, 1997). [19] J.R. Chipperfield, Non-Aqueous Solvents, Oxford Chemistry Primers, 1999. [20] K. Isutzu, Electrochemistry in Nonaqueous Solutions, John Wiley, 2002. [21] B.P. Nicolsky, Acta Physicochim. USSR 7 (1937) 597. [22] G. Eisenman, Glass Electrodes for Hydrogen and Other Cations, Principles and Practice, Marcel Dekker, 1967. [23] N. Lakshminarayanaiah, Membrane Electrodes, Academic Press, 1976. [24] B. Tr´emillon, La Chimie en Solvants Non-aqueux, Presses Universitaires de France, Paris, 1971. [25] Y. Marcus, Ion Solvation, John Wiley, Chichester, 1985. [26] H. Strehlow, Z. Elektrochem. 56 (1952) 827. [27] H.M. Koepp, H. Wendt, H. Strehlow, Z. Elektrochem. 64 (1960) 483. [28] M. Br´eant, C. B´eguin, C. Coulombeau, Anal. Chim. Acta 87 (1976) 201. [29] L.P. Hammett, A.J. Deyrup, J. Am. Chem. Soc. 54 (1932) 2721. [30] R. Stewart, T. Mathews, Can. J. Chem. 38 (1960) 602. [31] B. Tr´emillon, Electrochimie analytique et r´eactions en solution, tome 2: R´eactions et m´ethodes e´ lectrochimiques, Masson, Paris, 1993. [32] A.J. Bard, L.R. Faulkner, Electrochemical Methods, Fundamentals and Applications, John Wiley, 2001.
Electrochemical determination of acidity level and dissociation of formic acid/water mixtures as solvent J.S. Jaime Ferrer, E. Couallier, M. Rakib, G. Durand ∗,1 Laboratoire de G´enie des Proc´ed´es et Mat´eriaux, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chˆatenay-Malabry Cedex, France Received 10 October 2006; received in revised form 23 February 2007; accepted 24 February 2007 Available online 1 March 2007
Abstract The autoprotolysis constant KHS of formic acid/water mixtures as solvent has been calculated from acid–base potentiometric titration curves. A correlation of the acidity scale pKHS of each medium versus pure water has been implemented owing to the Strehlow R0 (H+ ) electrochemical redox function. The results show that formic acid/water mixtures are much more dissociated than pure water; such media are sufficiently dissociated to allow electrochemical measures without addition of an electrolyte. It has also been shown that for a same H+ concentration the activity of protons increases with formic acid concentration. For more than 80 wt.% of formic acid the acidity is sufficiently increased to locate the whole acidity scale pKHS in the super acid medium of the generalized acidity scale pHH2 O . © 2007 Elsevier Ltd. All rights reserved. Keywords: Acidity scale; Autoprotolysis constant; Formic acid; Formic acid/water mixtures; Redox function
1. Introduction Formic acid is an alternative fuel to methanol in direct fuel cells for portable power applications. Many papers have recently been published concerning direct formic acid fuel cells (DFAFCs) [1–13]. In these polymer electrolyte membrane fuel cells (PEMFCs) formic acid is oxidised directly into carbon dioxide and H+ ions, which cross the membrane to the cathodic compartment and produce water from oxygen (air) reduction. Some advantages of formic acid for such devices are its strong dissociation (no need for electrolyte), the high theoretical voltage of the corresponding fuel cell (1.45 V for formic acid/oxygen system) and the possibility of operating with high formic acid concentrations (i.e., high power density with respect to the fuel volume) without strong leakage through the membrane. In fact, formic acid is not used pure but mixed with water. Several authors have shown that an optimum concentration of formic acid is required for best fuel cell performances. Rice et al. [1] empirically showed that an optimum formic acid concentration must be used, around 50/50 wt.% water–formic acid
∗ 1
Corresponding author. Tel.: +33 1 41 13 12 13; fax: +33 1 41 13 11 63. E-mail address: [email protected] (G. Durand). ISE member.
