J . Phys. Chem. 1991, 95, 1285-1294 electrostriction due to charge creation. This would mean that reaction 3 must proceed via bond formation, i.e., via
CUI
-
1,
+ 02 7cu'-o? I
A,'
CU"
+ 02-
(17)
whcrc k , = k , k , ' / k ,, and
AP = AV(k1) - AP(k-1) + AP(k3') = AV(K1) + AP(k3') (18)
The observed A P will mainly rcprcscnt A v ( K l ) , whose average value is -22 cm3 mol-', since reaction 3' involves a bond breakage (+A v') accompanied by a charge creation ( - A P ) , and therefore A P ( k , ' ) is expected to be close to zero. Recently, a similar value of ca. -20 cm3 mol-' was reported in the case of myoglobin for thc rcaction Mb + O2 MbO,.,, Thus, if A v ( K , ) = A P ( k , )- A P ( k - , ) is ca. -22 cm3 mol-', it follows from cq IS that A P ( k ? )must also be close to zero. This mcans that rcaction 2 cithcr is diffusion controlled (no pressure dependence in watcr) or involvcs a process that is not accompanied by a signirkant volurnc change. The mechanism of reaction 2 can be describcd via thc formation of (Cu'OJ as an intermediate:
-
cue,+ + cu+ cu2++ (Cu+02-)
(19)
whcrc formally no chargc creation occurs. Reaction 2 may also procccd via thc formation of CU'O~CU' as an intermediate where
CU'OZ
+ CUI
-
CU'O2CU'
(20)
If C U ' O ~ C Uis ' formed, it must be produced via a diffusion-controlled process, otherwise one would expect a volume collapse due to n bond formation. Nevertheless, reaction 2 is not elementary and occurs probably through an intermediate. A binuclear complcx with a peroxide bridge is very unstable and hydrolizes rapidly in aqueous solutions. Probably the rate of this dimer formation is limited by the lability of the Cu' coordination sphere and is
1285
charactcrizcd by a rate constant close to the diffusion-controlled limit.23 Thus, as it has been found that k I k 2 / k - = , (2.9 f 0.3) X IOx M-' s - ' , ~if we assume that k2 = 1 X IO9 M-' s-'? then K , 5 0 . 3 M-'. A similar value ( K , = 0.1 M-I) has been found in the case of bipyridine-Cu' and 02,where it was also assumed that reaction 2 proceeds via the formation of a dimer with a rate constant of about I X IO' M-' S K ' . ~ ~ Conclusions
By measurement of the volume of activation of the reduction of molccular oxygen by (phen),Cu', it was possible to show that under all experimental conditions the reaction proceeds via the formation of an intermediate with a copper-oxygen bond, Le., via Cu1-02. Dcpending on the concentration of (phen),Cu" present in the solutions, this transient may either react with another (phen),Cu' or may decompose to (phen),Cu" and 02-(eq I and If).
On the basis of the reported volume of activation, the formation of Cu'0,Cu' via pathway I cannot be demonstrated. I f this intermediate is formed, it must be produced with a rate constant approaching the diffusion-controlled limit. Acknowledgment. This research was supported by the Council for Tobacco Research, the Israel Academy of Sciences and Humanities, thc Council for Higher Education, the Israel Atomic Energy Commission, and G.I.F., the German Israeli Foundation for Scientific Research and Development. Registry No. (phen),Cu+, 17378-82-4; 02.7782-44-7. (23) Mruthynjaya, H. C.; Murthy, A. R. V. J . Electruanal. Chem. 1968,
(22) Projahn, H.-D.; Dreher, C.; van Eldik, R. J . A m . Chem. Soc. 1990, 112, 17.
18. 200.
(24) Orbunova, N. V.; Purmal. A. P.; Skurlator. Yu.1.: Travin. S. 0. Inf. J . Chem. Kine!. 1977, 9, 983.
Electron-Transfer Kinetics and Ternary Equilibria of the N02+/N02/N204System by Transient Electrochemistry K. Y. Lee, C.Amatore, and J. K. Kochi* Department o j Chemistry, University of Houston, University Park, Houston, Texas 77204-5641, and Erole Normale SupDrieure, Lahoratoire de Chimie. URA CNRS 1110, Paris 75231, France (Received: July IO. 1990; In Final Form: August 28, 1990)
The reversible redox potential is established for the N 0 2 + / N 0 2couplc by the cyclic voltammetric (CV) examination of the reduction of the nitronium ion as well as the microscopic reverse oxidation of nitrogen dioxide. The facile association of NO2 and dissociation of N 2 0 4are specifically included in the electrode kinetics by the successful computer simulation of thc cyclic voltammograms at rclativcly slow and fast CV scan rates. The kinetics of the N 2 0 4dissociation ( k , ) and NO2 associntion ( k , ) are determined with the aid of single-step chronoamperometry by developing the theoretical working curves bnscd on thc CE(mono) mechanism in Scheme I I . The strong dependence of the redox potential on the medium is associated w i t h significant NO2+coordination, as shown by the lincar corrclation with Gutmann's donor numbcr of thc solvcnt. The hctcrogcncous ratc constant (k,) Tor clcctron transfer to NO2+is found to be faster than k, for NO'. despite a significantly cnhanccd valuc of the intrinsic rcorganization cncrgy of NO2+comparcd to NO+ for outcr-sphcrc clcctron transfer based on the Marcus model.
Introduction
Oxidation-reduction bears an important relationship to the chemical reactivity of the various nitrogen oxides.' Among these, 'To whom correspondence should Houston.
be addressed at the University of
0022-3654/91/2095- I285$02.50/0
nitric oxide and nitrogen dioxide are particularly ubiquitous and especially relevant to atmospheric contamination.? The estab( I ) (a) Vospcr, A. J . Nitrogen Oxides and Oxyacids. In Main Group Elements. Groups lVand V; Sowerby, D. B., Ed.; MTP Int. Rev. Sci. Inorg. Chem. Series Two, Butterworths: London, 1975; Vol. I . (b) Jolly, W. L. The Inorgunic C'henrisrry uf Nitrogen; Benjamin: Ncw York, 1964.
Q 199 I American Chemical Society
1286 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
B
A
Lee et al. TABLE I: Electrochemical Parameters for the Reduction of NO2+ in Acetonitrileo
v
f'.
s-1
5 7
IO 20 30
1.4
1.0
1.8
E. V vs SCE
1.4
1.0
lishment of the redox equilibrium and kinetics for the nitrogen( 111) oxidc, i.c. (1)
is amenable to transient electrochemical technique~,~-l and the application of cyclic voltammctry to both the one-electron oxidation of nitric oxidc and thc microscopic reverse process involving thc reduction of nitrosonium salts has rccently providcd the reversible rcdox potentials as well as the rate constants for heterogeneous electron transfer for the NO/NO+ couple in various media." However the cxtcnsion of the same electrochcmical methodology to the analogous nitrogen(V) oxide led to redox potentials as widely varied as 1.29, 1.8, and 1.95 V vs SCE.'-'' We believe that such disparate results are understandable if spcciric cognixiincc is taken of the facile dimerization of nitrogen since this places a severe limitation on transient elcctrochemical measurements by shifting the redox equilibrium in Scheme I-particularly in measure with the magnitudes of the rate constants k , and k2.I4.l5
SCHEME I
NOz+ + e
.-- NOz &
1.41,
0.88 0.86 0.83 0.84 0.82
TABLE 11: Reversible Cyclic Voltammetry for the Reduction of NO,+BF;"
Figure I Initial ncgativc-scan cyclic voltammogrums of 2.0 m M NO?+BF4' in acetonitrile at scan rates of ( A ) 0.1 and (B) 7.0 V s-I a t 23 O C .
5NO
iliac
E,,: 1.32, I.32, 1.325 1.32, 1.32,
+
E. V vs SCE
NO+ + e
E,a I .38, I .38, I .399 1.405
From the cyclic voltammetry of 2 X IO-' M N 0 2 B F 4 in C H I C N containing 0. I M TBAA at 23 "C. All potentials measured relative to S C E with Eo = 0.41 V vs S C E Tor the ferrocene standard. " ( E ; t'i')/2 = E , , 2 . 'Cathodic peak current normalized by the anodic peak current 01' the fcrroccne rcferencc.
- -
I .E
E; I .2s9 1 .2s4 1.25, 1.235 I .22,
(2)
C,. m M
solvent ncc t on i t r i Ic
2.0 2.5 3.0 4.0
nitromet hane ethyl acetate sulfolane
0.h
V s-'
El12C 1.32, f 0.002 1.329 f 0.003 I .29, f 0.002 1.17, f 0.003
5-30
0.5-10 0.2-1 20-70
" From the initial negative-scan cyclic voltammogram of NO2BF4 solution containing 0.1 M TBAA, except for ethyl acetate 0.3 M TBAA at 23 OC. "Scan range for the observation of chemically re-
versible cyclic voltammograms. ' V vs SCE.
B
A
-
I .8
1.4
1.0
ci -
I .8
1.4
1.0
E,V VI SCE
(3)
E, V VI SCE Figure 2. Initial positive-scan cyclic voltammograms of 2.7 m M N 2 0 4 in acetonitrile a t scan rates of ( A ) 0.5 and (B) 7.0 V s-l a t 23 "C.
