402
H. D. Sharma and S. P. Sood
Isotopic Exchange Reactions between Nitrogen Oxides and Oxyhalides H. D. Sharma" and S. P. Sood Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada (Received August 14, 1973) Publication costs assisted by the Department of Chemistry, University of Waterloo
The kinetics of atom exchange reactions among ClNO, NO, and NO2 have been studied by using a timeof-flight mass spectrometer in two reactors of different surface-to-volume ratio, over a temperature range 15N02 CPNO2 I4NO, of 0-23". The reactions proceed according to the equations Cl14N0 15N02 Cl15N0 + 14N02, Cl14N0 15N0 Cl15N0 14N0, with the second-order rate Cl14N0 constant, k = (1.78 i 0.04) X lo5 exp[-(3350 f 1 5 0 ) / q M - I sec-I for the first two reactions and k = (1.64 f 0.10) x lo6 exp[-(3145 f 150)/!Q M - I sec-I for the last reaction. Bimolecular mechanisms for the reactions have been proposed similar to those for the corresponding reactions in NO-NO2 and NO2NO2 systems. However, the rates of reactions in the present systems are slower by a factor of -106 a t 23".
-
+
+
Introduction In a previous paper,l it was shown that bimolecular exchange reactions occur in N1s02-N1602 and 15N02-14N0 systems with the rate constants k = (3.0 f 0.1) x 106 and (4.9 f 0.8) X lo7 M - I sec-l, respectively, a t 25". It was concluded that the atom transfer reaction takes place through an associative mechanism. Freiling, Johnston, and Ogg2 studied the kinetics of the reaction ClNO, NO = NO2 -k ClNO (1) and proposed an elementary bimolecular mechanism with a rate constant, k = 0.83 X lo9 exp(-6900/RT) M-1 sec-l. However, they noted that there existed an ambiguity with respect to the path of the reaction, Le., nitryl chloride could pass an oxygen atom or a chloride atom to nitric oxide with the same chemical results. They suggested that isotopic exchange studies may be helpful in clarifying the ambiguity. In this paper we report the results of isotopic exchange studies of the reactions
+
+ +
-
+ +
(21 Cl14N0 "NO Cll'NO 14N0 Cl14N0 I5NO, -+ C1"NO 14N0, (3) Attempts to obtain rate data on reaction 2 by Kuhn and Butkiewicz3 were unsuccessful because of the speed of the exchange reaction.
Experimental Section Preparation of Gases. ClNO obtained from Matheson Co. was purified by the methods of Ray and Ogg4 and Burns and I I a i n t ~ n About .~ 20 ml of liquid ClNO along with 2 ml of NO was condensed in a glass vessel. The mixture was kept a t -60" in a dimethylformamide slush for 6-8 hr with occasional stirring. It was fractionally distilled with the middle 60% condensed onto P2O5. The condensate was allowed to melt and ClNO distilled under vacuum. Several purification cycles resulted in a pure ClNO sample which was stored at liquid N2 temperature in a dark vessel. lSNO gas was prepared by the reduction of H15N03 with Fez+ ions in 4 M HC1 and purified according to a method described by Sharma, e t al.l The preparation and purification of 15N0 and N1802 was also carried out in a manner similar to that described by Sharma, et a1.l The Journal of Physicai Chemistry, Vol. 78.
No. 4 , 1974
-
+
+
-
+
Static Reactor Experiments. The vacuum line used for the transfer of metered gases in all experiments has previously been described.l Two reactors were used. One of t h e reactors was a 2-1. flask with a three-way stopcock which provided access to the inlet system of a time-offlight mass spectrometer. The other reactor was made by fusing six 1 m x 22 mm 0.d. glass tubes to a 33-mm 0.d. glass tube. Each 22-mm tube had a 12-mm 0.d. tube inside it to provide a large surface-to-volume ratio. The reactors were exposed to appropriate gas mixtures prior to a run. Experiments were performed in the absence of light to avoid any photodecomposition. The exchange kinetics was followed by measuring peak heights in mass spectra in the mass range of 46 to 52. A small volume of gas from the reactor was trapped periodically such that the total pressure did not change significantly during the course of the reaction. The gas was allowed to leak into the inlet system of the mass spectrometer through a 75-c~pinhole. The residual gases were removed after the mass spectrum had been recorded. The change in the m / e 46 and 47 for the 15N exchange and 46, 48, and 50 for the I s 0 exchange provided the rate data, except for one case in which NO2 was not present, the peak heights due t o m/e 30 and 31 were followed. The peak heights due to ClN+ a t m / e 49, 50, 51, and 52 were small and therefore the rate data on the exchange kinetics showed a large scatter, Nevertheless, the latter measurements provided additional data on the progress of the exchange kinetics.