0013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2007.02.058
mixture. Replacing platinum black electrocatalyst with a Pd/C one, Ha et al. [8] recently showed that the optimum could be a 40/60 wt.% mixture. Another limitation of DFAFC pointed out by several authors is formic acid leakage through Nafion® membranes. Rhee et al. [2] observed that more formic acid permeates through the membrane when the formic acid reservoir is filled with 10 mol dm−3 formic acid than with 20 mol dm−3 formic acid. Miesse et al. [13] recently implemented a DFAFC portable power supply for a laptop computer and showed that the optimum formic acid concentration for this device is around 6 mol dm−3 . They also suggested that the decrease in performance over 6 mol dm−3 is due to formic acid leakage through the membrane. Formic acid is also a chemical widely used in many industries, such as textiles, natural rubber, leather processing, agriculture, cosmetics, disinfectants, detergents and pharmaceuticals. In textile manufacturing formic acid is used mainly in cellulose spinning. In this process further fibber washing steps lead to effluents containing diluted sodium formate. Considering this solution as a waste, it might be valuable to split this salt to recycle concentrated formic acid. The more concentrated the recycled formic acid, the more profitable should be the recycling process. Some works have already been done by Luo et al. [14,15] on formic acid concentration by electromembrane processes. But these authors do not really study formic acid
5774
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
regeneration from formate salt, only acid concentration. Jaime Ferrer et al. [16] studied a whole process coupling electrodialysis and bipolar membrane electrodialysis for diluted (0.1 mol dm−3 ) sodium formate splitting to produce concentrated formic acid (7 mol dm−3 ). Problems were encountered: leakages through the membranes and consequently limitation of HCOOH concentration reachable, questions about physicochemical behaviour of the concentrated solution when formic acid concentration increased from 1 to 7 mol dm−3 . The present work was stimulated by these studies on formic acid regeneration by electromembrane processes in order to understand limitations of the process. The first question concerns the degree of dissociation of formic acid/water mixtures. This point is important in electrodialysis. As formic acid is a weak acid in water (pKa = 3.7), do we consider that highly concentrated solutions of formic acid remain weakly dissociated [14]? The answer may be obtained by determining the value of the autoprotolysis constant KHS (pKHS = −log KHS ) of each formic acid/water solvent in different proportions. The pKHS values may be obtained from strong acid/strong base potentiometric titrations in each solvent [17–20]. The second question concerns the acidity levels of the formic acid/water mixtures compared to pure water. A correlation of all acidity scales’ zero point versus a generalized pHH2 O scale (referred to pH scale in water) would allow to know the variations of proton activity during formic acid concentration. Such a correlation between acidity scales in various solvents has been widely described [18]. It would also help explain proton leakage and the corrosion power of highly concentrated formic acid solutions. 2. Experimental 2.1. Apparatus Titrations were done with a Metrohm 736 GP Titrino apparatus. Acquisition and processing of data have been done by the TiNet 2.4 software. Acidity was measured with a combined glass/reference electrode Metrohm 6.0299.100 Solvotrode, the reference electrode being Ag/AgCl/LiCl sat. in ethanol. Current–potential curves were recorded with a PARSTAT® 2263 potentiostat/galvanostat from Princeton Applied Research (AMETEK Inc.). The Power PULSE® module from the Power SUITE® software was used to exploit the current–potential curves. The reference electrode was homemade. It was the Ag/AgCl/KClsat. system in each water–formic acid medium. The working electrode was platinum rotating disc electrode EDI 101 (2 mm diameter) connected with a speed control unit, CTV 101 from Radiometer Analytical. For the H+ /H2 electrochemical system the platinum disc was platinized according to the following recipe: H2 PtCl6 3.5% + Pb(CH3 COO)2 0.005% (w/v) in water, 1000 rpm, E = −200 mV/SCE, t = 90 s. The auxiliary electrode was a platinum wire from Radiometer Analytical.
Water traces in pure formic acid were controlled by Karl Fischer titration with a coulometric titrator, aquaprocessor type, from Radiometer Analytical. 2.2. Chemicals Formic acid 97% from Avocado Organics was used for the formic acid/water mixtures. Formic acid 99–100% NORMAPURTM for analysis from VWR Prolabo was used for pure formic acid medium. Perchloric acid 70% for analysis from Fisher Chemicals, pellets of sodium hydroxide 98% and sodium formate 98% from Avocado Organics were used for acid–base titrations. Potassium chloride for analysis used for the reference electrode was from Acros Organics. Ferrocene [bis(cyclopentadienyl)iron] 99% pure was from Avocado Organics. 3. Results and discussion 3.1. Potentiometric determination of autoprotolysis constant 3.1.1. Theory In formic acid/water mixtures the autoprotolysis (or autosolvolysis) reaction is H2 O + HCOOH ⇔ H3 O+ + HCOO−
(1)
with KHS = [H3 O+ ][HCOO− ]
(2)
