4648
I.
c. HISATSUNE,BRYCECRAWFORD, JR.,
of benefit in interpreting the data relative to the exchange of Clzand CCld initiated by y-radiation. Acknowledgments.-The author wishes to thank Henry Taube for his many helpful suggestions. Some of the early experimental work was done by T. S. Piper. The assistance offered by A. H. Zeltmann and P. J. Bendt in deriving the modified rate expression is appreciated. Appendix Derivation of Modified Rate Law.-For the conditions in which the loss of CCl, by decomposition is very small compared to the initial [CCl,] and the [Clz]is about to M , then the following derivation is valid for any one stated flux. The rate of exchange of C1 between C1, and CC14 is expressed as
-,
AND
R. A.
OGG, JR.
VOl. 79
where No = total number of Cl, atoms present a t time 0 and
where Po = number of C136atoms present as C1, a t time 0. P -R In - = -- In (1 + a t ) Po
At PIP0 =
t
=
CVNO
tl/,
and
1)
where d N = the number of tagged chlorine atoms disappearing from the tagged phase in time dt, and R is a constant for any stated flux.
where P = number C136atoms present as Clz a t time t and C = P / N . But since N increases with time N = No(1
+ at)
(A 3)
which would be the case for a stable system. This expression is in agreement with the work of other investigators16 who have derived equations to fit the general case of unstable systems in exchange reactions. (16) C. P. Luehr, G. E. Challenger and B. J . Masters, TxixS JOCR7 8 , 1314 (1956).
XAL,
Los ALAMOS,NEWMEXICO
[CONTRIBUTION FROM THE SCHOOL OF CHEMISTRY, UNIVERSITY OF MINSESOTA,~ AND DEPARTMENT OF CHEMISTRY, STANFORD UNIVERSITY~ ]
The Kinetics of the NO-N,05 Reaction1 B Y I. c. HISATSUNE,~ BRYCECRAWFORD, JR.," AND R. A. RECEI\'IID A4PRII, 5,
OGG,
Jr.O
1957
The decomposition of SnOj in the presence of S O has been studied with a fast-scanning infrared spectrometer at total pressures of 57 and 400 mm. using Nz as diluent and at temperatures of 20, 25 and 30". By using an excess of NzOs over KO, t h e unimolecular dissociation constant for X20jas well as the ratio of the rates for NO1 reacting with NO2 and with N o , respectively, was determined. The Arrhenius activation energies for these rate constants also were determined.
Introduction In earlier reports from this Laboratory,2 the applicability of our fast-scanning infrared spectrometer to kinetic studies of relatively fast gas-phase reactions has been described. One of these moderately fast reactions which can be studied conveniently with our instrument is the unimolecular decomposition reaction of N2Oj in the presence of KO. Not only is the half-life of this reaction within the limits of our scanning rates, but both NzOj and NO2 have intense infrared absorption bands around 6 so that we may follow both molecular species simultaneously through the course of the reaction. Furthermore, since extensive kinetic data for this reaction are available in the literature, we are able to compare our results to those obtained from other methods. (1) This work was supported by the U. S. S a v y , Bureau of Ordoance, through contract with the University of Minnesota. ( 2 ) G. R . Cowan, E. Vincent and B. Crawford, J r . , J . Ofif. SOC.A m . , 43, 710 (1953); R. E. Kightingale, G. R . Cowan and B. Crawford, J r . , J . Chcm. PAYS.,12, 1398 (1953).
Since the publication of our preliminary notes3 on this reaction, we have been able to improve the sensitivity and stability of our spectrometer and also have been able to overcome some of the experimental difficulties involved in the present method. This paper reports our final results on this reaction. A number4 of investigators have studied this reaction and have found that their experimental data can be interpreted adequately in terms of the simple mechanism proposed by Smith and D a n i e l ~ , ~ which is given below in equation 1. Our data ob(3) G. R . Cowan, D. Rotenberg, A . Downie, B. Crawford, Jr., and K. A . Ogg, Jr., i b i d . , 21, 1397 (1953); I. C . Hisatsune, A. P. McHale, R. E. Sightingale, D. L. Rotenberg and B. Crawford, Jr., i b i d . , 23, 24S7 (1955). (4) W. F. Busse and F. Daniels, THISJOURNAL, 49, 1267 (1927); J . H. Smith and F. Daniels, ibid., 69, 1735 (1947); R. L. Mills and H. S. Johnston, ibid., 73, 938 (1951); H. S. Johnston and R. L. Perrine, i b i d . , 73, 4782 (1951); H. S. Johnston, i b i d . , 75, 1567 (19.53); D. J. Wilson and H. S. Johnston, ibid., 75, 5763 (1963); R . A . O g g , Jr., J. Chem. P h y s . , 18, 572 (1950); R. A. Ogg, Jr., W. S. Richardson and M . K. Wilson, i b i d . , 18,573 (1950).