Experimental Results and Discussion The experimental results are summarized in Table I, giving the total pressure, P, and the initial concentratibns, [ClNOIo, [Nolo, and [NOa]o. Corrections for the presence of the dimer of NO2 have been applied by using the data of Giauque and Kemp.6 The isotopic exchange rate, R, for 15N and Is0 has been obtained by using the expression7
and
Exchange Reactions between Nitrogen Oxidesand Oxyhalides
403
TABLE I: S u m m a r y of Experimental D a t a and R Values Temp, [NOzla X [Nolo X [ClNOlo X loe Runno.
OC
P, mm
106 M
1
23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23
2.57 5.12 2.89 7.79 1.45 1.93 2.85 3.34 2.24 1.37 1.79 1.75 2.46 3.18 3.10 2.29 5.69 3.06 3.41 1.91 2.98 4.25 2.20 2.09 3.10
72.5 57.6 50.1 44.8 53.3 55.4 109.8 138.6 53.3 38.4 52.2 49 .O 46.2 32 . O 35.2
2 3
4 5 6
7 8
9 10 11
12 13 14 15 16 17" 18" 19a 20 21 22 23 24 25 a
11 11 11 0 0 0
106 M
0 .oo 0 .oo 0 .oo 0 .oo 0 .oo 0 .oo 0 .oo 0 .oo 0 .oo
0 .oo
5.60 12.90 22.70 45 .OO 80.80 51.80
0.0
.oo
56.4 59 .O 70.2 52.2 53.3 59.7 64 .O 52.2 74.6
0 0 .oo 0 .oo
12.90 11.48 0 .oo
14.60 12.90 0.00
x
M
R
78.60 243 .50 119 .go 413 ,70 32.10 58.00
14.72 14.06 17.01 62.25 4.37
58 .OO 58 $00
15.66 18.89 11.29 4.21 15.89 25.90 75.94 209.18 221.70 175.58 52.59 21.32 28.47 19.78 42.91 19.09 14.90 14.76 6.97
78.60 42 $00 47.70 41 .OO 76.10 109.90 66.40 83.20 278.40 121 .20 130.20 47.30 110.69 190 .46 51.10 58 .O 107.6
109 M
8.18
ks, M-1
ks, M-188c-i
f 0.28 f 0.24 f 0.68 f 1.02 f 0.07 f 0.12 f 0.80 f 0.19 f 0.12 f 0.09 f 0.19 f 0.52 It 1 . 5 1 f 3.10 f 8.75 f 4.31 i= 0.76 f 0.22 f 0.39 f 0.49 f 1.41 f 0.57 f 0.15 f 0.48 f 0.08
m-1
40.56 f 0.09
2.18 i 0.03
27.76 f 0.27
1.32 f 0.03
16.71 f 0.08
0.84 f 0.02
Runs were made in reactor B.