H3 O+ the solvated proton, also written H+ , is the strong acid; HCOO− is the strong base. So KHS value may be calculated from strong acid/strong base potentiometric titration curves between the pH values for [H3 O+ ] = 1 mol dm−3 (pH 0) and for [HCOO− ] = 1 mol dm−3 (pH = pKHS = −log KHS ). But this computation from two experimental points is imprecise. The best way is to compute the whole titration curve and to fit it with the experimental one. In formic acid/water mixtures, perchloric acid HClO4 is always a strong acid, and sodium hydroxide NaOH always a strong base [18] according to the solvolysis reactions: HCOOH + HClO4 ⇒ HCOOH2 + + ClO4 −
(3)
where HCOOH2 + is the solvated proton, written H+ and HCOOH + NaOH ⇒ HCOO− + Na+ + H2 O
(4)
where HCOO− is the strong base. So NaOH or sodium formate NaHCOO may be used as a strong base in formic acid/water mixtures. In pure water the strong acid/strong base reaction is H+ + (ClO4 − ) + OH− + (Na+ ) ⇔ H2 O + (Na+ ) + (ClO4 − )
(5)
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
in formic acid/water mixtures it is H+ + (ClO4 − ) + HCOO− + (Na+ ) ⇔ HCOOH + (Na+ ) + (ClO4 − )
(6)
All along titration the electroneutrality equation is [H+ ] + [Na+ ] = [HCOO− ] + [ClO4 − ]
(7)
3.1.2. Results Perchloric acid has been titrated by sodium hydroxide or sodium formate in pure water and in formic acid/water mixtures, varying formic acid from 4.6 to 98.3 wt.%. Titration curves have been recorded (E = f(V)). All titration curves have been collected on the same graph (Fig. 1). As foreseen, the curves are gradually translated when the solvent becomes different from water because of the additional junction potential. For each titration, the potential difference between the first part of the curve (acidic media) and the second part (basic media) is correlated to the solvent pKHS (relations
If a volume V0 of HClO4 , the concentration of which is CHClO4 , is titrated by addition of a volume V of a CNaHCOO solution of the strong base, and owing to relations (2) and (6)–(7), the H+ concentration may be calculated from the relation: −(VCNaHCOO − V0 CHClO4 )/(V0 + V ) + [(VCNaHCOO − V0 CHClO4 )/(V0 + V )]2 + 4KHS [H+ ] = 2 Nicolsky [21] and other authors [22,23] have shown that the emf of an electrochemical cell including a glass electrode is E = E0 +
2.3RT log aH + F
(9)
where R is the ideal gas constant (8.314 J K−1 mol−1 ); T the temperature (K); F the Faraday constant (96,485.34 C mol−1 ); aH+ is the activity of protons, linked to concentration and activity coefficient γH+ by the relation: aH+ = γH+ [H+ ]
(10)
Difficulties in computing activity coefficients in water lead to measure E versus H+ concentrations in solutions of constant ionic strength so that γH+ is constant (even = 1). The non-ideality of solutions is then included in E0 , with
E0 = E0 +
2.3RT log γH+ F
(11)
The use of a glass electrode (often with an aqueous inner solution) in non aqueous media introduces other deviations from ideality. But it has been shown [23] that the glass electrode is always usable in such media to measure H+ concentrations, with a linear relation E versus log[H+ ]. So combining relations (9)–(11), the H+ concentration may be measured from glass electrode potential according to E−E0
5775
(8)
(2), (5) and (6)). So at first sight it appears that pKHS strongly decreases from pure water (curve 1) to pure formic acid (curve 15), passing through a minimum. The very small potential variations appearing on Fig. 1 show that only fitting between experimental and calculated curves will allow one to obtain precisely the pKHS value of each solvent. Each theoretical curve is computed from relations (8) and (12), knowing CHClO4 , CNaHCOO , V0 , V, postulating the theoretical value for the glass electrode response (2.3RT/F) and estimating a pKHS value. Calculation is done for a lot of E/V couples of points (with a V increment of 0.01 cm3 and for E0 = 0). Fitting between experimental and calculated curves is achieved with Excel software according to the following steps. The experimental curve is first translated along the E-axis, so that the acidic part of the titration curve is fitted with the calculated one. This translation is justified by the fact that the experimental value of E0 is not known (the glass electrode is not standardized in formic acid mixtures). Then the theoretical curve is computed again, varying pKHS value until the whole experimental and calculated curves are superimposable. An example is given Fig. 2 where only some calculated couples of points E/V are reported for a best visibility of the fitting.
[H+ ] = 10 2.3RT/F
(12)
E − E0 is the sum of all potential differences of the potentiometric chain, including that of the reference electrode. When the combined glass/reference electrode is dipped in different solvents (formic acid/water of various percentages) the junction potential between the reference electrode (in ethanol media) and the solution is not constant. Its variation may be large. Besides, the asymmetry potential of the glass electrode also varies on account of the differences between the inner solution (aqueous) and outer one (formic acid/water mixtures). So E0 values, including junction and asymmetry potentials, are different in each formic acid/water solvent. Thus it is not possible to compare the experimental curves between them. But in a given solvent, E0 value is constant during the whole titration.