Sept. 5, 1957
KINETICS OF
THE
tained by using a fast-scanning infrared spectrometer also were found t o fit this mechanism and the rate equation 2. Our work establishes the first ki NOz
Nz0s
kz
NO
+ NOo
( 1)
NO-N2O6 REACTION
NzOs and NO2 in the 6 p region with our fast-scanning spectrometer. A single cycle of the photographic record of the oscilloscope signal is shown in Fig. 2. Optical densities of the two species were read from these films and plotted against the reaction time, which was calculated from the known film speed of the recording camera and the scanning speed of the spectrometer. A portion of the optical density vs. time plot for a typical run is shown in Fig. 3.
ks + NOa + 2NOa
-d(NzOJ /dt = kl(NzOd/ [ l
+ kz(xOz)/ks(NO) 1
4649
RUN H A - 8 SCANNING RATE
0 . 2 5 sec.
(2)
quantitative estimate of the inhibition constant kz/ks. Our values for the constant kl are of the same order of magnitude as those obtained by previous investigators, but are consistently lower than the earlier results. The Arrhenius activation energy for kl from our work was found to be in excellent agreement with the earlier values of Johnston and his c o - ~ o r k e r s . ~ Experimental The gases NO, NzOs and NO1 were prepared according to the methods published recently.6 Special precautions were taken to prevent the formation of HNO8 which hindered our earlier work, and spectroscopic evidence was obtained for its absence. Brief descriptions of the experimental technique and the treatment of the data are given in the earlier reports.a Previously, we had used a reaction cell where the reactants were expanded through two slightly off-centered jets from either side of the cell by opening the two taps with a mechanical crank. However, this system produced serious mixing difficulties and therefore a new reaction cell system shown schematically in Fig. 1 was used. The 10 cm. Pyrex
1616 cm:'
1750 cmrl N 2 0 5 BAND
Fig. 2.-A
NO2
BAND
single cycle of the photographic record with blank superimposed.
o$ 0
f Fig. 1.-Schematic diagram of the reaction-absorption cell system; path length = 10 cm., volume = 163 ml. Silver chloride windows were sealed on with a mixture of high-temperature Halocarbon wax and grease. absorption cell had a volume of 163 ml. and a surface-tovolume ratio of approximately 1.4. Silver chloride windows were sealed to the cell with a mixture of high-temperature Halocarbon grease and wax. The reactant bulbs on either side of the 3 mm., a-way, hollow-T t a p had approximately 100-ml. capacities. The T t a p was connected to the absorption cell through a ball-joint and by 4 mm. i.d. Pyrex tubing of approximately 10 cm. length. The reactants which were diluted with oil-pumped nitrogen gas were expanded from bulbs A and B through the 3-way tap into the reaction cell. To test for reproducibility, N ~ 0 6was placed either in bulb A or B and the 3-way t a p was always opened ctockwise from identical initial positions so that the reactant in A always emptied out from the same tap-hole. All of our runs were made in the above manner. For temperature coefficient measurements the entire laboratory was thermostated to 20,25 and 30" with variation of not more than 0.5'. The reaction was followed by observing the time variation of the two neighboring intense absorption bands of ( 5 ) R. E. Nightingale, A. R. Downie, D. L. Rotenberg, B . L. Crawford, Jr., and R . A . Ogg, Jr., J. P h y s . Chcm., 68, 1047 (1954).
RUN HA-8
.I
12
24
36
48
60
72
8
t (sed.
Fig. 3.-An
optical density vs. time plot for a typical run.