Results (2) Grosjean, D., Ed. Nitrogenous Air Pollutants; Ann Arbor Science: Ann Arbor. MI. 1979. SCCalso: National Research Council; Nitrogen Oxides; National Academy of Science: Washington, DC, 1977. (3) Bontempelli. G.; Mazzocchin, G.-A.; Magno, F. J. Electroanal. Chem. 1974, 55. 9 I. (4) Garcia. C. T.: Calandra. A. J.; Arvia, A. J. Electrochim. Acta 1972, 17. 2181. See also: Bianchi. G.:Mussini, T.; Traini, C . Chim. Ind. ( M i l a n ) 1963, 45, 1333. Topol. L. E.: Osteryoung, R. A.: Christie, J. H.J . Electrochem. Soc. 1965. 112, 861. Mussini, T. Chim. Ind. ( M i l a n ) 1968. 50, 783. ( 5 ) Cauquis, G.:Serve, D. C.R. Acad. Sci. Paris, Ser. C 1968, 266, 1591, (6) Lee, K. Y.; Kuchynka. D. J.; Kochi, J. K. Inorg. Chem. 1990,29,4196. ( 7 ) See Bontempelli et al. in ref 3. (8) Boughriet. A.; Wartel, M.; Fischer. J. C.: Bremard, C. J. Electroanal. Chem. 1985, 190. 103. (9) Boughrict. A,: Wartcl, M. J. Chem. Soc., Chem. Commun. 1989, 809. (10) See also: Cauquis. G.; Serve. D. C. R. Acad. Sci. Paris. Ser. C 1968. 267, 460. ( 1 1 ) Redmond, T. F.; Wayland, 8. B. J. Phys. Chem. 1968, 72, 1626. (12) Vospcr, A . J. J. Cheni. Soc. A 1970, 2191. (13) Addison, C. C. Chem. Reu. 1980, 80, 21. (14) For the quantitative effects of coupled (followup) chemical reactions on the cyclic voltammetry of EC processes, see: Nicholson, R. S.; Shain. I . Anal. Chem. 1964. 36, 706. For a general review, see: Heinze, J. Angew. Chem., Int. Ed. Engl, 1984. 23, 831. ( 1 5 ) See: Olmstead, M. L.;Hamilton, R. G.;Nicholson, R. S. Anal. Chem. 1969. 41. 260, for the electrode kinetics relating to followup dimeri-
zation.
Critical to the transient electrochemistry was the availability or a pure sample of the nitronium salt NO2+BF4-.Ih Since the contamination of the highly reactive nitronium salt" represented a serious ambiguity in all previous studies,'-'' special precautions were taken in this study to remove the nitrogen(ll1) oxides, and the level of the NO+ adulterant was carefully monitored by IRI8 and chemical" analysis (see Experimental Section). Similarly, dinitrogen tetroxide was repeatedly purified until it yielded a sample whose electronic spectrum coincided with that previously established by Addison et al.?" Solutions of dinitrogen tetroxide in rigorously purified acetonitrile remained colorless up to 30 mM. Increasing dissociation to nitrogen dioxideI3 was noted in 8 mM nitromethanc by thc faint yellow coloration of the solution, and (16) (a) Cook, D.;Kuhn, S.J.; Olah, G.A. J. Chem. Phys. 1960.33, 1669. (b) Kuhn, S.J. Can. J . Chem. 1962. 40, 1660. (17) Elsenbaumer, R. L. J. Org. Chem. 1988, 53, 437. (18) See: Savoie. R.; Pigeon-Gosselin, M.; Rodrigue, A.; Chenevert. R. Can. J . Chem. 1983, 61, 1248. (19) Yoshida, T.; Ridd, H. J. ACS Symp. Ser. 1976, 22, I IO. (20) Addison, C. C.; Karcher, W.; Hecht, H. Chemistry in Liquid Dinitrogen Tetroxide and Sulphur Dioxide: Pergamon: New York, 1967; p 37.
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 1287
The N 0 2 + / N 0 2 / N 2 0 4System TABLE 111: Electrochemical Parameters for the Oxidation of i>.
V
E:
s-I
7 10
1.39" 1.39,, 1.41, 1.42., 1.43,,
20 30
so
E,C 1.257 1.2.5, 1.24, 1.22x 1.223
7-50d I 0- 30"J s -30d.R
E1pb 1.324 1.32, 1.330 1.326 1.330 1.32, & 0.003' I .32, 0.006' I .5 I 2 h 0.002'
I
NO,"
'
I
I
I
i/ior 0.16 0.14 0.15 0.15 0.15
*
R
"From cyclic voltamnictry of 2.7 X M N 2 0 4 i n CHJCN containing 0. I M TBAA :it 23 O C unlcss indicated othcrwisc. All potentials mcasurcd rclativc to SCE with Eo = 0.41 V for thc fcrrocenc standard. * ( E t E,,9/2 = 'Anodic peak current normalized by thc anodic peak current of the ferrocene reference. dSweep range examincd. pAvcrage valuc. /With 1.4 m M N 2 0 4 in nitromethane. #With 2.7 m M N , 0 4 in dichloromethane.
+
a -3
-
in 3 mM dichloromethane by its distinctive yellow-brown hue (A, 400 nm).*' Redox Equilibrium Based on the Reduction of the Nitronium Salt, The initial negative-scan cyclic voltammogram of a 2 X M solution of the nitronium salt N02+BF4-in acetonitrile containing 0.1 M tetra-n-butylammonium hexafluoroantimonate (TBAA) as the supporting electrolyte at 23 O C showed only a partial chcmical rcversibility at a platinum electrode at a scan rate of u = 100 mV s-l (Figure 1 A). Thus the sharp, well-defined one-electron cathodic wave with peak potential Ep' = 1.26 V was accompanied by a severely broadened anodic wave at E," 1.4 V on the rcturn positive scan. The latter suggested the involvement of a chemical process immediately following the initial reduction of NOz+. Indeed, the cyclic voltammogram of the same solution obtaincd at an cnhanccd scan rate of u = 5 V s& showed high chemical reversibility, as indicated by the ratio of the anodic/ cathodic peak currents ip"/i{ of near unity. The standard redox couplc in cq 2 was cvaluatcd as El,* = 1.32 V vs S C E from the constancy in Tablc I of the values of (Ep" + E,C)/2 at scan rates up to 30 V s-I (using the normalized peak current based on the ferroccnc The same values for the reversible reduction of N02+BF; were obtained at both a gold and a glassy carbon electrode under otherwise the same conditions. Moreover, similar cyclic voltammctric bchavior of the nitronium salt was obscrvcd in anhydrous media such as nitromethane, ethyl acetate, and sulfolane. and the variation of the E,,? values with the solvent is prcscntcd in TLtble I I . Redox Equilibrium Based on the Oxidation of Nitrogen Dioxide. Thc initial positivc-scan cyclic voltammogram of a 2.7 X M solution of dinitrogen tetroxide in acetonitrile containing 0.1 M TBAA at 23 OC showed a broad anodic wave at E,:' 1.4 V coupled with a sharp, well-defined cathodic wavc at E,C = 1.30 V on thc return scan at u = 500 mV s-l (Figure 2A). The broadcncd anodic wavc of NOz persisted in the CV sweep range of 0.05 < I * < 1 .0 V s-l, and the normalized anodic peak current decreased as the scan rate was increased. However, the anodic wave sharpened progrcssivcly with increasing scan ratc until a pair of wcll-dcfincd anodic/cathodic waves was obscrvcd at Epil = 1.39 and E,' = 1.26 V at L' = 7 V s-l, as shown in Figure 2B. The constancy of the (Epil E,')/2 values and the normalizcd peak currcnts at thc higher scan ratcs are presented in Table 111. I t is important to note the close resemblance of the shapes of the couplcd pcaks in thc initial ncgativc-scan and positive-scan cyclic voltammograms of NO2' and NO, in Figures I B and 28, re-
-
-
+
(21) See, e&: Hall, T. C. Jr.; Blacct, F. E. J . Chem. Phys. 1952, 20. 1745. (22) For a chemically reversible redox system showing both cathodic-anodic CV waves, the standard oxidation/reduction potential lies within the interval (E; + 30 mV) < E' < (E," - 30 mV). For a discussion of this point. see refs 23 and 24. In this study, the redox potential as determined by cyclic voltammetry, viz., E l l > = (E; E;)/2 is taken as 6'. (23) Nicholson, R. S. Anal. Chem. 1965, 37, 1351. (24) Howell, J. 0.; Goncalves. J. M.; Amatore, C.; Klasinc, L.;Wightman. R. M.; Kochi, J. K. J. Am. Chem. SOC.1984, 106, 3968. (25) Brown, E. R.: Sandifer, J. R. Physical Methods ofChemistry; Rossiter, B. W.. Hamilton, J. F., Eds.; Wiley: New York, 1986; Vol. 11. pp 298ff.
+
I
-2
-1
0
log k 1 8 Figure 3. Theoretical working curves for the single-step chronoampero-
mctry of N,04 showing the variation of the normalized current function R for the CE(mono) mechanism in Scheme II as a function of the dimensionless parameter k,B. The curves are shown for different values of KC;' = 2, I , 0.54, 0.27, and 0.10.
