E. P. Parry, I . B. Goldberg, D. H. Hern, and W. F. Goeppinger
678
ffect of Water on the Titanium Complexes in Methanolic olutions Containing Hydrogen Chloride
. Parry," I .
B. Goldberg," D. H.
Hern, and W. F. Goeppinger
North American Rockweli Science Center, Thousand Oaks, California 91360 (Received October 16, 1972) Publication costs assisted b y the North American RockweN Corp.
The electrochemical behavior of the Ti(II1) ITi(1V) couple was investigated in methanol solutions containing 0.02-0.22 M chloride ion and 0.02-7.0 M water. The presence of two electrochemically distinct Ti(II1) complexes was observed and the mechanism of the electrode processes was shown to consist of the reactions e- + Ti(1V) ;t Ti(III)(a) (EI/z -0.4 V); Ti(III)(a) + HzO e Ti(III)(b) -k Cl-(K); Ti(III)(b)= Ti(IV) -t- e- (E1,z 0.1 V). The equilibrium constant K was evaluated from pulse polarographic and cyclic voltammetric data to be 0.029 0.006. The reaction rates have been calculated from the kinetic contribution to the kinetic polarographic current, and the parameters k , and CY of the first electron transfer reaction were estimated from pulse polarographic data. Combining these results with electron spin resonance measurements, the species Ti(III)(a) comprised [TiClz(CH30H)4]+and [TiCl(CH3011[)#+. These two species equilibrate rapidly on an electrochemical time scale. Ti(III)(b) was assigned the structure [ T ~ C I ( C E I ~ Q H ) ~ H Z OIn] ~addition, +. the Ti(IV) in methanol containing more than 0.3 M HzO contains at least one more water ligand than the Ti(III), based on the negative shift of the half-wave potential with the concentration of water.
-
-
*
Introduction A recent paper from this laboratory reported the oxidation state of ti-sanium after electrochemical dissolution in methanol-HCl so1utions.l Some evidence was given in this work to suggest that in the presence of more than 0.5% water Ti(II1) gave two electrochemically distinguishable comptex species. Electron spin resonance (esr) results, which have recently been obtained in this laborator ~ have , ~indicated that in dilute solutions of Tic13 in anhydrous methanol, two distinct Ti(1II) complexes are distinguishable at low temperatures. Other electrochemical studies of the Ti(II1) ITi(1V) couple in nonaqueous solvent^^-^ have been reported. This couple has also been studied by polarography in acetonitrile6 and methanol7 containing small amounts of water. A study of niethoxide complexes of Ti(1V) in neutral and basic solutions was also reported.8 Some studies have been reported in which esr has been used to elucidate the structure of the Ti(Il1) species in solution. Various titaniunw(11I) chelatesg in aqueous media, fluoride and methoxide complexes in methanol,l*a and the complexes in a 20% terd-butyl alcohol-water mixturelob have been studied. In this work the combination of normal and pulse polarography, linear sweep voltammetry, and esr spectroscopy has been employed to investigate the nature of titanium complexes in HC1-me thanol solutions containing various amounts of H20. Values of the equilibrium constants between different chloride complexes of Ti(II1) and the rates of conversion between the complexes have been estimated, structures of complexes have been postulated, and the heterogeneous rate constants for the Ti(1V)-Ti(II1) electron transfer process have been estimated.
Experimental ~~~t~~~ Anhydrous methanol solutions containing HC1 were prepared by adding gaseous EICl to Mallinkrodt Nanograde absolute methanol (Ha0 content -0.02%) to make a stoick solution which was standardized by acid-base titraThe Journal of Physical Chemistry, Yo/. 77, No. 5, 1973
tion. The approximate water content of these solutions was 0.05-0.06% as determined by coulometric Karl Fischer titration. Subsequent solutions were made by taking suitable aliquots of this stock solution. The stock solutions were prepared weekly since HCI reacts slowly with methanol to give nethyl chloride and water. A stock solution of Ti(IV) in methanol was made by adding a known amount of reagent grade Tic14 to a measured volume of Baker Nanograde methanol and calculating the concentration. Previous work1 showed that the calculated value agreed with the value obtained by complexometric titration to within 5%. For some experiments, Ti(II1) was required. This was prepared by complete reduction of a given concentration of Ti(IV) in the supporting electrolyte of interest at a large mercury pool or was prepared from Tic13 powder (Alfa Chemical Co.). The latter material was analyzed by titration with dichromate and found to be 99.4% TiCls. A multipurpose electrochemical instrument and a previously described pulse polarograph built in this laborato-
(1) E. P. Parry and D. ti. Hern, d. Electrochem. SOC., 119, f141 (1972). (2) I. 8. Goidberg and W. F. Goeppinger, lnorg. Chem., 11, 3129 (1972). (3) I . M. Kolthoff and F. G. Thomas, J. €iectrochem. Soc., 111, 1065 (1964). (4) V. Gutmann and M. Michlmayr, Monatsh. Chem. 99, 316 (1968); V. Gutmann, M. Kogelnig, and M. Michlmayr, ibid., 99, 707 (1968); V. Gutmann and E. Nedbalek, ibid., 88, 320 (1957); V. Gutmann and G. Schober, ibid., 88, 206 (1957); 93, 1353 (1962); G. Schober, V. Gutmann, and E. Nedbalek, Z. Anal. Chem., 186, 115 (1962). ( 5 ) H. G. Brown and Hsiao-shu Hsiung, J. Electrochem. Soc., 110.
