Hrmo IMAL AND PAULDELAHAY
1108
TABLE IV FREEENERGIESAND HEATSO F -4CTIVATIOiX (KCAL./MOLE) FOR DIELECTRIC RELAXATION IN NUJOLSOLUTIONS Solute
AF*
AH*
Quinoline Isoquinoline 2-Bromobiphenyl 2-Methoxybiphenyl 2-Iodobiphenyl 4-Iodobiphenyl
3.30 3.27 4.55 4.77 4.78 5.78
4.09 3.97 5.91 6.32 6.18 7.60
quinoline is to be expected from the similarity of
T r d . 66
their relaxation mechanisms indicated by their relaxation times. The larger values for the biphenyls result from the greater lengths of their molecules. The virtual identity of the values for 2methoxybiphenyl with those for 2-iodobiphenyl give further confirmation of the similarity of the rotation mechanisms for these two molecules and, consequently, of the absence of contribution from methoxy group rotation. The larger values for 4iodobiphenyl are, at least, qualitatively consistent, with the longer relaxation time resulting from its rotation about the short molecular axes.
FARADAIC RECTIFICATIOK AND ELECTRODE PROCESSES. 111. EXPERIMEKTAL METHODS FOR HIGH FREQUEKCIES AKD APPLICATION TO THE DISCHARGE OF MERCUROUS 10s BY HIDEOIMAI* ASD PAULDELAHAY Coates Chemical Laboratory, Louisiana State University,Baton Rouge, Louisiana Recezved December 81, 1061
Ex erimental methods are described for faradaic rectification studies up to 50 Mc. and are applied to the discharge of Hg(1Pon mercury. Apparent exchange current densities up to 10 amp. cm.-* were measured which correspond t o an apparent standard rate constant of k,O = 100 em. sec.-l for an electrode process involving both soluble oxidant and reductant of equal concentrations of C = 5 X mole per liter (n = 2, DO= DR = 10-6cm.2 sec.-1) or to liso = 1000 cm. eec.-l for C = 5 X mole per liter. The folloning topics are covered: design of a cell for dropping mercury electrode with low inductance and very small stray capacity; measurement of the cell impedance; determination of rectification voltages; heating of electrolyte; measurement of non-faradaic rectification; and experimental errors. A method of interpretation is developed which does not require independent determination of the differential capacity of the double layer. The k,O for discharge of Hg(1) on Hg a t 24 =t2" in 0.1, 0.2, and 1.1 Af HClO4 is 0.28, 0.35, and 1.3 cm. set.-', respectively, and the transfer coefficient 1y is 0.28. These variations of k,* are correlated with the double layer structure and are of the order predicted by approximate theory. The k,O's and a also are compared with data obtained by the double pulse galvanostatic method. The much lower value of Ira0 = 0.047 cm. sec.-l for 0.98 HClO, for the latter method suggests the occurrence of a coupled chemical reaction.
Theoretical and experimental methods for the study of fast electrode processes by faradaic rectification, previously reported from this Laboratory.*>a are applied in this paper to frequencies up to 50 Me. Such high frequencies are necessary in the study of fast electrode processes, and the development of the appropriate experimental methods is of interest. Results are given for the discharge of mercurous ion on mercury in perchloric acid and are correlated with the double layer structure. The instrument previously describedzbwas tested up to 51 Mc. but was not used extensively, and only frequencies up to 2 Me. were utilized in previous work in this Laboratory.2a Barker* used frequencies from 100 Kc. to 1.6 &!IC.and occasionally 6.4 Me. Experimental Solutions.-Solutions ayere prepared from analytical grade reagents and water that had been bidistilled over K M n 0 4 . The stock solution of Hg(1) was kept over Hg and was standardized by electrogravimetry . Solutions were treated with purified activated charcoal according to Barker,* (1) Postdoctoral research associate 1960-1962; on leave from Minami College, Hiroshima University, Hiroshima. (2) (a) P. Delahay, bI. Senda, and C. H. Weis, J. Am. Chem. Soc., 83, 312 (1961): (b) M. Senda, H. Imai, and P. Delahar, J . Phys. Chem.. 66, 1253 (1981); see ref. 2a for bibliography. (3) See also the related papers: (a) M. Senda and P. Delahay, J. Am. Chem. SOC.,85, 3763 (1961), (b) M. Senda and P. Delahay. J. Phys. Chem., 66, 1580 (1961). (4) G. C . Barker, "Transactions of the Symposium on Electrode Processes, Philadelphia, 1959," E. Yeager, ed., John Wiley and Sons New York, N. Y., 1961, pp. 325-365.