in the labeled gas, f t where is the fraction of l5N or is the fraction of 15N or l 8 0 at time t , f a is the fraction of l5N or 1 8 0 a t equilibrium, and n is the number of exchangeable atoms in the labeled molecule. The values of R and the associated errors (Table I) for each run have been computed by a least-square-fitting program from the exchange rate data after the chemical equilibrium among t h e species has been reached. The concentration of ClNO a t equilibrium has been evaluated from the kinetics and equilibrium d a t a of Ray and Ogg,4 Freiling, et a1.,2 and Martin and Kohnlein.8 If the trial assumption is made that the exchange takes place through bimolecular associations and that the exchange rate constants differ from those for the chemical reactions, since the exchange can take place without producing a net chemical change, the exchange reactions can be depicted by the following equations ClI4NO
+ 15N0,
k k-1
'k + I~NO, ~ ~ k Cl14N0 + I5NO rapid + 15~0,
~
1
+ '*NO
(4)
+
(5)
C116N02
c~1 l 5 ~0o C116N0
-
1 4 ~ 0 2
+ I4NO +
(6)
(7) where k1 and k-1 are the rate constants for the forward k' = k2 is the comand the reverse reactions for (4), k l bined rate constant for exchange reactions 4 and 5 and k 3 is the rate constant for reaction 6. The expression for [ClNOz] can be derived from eq 8. 1 4 ~ 0
14~02
+
d[ClNOJ/dt = h1{[NOJ - [CINOz])([CINOIo- [CINOZI) ~ - I { [ N O I+ ~ [Ch"zIJ[C1NOzI (8) [ClNOJ = [CINOz],q(tanh (0.5a.t)) X
{(a
+ b>(a+ b t a n h (0.5~t))-~l(9)
where [ClNO],, = ( a
- b)[2(k-,
- l2)I-l
(10)
+ 4 l ~ l ( h --~ k,~NOz]o[CINO]o~ b = h1([NO2], + [ClNOIOl - k...l[NO]o
a
= {b2
(11)
(12) The expression for R for the entire range of t can be derived from eq 9 and 13
R=-
+
[ClNO]{[NOI n[NOz])d ln(1 - 8')dt [CINO] [NO] n[NOp] h,[ClNOI[NOJ k3[ClNOI[NO]
+
+
+
(13)
for t h e case when
[NO],
=
0 and (a
+ b)(a + b tanh(0.5at)J-1 = 1
(14)
- [C~NO~I~~J{[C~NOIO - [ClNOJeq]t -Ik,{[ClNOI - [C1NOzIeq)[C1NOzIeqt - [(~3[ClNolok,([NOz]o [C1NO]o))[C1N02]eq][t - 2a-1 In cosh (0.5at)l 2{h3 - hz)a-'[C1NOZ],~ tanh (0.5at) (15)
Rt
= k,{[NOZIo
+
+
and for the case when [NO10 >> [ClN02],, and
(a
+ b)[a + b t a n h ( O . ~ C Z ~ ) ] - ~= 2(1 + tanh (0.5at)l-'
Rt
= kz([NOz],
- [CINOZ]eq)([ClNOIo - [ClNOzIeqJt -I(k3[NOlo [ClNOzIeqII[C1NOIo - CClNCZleqlt + exp(-at~[h3([C1NOl, - [NO],) - kz([NOzI,
+
(16)
+
[C1NOIo)I[ClNOzIeq + ( k , kz)[C1N0z]es2[0.5 exp(-at) - 211 (17) The values of kz and k3 are evaluated by following eq 9 from R values (after the chemical equilibrium has been reached). The In (1 - F) values for each run are then calculated as a function of t over the entire range of t and compared with the experimental data (Figure 1).The assumptions given in eq 14 and 16 have been justified by calculating [ClN02] as a function of t according to eq 9 and by evaluating the values of In (1 - F) us. t by numerical integration of eq 13. The complex factors in eq 15 and 17 serve to show the effect of initial nonequilibrium condition on R with respect t o time for the reactions. In this The Journal of Physical Chemistry, Vol. 78, No. 4 , 1974
404
H. D. Sharma and S. P. Sood 1
oo l -O’
’F
$’4O
L
C
0.4 33
0
0
I
10
3.7
36
3.5
T-’ x ~ ~ 3 , 0 ~ - 1
I, \ \
Figure 2. Log kl vs.