i. n_m _ [_ i~a--,. .m"
(6) P. J. Shirvington. Aust. J. Chem., 20, 447 (1967). (7) P. Desideri and F. Patami, Ric. Sci.. 30,125, 233 (1966). (8) . , R . Gut. E. Schmid. and J. Serrallach. Helv. Chim. Acta. 54. 593. ~~~. 609 (1971). (9) S. Fujiwara and M. Codell, Bull. Chem. SOC..lap., 37, 49 (1964); S. Fujiwara. K. Nagashima, and M. Codall, ibid., 37, 773 (1964); T. Watanabe and S. Fujiwara, J. Magn. Resonance, 2, 103 (1970). (10) (a) E. L. Waters and A. H. Maki, Phys. Rev., 125, 233 (1962); (b) R? Johnson, P. Wormington Murchison, and J. 8 . Bolton, J. Amer. Chem. SOC., 92,6354 (1970). I
Effect of Water on Ti Complexes in Methanolic Solutions
679
TABLE I: Effect of Water on the Normal Polarographic and Pulse Polarographic Reduction Waves of Ti(IV) in HCI-Methanol Solutionsa _l_l_-_l-l
IHzOl, IM 0.04 0.13 0.39
0.71 1.41 a
E I ) (nor~ mal pol.), V
€1 l Z (normal pulse), V
AE,/,a
Derivative peak halfwidth, V
i,cathodic (Pulse), wA
i, (Normal), P A
-0.360 -0.374 -0.390 -0.408 -0.424
-0.398 -0.413 -0.435 -0.455 -0.479
-0.038 -0.039 -0.045 -0.047 -0.055
0.123 0.120 0.107 0.115 0.114
27.6 28.5 28.8 29.6 28.4
4.27 4.49 4.31 4.20 4.22
Methanol, 0.02 I@ HCI, 1 X
M Ti(lV).
i P (derivative), PA
1.6
2.2 2.2 2.Q 1.8
* Difference between half-wave potentials measured by normal pulse polarography and normal polarography.
ryl were used for the electrochemical measurements and for the large-wale reduction. The water was determined using a Photovolt Model I1 Aquatest coulometric water titrator. Electron spin resonance spectra were obtained on a modified Varian V-4502 spectrometer equipped with a Hewlett-Packard X532B wavemeter, dual cavity, and Magnion l!j-in. magnet. The titanium sample was monitored with 100-kHz field modulation, and the DPPH (diphenyl picryl hydrazyl) reference with 18-kHz field modulation. Thia experimental procedure is described elsewhere.z To impi*ove resolution DzO, DC1 in DzO, and CH30D, obtained from Bio-rad Laboratories, were used as the solvent system for measurements of hyperfine splittrngs and 4 factors. The CH3OD was found to contain 0.04% DzO,
Results Polarogrctphy The cathodic scan normal pulse polarogram for the reduction of Ti(1V) in 0.02 M HC1 in methanol gives a well-defined wave. The half-wave potential shifts to more negative potentials with increasing amounts of water (Table I), but the single wave remains well defined. The plots of log [(id - i ) / i ] us E for the normal pulse polarograms deviate from linearity a t i > 3/4zd indicating irreversible behavior, although similar plots for polarographic waves are linear. The effect of various amounts of water on the half-wave potential and limiting current for both the polarographic and pulse polarographre reduction wave of Ti(1V) in methanol-0.02 M HC1 is shown in Table 1. The derivative pulse polarographic data weye obtained with a pulse amplitude of 10 mV. Both the polarographic and pulse polarographic waves shift about the same amount with increasing water content. The normal polarographic wave appears reversible even in 1.4 M water as indicated by the slope of the plot of log [(id L ) / I ] us. El1 and by the equivalence of the half-wave potentials for oddation of Ti(II1) and reduction of Ti(1V). This shows a t least quasireversible behavior. The difference between the normal and pulse polarograms results from the differenl time scales of these measurements. A piot of the polarographic E ~ / us. z log [HzO] is shown in Figure 1. The slope of the upper linear portion of the plot is 60 mV per decade. In anodic pulse polarography, the initial potential is set on the cathodic diffusion plateau ( e . g , -0.7 V) so that during mork of the drop life Ti(1V) is reduced to Ti(II1). For each drop successively more anodic potentials are then applied near the end of the drop life in order to reoxidize the Ti(Il.1). Polarograms recorded in this manner exibit two waves when sufficient water is present (Figure 2). This suggests that there is either a transient Ti(II1) species formed upon reduction of Ti(IV), or there is an
to
10
-0
-0
- -0 0
2
I
/
D
/I
/ -0
1
1
e I
I
I
0.36
0.38
0.40
AI 0.42
0.44
c1/2
Figure 1. Log [H20] vs. half-wave potential for the polarographic reduction of 1 mM Ti(IV) in methanol containing 0.02 M HCI.