and charcoal was removed by centrifugation. Complete removal of small charcoal particles was somewhat critical for the more dilute solutions of Hg(1) because of the instability of potential for improperly treated solutions. Oxygen was not removed from the solution as it did not seem to interfere. Cell.--A cell Jvith a mercury pool and a dropping mercury electrode was designed for high frequency studies. Conventional cells cannot be used above 1 Mr. (or even lower frequencies) because the stray capacity of the mercury reEervoir and the inductance of the mercury column in the polarographic capillary are much too high. These unfavorable features are eliminated by the use of a short capillary vith a constricted section and a small mercury reservoir connected to a manostat and a manometer (mercury column type). The ccnstricted capillary in the re11 of Fig. 1 was constructed from conventional polarographic capillary, and the drawn out capillary was rut t o proper length after grinding of a circular groove. Heating of mercury in the ronstrirted section caused interruption of the flow of mercury when a.c. pulses longer than 5-10 msec. were accidentally applied a t the higher current densities. The capillary, however, could be reclaimed by application of pressure and gentle heating. Mercury was added in reservoir RI every 30 min. t o maintain the level constant within 1 mm. This was done with the stopcock closed and by careful squeezing of the plastic bottle B . The cell of Fig. 1 was fitted with a saturated calomel microelectrode in the study of rectification by the double layer. S o liquid bath was used for temperature control because of increase in stray capacity (with a conducting bath) and the relative uncertainty in temperature resulting from heating of the electrolyte a t the higher frequencies (see Discussion). The capillary characteristics were as i'ollows for the 0.1, 0.2, and 1.1 M HClO4 solutions: m = 0.896, 0.133, and 0.263 mg. sec.-l; drop time at open circuit without hammer, 9.0, 44.0, and 21.0 sec.; head of mercury in manostat and
1109
FARADAIC RECTIFICATIOX AND ELECTRODE PROCESSES
June, 1962
manometer connected to reservoir R1, 250,326, and 370 mm.; drop time with hammer, 3.33, 3.33, and 5.00 see.; time of application of a x . pulse, 1.66, 2.88, and 1.32 see.; area, 1.11 X lo-%,4.59 X and 4.21 X cm.2. Cell Impedance.--The cell im edance, which must be known for the evaluation of the vof7tage amplitude across the electrode impedance, was measured with a General Radio radio-frequency bridge, type 1606-A (400 kc. to 60 Me.). The bridge was connected to a Hewlett-Packard signal generator, type 6068, whose output was modulated by a Tektronix pulse generator, type 161. The latter was triggered vaa a Tektronix wave form generator, type 162, by the rotating disk with contarts which actuated the magnetic hammer of the d.m.e. The balance detector was a Sational receiver, type HROdOTI, the output of which was displayed on a Tektronix cathode-ray oscilloscope, type 535. Data in ‘Table I Bhow that the non-resistive part X of the cell impedance is essentially proportional to the frequency. Hence, X was purely inductive and the cell stray capacity was negligible, a t least up to 50 Me. The resistive component which depends on the electrolyte relaxation and the “skin” effect was nearly independent of frequency. Similar conclusions were reached for the other solutions in this work.
TABLE I CELLIMPEDASCE~ FOR 1.1 M HClOp f, Me.