,
spectively. This together with the coincident values of E , in Tables I1 and I11 led to the reversible potentials for the NO,+/kO2 couple in dichloromethane, acetonitrile, nitromethane, ethyl acetate, and sulfolane as 1.51, 1.32, 1.33, 1.29, and 1.18 f 0.005 V vs SCE, respectively, at 23 OC. Effect of the Nitrogen Oxide Concentration on the Cyclic Voltammetry. The cyclic voltammetry of N02'BF4- on the initial negative scan was well-behaved at the relatively low concentrations of 1-3 m M in a medium such as acetonitrile. [At higher concentrations, the CV waves were not diffusive and somewhat irreproducible owing to competitive adsorption on the platinum electrode.] Contrastingly, the cyclic voltammetry for nitrogen dioxide showed (a) an increase in the normalized anodic peak current at a given scan rate, (b) a sharper, more distinctive anodic wave in the sweep range 0.05 < L' < 5.0 V s-l, and (c) a negative shift of both Ept' and E,C (e.g., 1.42 to 1.39 V and 1.30 to 1.27 V ) at the slow scan rate of c = 0.5 V s-l, when the initial concentration of dinitrogen tetroxide was merely halved from 2.7 to 1.4 mM. Such a cyclic voltammetric behavior was highly diagnostic of the increased importance of the electroactive species (NO,) upon dilution, such as that obtained by dissociation, i.e.26.27 h
NzO, G 2NOl
(4)
Accordingly, the elcctrodc process for dinitrogcn tctroxidc must spccifically include its dissociation. Single-Step Chronoamperometry of Dinitrogen Tetroxide. The precquilibrium dissociation of dinitrogcn tctroxidc was included in the anodic process as the CE(mono) mechanism,'? i.c.
SCHEME I1 1.
N 2 0 4& 2 N 0 , A!
(5)
(26) For the effect of thc NO?mole fraction on (a) the normalized current, (b) wavc shape. and (c) peak potential, see the Experimental Section. (27) For the independent measurements of N L 0 4dissociation, see refs 8, 21, and 28-31. (28) (a) Redmond, T. F.; Wayland, B. B. J. fhys. Chenr. 1968, 72, 1626. (b) Vosper, A . J. J. Chem. Soc. A 1970, 2191, and references therein. (29) Gray, P.; Rathbone, P. J. Chem. Soc. 1958, 3550. (30) Whittaker, A. G. J. Chem. Phys. 1956, 24. 780. (31) James, D. W.; Marshall, R. C. J. Phys. Chem. 1968, 72, 2963. (32) SavCant, J. M.; Vianello. E. Electrochim. Aria 1967, 12. 1545.
1288 The Journal of Physical Chemiszry, Vol. 95, No. 3, 1991
A . MeCN
'I
Lee et al.
c. CH,CI,
B . MeNO,
-
L
z
L
i"
t A-
1 - O -3
-I
-3 log 0
log
I
e
I
log
Q
Figure 4. I i t of ~ h single-stcp c chronoamperometry data (filled circles) of N204in ( A ) acetonitrile, (B) nitromethane, and (C) dichloromethane at 23 OC with the theoretical working curve (smooth lines) for the values of log k , = 0.39, -0.05. and I .05 and KC,-' = 0.04.0.15, and 0.35, respectively. TABLE IV: Kinetic Parameters for the Dissociation of Dinitrogen Tetroxide by Single Potential Step Chronamperometry"
TABLE V: Kinetics Parameters for Heterogeneous Electron Transfer Relating to the NOZt/NOz Couple"
10-4k2:
solvent
C., mM
104K,hM
log k I b
k , , s-I
M-I
CII,CN C11,N02
0.65 0.65 1.3 1.8
IO
1.7
0.39 -0.05 -0. I6 0.90 0.2 f 0.5d 1.05
2.5
CH2CI?
0.26 0.98 1.3 1.8 1.4 f 0.4" 6.0
2 II
SKI
I f 2 1.8
" From solutions of N20, containing 0. I M TBAA at 23 OC. From the working curves (see text) with K = K'C,. where K ' is the dimensionless equilibrium constant. Calculated from K and k,. dAverage.
The kinetics of the dissociation in cq 5 was examined by single-step chronoanipcronictry, which is independent of heterogeneous kinetics of the electron-transfer step (eq 6 ) when the potential pulse is tnkcn to at lcnst 200 mV bcyond the peak p~tcntial."~'~ Accordingly, the current function ( i d ) was obtained from the experimental decay of the current at va_rious relaxation times 8. The theoretical currcnt function based on the purely diffusion-controllcd oxidation of NO, was obtained from the Cottrell i.c. (7)
whcrc F is thc faraday constant, A is the area of the clcctrode, and C and D arc thc Concentration and diffusion coefficient, respcctivcly, of NO, (see Experimental Section). The normalized currcnt ratio
R =(id)/(id)d
(8)
was defined as unity for the completely dissociated N,04,i.e., C = 2C,, where C, is the initial concentration of dinitrogen tetroxide. A scrics of working curves for the correlation of R versus log k,B wcrc generated Tor various valucs of KC,;' by the finite difference method for numerical integration (see the Experimental Section)." Figure 3 shows that a single limit is attained at R = 1 for large values of 8.)' and at the other extreme, R is strongly dependent on the dissociation constants, as expected for the frozen equilibr i u ~ i i . ' ~Thc values of thc dissociation rate (log k , ) and the dissociation constant ( K ) in Table iV were obtained by matching (33) Bard. A. J.: Faulkner, L. R. Electrochemical Methods; Wiley: New York. 1980: pp 136ff. (34) Kuchynka, D. J.; Amatore, C . ; Kochi, J. K. Inorg. Chem. 1986. 25, AnX 7 ,
(35) See: Bard, A . J.; Faulkner, L. R. In ref 33, p 143. (36) Amatore. C . ;Garreau. D.; Hammi, M.; Pinson, J.; Saveant, J . M. J . Electroanal. Chem. 1985. lR4, 1 ,
(37) Ab such, thc current function in this limit is unaffected by the dissociation kinctics. and thc current is solely dependent on NOI diffusion. (38) Thc limiting current at this cxtrcmc is determined solely by the equilibrium concentration of NO2.
solvent CH2CI2 CH3N02 CHJN EtOAc suiroianc
NO2+" k,, cm 5-l
N02' I05~. k,. cm s" (Y cm2 s-I 0.017 f 0.003 0.49 I .4 0.031 f 0.002 0.47 0.017 f 0.003 0.47 l.ld 0.031 0.005' 0.48 0.032 f 0.004 0.47 1.8 0.019 f 0.0005 0.54 0.73 (Y
-
*
0.01 f 0.001
0.51
0.06d
"At a Pt electrode in solutions containing 0.1 M TBAA (except for cthyl acctatc containing 0.3 M TBAA) at 23 O C . "From the reduction of N02+BF4-. From the oxidation of N,O,. From ref 8. 'The value or I\, = 0.03 cm s-' evaluated at a gold clcctrodc, and k , = 0.01 cm s d at a glassy carbon electrode. the experimental plot of R versus log B to the appropriate working curve for the correlation of R versus log k,B. The typical fits of the data in acetonitrile, nitromethane, and dichloromethane are shown in Figure 4. Electron-Transfer Kinetics for the Reduction of NO2+and the Oxidation of NO,. inspection of the cyclic voltammetric peak separations of the cathodic/anodic waves (i.e., AE, = E,C - E:) in Table I reveals magnitudes that are considerably larger than the 60 mV predicted for the Nernstian process for the fast heterogeneous rate of electron transfer.39 Moreover, the sweep-rate dependence of the peak separation of a(AE )/a log L' = 120 mV per decade of scan rate indicated the NOz' reduction to be far removed from electrochemical rever~ibility.~"W e note further that the cyclic voltammograms in Figures 1 B and 29 are quite symmetrical-more or less independent of solvent polarity. Such coupled cathodic and anodic waves of comparable shapes were suggestive of the electrochemical transfer coefficient CY of a half!' indeed the latter was quantitatively evaluated from the plot of the cathodic peak potential against log u as4? CY
= -29.6/(aEp/d log C )
(9)
The values of the transfer coefficient evaluated in various solvents are included in Table V. The measurement of the heterogeneous rate constant k , for electron transfer was based on Nicholson's procedureJy for the scan rate function J. = k , / ( D b c ) i / 2
(10)
where b = a F / R T and D is the diffusion coefficient for NO2+ (see the Experimental Section for details). The original tabulation (39) See: Nicholson, R. In ref 23. (40) For electrochemical reversibility the value of a E , / a log u is nil. See: (a) Amatore. C.;SavQnt, J. M.;Tasier, D. J . Electroanal. Chem. 1983, l46, 37. (b) Klinglcr, R. J.; Kochi, J. K. J . Phys. Chem. 1981, 85, 1731. (41) Vcttcr. K. J . Electrochemical Kinetics; Academic: New York, 1967. Scc also: Calus, Z. Fundamentals of Electrochemical Analysis; Wiley: New York. 1976. (42) Nadjo, L.; Saveant. J. M. J . Electroanal. Chem. 1973, 48, 113.