equilibrium between two Ti(1II) species which are oxidized at different potentials. In 0.24 M H20 the half-wave potential of the first anodic wave was -0.37 V (as compared to -0.41 V for the cathodic wave) and that of the second wave was -0.11 V. The total anodic wave height in methanol containing up to about 1.5 M HzO was constant, and was also approximately the same height as that of the cathodic wave. The relative heights of each of the oxidation waves to the total wave height and the half-wave potentials as a function of water content are given in Table 11. The relative wave height ratios were also found to be a function of chloride ion concentration as shown in Table 111. Moreover in the pulse polarographic anodic scan in (11) A plot of log [(id - i ) / i ] vs. € for the pulse polarographic wave as well as tables of results for cyclic voltammetry, measured values of
the equilibrium constant, and kinetic currents will appear following these pages in the microfilm edition of this volume of the journal. Single copies may be obtained from the Business Operations Office. Books and Journals Division, American Chemical Society, 1155 Sixteenth St., N. W., Washington, D. C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number JPC-73-678. The Journal of Physical Chemistry, Vol. 77, No. 5 , 1973
E. P.Parry, I. B. Goldberg, D. H.Hern, and W, F. Goeppinger
680
TABLE 11: Effect of Variation of Water Content on Normal Pulse Scan for 1 X
0.0388
-0.398 -0.373 -0.402 -0.428 -0.455
0.133 0.392 0.705 1.41
" First oxidation wave of T i ( l l l ) .
-0L
-0I
-03
27.6 23.3 19.5 15.7 11.9
No second wave -0.093 -0.110 -0.116 -0.140
-04
-05
-06
-07
-08
Figure 2. Anodic and cathodic pulse polarograms of the T i ( l I I ) Ti(lV) couple in methanol containing 0.02 M HCI and 0.24 M H 2 0 .
I
H20.
TABLE I l l : Effect of L.i%hium Chloride on the Relative Wave Heights lor Anodic Pulse Polarographic Scan at 1.1 M Water Contenta LiCl concn Added, M
0.0 0.067
0.10 0.10 0.20 0.20 c/
[Ti(lV)]
=1X
5.4 10.0 15.0 17.8
Second oxidation waveof Ti(llI). Starting potential -0.7 V; anodic scan.