R, ohms
X , b ohms
Z,c ohms
45 5 45.5 0 1 1.1 43 6 43 6 3 5 2.5 43.5 43.4 7 5.6 44 8 14 44.4 8 6 45 4 21 44 6 I1 8 45.4 28 45 0 50.2 50 45 2 22 2 a D.m.e. characteristics: m = 0.263 mg. sec.-I, t (magnetic hammer) 1.32 see., T = 26.0’. b Non-resistive component of impedance. c Total impedance. Faradaic Rectification.-Rectification voltages were measured directly from rathode-ray oscilloscope display. The instrument was as previously described except for two changes. (a) The amplitude of the a x . pulse applied to the cell was displayed on a Tektronix, model 585 with plugin unit 80 and probe P80, in the higher frequencies range; this high frequency oscilloscope (up to 100 Me.) was not available in our previous work. (b) The filter circuit was modified to improve its characteristics below 1 Me.: a 0.5 millihenry choke was connected between the d.m.e. and the input of the low-pass filter previously used, and a 0.01 pf. capacitor was connected across the input of the filter. The connection between the choke and the d.m.e. was short (5 cm.). The double pulse method previously describedzb was used a t the higher frequencies to shorten application of the a.c. pulse to a few milliseconds and minimize heating of the supporting electrolyte (See Discussion). Rectification by the Double Layer.-h’on-faradaic rrrtification was studied with the same instrumentzh as above except that the mean potential of the d.m.e. was controlled against a saturated calomel electrode and the charge due to rectification was compenqated by a square pulse of 10 pscc. duration (Fig. 2). Compensation was ascertained with a Tektronix Oscilloscope, type 535, which was fitted with a plug-in amplilier E and operated at the maximum sensitivity of 50 MV. em.?. il limitation of the equipment previously describedzh became apparent in this work, namely that the modulated a x . signal from the two transmitters is not sufficiently free of trawients to allow unambiguous detection of compensation. This limitation disappeared when the Hewlett-Packard signal generator, type 606A, was substituted for the transmitters but the limited output power of the generator prevented application above 7.5 Me. The Hewlett-Packard 4608R which has rather poor trandent characteristics also was eliminated from the instrument previously described.Zb
Analysis of Data The general equation for the rectification voltage €or control of the mean faradaic current to zero (cf. eq. 9 and 23 in ref. 2a) has the following form in
H-
Its
I 0 v)
Fig. 1.-Cell for very high frequency measurements: B, plastic bottle; R , RP,mercury reservoirs; M, connected t o manometer and manostsat; S, graded seal between Pyrex and soft glass (lower part with capillary); H, magnetic hammer; T,, P t terminal, 18 gage; TZ, Pt terminal, 22 gage; TL, Teflon stopper. A reference electrode (e.g., s.c.e.) can be inserted in the right-hand side bulb, if necessary.
n FILTER
HG POOL
-L Fig. 2.--Cell circuit €or study of rectification by the double layer: R, = 5.5 megohms; R? = 3000 ohms; C = 1 pf‘.
the particular case of the discharge of Hg(1) on B g where Al?- is the rectification voltage for t +- co ; V4 the amplitude of the sinusoidal voltage across the faradaic impedance; 01 the transfer coefficient,; e, the phase angle between the resistive and capaci-
HIDEOIILLIAXD PAUL DELAHAY
1110
Vol. GG
tive component,s of the faradaic impedance; n= 2; and R, 2’,and F are as the usual. At sufficiently high frequencies (cf. eq. 27 in ref. 2a) one has
Similar results were obtained for 0.1 M €IC104 but are not plotted for the sake of clarity. Xote that the plots in Fig. 4 are linear in the upper frequencies range and that the intercept a t w-’/2 = 0 is the same for all solutions (cf. eq. 3 ) . The values of kao where Iaois the apparent exchange current den- and I , O in Table I1 correspond to a very fast electrode sity; C the bulk concentration of Hg(1); D the process, and Barker’s observation* that faradaic diffusion coefficient of Hg(1); and w = 27$, ,f rectification is entirely diffusion controlled for C = 0.05 mM Hg(1) in 1 114 HC104 up to 6.4 Mc. is in being the frequency. agreement with the present findings. The preciWhen the faradaic impedance Zf is very large in comparison with the double layer impedance l/wcl sion for a and ka0, as estimated for oscillographic (e1 differential capacity), one has VA = I A / w c l (I* determinations and other measurements, correcurrent amplitude), and there follows from eq. 1 sponds to a relative error of =tlo%, or perhaps a higher error. The differential capacity for E and 2 = 0.71 to E = 0.67 v. vs. n.h.e. was 43 pf. cm.-2. This value is of the order of the approximate value, c1 = 39 pf. a t E = 0.65 v. DS. n.h.e., reported It will be assumed that (a) the differential ca- by Grahame6 for 1 114 HC104. It also agrees well pacity c1 is not affected by variations of the Hg(1) with c1 = 39 pf.cm.-2 as calculated by Matsuda7 concentration in the presence of a large excess of sup- from data reported by Matsuda, Oka, and Delahay* porting electrolyte; (b) that c1 is constant in the in a study of Hg(1) discharge by the double pulse range of potentials corresponding to the variations TABLEI1 in C; and (c) that c1 is frequency independent. The first two assumptions are realistic and the KIXETICDATA“FOR THE DISCHARGE OF Hg(1) ON Hg IN third one was verified experimentally. Further, it HClOd will be assumed that I a O in this case is hO, IS0, CHClOb CH (I) Iao
=
nFk,O
C1-a
(4)
M 1. --I
0 1
m*lf 1.