The N O z + / N O z / N z 0 4System
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
B
A
1.R
1.4
1.4
I 0
E, V vs SCE Figure 5. Simulated cyclic voltammograms of N02+BF[ from the clcctrochemical and kinetics parameters in Tables V and IV, respectively, at C V scan rates to match those shown in Figure 1 . Note the charging current is not included in B. E, V VI SCE
TAB1.E VI: Peak Potentials Obtained from the C V Simulation o f NLOP(I I.. V EnC.V E.", V u, V s-I E:, V E,", V 7 10
1.26
20
1.24
1.25
1.39 1.39 1.41
30 50
B
A
-
I .8
1.0
1.23 1.22
P 6
-
I .8
1289
I .4
-
I .(I
1.8
1.4 E, V vs SCE
E, V vs SCE
1.0
Figure 6. Simulated cyclic voltammogram of N , 0 4 Trom thc clcctrochemical and kinetics parlimetcrs in Tablcs V and IV, respectively. at C V scan rates to match those in Figure 2. Note the charging current is not added in B.
1.41 1.42
OWith 2.7 m M N , 0 4 in CHJN. Input parameters arc Eo = 1.32 V vs SCE,h , = 0.03 cm s-l. (1 = 0.47, k , = 5 s d , k , C, = 150 s-l, and D = 1 . 8 x lo-s c m 2 s-l.
for IJwith the peak separation AEp was replotted as a function of the experimental variable u in the range where the cyclic voltammograms exhibited chemically reversible behavior (vide supra). Sincc thc method allowed the heterogeneous rate constant to be obtained from a single cyclic voltammogram, the value of k , prcscntcd i n Table V is the average obtained from a series of CV curvcs mcasurcd bctwccn thc limits of u given in Table 11. Thc hctcrogcncous ratc constants for clectron transfer to N O z + at both a gold and a glassy carbon electrode as well as those obtaincd in various solvcnts arc also included in Tablc V for comparison. The rates of heterogeneous electron transfer from nitrogen dioxide were evaluated at scan rates that were sufficiently fast to show chemically reversible CV behavior in Table 111. The values of the rate constant k, and the transfer coefficient (Y for the anodic oxidation of N O z in various solvents were determined by the same procedures used for NO,', and they are included in Table V.43 Conrputcir Simulation of the Cyclic Voltammograms of NOz' and N 2 0 , . The electrochemical kinetics for the cathodic reaction of NO2+and anodic oxidation of N 2 0 4are based on the EC(dim)44 and C E ( m o n ~ mechanisms )~~ in Schemes 1 and I I , respectively. Since these mechanisms share in common the redox equilibrium of N 0 2 + / N O ? and the dissociation/association equilibrium of N?O,/NO?, the same electrochemical parameters should be applicable to both NO2+ reduction and N z 0 4oxidation. Accordingly the digital simulation of the initial negative-scan cyclic voltammogram of NO?+ was carried out by using the method of finite ~ ~recently diffcrcnccs, as originally dcscribcd by F ~ l d b c r gand elaboratcd by Gosscr and R i ~ g e r . The ~ ~ electrochemical paramctcrs Eo.k,, and (Y were taken from Tables l and V, and the dissociation data were k , and k z from Table IV. Figure 5 shows thc computcr-simulatcd cyclic voltammograms to reproduce the changes in peak shapes attendant upon the variation of v at both the slow-scan ( A ) and fast-scan (B) limits that were originally prcscntcd in Figure I .47 importantly the same parameters were (43) Thc diffusion coefficient of NO? was taken to be the same as that for NO2+. Compare: Adams, R. N. Electrochemistry at Solid Electrodes; Dekkcr: Ncw York, 1969. ( 4 4 ) Scc: Amatorc ct ill. in rcf 36. (45) Fcldbcrg, S.W. Eluclroanal. Chem. 1969, 3, 199. ( 4 6 ) Cosscr. D. K.; Ricgcr, P. H . Anal. Chem. 1988, 60, 1159.
I/lo
0
-I
0 log v
I
,
vs-'
Figure 7. Variation of the normalized anodic peak current with scan rate
( 1 . ) Tor 1.7 (m) and 1.4 (0)m M N,O, i n acetonitrilc u t 23 'C. The smooth curvc corresponds to the currcnt changcs prcdictcd by simulation.
applicable to the initial positive-scan cyclic voltammogram of N 2 0 4 ,as shown by the match of the computer-simulated cyclic voltammogram in Figure 6 to the experimental voltammograms in Figure 2.4' Furthermore, the variation in the CV peak potentials with scan rate, as noted in Table I l l , was reproduced in the CV simulation (Table Since the CV peak currents were scnsitivc to slight changes in N 2 0 4dissociation, the values of k , and k 2 wcrc optimized,49and the resultant fit of the normalized peak currents to the experimcntal valucs at various scan rates is shown in Figure 7 . The excellent match at both high and low concentrations of N z 0 4 thus provides strong support for the mechanistic formulation in Scheme I I . 5 0 (47) Note that the experimental cyclic voltammogram (B) at high scan rate was uncompensated for the sizeable charging current. (48) The CV peak potentials were not sensitive to changes in k , and k? at O > S V S ' .
(49) The optimized values of k , = 5 s I and kl = 6 X IO4 M I s I are comparable to 2.5 s I and I X IO' M I s I in Table IV. (50) Other equilibria of Nz04," such as the ionic dissociation to NO' and NO, 5 2 or NO?' and NO? ,x are unimportant in these aprotic media and not rcquircd for the CV simulation. (51) Cotton, F. A.; Wilkinson, G.Aduanced Inorganic Chemistry. 5th ed.; Wilcy: New York, 1988; pp 324ff. (52) Wartcl, M.; Boughriet, A,: Fischer, J . C. Anal. Chim. Acta 1979, 110. 21 I .
1290 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 TABLE VII: Reversible Reduction Potentials and Heterogeneous Electron-Transfer Rate Constants for Nitronium and Nitrosonium Cations E , p : V vs FC k,, cm s-' solvent Z ' DNb NO,' NO' N02' NO' CH2C12 64.7 0.0 1.03 (1.51) 1.00 (1.48)d 0.017 0.008d
Lee et al. ,'
I.I
I
~~
CH3N02 CH3CN sulfolanc EtOhc DMF
71.2 2.7 71.3 14.1 77.5 14.8 59.4 17.1 68.4 26.6
0.98 0.91 0.76 0.71
(1.33) (1.32) ( I . 18) (1.29)
0.98 0.87 0.76 0.75 0.56
0.015 O.OOSd (1.28)d 0.032 O.OOSd ( I .17) 0.01 0.001 5 (1.33) 0.019 0.003 (1.06) 0.006
1.0
-
0.9
-
(1.33)d
-
" Z value in kcal mol-' from refs 65 and 66. bDonor number from ref 71 arc refcrenced to dichloroethane and given in kcal mol-'. 'Potentials relative to ferrocene with E l j 2 = 0.41 (CH3CN), 0.35 ( M c N 0 2 ) , 0.48 (CH,CI,), 0.41 (sulfolane), 0.58 (CH3COOEt), and 0.50 ( D M F ) V vs S C E according to ref 68. Values in parentheses are rererenced to S C E in the particular solvent. dFrom ref 73.
I
I 0.9
1.0
1.1
E ~ ( N O + / N O ) vs FC Infrared Spectrum of N02+BFs- in Solution. The infrared spectrum of N02+BF4-taken in a Nujol mull showed a strong Figure 8. Correlation of the reduction potentials of NO2+and NO' in band at 2384 cm-' and a weaker band at 600 cm-I that correspond various solvents with EIl2referenced to ferrocene. to those also found previously in the perchlorate (2360,570 ~ m - ' ) ? ~ fluorosulfonate (2390,750 cm-'),S4 and nitrate (2375, 538 ~ m - ' ) ~ ~ salts. Dissolution in anhydrous acetonitrile also afforded an infrared spectrum with the same general appearance but with I.o sharpened lines-the higher energy band slightly blue shifted to 2391 cm-I and the other slightly red shifted to 570 cm-I. The complete vibrational spectrum of the nitronium ion in NO2+BF; consists of three well-resolved bands at 605, 1399, and 2380 cm-' 56 that were assigned by normalaordinate analysis to the bending (ub), symmetric (us), and antisymmetric (u,) stretching El/, mode^.^^.^' Of these, the band at 2380 cm-' is particularly sensitive to the c o u r ~ t e r i o n . ~Indeed ~ - ~ ~ the pronounced red-shift by -600 cm-' in covalent complexes, such as FN02,59C1N02,59 and HONOIm with u, = 1792, 1685, and 1708 cm-I, respectively, can be associated with the decrease in the 0-N-0 bond angle to 130°hld3as a result of the coordination of nitrogen to a single ligand center. Be that as it may, the minor perturbation of both u, and u b suggests that NO2* maintains its essentially linear structureh4when dissolved in acetonitrile.