To test for heterogeneity in the reaction, we packed the absorption cell with Pyrex glass rods, 3 mm. diameter by 25 mm. length. However, we were only able to increase the surface-to-volume ratio to 2.7 (compared to 1.4 in the unpacked cell) without blocking out the infrared beam. Two runs were made with this packed cell a t 20" and a t total pressures of 400 and 57 mm., respectively; in both cases
1. e. HISATSUNE, BRYCE
4650
CRIZWFORD, JR., AND
a n excess of NO was used so that only the rate constant kl was obtained. T h e results were as follows Unpacked cell
Packed cell
400 mm. 0.028 set.-' 0.027 57 mm. 0.018 0.018 In the high pressure runs, the difference in tlie tuw values of k, is within the limits of experimental uncertainties. However, in the low pressure runs, the difference is probably significant, although not large. It is reasonable for us t o conclude that no heterogeneity affects our k1 values beyond the limits indicated below. Treatment of the Data.-Smooth curves were drawn through the optical density us. timg plots arid readings from these curves were used for the following calculations. These smoothed optical densities were converted into pressures by using calibration curves which were obtained for S205 and NO2 a t every different temperature and total pressure used in t h e runs. Corrections were made for the Se04 equilibrium, using the constant given by Yerlioe Daniels,G and for the slight overlap of the N?Odand S20s absorption bands. For every run a “stoichiometry plot” of Sz05 v s . total NOe (;.e., 9 0 2 2S204) \vas made; Fig. 4 represents such a plot for a typical run. I n ever>-C:IX tlie slope was found to be ’ / 3 as predicted by the owr-:ill equxtion for the reaction, within the limits of esDeriinenta1 uiicertainties.
R.A . OGG, JR.
(Snob)- ( S Z O 5 ) - . The values of to and pressures corresponding to the completion of the reaction were chosen t o give the best linear y--w plots. T h e intersection of the experimental y-e plot n i t h a line y = w / / 3 gives k: and the w intercept gives k l t ~ j k ~\L. typical example of sucli >-w plots i5 shon xi in Fig. 3.
0.03
1I-
RUN H A - B
+
L-----L.
.
~~
L---p~L-i_
0.1
0.2
0.3
0.5
0.4
p.5
rv. Fig. S.-A
t
VOl. 79
y x plot ~ for a typical run. The line through the origin is y = w / 3 .
Results
IO
The average values of the rate constants obtained in the above manner are given in Table I.’ The estimated errors are average errors. For k1 the maximum deviation from the mean value was approximately 2Oy0. However, for k l k , ’ k z and the calculated constant kz ’kg this deviation was approxiniately 5 0 5 , since the w-intercept involves larger uncertainties. The inhibition constants k? ‘k6 listed in Table 1 are the averages of the values calculated from the separate runs. TABLE I EXPERINESTAL RATE COKSTASTS AT VARIOUS ‘rOTA1, P R E S S L I E S
h-0 ” tC. .
rutis of
k: a:;‘
klka,/k2 (sec:‘)
.-1j
( a ) 400 inm. 2.j 30
13 12
Od3a-+ ,Ii!)21 t
I\
I
3
2
N2O5 b-“,
Fig. 4.-A stoichiometry plot for a typical r u n . ?’ot,il SO2 refers t o NO2 21\‘,04. The line is of slope l / 3
+
T h e experimental pressures are substituted into the integrated form of the rate equation given below, valid for (N205)o > (N0)o. y = -k’(l - 3k’)-’w ki(1 - 3 k ’ ) - ’ (3) where k’ = ke/k6 y = ( t - to) -1 In[(SzOs)o(r\TzOs) -‘I and
+
The subscripts “0” and “ m ” denote pressures a t some initial time t o atid a t the end of the reaction, respectively. ?’he pressure of NO is calculated from the relation ( S O ) = .
(b)
F. H. V ~ i l i ~ eand h 11. Daniels. THISJ O C R P ;
11,
53, l 2 X (l!i.’i!l
*
0 =t
nii.:t) l . O i i .OltiO
1
3
z
.12
.O
f
.I7
.i)
( b ) 571nm. o . o m o 4t:i -r 0 . 1 2 2 o o:w:3 ,0010
0.‘310
.oow
LOO
2
.:I)!)