0 058 12 23 47
a
cm. see.-’
amp. om.-l
0 25 26
0 26 28 28 28 __ 28
0 32
where hao is the apparent standard rate c o n ~ t a n t . ~ 55 (The validity of this equation is discussed below.) 92 It then follows from eq. 3 that the ratio of the 28 1 50 __ slopes of the plot AE,w2/IA2 against w-’/2 for two Av. 26 concentrations of Hg(I), C1 and Cz, is (C2/C1)a. The coefficient a thus can be evaluated from the 0 2 0 058 0 28 0 35 0 43 directly measurable quantities AE,, IA, and w 12 28 35 0 70 without independent determination of the diff eren23 35 1 15 tial capacity el. The latter now can be evaluated 47 28 36 1 9 __ __ from the intercept of the line A E , w ~ / I Aagainst ~ Av. .28 36 w-‘/2 for w-’/2 = 0. Finally, laois calculated from the slope of the line AE,W*/IA~ against u - ’ / ~ . 11 0 067 0 26 1 3 1 7 35 30 1 4 5 9 Description and Discussion of Results .. 1 3 9 8 .73 Determination of cl, a , Iao,and kao.--Conditions for control of the voltage across the electrode Av. 28 1 3 impedance by the double laye: capacity were detera Differential capacities: 43 pf. cm.-z for the three acid mined from plots of log (iAE,I/IA2) against log w (Fig. 3 ) . When Zt >> l/wcl, V-4 = I*/wcl, and concentrations. ~ A E , / / I A is ~ inversely proportional to w z for pure galvaiiostatic method. One readily verifies from charge transfer control or inversely proportional to the IaO’sin Table I1 that the electrode impedance in the range of frequencies in which Zf varies was essentially controlled by the double layer at the linearly syjth w-’/2. Conrerjely, when Zf > l / w c l which is for the lowest frequency (0.2 Mc.). prescribed in the analysis of data above is fulfilled The rate constant, k,O = 1.3 cm. sec.-l for 1.1f d l at the higher frequencies. This conclusion was con- HC104 in Table 11, is much larger than the value firmed by comparison of the values of Zf and l / w c ~ kaO = 0.047 cm. sec.-l for 0.98 M HCIOl one dededuced from experimental data. duces from data obtained by the double pulse galValues of A E , w ~ / I A are ~ plotted against wT1I2 (6) D. C Grahame, Chem. Revs., 41, 441 (1947). in Fig. 4, and kinetic data are listed in Table IT. (7) H. Matsuda, doctoral dissertatlon, Faculty of Englneenng, u6/2
( 5 ) For a review, we, e.g., P. Delahay in Vol. 1, “Advances in Electrochemistry and Electrochemical Engineering,” P. Delahay, ed., Interscience Publishers, I n c , New York, N. Y . , 1961, pp. 233-318.
Tokyo University, 1961, p. 407. (8) H. Matsuda, S Oka, and P. Delahay, J . A m . Chem SOC.,8 1 , 5077 (1989).