Fig. 1. Titration curves of ≈0.2 M HClO4 by a 5 M strong base (NaOH or NaHCOO) in formic acid/water mixtures as solvent. Formic acid percentages (by wt.) are: (1) 0%, (2) 4.6%, (3) 9.0%, (4) 17.7%, (5) 26.0%, (6) 34.1%, (7) 41.9%, (8) 49.5%, (9) 56.9%, (10) 64.1%, (11) 71.1%, (12) 77.9%, (13) 84.6%, (14) 96.6% and (15) 98.3%.
5776
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
Fig. 2. Experimental curve for titration of 0.28 M HClO4 by 5 M NaHCOO in formic acid/water 71.1/28.9 wt.%; () calculated curve (the potential scale is shift from experimental one by E0 value).
In order to check that the experimental glass electrode response is always close to the theoretical (and postulated) one, each experimental curve is straightened for the fitted pKHS values. The average 2.3RT/F values obtained (Table 1) are always close to the theoretical one at 20 ◦ C and then justify the former hypothesis. So autoprotolysis constants KHS values are obtained by fitting experimental and calculated titration curves for each formic acid/water mixture. The corresponding values of pKHS are collected in Table 1. Fig. 3 shows the variations of pKHS from pure water to “pure” formic acid (98.3% i.e. ≈1.1 mol dm−3 residual water). The three series of experiments point to a good reproducibility of values. The curve shows a strong and rapid decrease of pKHS when formic acid is added to water. pKHS value is minimum for about 50/50 wt.% water–formic acid mixture and then increases again, the more when formic acid is pure. In fact, a small value of pKHS means a high value of the autoprotolysis constant KHS , and then a great dissociation of the solvent. The graph shows that formic acid/water mixtures are more dissociated than pure water, and then are more conducting media. The maximum of dissociation is obtained for the range 25–65 wt.% HCOOH. In 50/50 wt.% formic acid/water mixture, for example,
Fig. 3. Experimental values of autoprotolysis constant pKHS in formic acid/water mixtures. () First series of measures, () second series, ( ) third series (the point for pure water, pKHS = 14, is omitted).
the pKHS value shows that [H+ ] = [HCOO− ] = 0.07 mol dm−3 . In this case, the conductivity increase may be enough to carry out electrochemical measurements without addition of an electrolyte. 3.2. Correlation of acidity scales 3.2.1. Theory As shown above, the acidity scales, i.e., the number of pH units reachable in formic acid/water mixtures as solvents, strongly vary from pure water (pH = 14) to pure formic acid (pH ≈ 5), passing through a minimum (pH ≈ 2.3) for 50/50 wt.% mixture. But the values, pH 0 in water and in each formic acid/water mixture, are not comparable. What is obtained in each solvent (and water) is [H+ ] = 1 mol dm−3 . But a same concentration of H+ ions do not imply a same activity of proton. In a given solvent the activity of an ion i is linked to its concentration by the relation ai = γi ci . In the same way the activities of an ion i at the same concentration in water and in another solvent are bound by
Table 1 pKHS values of formic acid/water mixtures as solvents (for three series of titration) HCOOH
First series
Second series
Third series
mol dm−3
wt.%
Slope (V)
pKHS
Slope (V)
pKHS
Slope (V)
pKHS
0 1 2 4 6 8 10 12 14 16 18 20 22 25.7 26.2
0.0 4.6 9.0 17.7 26.0 34.1 41.9 49.5 56.9 64.1 71.1 77.9 84.6 96.6 98.3
0.0554 0.0577 0.059 0.0572 0.0586 0.0584 0.0576 0.0579 0.059 0.0574 0.0563 0.0591 0.0564 0.0566 0.059
14 3.45 3.1 2.8 2.46 2.36 2.3 2.26 2.26 2.4 2.56 2.75 3.23 4.4 5
0.0546 0.059 0.0585 0.0578 0.0589 0.0578 0.0584 0.0579 0.0568 0.0589 0.0586 0.058 0.0577 0.0575 0.0572
14 3.45 3.17 2.82 2.57 2.46 2.375 2.3 2.28 2.33 2.62 2.85 3.1 4.27 4.72
0.0599 0.0586 0.0582 0.0587 0.0586
2.5 2.465 2.42 2.45 2.47
0.0583
3.12
Average values (V)
0.0577
0.0578
0.0587
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
5777
the relation: (ai )S = Γt (i)H2 O→S (ai )H2 O
(13)
where Γt (i)H2 O→S is the activity coefficient of solvent transfer from water to S. Relation (13) shows that a same concentration of an ion in two different solvents does not imply a same activity in each of them. In fact there is no reason that the ion i would be solvated in the same manner in water and in another solvent, and then that its activity would be the same. This problem has been widely studied in the past [18,24,25]. The activity coefficient of solvent transfer Γ t allows one to evaluate the differences of solvation of ions from water to non aqueous solvents. If we consider the H+ ion, its activity coefficient of solvent transfer is expressed as log Γt (H+ )H2 O→S = −