t o . o i 1:1 , 0 3 2 8 k .lJ!I)lJ
.L’.-)
,om*
.on81
The activation energies arid frequency factors calculated far k l and k1kGl/k2from a least-square treatment of the entire data are listed in Table 11. The Xrrhenius plots for these constants are shown in Fig. 6, It -rc-uuld be cliEicult to estimate the temperature coefiicients for k a ’k6 from the values in Table I because oi the large uncertainties (see Fig. 7 ) . Hence, the final values of this constant were calculated from those of k l and hlkg/k?, both from Table 11. These values were found to be (7) Tables of complete < l a t a Iia\-e been deposiikd as Document number S I O I ~ w i t h t h e AD1 Avxiliary Publicatii?ns Project, Photoicatirln S e r v m , L i b r a r y of Ciongrrss, \Vashington 2.5, D. C . A ‘ m a y hv swurcd h y ritinx !lir Ducument nunilxr a n d rrtnilling rhFi.1. 5 i l x ph > iiJr i 4 . i mm mirrtifilm in advanw I>? or mmey qnlcr [ ~ y a h l c1 , ) C h i e f , PI, d i i 111 iciit ion S e n icr , I i hru! I L’,mj:rc\s
KINETICSOF
Sept. 5 , 1957
2 0
1,'"
57 mm.
4651
I
1 1
PT :400mm. P =
NO-Nz06 REACTION
THE
.IO
1
I
T
,.04 0 4-1
.04
T
-I!
t
.08 .06
I
I
A
.02
.oI
X
I
.02
CALCULATED
AVERAGED
A
PT ,400mm 0 PT
t
-
A
57".
1
.2
I
I
1
I
1 .01
3.30
3.35
3.40
3.45
W T ) x 103
see text.
plot for kg/ka;
Fig. 7.-Arrhenius
within the limits of the errors in Table I, as shown in Fig. 7. TABLE I1 FREQUENCY FACTORS AND ACTIVATION EXERGIES Constant
-
400 mm.
kl (sec. - 1 ) kiko/kr (sec.-l)
1 0 > 1 . 1 e-21.0iRT
kdks
10-2.2
Total pressure--
1016.a eti.i/lZT
* 5 7 mm
Ps
(KCAL./MOLE)
e
-22.4,
t '20.C
57 mm. 1013.! e - 2 0 . 0 1 R T
-
R
'o\o
io-a.? e - 2 . a I R T
h 0'
Discussion
->
0.0147
1
-
-
0'
In our earlier work3 we encountered serious diffi- ", culties arising from the mixing of the reactants in '\. 20the absorption cell. The values of the constant rE.1 were of the right order of magnitude but the calculated activation energy was found to be anomalously low. In the present work we feel that 1.0: this difficulty has been removed. As another pre6caution, we made at least two runs at each total pressure and temperature in which an excess of 4N O was used. In these runs the plot of log(NzOs) against time gave straight lines over the entire ,2period of the reaction. Two of these plots are shown in Fig. 8. The values of kl obtained from the slopes of these plots were found to be in good agreement with those calculated from the y-w f
-.e
HA-21
o'aCy,o.
0-3. O.O.o
\o,
-
kaO0143 O ..-
0
-
O\
-
-
I
I
I
I
25
I
I
I
I
I
50
1
,
1
,
,
75
,
,
1
,
l
,
100
I
I
,
,
I
125
I
4652
W. D. WILLIAMS, J. A. ELLARDAND L. R. DAWSON
400 and 57 mxn., nevertheless, the decrease in the energy is in the correct direction. As for the frequency factors, we can only conclude that they are reasonable, since a rather limited temperature range was used in their evaluation. The constant klke,/k~ is found to be independent of the total pressure within the precision of our measurements. This result is in complete agreement with the proposed mechanism. From this value one could estimate the equilibrium constant for the dissociation of N205 into NO2 and NO3 if one knew the value for k ~ or , vice versa. I t is interesting to note that the temperature coefficient for kz/k6 is small and negative. This of course means that the activation energy E2 associated with k2 is slightly less than E6 associated with k6. Our accuracy is such that we can with confidence say only that (E2 - E6) is small, and that if we regard E2 as probably small because the reaction is merely a recombination, then E6 must also be small. I t is however interesting to note that the trend of activation energies with pressure, ~ like that found for kl by Johnston, et ~ l .is, consistent with the prediction of unimolecular rate theorya that the activation energy of a unimolecular decomposition should fall off a t low pressures, and that a bimolecular association with no activa(8) L. S. Kassel, “Kinetics of Homogeneous Gas Reactions,” X e w York, N. Y.,1932, pp. 95-100; A. F. Trotman-Dickenson, “Gas Kinetics,” New York, N. Y., 1953, pp. G2-S4.