June, 19G2
1111
FARADAIC RECTIFICATIOK A X D ELECTRODE PROCESSES
vanostatic method.s>g The transfer coefficient is esf (MC). A .6 .8 I 2 3.5 7 14 21 28 sentially the same in both methods, L e . , 0.28 (Table 11) vs. 0.24. Barring experimental or calculation mistakes, which it is hoped are unlikely, one must account for this discrepancy. It is suggested that the lower value obtained by the galvanostatic method results from the over-all effect of charge transfer and a coupled chemical reaction. The higher value of kao obtained by faradaic rectification would correspond to conditions in which the influence of the coupled chemical reaction is eliminated or at least minimized. The galvanostatic results were obtained by extrapolation to time t = 0 of data for t 2 1 psec., whereas extrapolation to w - ' / z 3 0 of data obtained up to 50 >IC.in faradaic rectification is equivalent to extrapolation to t = 0 for t 2 2 X IO-* sec. Hence, it is possible that the effect of the coupled chemical reaction is eliminated or greatly minimized in fara-7I I I I I I daic rectification, but is not in the galvanostatic 7 25 0 0.5 6 6.5 method. Further, the overvoltage corresponding log w. to the chemical reaction in the galvanostatic method would be constant lo for sufficiently long Fig. 3.-Plot of log( I A& 1 /Z") against log w for the discharge of Hg(1) in 0.2 M IEClOl a t 23.5 dz 0.5". times, and consequently no distortion was noted in the extrapolation plot which might have led one to suspect a coupled chemical reaction. f (MC). 7 3.5 2 I 80 26 21 14 The na,ture of the chemical reaction could not I I I I I I be ascertained although one reaction can be ruled out as being rate-controlling, namely dissociation of the ion pair HgC104+ in the bulk of the solution. The formation constant for HgC104+ a t 25' is approximatelyll 0.9, and consequently the species Hg2++and HgC104+are present a t about the same concentration in 1 M HC1o4. The discrepancy in the kao therefore would be much smaller than observed. It is possible that the coupled reaction is 2Hg+ = Mg2++ but this i s pure speculation as information on Hg+ in aqueous solution is very meager.12 I
Influence of Double Layer Structure.-The variations of k,O with HClOa coneentration is interpreted as a double layer effect. No detailed quantitative study was made because it would have required the determination of specifically adsorbed clod-, but it will be shown that the variations of li,O with HC104 concentration are of the order of magnitude one would expect. Both Ng,++ and HgC104+ must be considered's in 1.1 LM HC104 (see above) whereas Hgz++ is markedly predominant in 0.1 and 0.2 31 HC104. We shall assume that kO , must be corrected for variations of the potential +Z in the outer Helmholtz plane (with respect t o the potential +B in solution) according t o the Frumkin theory.14 This is only 3 fair approximation but on? which is reasonable since Hg(1) is, in all likelihood, not specifically adsorbed. The potential qh can be evaluated from the Gouy-Chapman theory, provided one makes allowance for the component of the charge on the electrode corresponding to specific adsorption of Clod-. As a coarse approximation (9) H. Gerischer and M . Krause, Z . p h y s i k . Chem. (Frankfurt), 14, 184 (1958). One calculates from their data, which were not corrected for mass transfer overvoltage, hao = 0.025 em. see. -1; also o 0.30. (10) H. JIatsuda, P. Delahay. and M. Kleinerman, J . Am, Chem.
-
Soc., 81, 6379 (1969).
(11) J. Bjerrum, G. Schwarzenbach, and L. G. Sillen, "Stability Constants. P a r t 11," The Chemical Society, London, 1958, p. 111. (12) W. C. E. Higginson, J. C h e m . Soc., 1438 (1951), reported ( H E + ) ~ / ( H ~ ~= + +10-6 ) to 10-8 on the baais of ultraviolet absorption spectra of dilute mercurous perchlorate solutions. However, A. 31. Armetrong, J. Halpern, and W. C. E. Higginson, J . Phys. Chem., 60, 1661 (1956), suggest that Higginson's results could be int,erpreted on the assumption of the dismutation Hgz++ = H g + + Hg. (13) The species HgzOH+ can be neglected: cf. ref. 11, p. 18. (14) For a review, cf., e.g., R. Parsons, in ref. 5, pp. 1-64.