, \ ,
system, the chemical equilibrium is reached long before isotopic species attain statistical distribution among the molecules (Figure 1).The errors associated with 122 and 123 have been evaluated by using a least-square-fitting program. The rate data for any given run fit the appropriate expressions. It can, therefore, be surmised that the exchange reactions are first order with respect to each reactant. The initial concentration of the reactants has been varied fourfold and the second-order rate constants are given in Table I. Runs 17 to 19 made in reactor B, having a tenfold change of surface-to-volume ratio, have been found to give the same rate constants within the experimental errors. This provides evidence for the homogeniety of the exchange reactions. In order to determine the activation energy, runs were made in the temperature range 0-23”. A plot of log k us. T-I is shown in Figure 2. The rate constants can be expressed by the Arrhenius equation for reactions 4 and 5 as 122 = (1.78 i 0.04) x lo5 exp[-3350 150/T] and for reaction 6 as 123 = (1.64 i 0.10) X lo6 exp[-(3145 150)/T]. The value of the activation energy for reactions 4 and 5 is similar to that found for the chemical reaction8 for the oxidation of ClNO by NOz. It is, however, interesting to note that k2 is 2.5 times larger than kl for both 16Nand 180 exchange and that 122 has the same value for both l5N and 1 8 0 transfer reactions. It appears that the exchange can occur through another path which does not lead to the oxidation of ClNO. In the N1602-N1802 system, it has been shown that the transfer of oxygen atom can only occur through the formation of a bridged “intermediate dimer” of N0z.l In ClNO-NO2 system, the possibility of the formation of such a bridged species is indicated. The “intermediate species” (not differentiated from a “transition state” configuration) may be depicted as follows
*
The Journal of Physical Chemistry, Voi. 78, No. 4, 1974
T-l
( A ) and
0
I
20 30 40 50 TIME(mins1 Figure 1. Ln (1 - F ) vs. time: run np. 4, A (with I5N); run no. 12, 0 with 15N); run no. 2, 0 (with l a g ) ;-, according to eq 10 and 16. 0
3.4
*
0-N’
cl\ N,O/ I
o\N,o,
N-0
---f
NO
+ NO
C1/
log k3 vs. T - ’ ( 0 ) .
+ ClNO,
+ ClNO,
15N and ”0 exchange
no “N and
exchange
11 0
Cl-N/
\N-0 \O/ I11 C1
0-N’
“-0
-+
NO,
+ ClNO
no I5N exchange exchange
but
NO,
+ ClNO
I5N and “0 exchange
‘0’
Iv If the intermediate species involved one or two oxygen atoms, as shown in I1 and I11 and particularly 111, 122 for ISO atom transfer should have been higher. Failure t o observe any significant difference in 15N and 1 8 0 exchange rate implies that the chlorine atom is involved in forming the intermediate species as shown in I and IV. In ClNO, the N-Cl bond length (1.95 A)Qis longer than the normal N-C1 bond length (1.73 A ) . The low value of the NQR coupling constant10 and high value of dipole moment indicate that the electron density is shifted toward the chlorine atom. In a bimolecular collision the C1 atom will orient itself toward the positive end of NO2, ie., toward the nitrogen atom, thus leading to I. The evidence, though inconclusive, favors the path which involves transfer of the C1 atom rather than the oxygen atom in the oxidation of ClNO by NO2. Further evidence can perhaps be obtained by spectroscopic studies of the unstable species by the matrix isolation technique. The possibility of a dissociative mechanism involving NO and C1 radicals can be excluded on the grounds that the reaction has a very high value for the activation energy (158.8 kJ mol-I). An intermediate species, V, involving the chlorine atom 0-N
/a*...N-0 V
for N transfer in ClNO-NO system similar to that postu-
Isotherm for
Mobile Physisorption of Noble Gases
lated for N O - N O Z ~ can . ~ ~provide satisfactory explanation for the exchange rate. It is interesting to note that the atom transfer reactions between oxides of nitrogen proceed lo6 times faster than those between the corresponding oxide and oxyhalide at room temperature. In the former cases the activation energy is almost 0 while in the latter cases the value is -27 kJ. It may, however, be noted that in oxides both the reactants can be considered as radicals whereas in the latter cases the reaction is between a radical and a molecular species. It will be of interest to investigate whether isotope exchange will occur between oxyhalides by the double labeling technique.
-
Acknowledgments. The authors are grateful’ to the National Research Council of Canada for providing financial
405
support through the provision of research grants and a Research Fellowship to s. P. s.