-
Discussion The chemically reversible CV behavior of the nitronium ion and dinitrogen tetroxide on the initial negative and positive scans (as shown in Figures 1 and 2, respectively) provides reliable values of the reversible redox potentials for the N02+/N02couple in various solvents. Solvent Effects on the Redox Potential of the N 0 2 + / N 0 2 Couple. Although the values of E I l 2show a significant decrease from dichloromethane (1 -51 V) to sulfolane (1.18 V), the trend in Table VI1 does not follow any em irical measure of solvent polarity, such as the Kosower Z scale.6 66 Thus dichloromethane
31
~~
~
(53) (a) Nebgen, J. W.; McElroy, A. D.; Klodowski, H. F. Inorg. Chem. 1965,4, 1796. (b) Soulen, J . R.; Schwartz, W.F. J. Phys. Chem. 1962,66, 2066. (54) Qureshi, A. M.; Carter, H. A.; Aubke, F. Can. J. Chem. 1971, 49, 35. (55) Teranishi, R.; Decius, J. C. J. Chem. Phys. 1954, 22, 896. (56) Evans, J. C.; Rinn, H. W.; Kuhn, S.J.; Olah, G. A. Inorg. Chem. 1964. 3, 857. (57) The Raman-active band at 1399 cm I corresponds to the IR-active band a t I396 cm in carbon dioxide.'x (58) Osberg, W. E.; Hornig, D. F. J . Chem. Phys. 1952, 20, 1345. (59) Bernitt, D. L.; Miller, R. H.: Hisatsune, 1. C. Spectrochim. Acra 1%7, 23A. 237. (60) McGraw, G . E.; Bernitt, D. L.; Hisatsune, I. C. J. Chem. Phys. 1965, 42. 237. (61) Legon, A. C.; Millen, D. J . J. Chem. SOC.A 1968, 1736. (62) Bird. G . R.; Baird, J. C.; Jache, A. W.; Hodgeson, J. A.; Curl, R. F.,
'
Jr.; Kunkle. A. C.; Bransford, J . W.; Rastrup-Andersen, J.; Rosenthal, J. J. Chem. Phys. 1964, 40, 3378. (63) Luzzati, V. Acra Crystallogr. 1951, 4, 120. (64) Truter, M. R.; Cruickshank, D. W. J.; Jeffrey, G . A. Acra Crystallogr. 1960, 13. 855. (65) Kosower, E. M. Introduction to Physical Organic Chemistry; Wiley: New York, 1968.
0
.8
.4 DN,
1L2
eV
Figure 9. Correlation of the reduction potentials of various cations with Ag' (0),TI' the donor number of the solvent for NO2+ (b),NO' (a), (01, and Na' ( 0 ) with referenced to either ferrocene or bis(diphenyl)chromium(l) in volts and DN given in electronvolts.
(Z= 65 kcal mol-') and ethyl acetate (Z = 59 kcal mol-') are solvents of more or less comparable polarity,h7 but they lie at opposite extremes of Table V11, insofar as their effect on E O . Likewise, nitromethane and sulfolane are both considered to be rather polar solvents with Z = 71 and 77 kcal mol-', but the values of E l j 2in these solvents are strongly distinguished (compare entries 2 and 5, Table VII). However, a closer inspection of the solvent variation of El12.68reveals a linear correlation with the donor number (DN),simply expressed as7! Eli2 = -0.4DN
+ 1.03
(11)
(66) (a) Kosower, E. M.; Mohammed, M. J. Am. Chem. Soc. 1968, 90, 3271. (b) Kosower, E. M.; Mohammed, M. J . Am. Chem. SOC.1971, 93, 2713. (c) Kosower, E. M.; Mohammed, M. J . Phys. Chem. 1970, 74, 1153. (67) Reichardt, C. Soluenr Effects in Organic Chemistry; Verlag Chemie: New York, 1979. (68) Referenced to a ferrocene standard to correct for the difference in the
junction potentials in various solvent^."^^'^ (69) (a) Gagne, R. R.; Koval, C . A.; Lisensky. G. C . Inorg. Chem. 1980, 19. 2854. (b) Gritzner, G . ; Kuta, J. Pure Appl. Chem. 1984, 56, 461. (70) Kadish, K. M.: Cornillon, J.-L.; Yao, C.-L.; Malinski, T.; Grittner, G.J. Electroanab Chem. 1987, 23.7, 189.
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
The N 0 2 + / N 0 2 / N 2 0 4System The existence of such a relationship is understandable if cognizance is taken of the redox equilibrium of the N 0 2 + / N 0 2couple that is dominatcd by the highly reactive nitronium cation, owing to its small size and coordinatively unsaturated ~ h a r a c t e r . ~As ' such, thc role of the medium is directed strongly toward the distribution of thc NO2+ charge, particularly by solvent coordination. Indeed, measures of thc latter are provided by the donor number (or donicity), as defined by Gutmann7' in terms of the enthalpy change for 1 : 1 adduct formation of antimony pentachloride with electron-pair donor solvents,'? i.e. SbC15 + D
D-SbC15
(12)
relative to that in the noncoordinating I ,2-dichloroethane as the reference solvent. On this basis, nitromethane (DN = 2.7 kcal mol I) is indccd a significantly weaker donor solvent compared to sulfolane (DN = 15 kcal mol-')-in contradistinction to their comparable solvent polarities. The dominant role of donicity in the solvent variation of E , for the N 0 2 + / N 0 2couple also applies to the N O + / N O couple)' as shown by the unit slope of the linear correlation established in Figure 8. Moreover the same applies to a variety of other cationic spccics including silver( I), thallium( I), and sodium ion.74 Despite the experimental scatter about the linear correlations of El,2with solvent for the family of cations shown in Figure 9, their strong dependence on the donor number is ~ n m i s t a k a b l e . ~Since ~ the strong coordination of solvent as ligand to Ag+ is known,7h a similar interaction with solvent of NO2+and NO' is reasonable in view of the linear correlations obtained in Figures 8 and 9. Howcvcr such an explanation is clearly an oversimplification of solvent effects for several reasons. Thus the infrared studies (vide supra) indicate that the nitronium ion NOz+ dissolved in acetonitrile largely retains its linear structure extant in crystalline N02+C104-,64as indicated by the minor shift (7 cm-I) of the charactcristic antisymmetric stretching band to 2391 cm-I. On the other hand, the strong coordination of NO2+ to a single molcculc of acetonitrile would result in a trigonally bent adduct and lead to a marked red-shift in antisymmetric stretching band at 2384 cm-' (Nujol mull), as found in the pyridine complex ) ~ simpler ~ covalent derivatives pyNOz+BF4-(u,, = 171 5 ~ m - ' and XNO, with X = F, CI, and H O with u , = 1792, 1685, and 1708 cm-I, re~pcctively.~~.~" The retention of the linear structure suggcsts that NOz+ is solvated by more than one molecule of acctonitrilc that arc isotropically distributed about the Dmhaxis. I n contrast, the nitrosonium ion NO+ undergoes a substantial shift of almost 500 cm-' to lower energy in the N - 0 stretching frequency in acctonitrilc rclative to that in the crystalline NO'BFL.~~ Thc observation of 11 = 187 1 cm-' for NO+ dissolved in acetonitrile is strongly rcminisccnt of that mcasured for the cation covalently bound to a singlc ligand X N O as in X = py, F, and CI at u, = 1801, 1844, and I800 cm-I, r e ~ p e c t i v e l y ,or ~ ~in- ~metal ~ complexes such as F?HgNO, CI?SnNO, and F 2 P b N 0 with u, = 1892. 1892, and 1891 cm-I, respectively.'" (71) Mayer, U.; Gutmann, V. Struct. Bonding 1972, 12. 113. For the correlation in eq 1 I, the values of the D N (Table VI1) in kcal mol were convcrtcd to volts. (72) (a) Olofsson, G.;Lindquist, 1.; Sunner, S. Acta Chem. Scand. 1963, 17,259. (b) Gutmann. V.; Steininger, A.; Wychera, E. Monatsh. Chem. 1966, 97, 460. (73) Lee, K . Y. et al. in ref 6. (74) (a) Duschek, 0.;Gutmann, V. Z . Anorg. Allg. Chem. 1972,394, 243. (b) Gutmann. V.; Schmid, R. Monatsh. Chem. 1969, 100, 21 13. (75) For bivalent cations. the slopes of the E,,: correlations with DN are gencrally in the rangc 0.6-0.7. See: Giitzner, G. J . J . Phys. Chem. 1986, 90, 5478. (76) Morkovnik, A. S.; Morkovnik, 2.S.; Bcssonov, V . V . Russ. J . Inorg. Chem. (Engl. Tran.7.)1987. 32, 1799. (77) Olah, G . A.; Olah, J . A.; Ovcrchuk, N . A . J . Org. Chem. 1965, 30, 3373. (78) Kim, E. K. 1Jnpublished results. (79) Laane, J.; Ohlscn, J . R . Prog. Inorg. Chem. 1980, 27, 465. (80) (a) Tcvault. D.; Nakamoto, K. Inorg. Chem. 1976, 15, 1282. (b) Tevault. D.; Strommcn. D. P.; Nakamoto, K . J . Am. Chem. Soc. 1977, 99, 2997.