E Y S SCE
--
M Ti(IV) in Methanol Containing 0.02 M HCI
-
Relative height of wave at -0.35 V
Relative height of wave at -0.1 V
0.54 0.79 0.83
0.46 0.21 0.17 0.18 0.12 0.1 1
0.a2 0.88 0.89
M. [HCl] = 0.02M.
methanol solutions containing up to 1.5 M HzO,the limiting current for both waves is diffusion controlled as indicated by the constancy of the product of the current and the square root of the measuring time. In a similar manner the pulse polarographic limiting current for the reduction of Ti(1V) was shown to be diffusion controlled. In order to study the oxidation process of Ti(II1) independently, solutions of Ti(1V) were reduced a t a large mercury electrode at constant potential until the current decayed to less than 170of the initial value, and an anodic pulse polarogram was recorded. Such an experiment would indicate whether the two Ti(II1) species noted in the anodic pulse polarogram were in equilibrium or one was a transient species. It was observed that the pulse polarogram obtained with the Ti(II1) from bulk reduction was identical with the above anodic waves. It was also found that the wave heights were independent of whether the addition of up to 1 M deaerated water was made before or after reduction of Ti(1V). Moreover, pulse polaroThe Journal of Physical ChemisPry, Vol. 77, No. 5, 1973
-0.398 -0.413 -0.435 -0.455 -0.479
27.6 28.4 28.8 29.6 28.4
Starting potential -0.0 V; cathodic scan
grams recorded on methanol-water solutions in which Tic13 was added directly to the electrochemical cell gave equivalent results to both of the other experiments. These results thus suggest two electrochemically distinguishable species of Ti(lI1) in equilibrium in the methanol-water system. Since the pulse polarographic waves are diffusion controlled, the equilibrium concentrations of the two species can be determined from the pulse polarographic wave heights. Normal polarograms of Ti(II1) solutions prepared as described above also exhibit two waves. The relative heights of the first oxidation wave to the second oxidation wave are considerably greater than those recorded by pulse POlarography. Measurements of the dependence of the current on the mercury height show that the current increases more slowly than the expected proportionality to the l/2 power of the mercury height. The data therefore suggest that there is a kinetic contribution to the first polarographic wave. In solutions containing 7 M HzQ, where the first wave is considerably smaller than the second, a plot of log [(id - i)/i]us. E for the second wave is linear with a slope of 0.059 V. A t this water concentration the half-wave potential is -0.022 V. Cyclic Voltammetry. Cyclic voltammetric studies of the Ti(II1)-Ti(1V) systems were carried out at sweep rates between 50 and 400 mV/sec. Several typical results are shown in Figure 3. A negative shift of the Ti(XV) reduction potential at maximum current (E(p,) ) with water is found to be similar to that of the polarographic measurements. Only one cathodic peak is observed throughout the range of water concentrations studied. One reoxidation wave is observed at about -0.3 V in solutions with less than 0.1 M HzO. However, at 0.2 M HzO, a shoulder on the positive side of the oxidation wave can be observed. At concentrations of water greater than 0.5 M, a second oxidation peak at about -0.1 V becomes evident (Figure 3a). The height of the peak (i(pa)I) at -0.3 V decreases with water content (Figure 3b) and sweep rate (Figure 3c) while the height of the peak a t -0.1 V (i(p,I2) increases. At 5 M HzO, the peak near -0.3 V is barely visible. These results also suggest an equilibrium between two different Ti(II1) species where the rate of conversion from one complex to the other is significant a t the slower sweep rates and higher water concentrations. Esr Studies. Spectra of Ti(II1) produced by controlled potential electrolysis of Tic14 in HCl-WzO-CH3OH media were obtained and were identical with those obtained from solutions prepared directly from Ti613. Since it has been shown that there is significant unresolved hyperfine interaction with the protons of the solvent,12 better resolution is obtained if deuterated solvents are used.lOb Re(12) A. M . Chmelnick and 0.Fiat, J . Chem. Phys., S i , 4238 (1969)
Effect of Water on Ti Complexes in Methanolic Solutions
681
I
I
Figure 3. Cyclic voltammetry of 1 m M Ti(IV) 'in methanol containing 0.02 M tic1 and water: (a) 50 mV/sec, 0.5 M H20; (b) 200 mV/sec, 0.5 fin HaO;(c) 50 mV/sec, 2 M H20; (d) 200 mV/sec, 2 M H20.
sults obtained using CW&D as the solvent are reported here. Figure 4 shows typical esr spectra obtained from solutions of Ti613 in CH30D a t -10". In each spectrum a lowfield (1) and high.field (h) absorption can be observed. When the concentration of T i c 4 is decreased from 7.8 (Figure 4) to 3.1 mM (Figure 4b), the amplitude of h decreases relative to 1. The addition of 0.064 M LiCl to 7.0 mM Tic13 decreases 1 relative to h, whereas the addition of 0.4 M DzO iincreases 1relative to h.
Discussion Equilibrium The results from the electrochemical measurements suggest that the following reactions and equilibria are important in the titanium-HC1-methanol system in the presence of water Ti(IV) 4- e -*Ti(III)(a) ( E % -0.4 V) (1)
-
Ti(III)(a)
i-H,O
+Ti(III)(b)
Ti(III)(b) e TdJV)
+ le
+
C1-
(slow) (2)
( E y 2 - -0.1. V) (3)
where Ti(IIl[)(a)and Ti(III)(b) are two different complexes of Ti(D1) which are electrochemically distinguishable. Reactions 1 arid 3 appear reversible by normal polarography but kinetically controlled by pulse polarography whereby it is possible to evaluate the kinetic parameters of the electron transfer (see below). The conversion from Ti(lII)(a) to Ti(Ul)(b) is slow and thus allows both species to be observed electrochemically. In solutions of low water content, a Ti(1V) complex containing no water is reduced to a Ti(II1) complex which also contains no water and the polarographic half-wave potential is independent of water. As more water is added and a significant amount of aquated complex is formed, the half-wave potential shifts to reflect an elimination of one water molecule per ion of Ti(IV) reduced ( i e . , a slope of 60 mvldecade, see Figure 1). Since the exchange between methanol arid water i s rapid in Ti(IV),I3 only one reduction wave is observed. The esr data definitely indicate two different species a t low temperature. In anhydrous methanol, absorption 1 (see Figure 4) has been attributed to [TiC1(MeOD)6l2+ and absorption h to [TiC12(MeOD)4]+.2 This was based on the following: (I) Glnmelnick and Fiat found that in con-
(Cl
I;
Figure 4. Esr spectra of TiCI3 in C H 3 0 D at --IO". Solutions contain (a) 7.1 mM TiC13, (b) 3.1 mM Ti&, (6) 7 0 mM Tic13 and 65 mM LiCl, and (d) 7.2 mM Tic13 and 0.5 M D20.