+
Fig. 4.-Plot
I
I
of AwE,~/PA against ~ ~ for' the2 discharge of Hg(1) in HCIOl a t 24 i 2".
one has in the present case, i.e., for potentials sufficiently different from the point of zero charge $2
Thus, +Z Further
-
=
-
- Ips < 0, and 9, -
In cHoio4
+ constant
(5)
decreases as Caoloa increases.
where kO is the standard rate constant; n the number of electrons in the rate-determining step; and z the ionic Val. ence of Hg(1). There follows from eq. 5 and 6 that k,O should be proportional to C ~ ~ l ~ p - aHence, n. hao should be proportional t o C H C ~ Ofor ~ ~z .= * ~2 , n = 2, and a! = 0.28 and to ( 7 ~ ~ lfor o z~ ~ 1 . and ~ ~ n = 2. The former correction should hold for 0.1 and 0.2 A4 HClO, for which Hg(1) is mostly Hgz++whereas the correction for 1 .I M HCIO, is in~ ~ .CHClp4°'44. ~ ~ The ratio termediate between C a ~ 1 o and of the k.0'~ for 1.1 M HCIO, (Table TI) IS 4.6 as compared with the predicted ratio of 3.5 for z = 1 (using C E C ~ O ~ O . ~ ~ ) . 3
HIDEOIMAIAND PAUL DELAHAY
1112
Yol. GG
marily of the Helmholtz double lager since the contribution of the diffuse double layer is quite negligihlc for 1 M HC104-need not be considered in this case up to 7.5 Me. It was assumed that the same conclusion held up to 50 &IC.though no experimental evidence was available above 7.5 &IC. The interpretation based on this assumption was selfconsistent . TABLE I11 NO>-FARADAIC RECTIFICATION O F D.M.E.IU 1.1 N HCIOa AT E = 0.18 v. us s . c . E . ~ q,
IO m s e c
I Fig. 5.-Osrillogram traring showing drift of potential caused by heating of the electrolyte (0.1 111 HCIOa)a t 14 Mc. and l~ = 31 amp. cm.-2. Rectification for 0.47 mM Hg(1). I
This calculation is very crude because eq. 5 is approximate, a t a n j rate, and the approximation is made even poorer because specific adsorption of CIQ, - was neglected. Further, ko is probably different for Hg,++ and HgC104+, and the double laver effect is complicated by the dissociation of HgClod+which is coupled with the charge transfer reaction and possibly bv any other coupled reaction (see above). The use of a Frumkin-type correction, even with rigorous calculation of +2 - &, is approximate because of the uncertainty on the proper value of the potential in the double layer to be used and, moreover, the structure of the double layer was not considered in the solution of the boundary value problem in the derivation of the faradaic impedance. This simplification is entirelv justified when the diffusion layer thickness (6 = [ 2 D / w ]' 1 2 ) is very large in comparison with the diffuse double layer thickness l / ~ .The Frumkin correction for the double layer structure then can be made a cm.2sec.-1, 6 posterzorz. One has for 50 Mc. and D 5 = 2.5 X 10-7 cm., whereas 1 / = ~ 10-7 cm. for 0.1 M HC10, and 1 / ~= 3 X 10-8 cm. for 1 M HCIO,. The above "nonFrumlcin" correction therefore should not be entirely negligible. The quantitative analysis is difficult and equations published thus*b far correspond to conditions which are not fulfilled here. It must be noted, however, that the dependence of Zo, on the concentration of Hg(1) is more involved than that given by eq. 4 when the non-Frumkin correction is significant. Since a self-consistent interpretation of data on eq. 4 could be developed, it appears that the non-Frumkin correction is not too large.
Possibility of Frequency Dispersion of the Double Layer.-It n-as assumed above that the differential capacity of the double layer is Erequency independent. This assumption was examined by study of non-faradaic rectification at the d.m.e. in 1.1 nd HCIOl up to 7.,3 hlc. Higher frequencies could not be used because of instrumentation limitation (see Experimental). A fixed charge (passed in 10 psec.) was supplied to the cell to compensate non-faradaic rectification, and the amplitude U of the alternating voltage across the cell was measwed when compensation was achieved. Sincesa 4
(VA amplitude of a.c. signal across the double layer), the qiiantity U ' j Z , ( Z , impedance of the cell) should be frequency independent in the absence of double layer dispersion. This was the case for E = -0.70, -0.88, and 0.18 v. vs. s c.e. from 0.25 to 7.5 Mc. (partial data in Table 111). This conclusion is in agreement with Barker4who made a similar study for 1 i l l HC104 between 0.1 and 1.6 Mc. Frequency dispersion of the double layer-pri-
pp
coulombs
f, Mc.