'
1291
Activation Barriers for the Reduction of Nitronium Ion. The results summarized in Table VI1 show that the redox equilibria of the nitronium ion are comparable to those of the nitrosonium ion, despite its being in a higher formal oxidation state of nitrogen(V) compared to nitrogen( Moreover NO+ is widely employed in electron transfer as an oxidant:' whereas NO2+ is rarely used in this capacity but more commonly exploited for its electrophilic properties.62 These considerations raise the question as to how the structural change from N O + / N O to N 0 2 + / N 0 2 affects the kinetics barrier to electron transfer in solution, particularly in view of their thermodynamics similarity. For the comparison, the rate constant k, for heterogeneous electron transfer is related to the activation free energy as
k , = A exp[-(AG'
+ w)/RT]
(13)
where w is the electrostatic work term required to transport the electroactive species from the bulk solution to the electrode. According to the preequilibrium model,R3the preexponential factor A = 6reI',lu,lcan be evaluated as 3 X 1 Os cm s-I for rn = I , br, =1X cm, and u, = 3 X I O l 3 s-1.84 However for the comparison of the two redox couples, the relative rates simplify toB5
k , l / k , 2 = exp[-(AGII - AG'z
+ w I - w2)/RT]
(14)
where the subscripts 1 and 2 refer to the N 0 2 + / N 0 2 and N O + / N O couples, respectively. The work term describes the average electrostatic interaction,Rhand it is (according to the Gouy-Chapman-Stern model of the diffuse double layer67)directly related to the charge density on the electrode and most importantly determined by the potential.@ Since NO2+and NO+ are reduced in the same potential range (and they are of roughly comparable size), the difference in work terms is likely to be small. Accordingly, the difference in activation free energy for electron transfer can be approximated as
AG2* - A G l * = -RT In k , , / k , ,
(15)
From the measured values of k, of 0.03 and 0.005 cm s-I for NO2+ and NO+, respectively, the free energy difference is evaluated as I . 1 kcal mol-'. Thus the slower rate of heterogeneous electroll transfer to NO'73 results from a reorganization energy that is actually - 4 kcal mol-' higher than that to NO2+. Such a difference is likely to arise in outer-sphere electron transfer from the inner-sphere reorganization terms given asR9 A, =
E- LRP (A# + E- f b R f b o J
f\R +.Lo
J
fbR
(Au)?
(16)
+fbo
where the subscripts s and b refer to the stretching and bending force constants and the superscripts R and 0 refer to NO,(NO) and NO,+(NO+), respectively. From the structural parameters " ~ ~sumof the nitrogen oxides in the published l i t e r a t ~ r e ~ and (81) (a) Musker, W. K.; Wolfold, T.L.; Roush, P. B. J . Am. Chem. Soc. 1978. 100,6416. (b) Eberson, L.; Radner. F. Acto Chem. Scand. 1984, B38, 861. (c) Bandlish, B. K.; Shine. H. J . J . Org. Chem. 1977, 42, 561. (d)
Mocella, M. T.; Okamoto, M. S.; Barefield, E. K. Synrh. React. Inorg. Met.-Org. Chem. 1974, 4, 69. (e) Caulton, K . G . Coord. Chem. Rev. 1975, 14, 317. (82) (a) Olah, G . A.; Kuhn, S. J . Friedel-Crafts and Rrlaied Reactions; Olah, G . A., Ed.; Interscience: New York. 1964; Vol. I l l , Chapter 43. (b) Guk. Y. V.: Ilyushin, M. A.; Gold, E. L.; Gidaspov. B. V. Russ. Chem. Reu. (Engl. Trans.) 1983. 52, 284. (83) (a) Brunschwig, B. S . ; Logan, J.; Newton, M. D.; Sutin. N . J . Am. Chem. SOC.1980. 102, 5798. (b) Marcus, R. A . Inr. J . Chem. Kinet. 1981, 13, 865. (84) Hupp. J . T.; Weaver, M. J . J . Electroonab Chem. 1983, 152. I . (85) Compare Table VI11 for the comparable structural parameters of NO' and NO:' for the cancellation of the preexponential factor. (86) Frumkin, Z. Phys. Chenr. Absfr. A 1933, 121. (87) See: Bard, A . J.; Faulkncr, L. R. In ref 33, pp 488ff. (88) Stern. 0. 2. Elektrochem. 1924, 30, 508. (89) Marcus. R . A . J . Phys. Chem. 1963, 6 7 , 853. (90) See: Truter et al. in ref 64. (91) Weslon, R. E., Jr.; Brodasky, T. F. J . Chmt. Phys. 1957, 27, 683.
1292
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
marized in Table VI I I, the reorganization energy X i = 78 kcal mol-' y w for NO2+ is calculated to be substantially greater than A, = 2 I kcal mol-' for NO+ when electron transfer proceeds via an outer-sphcrc activated complex. The failure of the Marcus theory to account for thc significantly faster rate for the electrochemical rcduction of NO,+ relative to NO+ may be attributed to the participation of an inner-sphere pathway at the electrode, as prcviously obscrvcd in thc rcduction of chromium(ll1) comp l c x c ~ . Indeed ~ the strong dependence of El,? on solvent donicity (see Tablc VII) undcrscores the importance of NOz+coordination as an indication of thc inner-sphere activated complex a t the electrodc intcrfacc.IM Moreover it is likely that electrochemical reduction of NO+" also contains a strong component of an inner-sphcrc pathway."" Experimental Section Matcriols. Thc nitronium salt N02+BF4-was prepared from nitric acid, hydrogen fluoride, and boron trifluoride according to thc proccdurc dcscribcd by Elsenbaumer." T o avoid adulteration by NO+BF4-, 250 m L of fuming nitric acid (Fisher reagent grade) was first trcatcd with 2.5 g of urca and an equal volume of conccntratcd sulfuric acid at 0 "C; and the mixture distilled in vacuo to yield purc nitric acid (colorless). The subsequent reactions wcrc a11 carricd out with plastic (poly(methylpentene), polycthylcnc, and Tcflon) cquipment and either undcr an inert argon atmospherc (Schlcnk techniques) or in a Vacuum Atmospheres MO-41 drybox to maintain < I ppm dioxygen and water. The purity of N02+BF4-(after recrystallization from acetonitrile at -25 "C) was assayed by gas chromatographic and NMR spectral analysis of thc nitration product 4-nitrotoluene." The complcx with 18-crown4 in dichloromethane was colorless (which confirmed the absence of the yellow NO+ complexIo2) and showed thc charactcristic bandIn at 2383 cm-' in the IR spectrum. Dinitrogcn tctroxide (Matheson, reagent grade) was initially treated with dioxygcn at 0 "C then dried over P 2 0 5 ,and finally redistilled twicc prior to USC.Thc UV-vis spectrum of dinitrogen tetroxide in hcxanc showcd A,,,,,, at 343 nm, and the extinction coefficients at the thrcc sclcctcd wavclcngths of 270, 301, and 343 nm coincidcd with thc valucs rcported in the literature.20 Tetra-n-butylammonium hcxafluoroantimonate (TBAA) crystallized from an aqucous solution of tctra-n-butylammonium bromide (Fluka) and sodium hcxnfluoroantimonate (Ozark-Mahoning), The colorless crystals wcrc dricd and rccrystallizcd from a mixture of ethyl acctatc and diethyl cthcr. Crystalline TBAA was pulverized and dricd in mcuo at 140 O C prior to use. Acctonitrilc (Fishcr, rcagcnt grade) was stirred with KMn04 for 24 h at room temperature, and the mixture was heated to reflux until thc liquid was colorless. After removal of the solid (MnO,), the acctonitrilc was rractionatcd from P,05 undcr an argon atmosphcrc. It was rcfractionated from calcium hydride and stored in a Schlcnk flask (Tcflon stopcocks) under an argon atmosphere. Nitromcthanc (Aldrich, 96%) was fractionally crystallized at -78 OC. Thc palc ycllow liquid from the partially frozen mixture was decanted, and thc colorless crystals werc resubjcctcd to this proccdurc thrcc timcs. The resulting colorless nitromethane was passed through a column of ncutral alumina, followcd by frac(92) Field, R. W. J. Mu/.Specfrosc. 1973, 47, 194. (93) Nicholr. N. L:Hause, C . D.;Noble, R. H. J. Chem. Phyr. 1955, 23, 51. (94) Qureshi. A. M.;Carter, H. A.; Aubke, F. Can. J. Chem. 1971, 49. 3s. (95) (a) Bird, G. R.; Baird, J. C.; Jachc, A . W.; Hodgeson, J. A,; Curl, R. F.. Jr.: Kunkle. A. C.; Bransford, J. W.: Rastrup-Andersen. J.; Rosenthal. J . J. Chem. Phys. 1966, 40. 3378. (96) Scc Laanc ct al. in ref 79. (97) Scc Ebcrson ct al. in rcf 82. ( 9 8 ) The strong dcpcndcncc of A, on the 0-N-0 angle is indicated by the 20'88 increase accompanying the change to the linear structure.'" (99) Wcnvcr. M. J.; Anson. F. C. J . Am. Chem. Soc. 1975, 97, 4403; Inorg. Chem. 1976, 15. 1871. (100) Thc adsorption of NO2+on the platinum electrode is qualitatively notcd by thc sharp. nondiffusive CV wavc. especially at high concentrations. (101) Kochi. J . K. Acfu C'heni. Scund. 1990. 44. 409. (102j Hco, G . S.; tiillman. P. E.; Rartsch, R. A. i. Hererocycl. Chem 1982. 19. 1099.