[CONTRIBUTION FROM
THE
tion energy a t high pressures will have a negative “activation energy” a t low pressures. Thus if we assume that the high pressure limit of E2 is zero, we may interpret the data to mean that the high pressure limit of El, 21.0 kcal./mole, represents the dissociation energy of NzO5; that E6 is also nearly zero; and that the negative quantity (E2 &) essentially measures the predicted “negative activation energy” of the association of NO2 and NO3 a t low pressures. Conclusion.-We have investigated the unimolecular decomposition reaction of NzOa in the presence of hTO with our fast-scanning infrared spectrometer. The results obtained from this method were found to be consistent with those obtained from other methods. In addition, we have been able to obtain for the first time a quantitative estimate of the inhibition constant k d k s . Finally, we can reasonably conclude that this spectroscopic method can be applied equally well to other relatively fast gas-phase reactions. Acknowledgment.-\&’e wish to thank hlr. David Rotenberg for preparing the ozone samples used in this work and Miss Ann McHale for undertaking the tedious but critical task of processing our photographic data. Our discussions on this problem with Professor Harold S. Johnston have been a pleasure. MINNEAPOLIS, MINSESOTA STANFORD, CAL.
DEPARTMENT O F CHEMISTRY, USIVERSITY
Solvents Having High Dielectric Constants. VI. B Y WILLIAMD.
W I L L I A R I S , JAMES
Vol. 79
OF
KENTUCKY]
Diffusion in N-Methylacetamide’s2
A. ELLARD A N D LYLER. DAWSON
RECEIVED APRIL 18, 1957 The self-diffusion coefficients of N-~ncthylacet;ltnitlcOver the temperature range 35 to t i O ” , and the sodium ioii iii sodium chloride solutions in N-methylacetamide at 40”. have been determined. Concentrations of the salt varied from 2.5 X t o 0.25 molar. The capillary method was employed with stirring accomplished by rotating the capillary holder. For the pure solvent the diffusion coefficient increases from 4.11 X 10-0 to 7.33 X 10-6 cm.*/sec. as the temperature is raised. The value for the sodium ion decreases from2.58 X 1 0 P to 1.9; X 10-6 cm.*/sec. as the salt concentration is increased one hulldred fold. The activation energy for self-diffusion in the amide is equal t o that for viscous flow. Also it is equal to the activation energy for the self-diffusion of water.
Interest in N-methylacetamide as a s o l v e i i t to be used in diffusion studies arises from its unusual properties. It dissolves readily both organic and inorganic solutes. At 40” its dielectric constant is 165.5 and its viscosity is 0.03019 poise.3 Sodium chloride was chosen as the solute for this study because the literature contains diffusion data for this salt in water4 and its conductance and transference numbers in N-methylacetamide have been calculated from measurements in this Lab0ratory.j Wang6 has discussed the theory and described the procedure for measuring diffusion coefficients (1) Abstracted from a dissertation submitted by William D. ‘A’illiams as a part of the requirements for the Pb.D. degree a t the University of Kentucky. (2) This work was supported in part by a contract with the Office of Ordnance Research. (3) L. R . Dawson, P. G. Sears and R. 13. Graves, THISJ O I J R N A I . . 7 7 , I98F (1955). (4) J. H. Wang ~ n S. d Aliller, ibid., 74, 1611 (196%) (5) E. D. Wilboit, Dissertation, University of Kentucky, l!Kjti. (fi) J . H. Wung, TIHSJ O U R N A L , 74, 1182 (1952)
by the capillary method. Mills and Kennedy7 and Mills and Adamson8 reported studies of probable experimental errors in this method and have described some improvements in techniques. These procedures together with a technique modified for viscous media have been used in the present work. Experimental Materials.-Reagent grade sodium chloride was recrystallized and fused. Sodium-22 chloride was obtained from the Isotopes Division, U.S.A.E.C., Oak Ridge, Tennessee. K-Methylacetamide was prepared by the method described in an earlier paper from this Laboratory.s The solvent which was used froze above 29’ and had a specific conductance of 2 X 10-60hm-1cm.-1at 40”. Active N-methylacetamide was prepared from C14enriched BaC03, obtained from Oak Ridge, by first synt liesizing acetic acid-1-C”. This synthesis was arrotn( 7 ) R. Mills and J. W. Kennedy, i b i d . , 7 6 , 5G9G (1953). (8) R. h‘iills and A. W. Adamson, i b i d . , 77, 3454 (1955).