U , volts
U/fZo
3 4 x 10-8 3 5 3 5 .75 3.4 1 3 5 2.5 4 54 1 1.3 x 10-8 2 1.1 4 1 2 6 1.2 7 5 7 1 I .3 a Capillary characteristics: m = 0.062 mg. set.-'; a x . pulse applied at I = 3.7 sec. 36.4
0 25 .5
0 54 1.1 1.7 2.2 5.6 0 81 1 5 33 5.2
Heating of the Electrolyte.-Heating of the electrolyte was appreciable a t the higher frequencies and the lower concentrations of HC104. There resulted a shift in the equilibrium potential (Fig. 5 ) which did not exceed approximately 2 mv. in the HC10, most extreme conditions, namely 0.1 and 28 Mc. The temperature coefficient of Hg,+' 2e = 2Hgis15approximately -0.045 mv. degree-I and consequently the increase in T for Fig. 6 is approximately 18' over 7 msec. Since rectification voltages could be measured within 200-300 psec. after application of the a.c. pulse, the increase in temperature actually affecting the measurement did not exceed 0.54.8' in this instance and 2' for the most extreme conditions of frequency and electrolyte concentration. The resulting error on the exchange current is rather small. The measured increase in T has approximately the value one calculates on the assumption of no heat transfer to the electrode and the bulk of the solution. One then has2&at the electrode surface dT/& = 0 24(1~~/2)(1/h, GoCh), K~ being the specific conductance of the electrolyte, Ch its specific heat, and 80 its density. One has approximately for 31A2At, i . e . , AT = 20' over 7 msec. Fig. 5 AT as compared t o A T = 18' from experiment. The experimental A T is a little smaller than the calculated AT because of heat transfer to the electrode and the bulk of the solution and experimental errors. Conclusion It would appear from this work that the kinetics of fast electrode processes can be studied by faradaic
+
(15) As evaluated fron the e m f of a n H-cell 731th the arms a t the temperatures T I and T2. The cell nas filled wlth 1.46 m.M Hpz++ in 0.1 A4 HClOa. The e.m.f. was measured with the Hewletf-Packard DC microvolt-ammeter, Model 425A. Exact interpretation of such A non-isothermal cell is dlfficult, but the older of magnitude of AB/AT is obtained. T h e temperature coefficient could not be calciilated be cause AS0 foi Hgt++ could not be found in the literature.
June, 1962
PEIOTOCIIEMICAL DECOMPOSITIOS OF BARIUM AZIDE
rectification up to 50 &IC.(and possibly a t higher freqitencies with electrolj4es of high conductivity). Apparent exchange current densities up to 10 amp. cm.-2 were measured which correspond to an apparent standard rate constant of approximately 100 cm. sec.-l for an electrode process involving both soluble oxidant and reductant a t equal conM (n = 2, D o = D E = centrations of 5 X I 0-5 cm. sec.-l>. Somewhat faster processes could even be studied with more dilute solutions. The
1113
method should prove most useful in the study of a number of processes which arc too rapid for other methods presently available. Moreover, the investigation of relatively slow electrode processes at high frequency may allow the detection and the study of coupled chemical reactions which are too rapid to be detected by other methods. Acknowledgment.-The support of this work by the National Science Foundation is gladly acknowledged.
THE PHOTOCHENlICAL DEGOMPOSITIOY OF BARIUM AZIDE BY P. W. M. JACOBS, F. C. TOMPIZINS, AND V. R. Par VERNEKER Department of Chemistry, Imperial College, London, S.W. 7 Received December 21 1061 ~
The kinetics of nitrogen evolution from barium azide irradiated with ultraviolet light from low and high pressure mercury arcs has been investigated as a function of intensity, temperature, and time of irradiation. These results emphasize the important role played in the reaction by the barium product formed as a result of photolysis. Two mechanisms of the photodecomposition which are consistent with these detailed kinetic results are proposed and discussed in the light of our present knowledge of the physical properties of azide crystals. The first of these, which occurs chiefly in fresh salt, is the formation of barium atoms (prsnuclei); the second is the thermal production of positive holes by the transfer of electrons to barium pre-nuclei which have become ionized by photoemission of an electron into the conduction band. The significance of a purely thermal contribution to the photolytic rate also is assessed.