G0t (H+ )H2 O→S 2.3RT
(14)
where G0t (H+ )H2 O→S is the molar free energy variation for H+ ion transferred from water to solvent S (variation of solvation energy by changing the solvent). A value of Γ t (H+ ) higher than unity (log Γ t (H+ ) > 0) means an H+ solvation more energetic in the solvent S than in water (the contrary if Γ t (H+ ) < 1). The more solvated the H+ , the less reactive it is. A potentiometric evaluation of activity coefficients of solvent transfer has been proposed by Strehlow [26,27] through the use of the ferrocene/ferricinium redox couple (ferrocene is dicyclopentadienyl-iron(II)). Strehlow postulated that solvation of ferrocene and its oxidised form ferricinium (complex dicyclopentadienyl-iron(III)) are similar in all solvents. This electrochemical couple may thus be considered as a “universal” potential reference electrode in all solvents. (Its redox power is not influenced by change of solvents because oxidant and reducer are solvated in the same manner.) Consequently, Strehlow defined an experimental parameter, designated by R0 (redox function), allowing one to determine the ion activity coefficients of solvent transfer. The redox function corresponds to the difference of potential measured between two electrochemical couples, one of them being ferrocene/ferricinium, in water on the one hand and in a solvent S on the other hand. If the second electrochemical couple is H+ /H2 (hydrogen electrode), we have R0 (H+ )H2 O→S =
0 )H −(ENHE/Fec
2.3RT/F
2 O→S
= log Γt (H+ )H2 O→S (15)
where NHE is normal hydrogen electrode and Fec is ferrocene/ferricinium couple. So the activity coefficient of solvent transfer for H+ ion can be potentiometrically measured. This allows one to correlate acidity scales of solvents with that of water. In water, the standard potential E0 for hydrogen electrode is 0 −0.40 V versus Fec (Fec/Fec+ couple). Measures of ENHE in a + 0 solvent S allow one to calculate the value of R (H ) according
Fig. 4. Current–potential curves of the H+ /H2 electrochemical system for several concentrations of formic acid in water: (1) 6 M, (2) 8 M, (3) 10 M, (4) 14 M, (5) 16 M, (6) 22 M, (7) 25.7 M and (8) 26.2 M. The working electrode is a rotating platinized platinum one (3.14 mm2 area, 1000 rpm). All scans are recorded at 1 mV s−1 . Potentials are given vs. Ag/AgCl/KClsat. in corresponding media. The solution is hydrogen saturated and contains HClO4 1 M.
to Koepp et al. [27]. This value gives the shift between pH 0 in water and pH 0 in S. This is the difference of acidity level for pH 0 in the two solvents. To compare the acidity levels of all solvents (and solvent mixtures), a generalized acidity scale pHH2 O called R(H+ ) was defined. In water, the acidity scale stretches from pHH2 O = 0 to 14. Some works have been done to correlate the acidity scales of water and anhydrous formic acid [28–30]. A R0 (H+ )H2 O→HCOOH value equal to −7.4 has been estimated by Br´eant et al. [28]. So the acidity scale origin in anhydrous formic acid would be pHH2 O = −7.4. Consequently, the activity of a proton is strongly increased in formic acid, owing to its least solvation, from that in water. Apart from this determination for anhydrous formic acid, nothing is known about formic acid/water mixtures. It is why a correlation between the acidity scales has been achieved in order to know the acidity level variations of formic acid/water mixtures. 3.2.2. Results 3.2.2.1. Hydrogen electrode potential. Current–potential curves have been recorded for a hydrogen system corresponding to the reaction: 2H+ + 2e− ⇔ H2 on platinized platinum in formic acid/water mixtures of several percentages. For each medium, HClO4 concentration was 1 mol dm−3 and hydrogen gas saturated the solution. The curves are represented on Fig. 4. Their shapes are similar. It only appears that hydrogen solubility increases slightly with formic acid concentration. More important is the potential shift (≈+300 mV) from formic acid 6 mol dm−3 (26 wt.%) to 26.2 mol dm−3 (98.3 wt.%). The H+ /H2 potential is negative versus the reference electrode when formic acid percentage is low and becomes positive with high formic acid percentage. This shows that it is easier to reduce H+ ions when formic
5778
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780 Table 2 Determination of standard potential E0 of H+ /H2 system in water–formic acid mixtures HCOOH
Fig. 5. Experimental and calculated current–potential curves for H+ /H2 electrochemical system. Continuous lines: experimental curves. Calculated points for HCOOH: () 6 M, (♦) 16 M and ( ) 25.7 M.
