Chemiluminescent Reactions of Excited Helium with Nitrogen and

---

9 Chemiluminescent Reactions of Excited Helium with Nitrogen and Oxygen MARK CHER and C. S. HOLLINGSWORTH Downloaded by CORNELL UNIV on July 23, 2016 | http://pubs.acs.org Publication Date: June 1, 1969 | doi: 10.1021/ba-1969-0080.ch009

North American Aviation Science Center, Thousand Oaks, Calif. 91360

Active species created in a fast flow of helium by a micro­ wave discharge react outside the discharge with nitrogen or oxygen causing the emission of visible bands ofN +and O +. The emission intensity in the "flame" zone decays exponentially with distance, and the decay coefficient de­ pends on both theflowrate of helium and theflowrate of the added gas. A mathematical analysis is developed to predict the intensity dependence on distance and flow parameters. Comparison of experimental and theoretical results permits the calculation of the rate constants for the reactions populating the emitting states and the diffusion coefficients of the excited helium species. Evidence is pre­ sented to suggest that the dominant reactive species is the metastable He atom in the2 Sstate. 2

2

3

Tong-lived reactive species, produced when helium gas is subjected to an electrical discharge, react with many other gases and generate characteristic emissions of visible light. The nature of some of these chemiluminescent reactions has been discussed recently in a number of papers (3, 4, 5,9,16). The reaction with nitrogen gas produces an intense bright blue flame consisting of the first negative system of N ( B 2 „ —> X 2 ) . With oxygen a bright yellow-green flame is observed owing to the excitation of both the first negative system of 0 (b 2 ~ -> a n „ ) and the second negative system of 0 ( Α Π „ —> X n ) . In this paper we report the results of our measurements of the spatial variation of the emission intensity in a fast flow system for various flow conditions, and show how these measurements can be used to evaluate the rate constants for the reactions populating the emitting states. 2

2

+

+

2

g

2

2

+

2

2

+

4

}i

4

s

118 Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

+

9.

CHER AND HOLLiNGsWORTH

119

Chemiluminescent Reactions

Apparatus The reaction cell and associated equipment are shown schematically in Figure 1. The reaction cell consisted of a pair of concentric boro­ silicate tubes. The inner tube, which carried the helium gas, was 0.955 cm. i.d. and 55 cm. long. The titrating gas was introduced into the helium stream via the outer tube through a 0.2 mm. inlet gap in the inner tube. High velocity flows of about 10 cm./sec. were maintained by three mechanical pumps connected in parallel, each of which was rated at 425 liters/min. The flow rates of the gases were measured using a pair of calibrated critical velocity orifice flow meters described by Andersen and Friedman (1). The pressure in the reaction cell was taken as the average value measured by two oil manometers located approximately 20 cm. upstream and 35 cm. downstream from the inlet gap. The ob­ served pressure drop between the two manometers was approximately 75% of the average pressure.

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4

ι—ι

Valve &

N * + X

(1)

N * -> N

(2)

2

2

+

2

2

+

+

+ h

v

At this point the identity of X* remains unspecified. -X* could be, for example, the metastable 2 S helium atom, in which case X represents a ground state He atom plus an electron. Alternatively X* could be the H e molecule-ion, and X would then represent two ground state helium atoms. For simplicity we assume that under any one set of conditions only one excited helium species is dominant, although we can expect several processes occurring simultaneously. The natural lifetime of N * or 0 * is short compared with the time scale of the experiment, and thus the emission intensity is proportional to the rate of Reaction 1. If the concentration of nitrogen is uniform and constant along the tube, which should be the case after some distance of travel, the intensity 3

2

+

2

2

+

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

+

9.

121

Chemiluminescent Reactions

CHER AND HOLLINGSWORTH

becomes proportional to the concentration of X*. We therefore need to derive an expression for the concentration of X* as a function of position. We consider a semi-infinite cylinder of radius r . Let η be the con­ centration of X* and Ν the concentration of the added gas, say N . We assume that the two major mechanisms responsible for the decay of η are diffusion of X* to the walls where η = 0 and the chemical reaction represented by Equation 1. Under these conditions the rate of change of η is given by ()

2

u ^ = D V n - kNn dx

(3)

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2

where u is the stream flow velocity, χ is the axial coordinate, D is the diffusion coefficient of X*, and k is the specific rate constant for Reaction 1. Since transport along the axial direction by convection is much greater than by diffusion, we need only consider radial diffusion, and for this case the solution of the axial part of Equation 3 assuming a constant average flow velocity u is (10) Q

+ *N)

n(x)=n exp[0

.