centrated solutions of TiC13, the Ti(II1) ion is solvated by four methanol ligands;12 and (2) [Ti(MeOH)a]3+ would exhibit a very broad line and would be difficult to observe above liquid nitrogen temperatures in dilute solutions. It was further observed that at room temperature, absorptions 1 and h begin to broaden which suggests that there is an exchange between ligands of each complex in solution. For this reason the complexes containing only methanol and chloride ligands would not be expected to be distinguishable by electrochemical measurements. As a result, the species labeled Ti(JJI)(a) in eq 1 and 2 is a combination of chloro and dichloro complexes, which do not contain water. The following reaction, eq 4, therefore, must be added to eq 1-3 [ T i C 1 2 ( C H 3 0 H ) 4 ] + 6[TiC1(CH30H)5]2+f 61- (4) Since the amplitude of 1 increases and that of h decreases with the addition of DzO, a complex containing water must contribute to 1. Because water and methanol exhibit similar crystal field effects on titanium ions,14 the complexes containing different ratios of water to methanol would be expected to give nearly the same esr absorption. Thus, the esr spectrum of [TiC1(D20)(CH30D)4]2+would be expected to be almost identical with the spectrum of [T~C~(CH~OD}F,]*+. Esr measurements of solutions of Tic13 a t 25" which were equivalent to those used in the electrochemical ex(13) A. Fratiello, R . E. Lee, D. P. Miller, and V. M. Nishida, Mol. Phys., 13, 349 (1967). (14) R. J. H. Clark, "The Chemistry of Titanium and Vanadium," Elsevier, Amsterdam, 1968, Chapter 6.
The Journal of Physical Chemistry, Vol. 77,No. 5, 7973
82
E. P.
periments, except that deuterated solvents were used, show that the Contribution of the dichloro complex to the amplitude of the spectrum is in the order of 10% when 0.5 hf DzO and 0.02 M DCl is present. At DzO concentrations of about 1 M only a relatively small contribution to the spectrum can be seen. This appears as a high-field broadening of the line rather than a second absorption. When Hz0 and CH&H are used as the solvents, the distinction between two complexes i s more difficult because the spectra appear to be high-field broadened. This broadening had previously been attributed by other authors both to slow rotation time of the Ti(II1) in methanol and to vibrational interactlons. l5 Combining these observations with the results of the electrochemical measurements, we can define in greater detail the nature of the Ti(II1)la) and Ti(III)(b) species. As indicated above, [TiClz(CH30H)4]+ and [TiCl(CH30H)5I2+ are indistinguishable electrochemically, so this combination represents Ti(III)(a). The equilibrium of eq 2, therefore, is better given by eq 4 and [TiCl,(CH,OH),]'
-+
H,Q ; . 1 [TiC1(I120)(CH,0H),]2+ + Cl- ( 5 )
where Ti(III)(b) IS the complex [TiCl(HzO)(CH,OH)4]+. Ti(lII)(a) oxidation gives rise to the first polarographic wave (-0.3 V) and Ti(III)(b) oxidation to the second wave (-0.1 V). The fact that certain complexes which are indistinguishable by electrochemical measurements can be defined by esr (and vice versa) illustrates the power of the combined technique for studies of transition metal complexes. As the results have indicated, the rate of conversion of b LO a is on the same time scale as that for normal polarography so the wave for the oxidation of a (first wave) has a kinetic contribution However, because there is a difference of 15O-fold in the current measurement time scale between normal polarography and pulse polarography (i e., 3 us. 0.02 sec), the pulse polarographic waves are diffusion controlled and thus give the equilibrium concentrations. With known concentrations of water and chloride ion, the equilibrium constant K for eq 2 can be calculated. The equilibrium expression, neglecting activity coefficients, is given by . I
K = [ C1 -][Ti(III)(b)]/[H20J[Ti(III)(a)]
(6)
Values of 1< were calculated for variation of both the water content between 0.1 and 7.0 M a t constant chloride ion concentration and for variation of the chloride ion concentration between 0.02 and 0.22 M at constant water. The average value for K was found to be 0.029 with a standard deviation of k0.006. Even though no corrections were made for ionic strength effects or for changes in the solvent activity, the values were reasonably constant. It was assumed that HC1 and LiCl are conipletely dissociated. The value for the dissociation canstrmt of MCl in anhydrous methanol is reported to be 6 x H O - Z . 1 6 Thus, 0.02 M HC1 would be about 75% dissociated. In methanol containing about 2.4 M water, however, the dissociation constant increases by lbout threefold 16 Thus, in the range of water content covered by these experiments, the dissociation of HCl may actually incrcwse to atbout 90 or 95%. No dissociation constant for LiCI in methanol has been reported,'? but at concentrations as high as 0.2 M , it would be expected to be partially associated The Journal of Physical Chemistry, Vol. 77, Na. 5, 1973
Parry, I .