(k0 /(kD )R )IR 10β(E−E
0 )/(2.3RT/2F )
1 + (k0 /(kD )R )10β(E−E
+ (k0 /(kD )Ox )10−α(E−E
where k0 is the standard rate constant (cm s−1 ); kD the diffusion rate constant (cm s−1 ); α and β the charge transfer coefficients for reduction of H+ and oxidation of H2 ; IR and IOx the limiting currents for reduction and oxidation; E0 is the standard potential of the H+ /H2 system. The theoretical current–potential curves have been calculated assuming that α = β = 0.5, IOx » IR (IOx /IR ≈ 1000) and 2.3RT/F = 0.06 V for postulated k0 /kD and E0 values. The IR values are measured from experimental I–E curves subtracted from residual current. The theoretical equation of Iresidual –E curves, considered as straight lines, is calculated by fitting from the experimental corresponding curves. Then the (I + Iresidual )–E theoretical curves are calculated and compared to experimental recorded ones. Fitting is achieved by variation of E0 values until good superposition of curves is found. If necessary, k0 /kD values are then adjusted for a better fit. Fitting between experimental and calculated curves is very good for each medium, as shown on Fig. 5 for three of them (only some calculated I–E couples of points are reported). The standard potentials thus obtained are collected in Table 2. 3.2.2.2. Ferrocene/ferricinium potential. Correlation of acidity scales through relation (15) needs knowledge of the standard potential of the ferrocene/ferricinium couple. According to Strehlow, this one may be considered as a reference potential system valid in all solvents (independent of solvation). The standard potential E0 of the reaction: Fec − e− ⇔ Fec+
6 8 10 14 16 22 25.7 26.2
26.0 34.1 41.9 56.9 64.1 84.6 96.6 98.3
0.4 0.7 0.7 0.7 0.6 0.1 0.55 0.4
−0.223 −0.211 −0.194 −0.146 −0.117 −0.008 0.112 0.098
where Fec is dicyclopentadienyl-iron(II) is obtained by fitting experimental and calculated current–potential curves of ferrocene oxidation. The theoretical curve is calculated from the Nernst relation applied to equilibrium at electrode interface: E = E0 +
+ (k0 /(kD )Ox )IOx 10−α(E−E
0 )/(2.3RT/2F )
wt.%
E0 vs. Ag/AgCl, KClsat. (V)
Potentials are referred to Ag/AgCl/KClsat. in each media, computations have been done for α = β = 0.5, IOx » IR , 2.3RT/2F = 0.03.
acid concentration increases, in connection with its higher activity. To correlate the acidity scales of water and formic acid/water mixtures, the standard potential of the H+ /H2 system must be known. This one has been calculated by fitting theoretical and experimental curves in each medium. Theoretical current–potential curves are calculated from the Butler–Volmer relation applied to the hydrogen system [31,32]: I=
mol dm−3
k0 /kD
2.3RT [Fec+ ]el log F [Fec]el
0 )/(2.3RT/2F )
0 )/(2.3RT/2F )
(16)
where [Fec+ ]el = I/dFec+ , [Fec]el = (IFec − I)/dFec ; dFec and dFec+ the diffusion coefficients of ferrocene and ferricinium species; IFec is the limiting diffusion current for ferrocene. Then I=
IFec 10(E−E1/2 )/(2.3RT/F ) 1 + 10(E−E1/2 )/(2.3RT/F )
(17)
with E1/2 = E0 + 2.3(RT/F )log((kD )Fec /(kD )Fec+ ) ≈ E0 . Experimental current–potential curves for ferrocene oxidation have been recorded in several formic acid/water mixtures (Fig. 6). Values of IFec are firstly deduced from recorded I–E curves for ferrocene oxidation and corresponding residual currents. Theoretical current–potential curves are then calculated according to relation (17), postulating the theoretical value for 2.3RT/F and estimating an E1/2 value. The equation of Iresidual –E curves, considered as straight line, is deduced from experimental recorded curves. I + Iresidual versus E curves are then calculated. For each formic acid/water mixture, experimental and calculated current–potential curves are fitted. E1/2 is varied until a good superposition is obtained. If necessary, the 2.3RT/F value is slightly modified to obtain a best fit (2.3RT/F values deduced from experimental curves remain in a narrow gap (0.056 to 0.064 V)). The half-wave potentials E1/2 for each medium are collected in Table 3. From these values and those of H+ /H2 standard potentials (Table 2), the H+ redox function of transfer from water to formic acid/water mixtures, R0 (H+ ), is calculated according to (15) (Table 4).