(4)

Λ, the characteristic diffusion length is given by Λ = r /2.405, and is obtained from the solution of the radial part of Equation 3 using the assumed boundary condition η = 0 at the walls (12). The radial de­ pendence of n(x) is taken care of by the experimental arrangement, since the photomultiplier tube views an entire cross section of the flame, and its response is proportional to the integrated average intensity. The average flow velocity u and the concentration Ν are calculated by Equations 5 and 6 o

0

tt = RT2F/p*r e

0

(5)

2

(6)

N=(F /%F)(p/KT) N

where ρ is the pressure, Τ is the temperature, F is the flow rate of the added gas in moles/sec, and 2F is the total flow rate, which in these experiments is essentially equal to the flow rate of helium. If the emitted intensity I(x) is proportional to n(x), it follows that a plot of In / vs. χ should be a straight line with slope N

(D )(2.405)2 7602FRT

dlnl dx

oPo

7 +

* - ( ^ Η Γ ) ^

(

7

)

In Equation 7 we make use of the fact that D is inversely proportional to pressure and (D p ) is the diffusion coefficient at pressure 1 mm. Hg. Using Equation 7 it should be possible to evaluate k and D p from the predicted linear dependence of S on the flow rate of added gas F . 0

0

0

0

N

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

122

CHEMICAL REACTIONS IN ELECTRICAL DISCHARGES

In the derivation of Equations 4 and 7 we have used a constant average flow velocity u and neglected to allow for the parabolic velocity profile that must exist under our laminar flow conditions. If we let u in Equation 3 be a parabolic function of r, namely u = 2w (l — r /το ), then the equation becomes considerably more complicated, and this case does not appear to have been heretofore treated satisfactorily. The solution is worked out in the appendix and the final result is shown in Equation 8 0

2

0

__

S

{DQVOU

(K?\

+

(

h

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760XFRT V 2 ) -

«

-

y / l +

Pro

\760XFRT)

(

^

(

^

"

Ϊ

'

\ "

e i

1

\

2 )

N

·

where λ = 2.710, = 0.237 and e = 0.00115. Except for the value of the empirical constants and the appearance of the quadratic third term, which turns out to be essentially negligible, Equations 7 and 8 are similar. Thus, the effect of considering the parabolic flow field in the tube is to increase all the values of D p and k over those obtained in the simpler treatment by factors of 1.58 and 1.62, respectively. 0

2

C l

Q

0

Results Measurements of intensity vs. distance were recorded for nitrogen at 3914 A. and for oxygen at 5586 A. and 4116 A. These wave lengths are the heads of intense vibrational bands of the first negative system of N and the first and second negative systems of 0 . Flames were 5—20 cm. in length, and over this distance the intensity varied by factors of 100 or more. Typical plots of the logarithm of the intensity vs. distance for various nitrogen flow rates at constant helium flow rate are shown in Figure 2. These results demonstrate both the linear behavior and the increased rate of decay of intensity with increasing flow rate of added gas, as predicted by Equations 7 and 8. Rates of decay of intensity S for various flow rates of helium were plotted against the flow rate of added gas, and the results are shown in Figures 3 and 4. A linear dependence is obtained for nitrogen, but for oxygen some downward curvature is evident. The quantities k/T and D p /T were calculated from the slopes and intercepts (initial slopes in the oxygen experiments) using Equation 8, neglecting the quadratic third term, and the results are shown in Table I. From the values of k/T and D p /T obtained in this way, the magnitude of the third term was then calculated for the largest value of F used, and it was shown that the ratio of this term to the first two terms was less than 1% for nitrogen and 4% for oxygen. Taking an average value of the temperature in the reaction zone from the spectro2

+

2

2

0

2

+

0

0

0

N

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

9.