B. Goldberg, D. H. Hern, and W. F. Goeppinger
The effect of the two methanol-chloride species which comprise Ti(III)(a) can also be considered. For simplicity we can represent [TiC1(CH30H)5I2+ by TiC12+ and [TiClz(CH30H)4]+ by TiC12+. Assuming constant activity of methanol and neglecting activity coefficients, the equilibrium constant KZfor these complexes is ITiCl2'J1C1-]/[TiCl,']
= K,
( 7)
Since Ti(III)(a) is the sum of two complexes given by [Ti(III)(a)J = [TiCl"] + [TiCl,'] = [Tiel2'] (1 f ( K , / [Cl-l) 1 (8) the equilibrium expression for K becomes
K = [C1-J[Ti(III)(b)]/[H20][TiCl,] (1 I- ( K2/[C1-])} (9) If KZ is small, or the equilibrium is shifted toward the dichloro species, then the measured values of K would be approximately constant. However, in more dilute chloride media, deviations of K calculated from eq 6 might be observed. The most likely source of deviation in the values of K , however, appears to arise from measurements of the diffusion currents from the incompletely separated polarographic waves. If we assume that a 20% deviation from the value of K = 0.029 for a tenfold change in chloride can be observed, then an upper limit for K2 is estimated to be about 5 x M . Thus, at a concentration of 0.62 M HCl and 0.001 M Tic13 in methanol in the absence of added water about 20% of the Ti(III)(a) could be in the TiC12+ form. Rate of Conversion of Ti(III)(b) to Ti(III)(a). In normal polarography the oxidation wave of Ti(III)(a) is larger than that observed in pulse polarography, During the time of the polarographic measurement, the reverse reaction of eq 2 contributes to the amount of Ti(ILI)(a) a t the electrode surface, and the amount oxidized is greater than would be predicted from the equilibrium concentrations. From this kinetic contribution to the polarographic wave, the rate constant for the conversion of Ti(III)(b) to Ti(III)(a),eq 10, can be calculated. Ti(III)(b)
+
C i - L T i ( I I I ) ( a ) -1- H,O
(10)
If the concentrations of C1- and 2 0 are sufficiently greater than the concentrations of the titanium complexes, the reaction is pseudo first order, and first-order reaction rate expressions, eq 11, can be used, where k' is the pseudo-first-order reaction rate constant -d[Ti(III)(b)]/d t = h [Ti(III)(b)][Cl-j = h '[Ti(III)(b)] (11)
After Brdicka and Wiesner,lg we can write zk = nF103Aph' [Ti(III)(b)],, (12) where ik is the kinetic current, n the number of electrons transferred, F the Faraday, A the electrode area, p the (15) N. F. Garif'yanov, E. I. Semenova, N. F. Usacheva, Zh. Strukt Khim., 3, 596 (1969); J. Strukt. Chem., 3, 570 (1962); N. S. Garif'yanov and E. I. Semenova, Dokl. Akad Nauk SSSR, 140, 157 (1961); Dokl. Phys. Cherri., 140, 568 (1961): A. V. I. Aurakova, N. S. Garif'yanov, and E. I . Semenova, Sov. Phys. J E W , 12, 847 (1961); 14, 243 (1962); N. S. Garif'yanov, A. V. Danilova. and R . R. Shagidvllin, Opt. Spectrosc., 13, 116 (1962). (16) T. Shedlovsky and R. L. Kay, J. Phys. Chem.. 60, 151 (1956). (17) G. Charlot and B. Tremillon, "Chemical Reactions in Solvents and Melts." Pergamon Press, New York. N. Y . , 1969, p 276. (18) R. Brdicka and K. Wiesner, Collect. Czech. Chem. Commun., 12, 138 (1947); see also I. M. Kolthoff and J. J. Lingane, "Polarography,"2nd ed, Interscience, New York, N. Y , 1952, pp 269-273.