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
Fig. 6. Current–potential curves for oxidation of ferrocene in H2 O/HCOOH mixtures. HCOOH: (1) 6 M, (2) 8 M, (3) 10 M, (4) 14 M, (5) 16 M, (6) 22 M, (7) 25.2 M and (8) 26.2 M. Potentials are vs. Ag/AgCl/KClsat. reference electrode. Ferrocene 0.0043 mol dm−3 is introduced in each solution containing HClO4 0.25 M (only a part is soluble). Table 3 Values of the half-wave potentials E1/2 for ferrocene oxidation in formic acid/water mixtures HCOOH mol dm−3
wt.%
6 8 10 14 16 22 25.7 26.2
26.0 34.1 41.9 56.9 64.1 84.6 96.6 98.3
IFec (A)
E1/2 (V)
2.8 4.6 5.8 8.5 19.8 43 36 56
0.193 0.197 0.202 0.202 0.202 0.193 0.185 0.153
Potentials are referred to Ag/AgCl/KClsat. .
3.2.2.3. R(H+ ) scales. Owing to these R0 (H+ ) values and to the pKHS values determined by titration, the water–formic acid mixing diagram is drawn (Fig. 7). This diagram shows the variation of the acidity limit from pure water, R0 (H+ ) = 0, to pure (98.3 wt.%) formic acid, R0 (H+ ) = −5.95. This means that in 98.3 wt.% formic acid the activity of a concentration equal to 1 mol dm−3 of H+ is largely increased versus in pure water (Γt (H+ )H2 O→HCOOH = 10−5.95 ). The diagram also shows that until about 50 wt.% formic acid, the basicity of water molecules limits the acidity scale (R0 (H+ ) ≈ 0). For HCOOH 98.3 wt.%, the whole acidity scale is in the super acid medium
5779
Fig. 7. Water–formic acid mixing diagram showing variations of the acidity level and pKHS values vs. the generalized acidity scale R(H+ ). (), ( ), (♦) and () are experimental values. Continuous lines are calculated by polynomial regression from experimental values. Dotted line is the acidity neutrality.
(R(H+ ) = pKHS < 0). So even 1 mol dm−3 of the strong base (formate) gives an acidity level higher than 1 mol dm−3 of H+ in pure water. This diagram also shows that from formic acid percentage over 9% (≈2 mol dm−3 ), the medium is much more dissociated than pure water ([H+ ] = [HCOO− ] ≥ 0.03 mol dm−3 ). The maximum of dissociation is for a 50/50 wt.% mixture (0.07 mol dm−3 ). 4. Conclusions The autoprotolysis constants of formic acid/water mixtures have been determined by potentiometric titrations of a strong acid by a strong base in a series of mixtures. Fitting of experimental curves with calculated ones allowed an accurate determination of pKHS values, giving the extent of acidity scales. The obtained values show that the addition of formic acid in water leads to more dissociated media than pure water. The pKHS value varies from 3.45 to 5 (HCOOH 4.6–98.3 wt.%) with a minimum value of 2.3 around 50 wt.%. In the range HCOOH 4 mol dm−3 (17.7 wt.%) to 22 mol dm−3 (84.6 wt.%), the ionic strength is above 0.03. A correlation between acidity scales of formic acid/water mixtures and the acidity scale of pure water has also been achieved by determination of the redox function of Strehlow in each medium. This correlation shows that the acidity level in acidic media is limited by the basicity of water molecules from
Table 4 Values of the redox function R0 (H+ ) in formic acid/water mixtures (computation with 2.3RT/F = 0.058 V) HCOOH
Potential (V) vs. Ag/AgCl/KClsat.