There have been several previous investigations of the effects of radiation on barium azide. Irradiation with soft X-rays’ produces barium nitride and nitrogen. Pre-irradiation of barium azide with aparticles2 or ultraviolet light3 accelerates the rate of subsequent thermal decomposition. Irradiation with ultraviolet light4causes the evolution of nitrogen at a rate proportional to the square of the intensity and with a temperature-dependence corresponding to a n energy of activation of 5 kcal./ mole. Failure to detect photoconductivity5 was held to imply that the primary process was the formation of excitons4 rather than of free electrons and positive holes.6 Recent investigation^,^ however, have shown that the mechanism of photolysis must be more complicated than the bimolecular decomposition of excitons a t traps.4 In particular, the rate of photolysis under irradiation with a high pressure lamp at first decreased and then increased again, finally attaining a constant value. The intensity-dependence appeared to be complicated, the exponent n in the equation R = Clnvarying from 0.5 to 2. This work, though valuable in pointing to the role of the metallic product, in photochemical as well as thermal decomposition, was unsatisfactory in that the temperature dependence was not examined and also because insufficient account was taken of the effects of the “dark rate” in determining the value of n. (1) P. Gunther, L. Lepin, and K. Andreew, 2. Elektrochem., 3 6 , 218 (1930). (2) W. E Garner and C. H. Moon, Nature, 131, 513 (1933). (3) W. E. Garner a n d J. Maggs, Proc. Roy. Soc. (London), 8172, 299 (1939). (4) J. G. N. Thomas and F. C. Tompkins, zbzd., 8209, 550 (1951); 8210, 111 (1961). ( 6 ) P. W. M. Jacobs and F. C. Tompkins, %bid., 8216, 254 (1952); 216, 265 (1952). ( 6 ) N. F. Mott, ibid., 8172, 325 (1939). (7) P. W. h1. Jacobs, F. C. Tompkins, and D. A. Young, Discussions Fainday SOL, 28, 234 (1959)
Consequently, the kinetics of nitrogen evolution under ultraviolet irradiation has been re-examined in some detail and the results of this investigation are recorded below. Experimental Barium azide was prepared by neutralization of an approximately 5% solution of hydrazoic acid with barium hydroxide of A.R. quality. The solution was maintained neutral to phenolphthalein during evaporation on a water bath to incipient crystallization and the azide then was precipitated by addition of absolute alcohol. The fine white precipitate was filtered, redissolved in the minimum amount of distilled water made slightly acidic with hydrazoic acid, and the barium azide obtained either by addition of absolute alcohol or by slow evaporation of the acidic solution. The former method yields a white amorphous powder, the latter a mass of tiny crystals. The azide was dehydrated over phosphorus pentoxide in a desiccator. The hydrazoic acid was obtained by two methods: (i) by dropping sulfuric acid onto a solution of sodium azide and sodium hydroxide and distilling off the hydrazoic acid into water and (ii) by passing a 10% solution of sodium azide through a cation exchanger in the hydrogen form. No differences were observed in the behavior of products obtained by these slight variations in technique. The azide was contained in a transparent silica cell with a flat window, connected via a B.14 standard joint t o the vacuum line. This consisted, in sequence, of a trap immersed in li uid nitrogen, a standard volume, a pirani gage (PI),a cut (CI?,a diffusion pump @I), a second trap, a second pirani gage (P$),a McLeod gage, and a second cut off (C,) which separated the line from the second diffusion pump (Dz)and the backing pump. This enabled the rate of nitro en evolution t o be measured either on PI with CI raised ?the accumulatory method) or on PI with CI lowered and CI raised. I n the accumulatory method the azide is in continual contact with the nitrogen evolved, which may reach a pressure of several microns. I n the second method (referred to as “pumping”) the diffusion pump DI maintains a pressure of