Effect of Water on Ti Complexes in Methanolic Solutions
683
TABLE IV: Values of Ihe Rate Constant for Conversion of Ti(lll)(b) to Ti(lll)(a)a
0.5 1.o 2.0
5,0 a
4.19
4.0 3.6 2.6
2.17 1.47
0.88 0.31
2.12 2.53 2.74 2.3
thickness of the reaction layer, and [Ti(III)(b)]o is the concentration of the species at the electrode surface. We also have the rrlation I , = {[Ti(III)(b)]m- [Ti(III)(b)]ol (13) where [Ti(III)(b)] is the concentration of these species in the solution bulk, and x is 706 X lo3 nD1/2m2/3t1/6 when the maximum current is taken. Equation 12 can be rewritten as ik = id(?(i(ITI)(b)) - ,y[Ti(III)(b)l0 (14) where id(Ti(II[)(b) would be the diffusion current of Ti(III)(b) if no ,reaction occurred. Koutecky and Brdickalg have derived an expression for the thickness of the reaction layer
15)
where 7 is the mean life time of the depolarizer. The mean life time of a first-order reaction is the reciprocal of the rate constant. Using pseudo-first-order rate constants for the forward and reverse reactions, it can easily be shown that the thickness of the reaction layer is given by
where K i s the equilibrium constant of eq 2, k' is the pseudo-first-order rate constant of eq 10, and D is the diffusion coefficient of the Ti(III)(a) complex. If we assume that the diffusion coefficients of both titanium complexes are equal, we can combine eq 13, 14, and 16 to obtain the expression
k!% =
4.3
1.8 1.9
2.0
231
100
3.3
1.4
4.0
167 198
Av
Chloride ion c:oncentratton constant at 0.02 M
/A==*
1.7
iK([&O]/[CI-])706mY3t1h zk . (17) FA z d [ T ~ ( l I I l ( b ) l - lk
Values of h' and h for eq 10 calculated from eq 17 are given in Table TW. For these conditions mz13t1/6 and A were 2.30 nig2/3sec1/6 and 0.036 cm2s respectively. The data for the equilibrium values of id(Ti(III)(a)) and id(Ti(III)(b)) were obtained by multiplying the appropriate fraction of the total c x r e n t as determined by the ratio of wave heights of the pulse polarograms by the total current of the polarogram. Considering that no corrections have been made for double layer and activity effects and possible changes in ionization, we consider the agreement very good. It is evident from Table IV that the value of id decreases significantly a t water concentrations greater than 2 M . Since Ti(1V) is easily hydrolyzed, as shown by Shirvington for TiC14 in acetonitrile containing 0.03 M water,6 it seems likely that a t high water contents in methanol even in 0.02 M WC1, some hydrolysis can occur. This product may be clectroinactive a t the low values of the negative poteniials which can be reached in acidic metha-
1 7 4 ~ 7 55
nol. The additional possibility that an electroinactive product of Ti(II1) is formed must also be considered, but this appears less likely. These questions are under current investigation. To verify the magnitude of the rate constants obtained by the above calculations, digital simulations20 of the cyclic voltammetry were carried out, Although many parameters could be varied in the simulation process to find the optimized results, only the equilibrium constant and rate constant were varied. The electron transfer was treated as Nernstian, and the rate constants were again pseudo first order. Linear diffusion was also assumed. The best values of the equilibrium constant obtained here based on superposition of the simulated and actual current voltage plots was 0.03 f 0.01 for K and 1.6 ds 0.3 sec-l for the pseudo-first-order rate constant k'. This corresponds to a value of about 80 M - l sec-I for the value of k . These results agree well with the values obtained from polarographic data, especially Considering the assumptions made in the digital simulations as well as the method for calculation of k' from the kinetic current. Heterogeneous Kinetics The reversibility of the normal polarographic wave for the Ti(1V) ITi(IK1) couple in methanol with and without water present is evident from the data. Plots of E us. log [(id - i ) / i ]are linear with a slope of 0.059 V, and the oxidation of Ti(1II) and reduction of Ti(1V) have the same half-wave potentials. However, the electrode reaction is not fast enough for the pulse polarographic wave to be diffusion controlled. The heterogeneous rate constant for the electrode reaction and the transfer coefficient can be estimated from the normal and derivative pulse data of Table 11. It is acknowledged that these values will also reflect the presence of homogeneous chemical reactions, and possible uncompensated zR. Using a small pulse amplitude (-10 mV), the width a t half height of the derivative pulse polarogram ( Wj12)can be used to obtain a value of n a for the electrode reaction. The equation for this calculation21 is given by = (0.0835/ W % )V
(18)
Since the half-width does not change significantly with water content, the value of a is not markedly affected by addition of water. In a previous paper,21 it was shown that the electrochemical rate constants can be determined from the normal pulse polarographic wave from a simple algebraic expression rather than from graphical or tabular interpolation. A (19) J. Koutecky and R. Brdicka, Collect. Czech. Chem. Commun., 12, 337 (1947); see also J. Heyrovsky and J. Kuta, "Principles of Polarography," Academic Press, New York, N. Y . , 1966, p 346. (20) S. W. Feldberg, "Electroanalytical Chemical," Vol. 3, A . J. Bard, Ed., Marcel Dekker, New York, N. Y., 1969, p 299 ff, S. W. Feidberg, J. Phys. Chem., 75, 2377 (1971). (21) K. B. Oldham and E. P. Parry, Anal. Chem., 48, 65 (1968). The Journal of Physical Chemistry, Val. 77, No. 5, 1973
E. P. Parry, I. 8 . Goldberg, D. H. Hern, and W. F. Goeppinger
4
TABLE V: Electrochemical (Heterogeneous) Rate Constant and Transfer Coefficient for Ti( I V ) Reduction in Methanol-HCI as Function of Water Content'
t
1.0
Water concn, M .