CHER

AND H O L L i N G S W O R T H

Chemiluminescent Reactions

123

scopic measurements, we then calculate absolute values of k and D p . The magnitudes of the rate constants are in the range of 10" cc. mole­ cule" sec." . Thus, these reactions are very fast indeed, being of the order of the collision frequency. The rate constant for the reaction with N is about one-third as large as those for the reaction with 0 . Quali­ tatively this is observed, since the nitrogen flames are generally longer than the oxygen flames. The small difference in the rate constants for the oxygen reaction, as determined from the data at the two wave lengths, is real and not caused by experimental error. This is shown by the fact that in a given flame the first negative band system decays with distance slightly more rapidly than the second band system. The unusual square dependence of the rate constants on temperature shown in Table I is found in both sets of reactions. The diffusion coeffi­ cient D p of the excited helium species shows a similar temperature behavior. The magnitude is reasonable for any one of the excited helium species (13), and it is interesting that essentially the same value is ob­ tained for both sets of reactions. 0

0

10

1

1

2

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2

0

0

ΙΟΟι

—

\

X4.4

^^^^

\l6.5 —

27.4 s!34.8

X.

\·

0

I 2

1 4

1 6

\59.2 81 11 0 \ 1 12 Distance

I 14

I 16

18

Figure 2. Intensity vs. distance plots for nitrogen titration at 3914 A. F = 16.1 X 10~*< moles/sec. The intensity was normalized to 100 arbitrary units in all runs. Distance scale: 1 unit = 0.531 cm. The num­ ber in each run refers to the pressure of nitrogen upstream of the flow­ meter orifice and is approximately proportional to theflowrate of nitrogen He

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124

CHEMICAL REACTIONS IN ELECTRICAL DISCHARGES

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Discussion The experimental data obtained in the nitrogen titrations fit the equa­ tions predicted by the model remarkably well, as evidenced by the results in Figures 2 and 3. In the oxygen titrations, the results are not as good; while the intensity curves obey the exponential decay law (Equation 4), the decay coefficient S shows a greater downward curvature than we would predict on the basis of Equation 8. A likely explanation is that photo-ionization and excitation of the oxygen by trapped 587 A. resonance radiation from the helium discharge acts as an additional source of excited molecules, and consequently the intensity of the emitted light decays less rapidly than expected at higher flow rates (and hence con­ centration) of added gas. Evidence for this effect is provided by our early experiments which were carried out with only one-third the ultimate pumping capacity. These experiments showed greater deviations from 1.6,

Titration He* with N at 3915 Δ 2

0

0.5

Figure 3.

1.0

1.5

2.0

(moles/sec)

2.5

3.0

Plot of —dlnl/dx vs.flowrate of nitrogen

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

9.

CHER AND HOLLiNGsWORTH

Chemiluminescent Reactions

Titration He* with 0 F xl0 moles/sec • 16.1 Ο 16.1 • 30.6 • 30.6 • 46.5 Δ 46.5 He

1.8

-

4

125

2

Ρ mm Hg 4.17 4.17 6.60 6.60 8.74 8.74

Wave length 5587 4118 5587 4118 5587 4118

·/

1.4 -

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-

-

/ •

0.(

0."

—

ο.;

0

I 0.5

1

1 1.5

1.0

1 2.0

1

2.5

3.0

F Q X I0 (moles/sec) 2

Figure 4.

6

Plot of —dlnl/dx vs. flow rate of oxygen

linearity in both the oxygen and nitrogen systems, presumably because the resonance light is more efficiently absorbed at the resulting higher pressures. This indeed is the rationale for taking initial slopes to compute rate constants. Ferguson and co-workers (10) report direct evidence of the photo-ionization effect, although they find that the effect in oxygen is smaller than in nitrogen. The square dependence on temperature for the rate constants of both reactions is quite surprising, and we cannot explain it. It is difficult to believe that these fast reactions involving highly excited species should have activation energies associated with them, although one could cer­ tainly draw Arrhenius plots from the data. Because of the scatter of the data in Table I and the uncertainties introduced by the temperature gradient in the reaction zone we cannot rule out the possibility of a

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

126

CHEMICAL

R E A C T I O N S IN E L E C T R I C A L

DISCHARGES

somewhat less steep functional dependence on temperature. Additional experiments in which the gradient is removed will be required to establish more accurately the temperature coefficient. It should be noted that the determination of the temperature dependence comes out naturally from the mathematical model and the data of Figures 3 and 4 and does not depend on the measurement or knowledge of the actual temperature in the reaction zone. However, the solution of Equation 3 is based on the assumption of constant u and N, and both of these quantities depend on the ratio of temperature and pressure—i.e., density—as shown by Equa­ tions 5 and 6. The effect of the temperature gradient in the reaction zone is fortunately partially compensated by a corresponding drop in pressure because of the viscous drag. The net effect cannot be too serious in view of the excellent fit to the predicted exponential decay of intensity. Owing to the uncertainty in the temperature of the reaction because of the gradient, the error in the absolute value of k may be as large as 50%, whereas k/T is probably accurate to within 20%.