Lee et al. tionation in vacuo. Dichloromethane (Baker, reagent grade) was stirred with successive portions of concentrated sulfuric acid until the acid layer was colorless.'03 The resulting dichloromethane was washed with 5% aqueous NaHCO, and water. After drying ovcr CaCI2, the dichloromethane was distilled from Pz05 and redistilled from CaH2 under an argon atmosphere. Ethyl acetate (Fisher) was washed with aqueous NaHCO, and then with saturated aqueous NaCI. The resulting ethyl acetate was dried with CaCl, and then P 2 0 Sand fractionated under an argon atmosphere. Sulfolane (Shell) was passed through a column of activated 4A molecular sieves. Small portions of KMnO, were added to 50 OC until the pink color persisted for at least an hour. Excess KMnO, was destroyed with CaH,, and the sulfolane fractionated at 0.2 mmHg. N,N-Dimethylformamide was dried over anhydrous powdered BaO and then fractionated a t 5 mmHg.lo3 Electrochemical Instrumentation and Measurements. Cyclic voltammetry was performed on an iR-compensated potentiostatIM drived by a Princeton Applied Research (PAR) 175 Universal Programmer. The high-impedance voltage-follower amplifier was mounted external to the potentiostat to minimize the length of the connection to the reference electrode for low noise pickup. Current-voltage curves were recorded either on a Houston Series 2000 X-Y recorder or displayed on a Tektronix 5 I I5 storage oscilloscope. Fast-scan voltammograms (c > 1 V S K I ) were recorded on a Could Biomation 4500 digital oscilloscope interfaced to the Compaq Deskpro computer, with which all further data manipulation was performed. The cyclic voltammetric cell was of airtight design with highvacuum Tcflori stopcocks and viton O-ring seals to maintain an inert atmosphere without contamination by grease. The working platinum disk embedded electrode consisted of a 1 +"diameter in glass. The gold working electrode was prepared by sealing a gold wire ( r = 0.5 mm, Goodfellows) in glass. The glassy carbon electrode (r = I .5 mm) was obtained from Bioanalytical Systems Inc. The counter electrode consisted of a platinum gauze sheet separated from the working electrode by -0.75 cm. The S C E reference electrode and its salt bridge were separated from the working electrode compartment by a sintered glass frit. The SCE rcference electrode was connected to the counter electrode via a 0.02-pF capacitor to aid in the compensation of the iR drop. All potentials are reported vs SCE, and the E , , : values for the ferrocene/ferrocenium couple were measured as 0.41 (acetonitrile), 0.35 (nitromcthane), 0.48 (dichloromcthane), 0.58 (ethyl acetate), 0.42 (sulfolane), and 0.50 (N,N-dimethylformamide) V relative to SCE!' Thc platinum microelectrode for the determination of thc diffusion coefficient D was constructed from a IO-pm-diameter platinum wire scaled in soft glass. The electrode area was calibrated with the ferrocene standard'"? by using the relationship for the limiting current as i = 4nFDrC'Oh at slow scan rates (0.1-1 V S K I ) , The diffusion coefficient for N02BF, was measured with thc microelectrode under conditions at which the macroelectrode yielded reversible cyclic voltammograms in a given solvent system (see Table 11). However, thc diffusion Coefficient of NOz+ in CH2CI2could not be. determined due to the insolubility of the salt. The value of D in dichloromethane was estimated from its viscosity"" which is slightly greater than that of acetonitrile but less than that of nitromcthanc. Cydic P'oltanimrtry of the Nitroniuni Salt. In the drybox, N0,+BF4- (2.4 mg, 1.8 X IOT5 mol) was weighed and placed into the working electrode compartment of the cell. To the top of the cell was attachcd a column filled with activatcd alumina. that was baked at 300 "C in vwuo for 24 h. With the aid of a hypodermic syringc, 9 m L of thc 0. I M stock solution of TBAA was passed (103) Perrin. D. D.; Aramarego. W. L. F.; Perrin. D. R. Purification of Laboratory Chemicals, 2nd ed.: Pergamon: New York. 1966. (104) Garreau. D.; Saveant, J. M. J. Elecfroana/. Chem. 1972. 35, 309. (b) Garrcau. D.; SavSant, J. M. J. E/ectroonal. Chem. 1974. 50. I . (105) KuwanJ. T.: Bublitz, D. E.; Hoh. G . J . Ani. Chem. Soc. 1960.82, 581 I. (106) Howcll. J. 0.;Wightman, R . M. Anal. Chem. 1984. 56, 524. (107) Riddick. J. A,; Bunger, W. B. OrganicSolvenrs, Physical froperlies und Methods of Purification; Wiley: New York. 1970.
The N 0 2 + / N 0 2 / N 2 0 4System through thc alumina column and added to the working electrode compartment, and 3 mL was added to the reference compartment. Voltammograms were recorded at various scan rates. In all solvents studicd, the adsorption of NO2+ on the Pt working elcctrodc was apparcnt at conccntrations greater than 5 X IO--' M. Howcvcr at conccntrations less than 5 mM, the CV wave was reproduciblc and largely diffusive, as indicated by the constant values of i / v ' r that arc listed in Table I . The cyclic voltammogram o P N 0 2 +was also measured with gold and glassy carbon elcctrodcs from a 2 X IOT3 M solution of N 0 2 B F 4in acetonitrile containing 0.1 M TRAA. The same potential of E I j z= 1.32 V was obtaincd with both clcctrodes, but the peak separation appearcd to bc largcr with the glassy carbon electrode (e&, 300 mV at IO V s-l). Accordingly, the heterogeneous electron-transfer ratc constant at the glassy carbon electrode was estimated as 0.01 cni s - I by thc cxtrapolation of Nicholson's working curve.39 Cyclic Voltartiriietry of Dinitrogen Tetroxide. The column of activatcd alumina was attached to the working electrode compartmcnt of thc ccll in thc drybox, and 6 mL of the 0.1 M stock solution of TBAA was added to the working electrode compartmcnt through thc alumina column and 3 mL to the reference compartmcnt. In a separate Schlenk flask, a 0.32 M stock solution of N ? 0 4 was prepared at 0 OC, and 50 p L of the stock solution was added to the working electrode compartment and 25 p L to the rcferencc Compartment to minimize gaseous diffusion between the two compartments. All transfers of NzO4 were performed with a glass syringc cquipped with a platinum needle which was cooled to 0 "C undcr an argon atmosphere before use. N o contact of thc N,O, solution with metals other than platinum was made at any timc. Cyclic voltammctry was performed from a resting potcntial of I . I5 V as the zero current potential. Tetra-n-butylarnmonium hcxafluoroantimonate was the supporting electrolyte of choicc, sincc thc usc of the hexafluorophosphate, perchlorate, or tctrafluoroboratc salt introduced trace amounts of contaminant(s) that could not be removed despite multiple recrystalliza t ions. Thc anodic bchavior of N z 0 4 was scrutinized in detail owing to the current plateau in Figure 2A. Since the normalized current ; / i o (like the currcnt function i,,/v'u) is a constant for a pure diffusive wave.Ion it was used to correct for the background current and to minimizc thc systcmatic crrors in the measurement of the peak currcnts. Thc normalizing factor was obtained from the anodic currcnt of fcrroccnc at thc Concentration of N 2 0 4 . The plot of i / i o vs log I' showed that it monotonically decreased to a limiting minimum on going to fast scan rates. The constancy of thc nornializcd currcnt at thc lowcr limit indicated the absence of a chemical kinetics involvcmcnt on this time scale. The lower limit incrcascd as thc conccntration of N 2 0 4decrcased as a result of the incrcascd molc fraction of N O 2 in the N z 0 4solution. The negativc slopc ( ; / i nvs log u ) was also higher at low concentrations of N,O+ Thc maximum limiting currcnt (two-elcctron limit) expected at slow scans could not be obtained even at the lowest conccntration used (0.65 mM) in any solvent system with the scan ratc of I. > 0.01 V s-l. The decrease in the concentration of N2O4 (i.e., the increase of the mole fraction of NOz in solution) also affected the shape of anodic wavc and thc pcak potentials of both thc cathodic and anodic wavcs. Thc broad anodic wavc at slow scans (I. = 0.05-5 V s-I) was sharper (more diffusional) at low conccntrations of NzO+ Thc anodic and cathodic wavcs were shiftcd to morc ncgativc potcntials (closer to the E I l 2 of N 0 2 + / N O ? )at low concentrations. Thus the cyclic voltammograms could be made to resemble that for the NO2+/NOzcouple by increasing thc molc fraction of NO2. The rcvcrsiblc cyclic voltammogram for N 0 2 + / N 0 2was selected among those obtained at various scan rates by carefully tracing the normalized current, thc potcntial shift, and thc currcnt ratio. SingIi~-StcpChronoomperometry of Dinitrogen Tetroxide. The singlc-stcp chronoampcromctry of N z 0 4was performed with the samc ccll and clcctrodcs uscd for thc cyclic voltammctric mca(108) See: Amatore, C.: Verpeaux, J.-N.: Krusic, P. J . Organometallics 1988, 7. 2426.