.6
0.038 0.133 0,392
0.705 1,41
A€,
1,.
V
WIl9,
v
-0.038 -0.039
0.123 0.120
-0.045 -0.047 -0.055
0.1 17 0.115 0.1 14
an
0.68 0.70 0.71 0.73
0.73
IO3, k , cm sec-'
3.5 3.5 3.0 2.8 2.3
a l mMTi(lV),O.O2MHCI.
-.2 -.4
t
c
1 -.3C
-.32
-.34
-.36
-.38
-.40
E vs SCE
-.42
-.44
+
Figure 5. Plats of log [ ( i d - i ) / i ] and log [X2(1.75 X2)/(1 X i ] where X i / i d vs. E for the pulse polarographic reduction of 1 m M TiCL, in methanol containing 0.02 M HCI.
plot of log [Xzj1.75 iX2)/(1 - X)]us. E where X = i/id for a pulse polarographic wave will yield a straight line for an irreversible reaction with a slope of na/0.059 V - l and an intercept Ellz. The E I 1 2 value is related to the electrochemical rate constant by the expression E x = ICs 9 ( 0 . 0 5 9 2 / n n ) log ( 2 . 3 1 h s ( t / D ) ' 1 (19) where E, is the standard potential of the syitem, k , is the rate constant, t i s the time of measurement after pulse application, arid D is the diffusion coefficient which was found to be 1.0 =k 0.1 x 10-6 cm2 sec-1.I A plot,of log [(id - z)/i] us. E for an irreversible pulse polarographic wave has been shown to be nonlinear.21 Figure 5 shows a plot of log [X2(1.76 5 X p ) / ( l- X ) ] us. E, and the corresponding plot of log [id - ~ ) / i 11s ] E The value of an obtained from the slope of the line i s 0.06, while eq 18 gives a value of 0.68. By assuming that the normal polarographic wave is reversible and using this half-wave potential for the value of E,, the value of the electrochemical rate constant can be calculated from e1219. The values of k and LY are given in Table 'pi as a function of tvnter content.
The Journal of Physical Chemistry, Vol. 77, No. 5, 1973
The maximum variation of a over the range of water concentration is about 7% which is well within the accuracy of the method, especially considering the agreement (see above) between the value of 01 obtained from the halfwidth of the derivative pulse polarogram compared to that obtained from the slope of the log plot. For this reason the value of a was taken as 0.65 & 0.07 for all values of water concentration. Previous work has indicated that the upper limit of applicability for the determination of k , using normal pulse polarography is about 2 x cm s ~ c for - ~values of D and t of cm2 see and 20 msec, respectively. It is, therefore, expected that for values of k , in the order of cm s ~ c -the ~ precision of the measurement would not be high. The experimental techniques used did not optimize the accurate measurement of these small differences in half-wave potential. Therefore, when the uncertainty of the measurement of a is considered, the values of rate constant should be considered only as an approximation, and no real difference in the value of k , with varying water content can be suggested by these data. The value of the heterogeneous rate constant for the reduction of titanium(1V) in methanoL0.02 1l.I HCl calculated here is approximately 3 X em 8ec-l with an uncertainty of at least k50%. This rate is fast enough to appear reversible in normal polarography Possible reasons for the apparently slow electron transfer step may be the result of changes in the geometry or coordination between the electroactive reactant and product. It could be expected from the dependence on water of the normal polarographic values that a t high water concentrations Ti(IV) loses one € 3 2 0 ligand during reduction to Ti(II1). This could account for some degree of irreversibility. The effect of the homogeneous reaction (eq 2) on these measurements should be fairly small during the time scale of the pulse polarographic measurements. ~
Acknowledgments. The authors thank Dr. R. Lee Myers, Dr. Leo Topol, Dr. George Lauer, and W. M. Moore for many helpful discussions concerning these experiments.