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0

2

Table I.

Rate Constants and Diffusion Coefficients for the Reactions of Excited Helium with Nitrogen and Oxygen

F X 10' ρ Τ Run moles/sec. mm. Hg °K. T He

χ

1 Q 1 6

kXIO" cc-

DQPQ D XIO* Τ cm. mm. Hg O P O

2

molecule-sec.

2

sec.

Titration with N at 3914 A. 2

1 2 3 4

7.70 16.1 30.6 46.5

2.77 4.35 6.63 8.82

1 2 3

16.1 30.6 46.5

4.17 6.60 8.74

399 440 525 660 Average

4.2 4.5 4.3 3.4 4.1

0.66 0.87 1.2 1.5

1.8 2.4 3.0 4.2

7.3 11 16 28

2.0 3.1 3.1

8.6 16 20

1.9 2.6 2.5

8.4 14 17

Titration with Ο at 5586 A. (1st. Neg.) 2

440 525 660 Average

Titration with 0 1 2 3

16.1 30.6 46.5

4.17 6.60 8.74

440 525 660 Average

14 12 13 13 2

2.7 3.4 5.8

at 4116 A. (2nd. Neg.) 13 11 12 12

2.5 3.1 5.1

A question may be raised concerning the significance of an equi­ librium Boltzmann rotational temperature for N , and the propriety of equating it to the temperature of the gas stream, since under the condi2

+

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

9.

127

Chemiluminescent Reactions

CHER AND HOLLINGSWORTH

tions of our experiments excited N suffers two to five collisions during its radiative lifetime of 6.6 Χ 10" sees. (2). The answer must be that either these very few collisions are sufficient to attain rotational equi­ librium, or else the excited N is produced in Reaction 1 at the same rotational temperature as the neutral N . In a reactive collision between N and He(2 S) neither the He nor the Penning electron can carry away much orbital angular momentum, and thus the second possibility appears quite reasonable. 2

+

8

2

+

2

3

2

So far we have not considered the identity of the excited helium species X*. Collins and Robertson (3) have shown that the upper state of N giving rise to the blue emission is populated by reaction of N with both metastable 2 S He and He . Similarly, they have shown that 2 S He reacts with 0 to populate the upper state of both band systems of 0 , while H e reacts with 0 to populate only the upper state of the 5586 A. system. 2

+

3

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2

3

2

+

2

2

+

2

+

2

In our experiments with 0 we obtain rate constants which are almost the same whether we monitor the 5586 A. or the 4116 A. band systems. Also the diffusion coefficients appear to be the same in both oxygen and nitrogen titrations. These observations suggest that under our conditions metastable 2 S He is responsible for most of the reactions leading to emission. If H e were contributing significantly to the reac­ tion populating the upper state of the 5586 A. system, we would expect the differences between the results at the two wave lengths in oxygen to be a function of total pressure, since the population of H e is proportional to the square of the total pressure. This is not found. The small difference between the results at the two wave lengths shows that the reaction of H e cannot be excluded completely, however, and we would predict qualitatively that the rate constant for the reaction of H e with 0 is larger than the corresponding rate constant for the reaction of 2 S He. Quantitative comparisons for these reactions are not available. An inde­ pendent check on the identity of the excited helium species and the magnitude of the rate constants could be obtained by following the decay of the 2 S helium concentration using absorption measurements. Such experiments are being planned, and the results will be reported in future publications. 2

3

2

+

2

2

+

+

2

+

2

3

3

There are very few measurements of the rate constants for these reactions with which we may compare our results. Sholette and Muschlitz (17) give values of 19 Χ 10" cc. molecule" sec.' and 9 Χ 10~ cc. molecule" sec." for Reactions 9 and 10 11

1

1

1

n

1

He(2 S) + 0 -> He + 0 3

2

2

He(2 S) + N -> He + N 3

2

2

+

+e

(9)

+

+e

(10)