References and Notes (1) H. D. Sharrna, R. E. Jervis, and K. Y. Wong, J. Phys. Chem., 74, 923 (1970). E. C: Freiiina, H. S. Johnston, and R. A. Oaa, Jr.. J. Chem. Phys., 20,327 (I 953). L. P. Kuhn and C. Butkiewicz, J. Phys. Chem., 65, 1084 (1961) J. D. Ray and R. A. Ogg, Jr., J. Chem. Phys., 26,984 (1957). W. G. Burns and F. S. Dainton, Trans. FaradaySoc., 48, 21 (1952). W. F. Giauque and J. D. Kernp, J. Chem. Phys., 6, 40 (1938). H. A. C. McKay, J. Amer. Chem. SOC., 65, 702 (1943). H. Martin and E. Kohnlein, 2. Phys. Chem., 17, 375 (1958). L. E. Sutton. Chem. SOC. Soec. Pub.. No. 11 (1958): . , No. 18 (1965). (IO) D. J. Millen and J. Pannel, J. Chem. Soc., 1322 (1961). (11) F. S. Klein, W. Spindel, and M. J. Stern, J. Chim. Phys., 60, 148 (1963).
--
Isotherm for Mobile Physisorption of Noble Gasesia E. Bergmannlb Department of Physical Chemistry, The Hebrew University, Jerusalem, Israel, and Battelle Institute, Advanced Studies Center 1227 Carouge, Switzerland (Received August 2, 7973) Pubimbon costs assisted by the National Bureau of Standards
The solution of the scaled particle theory for hard disks is used with the temperature-dependent diameter corresponding to the R - 1 2 repulsive potential. This is combined with the contribution of the attractive potential to the second virial coefficient to a n improved equation of state for mobile adsorbed layers on homogeneous surfaces. For the intermolecular potential the parameters determined from surface gas virial data are used. The equation of state is thermodynamically related to an isotherm. Both the critical temperatures and the isotherm show satisfactory agreement with measurements.
I. Introduction The recent physisorption experiments of Thomy and D u v a P on exfoliated graphite have raised new interest in the fluid phase transitions on such surfaces.2b The data are currently interpreted in terms of the De Boer-Hill isotherm, which is based on the simple two-dimensional van der Waals equation. Tsien and Halsey3 have combined this isotherm with the Langmuir isotherm for localized adsorption and were thus able to explain the whole coverage range. Earlier, Stebbins and Halsey4 pointed out that one could use results for the virial coefficients of hard disks to improve the treatment of the repulsive shortrange interaction. Claiming the short-range interaction to reproduce the second virial coefficient correctly, they derived the adjusted Volmer equation. In contrast to this McAlpin and PierottiS used the significant structure model of liquids to obtain also a n equation of state for adsorbed layers. Meanwhile greatly improved solutions of the hard disk problem are available, e.g., the Pad8 approximant of Ree and Hoover6 which agrees excellently with the results of molecular dynamics calculations up to the liquid-solid transition. One purpose of this study is to use improved hard disk results. To avoid unnecessary complication, we will how-
ever use the simpler scaled particle result7 which also gives very good results at not too high densities. The longrange contribution to the equation of state is taken from the second virial coefficient. The approximations involved herein are discussed in section 111. For the interaction between adsorbed atoms we use the potential obtained by Everett8 from fitting of second virial data. The equation of state so obtained is integrated uia thermodynamic relations to an isotherm whose integration constant is determined by comparison with Hill’s classical r e ~ u l t . ~
11. Short-Range Interaction We choose as usual the short-range potential as an inverse power. V ( R ) = V , / R” = 4V,,,(Ro/ R)12 (1) As Everett8 we take for V,,, and Ro the parameters of the bulk gas, thus plugging the entire perturbation of the intermolecular potential by the adsorbent into the longrange repulsion. There is no real justification for this, nor for the special form chosen in (l),e.g., theoretical calculations fit much better to an exponential,l0 but the small amount of experimental results of intermolecular forces of adsorbed atoms precludes for the moment any improvement. The Journal of Physical Chemistry. Voi. 78. No. 4. 1974