The Journal of Physical Chemistry, Vol. 95, No. 3#1991
1293
surements. In a typical experiment, the PAR universal programmer was programmed to step from 1.15 to 1.80 V and held at 1.8 V for the time interval I?. The I? values ranged from 0.01 to 10 s, at which the constant value of id0 was obtained by using the ferrocene standard. The current decay was recorded on a Gould Biomation 4500 digital oscilloscope interfaced to a Houston 2000 X-Y recorder. The current data collected were corrected for the background current that was obtained by performing the same experiment without N204 present. The working curves in Figure 3 were simulated on the basis of Scheme 11, where NZ04, NOz, and NO2+ are hereafter represented by A , B, and C for convenience. The dimensionless variables are introduced as a = [ A ] / C n ,b = [B]/C,, A , = k,O, h2 = k2CoI?,K ' = A,/A2 = k , / ( k z C o ) = K/CO, T = t/I?, and y = x(DI?)-'12,in which Co is the initial concentration of A as introduced into the cell, 0 is the duration of the potential pulse, t is the time elapsed from the beginning of the potential pulse, x is the distance for the electrode surface, and D is the average diffusion coefficient of A and B. One obtains the following partial differential equations that govern the diffusion and reaction of species A and B within the diffusion Iayer:32.36 a u l a T = a2a/ay2
a b / a T = a2b/ay2
- X,U
+ A,b2
+ 2 4 0 - 2k2b2
(17) (18)
When the potential pulse is taken sufficiently positive for B to be oxidized completely at the electrode surface, the boundary conditions for this system are 0 C T II , y = 0 , aa/ay = 0 , and b = 0. The boundary conditions at time T = 0 for all y > 0 or at T > 0 for y m are equivalent to a = a,, and b = b,,, where aeqand b,, are the dimensionless concentrations of A and B resulting from the establishment of the dissociation equilibrium in eq 5 so that
-
a,,
+ b,,/2
= 1
(19)
K'a,, = beq2 from which it follows that aeq= 1
+ (K'/8)[1
- (I
+ 16K')'/2]
(21)
The solutions of the partial differential eqs 17 and I8 at the initial and boundary conditions given above were carried out by a classical numerical procedure involving explicit finite d i f f e r c n ~ e s . ~ ~ . ~ . ' . ' ~ ~ The dimensionless current was evaluated at time T = I ( t = 0) as32.36
and the normalized current ratio H in eq 8 was obtained as
R = (ifi)/(ifi)d = 9(~'/'/2)
(23)
since the dimensionless current that corresponds to pure diffusion is given qd=
( i f i ) d / ( ~ ~ ~ o=f2-11? i)
(24)
Simulations of the Cyclic Voltaninrogranis. The digital simulations of the cyclic voltammogrPms of NO2+ and N 2 0 4 were carricd out with the Fortran vcrsion of the Gosscr-Rieger program4" that was proccsscd with a Compaq Dcskpro personal computcr. The simulations wcrc bascd on the mechanisms in Schcmcs I and II, for which the initial input parameters were taken from Tablc V for E O , k,, N , and D and Table IV for k , and k z . Sincc the simulatcd pcak potential was in good agrccmcnt with that obtaincd from thc reversible cyclic voltammogram of NO2+ and NZO+only the chcmical kinctic parameters k , and kJ,, were changed to describe the anodic behavior of N2O4. The change of chcmical kinctics paramctcr did not affect the pcak potential of rcvcrsiblc CV at scan ratcs L' > 7 V s-l. The cyclic voltammogram of N 2 0 4 at diffcrcnt conccntrations (1-3 mM) with various scan rates (o = 0.01-5 V s I ) was first compared with output, and the CV of NO2+was chcckcd with thc samc paramctcrs. The final optimization was carricd out by comparing ihe
J . Phys. Chem. 1991, 95, 1294-1299
1294
cxperimental and simulated normalized current. The simulated normalized current i / i 0 was generated with k, = 1.O cm s-l, a = 0.5. and D = 2.4 X IO-' cm2 s-I.IoS l ~ l f i u r dSpcctrioir of N 0 2 B F , in Solution. In a Schlenk flask, a 0. I M solution of NO?+BFJ- in acetonitrile was made up under an argon atniosphcrc. The Schlenk flask was connected to a flowthrough AgCl ccll (0.1-mm Teflon spacer) using a 20-gauge Tcflon tubing. Another Schlenk flask was connected to the outlet (109) See also discussion by Bard and Faulkner in ref 33. The Fortran program is availablc on rcqucst.
of the cell by using a 20-gauge Teflon tubing. The system was thoroughly flushed with argon. With the cell placed directly in the beam of infrared spectrometer, the sample flask was pressurized with argon, and the sample was slowly injected (20 m L min-I) into the IR cell. At a constant flow of the sample solution, the 1R spectrum was measured every 5 s o n a Nicolet IO DX FT spectrometer with 2 cm-l resolution. Acknowledgment. We thank D. K. Gosser for kindly providing us with his CVSim program, the National Science Foundation, the R. A. Welch Foundation and the Texas Advanced Research Program for financial support.
Operational Procedure toward the Classification of Chemical Oscillators M. Eiswirth,+ A. Freund, and J. ROSS* Department of Chemistry, Stanford University, Stanford, Calrornia 94305 (Received: July 13, 1990)
A general approach is presented briefly to the mechanistic characterization of chemical oscillatory reactions, based on a ncw operational classification of simple chemical oscillators, i.e., oscillators that contain only one source of instability
(autocatalysis), and categorization of their species. We use stoichiometric network analysis to classify oscillatory reactions according to their basic unstable feature and the type of their dominant negative feedback loop. The species are first categorized into those essential and nonessential for the Occurrence of oscillations. The essential species are further divided into subcategories according to thcir rolcs in the mcchanism. The suggestcd proccdurc includes operational criteria for the assignment of a chemical oscillator to onc of the defined categories of mechanisms and for the identification of the roles of the species. Altogether 25 abstract modcls and realistic mechanisms of simple oscillators have been investigated; all fit into the four defined categories of incchanisms. Thc classification and proccdurcs prescntcd briefly here arc fully devcloped in an article to appear in Ado. C'hefH.PhYJ.
1. Introduction
Chcmical oscillators can display complicatcd dynamics such as pcriod doubling sequences, chaos, mixed-mode oscillations, and quasiperiodicity. In the present work we concentrate, however, on their common feature, the fact that they generally exhibit single or multiple stationary states and simple periodic oscillations in ccrtain regions of the parameter space. The goal of this investigation is to obtain information about the underlying oscillatory rcactions from these basic features. The strategy used to achieve this i s to find a classification of mechanisms and a categorization of thc chcmical spccics based on operational methods of assignment of ;I chcmic:il oscillator to its catcgory and a species to its role. I n the process we apply results of stoichiometric network analysis (SNA). This mathematical method has been developed by Clarke2 and allows the identification of the basic unstable features of a mcchnnism. Thc proposed clnssification of mechanisms is rcstrictcd to simple oscillators, i.e., oscillators that contain only one such unst:iblc fcaturc. The SNA method is briefly discusscd in scction 1. In scction 3, thc spccics arc categorized into those essential and noncsscntiLil for thc occurrence of oscillations. Nonessential species can be included in the parameters or replaced by flows. Two main catcgories of mechanisms are defined according to their unstable fcaturc. onc of which i s dividcd into three subtypcs. Typical skclcton modcls arc prcscntcd for ciich of thc rcsulting four categories. and the essential species in them are classified according to thcir rolcs in thc mcchanism. U p to four difrcrcnt rolcs arc dcfincd dcpcnding on thc typc of mcchanism. A gcncral proccdurc for assigning a rcaction to its class and a spccics to its cntcgory is prcscntcd in scction 4. I t uses cxpcrinicnhlly ;icccssiblc propcrtics such as bifurcation dingrams in two p:irnmctcrs and stabilizing and destabilizing effects as well ' Prcacnt address: Frit~Haber-Institutder MPG, D-IO00Berlin 33, FKC. * A u t h o r to whom corrcsaondcncc should he directed.
0022-3654/91/2095- I294$02.50/0
TABLE 1: List of the Abstract Models and Realistic Mechanisms Investigated in Ref 1 and Their Categories
I . Simple Oscillators ( a ) abstract niodcls
category
OrcgonatorI5 rcviscd orcgonator versions A and B!6 Franck modell"." Scl'kov model and its variationslJ.?' Brussclator?n cxothcrniic reaction in a CSTR29 Higgins model"'," Papain modc132,13 (b) realistic mechanisms FKN mechanisms.h S N B mechanism'4 OKN nicchanism'5,'h N FT m~chanisml~.~' BZ with oxalic acid ("modified oreyonator")'" BrO,-/Mn?+/SO,*-rci~ction~' BrO, /Mn?+/hypophosphik rcaclion4"
IB IB 1
2 2 I cx 2
category IB IB
1B
cw B
cw B
cw cw cw
BrO, / B r /CIO, r c a c t i ~ n ? ' . ~ ' RrOl-/l- rcaction?' C102-/1- r c n c t i o r ~ ~ ~ - ~ ~ Briggs-Kauscher rewtion45.J" mixed Landolt rcaction LI4','" mixcd Landolt reaction L2"" BrO, mixed Landolt oscillator"' nonisothcrnial hydrolysia of 2.3-epoxy- I -propanol" iaothcrmnl CO oxidation on Pt( I IO)'".'' peroxidase catalyacd N A Dt 4 oxidation'?
cx
-7
B
cx
Icx ICX 2 7
1 cs
I I. Nonsimplc Oscillators two furthcr Franck modclsl"." cxploduior"
rcviscd orcgonator version C?" ocill;~tor~~.~'
.Icnhcii
as shifts of stationary states during constant perturbations of spccics conccntrntions closc to a supercritical Hopf bifurcation. @ 1991 American Chemical Society