Potential (V) vs. Fec/Fec+
mol dm−3
wt.%
E0 [H+ /H2 ]
E0 [ferrocene]
E0 [H+ /H2 ]
6 8 10 14 16 22 25.7 26.2
26.0 34.1 41.9 56.9 64.1 84.6 96.6 98.3
−0.223 −0.211 −0.194 −0.146 −0.117 −0.008 0.112 0.098
0.193 0.197 0.202 0.202 0.202 0.193 0.185 0.153
−0.416 −0.408 −0.396 −0.348 −0.319 −0.201 −0.073 −0.055
R0 (H+ )
0.28 0.14 −0.07 −0.90 −1.40 −3.43 −5.64 −5.95
5780
J.S.J. Ferrer et al. / Electrochimica Acta 52 (2007) 5773–5780
0 to 50 wt.% formic acid. For high concentrations of formic acid (>80% by weight), the whole acidity scale is in the super acid part of the generalized acidity scale pHH2 O . The diagram also shows that formic acid/water mixtures are relatively dissociated media. This would explain problems encountered in formic acid regeneration from formate by electromembrane process [16]. On the contrary, this dissociation is favourable for implementation of electrochemical devices such as direct formic acid fuel cells. References [1] C. Rice, S. Ha, R.I. Masel, P. Waszczuk, A. Wieckowski, T. Barnard, J. Power Sources 111 (2002) 83. [2] Y.W. Rhee, S.Y. Ha, R.I. Masel, J. Power Sources 117 (2003) 35. [3] S. Ha, B. Adams, R.I. Masel, J. Power Sources 128 (2004) 119. [4] X. Wang, J.M. Hu, I.M. Hsing, J. Electroanal. Chem. 562 (2004) 73. [5] Y. Zhu, S.Y. Ha, R.I. Masel, J. Power Sources 130 (2004) 8. [6] Y. Zhu, Z. Khan, R.I. Masel, J. Power Sources 139 (2005) 15. [7] R.S. Jayashree, J.S. Spendelow, J. Yeom, C. Rastogi, M.A. Shannon, P.J.A. Kenis, Electrochim. Acta 50 (2005) 4674. [8] S. Ha, R. Larsen, R.I. Masel, J. Power Sources 144 (2005) 28. [9] X. Li, I.M. Hsing, Electrochim. Acta 51 (2006) 3477. [10] R. Larsen, S. Ha, J. Zakzeski, R.I. Masel, J. Power Sources 157 (2006) 78. [11] S. Ha, Z. Dunbar, R.I. Masel, J. Power Sources 158 (2006) 129. [12] J. Yeom, R.S. Jayashree, C. Rastogi, M.A. Shannon, P.J.A. Kenis, J. Power Sources 160 (2006) 1058. [13] C.M. Miesse, W.S. Jung, K.J. Jeong, J.K. Lee, J. Lee, J. Han, S.P. Yoon, S.W. Nam, T.H. Lim, S.A. Hong, J. Power Sources 162 (2006) 532.
[14] G.S. Luo, F.Y. Wu, Sep. Sci. Technol. 35 (2000) 2485. [15] G.S. Luo, S. Pan, J.G. Liu, Desalination 150 (2002) 227. [16] J.S. Jaime Ferrer, S. Laborie, G. Durand, M. Rakib, J. Membr. Sci. 280 (2006) 509. [17] J.J. Lagowski, The Chemistry of Non-Aqueous Solvents, vol.1. Principles and Techniques, Academic Press, New York, 1966. [18] B. Tr´emillon, Electrochimie analytique et r´eactions en solution, tome 1: R´eactions en Solution, Chapitre 6: Solvants Mol´eculaires, Masson, Paris, 1993 (translated: Reactions in Solution, An Applied Analytical Approach, John Wiley, Chichester, 1997). [19] J.R. Chipperfield, Non-Aqueous Solvents, Oxford Chemistry Primers, 1999. [20] K. Isutzu, Electrochemistry in Nonaqueous Solutions, John Wiley, 2002. [21] B.P. Nicolsky, Acta Physicochim. USSR 7 (1937) 597. [22] G. Eisenman, Glass Electrodes for Hydrogen and Other Cations, Principles and Practice, Marcel Dekker, 1967. [23] N. Lakshminarayanaiah, Membrane Electrodes, Academic Press, 1976. [24] B. Tr´emillon, La Chimie en Solvants Non-aqueux, Presses Universitaires de France, Paris, 1971. [25] Y. Marcus, Ion Solvation, John Wiley, Chichester, 1985. [26] H. Strehlow, Z. Elektrochem. 56 (1952) 827. [27] H.M. Koepp, H. Wendt, H. Strehlow, Z. Elektrochem. 64 (1960) 483. [28] M. Br´eant, C. B´eguin, C. Coulombeau, Anal. Chim. Acta 87 (1976) 201. [29] L.P. Hammett, A.J. Deyrup, J. Am. Chem. Soc. 54 (1932) 2721. [30] R. Stewart, T. Mathews, Can. J. Chem. 38 (1960) 602. [31] B. Tr´emillon, Electrochimie analytique et r´eactions en solution, tome 2: R´eactions et m´ethodes e´ lectrochimiques, Masson, Paris, 1993. [32] A.J. Bard, L.R. Faulkner, Electrochemical Methods, Fundamentals and Applications, John Wiley, 2001.