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

128

CHEMICAL REACTIONS IN ELECTRICAL DISCHARGES

while Fehsenfeld and co-workers (8) report 6 X 10 for Reaction 11 He + N ->2He + N 2

+

2

2

1 0

cc. molecule" sec. 1

1

(11)

+

Our results extrapolated to 300 °K. give values of 11 Χ 10" and 4 X 10' cc. molecule" sec." for Reactions 9 and 10 in reasonable agreement with those of Sholette and Muschlitz. 11

1

11

1

Acknowledgments

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The authors are grateful to D. A. McQuarrie for his help with the mathematical analysis and to G. Lauer for supplying the computer program.

Appendix The Effect of a Parabolic Velocity Profile on the Concentration Distribution of Excited Species We consider the differential equation

This equation differs from Equation 3 in that the flow velocity u is given by u = 2u (1 — r /r ); u is as before the average flow velocity, and r is the tube radius. As usual we let n(r,x) = X(x)R(r), substitute into Equation A - l , separate variables, and obtain two ordinary differential equations for X(x) and K(r), which are related by a separation constant b. 2

0

2

0

0

0

2

2u 1 dX

JL_

0

~D~li~dx~ dR

IdR

dr

r dr

2

2

(A-2)

W

The solution of Equation A-2 follows immediately X(x) = C exp [

- (§ + ) J L ] = C exp [ e

+ kN ) ^ - ] (A-4)

where C is a constant, and Λ and λ are parameters ( independent of r and x) defined by 1

λ

2

1

a

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

/ A K\

9.

CHER AND HOLLINGSWORTH

129

Chemiluminescent Reactions

Whereas in the solution of Equation 3 1/Λ = ( 2.405 ) /r , and λ is simply the number 2.405 corresponding to the first zero of the Bessel function J (fA/r ) evaluated at r = r , in the more complicated case of Equation A - l λ turns out to be function of a and hence a function of N. The problem is to find this dependence. We define a new variable 2

0

0

2

0

2

0

y=T

= T

( A

-

6 )

and simplify Equation A-3 to the non-dimensional form | H dy

i £ y dy

+

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2

Λ _ ^ \

+

y

Λ /

Η

=

0

( A

.

7 )

where R is now a function of y, and

Equation A-7 can be reduced to the confluent hypergeometric differential equation (14) dG - d *

.

2

z

+

{

~

1

z

)

dG i h -

a

G

=

0

where ζ=

βλτ /τ 2

2

0

a =(1/2) -

( /40) λ

exp[/?Ar /2r ]

G(Z)=R(^J

2

2 0

and its solution in terms of the real variable r is (14) R (^) Here F (a,l;z) 1

i

= e x

P

[

-

/

^ / W

1

(I

-

A

1

;

(A-9)

B f )

represents the confluent hypergeometric function rw

,

χ

Ξ

a(a + l)~-(a

j= o

+ j-1)

.

^'·'

The boundary condition η = 0 at the wall of the tube requires

MW^H

-

(A io)

The solution of this equation gives λ as a function of β, which in turn is a function of N. The first three roots of Equation A-10 were solved numerically for several values of β in the range 1 to 2.5, and the results are shown in Table II. It is interesting to note that the first three solu-

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

130

CHEMICAL REACTIONS IN ELECTRICAL DISCHARGES

tions for the special case β = 1 (i.e., no chemical reaction as Ν = 0) were obtained by Nusselt (15) in 1910 in connection with a heat flow problem, and he found values of λ equal to 2.705, 6.66, and 10.3. Although the complete solution of Equation A - l involves an infinite sum of exponentials of the kind represented by Equation A-4, each corresponding to a root of Equation A-10, only the first root contributes substantially to the sum. Consequently, we shall ignore all roots except the first, and hereafter λ refers only to the first root. Table II.

The First Roots of Equation A-10 as a Function of β

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(2)

λ

β

(1)

1.000 1.100 1.250 1.375 1.500 1.625 1.750 2.000 2.250 2.500

λ

2.7044 2.7776 2.9090 3.0408 3.1947 3.3715 3.5699 4.0178 4.5032 5.0004

6.679 7.017 7.656 8.301 9.013 9.752 10.500 12.000 13.500 15.000

10.673 11.320 12.561 13.759 15.001 16.250 17.500 20.000 22.500 25.000

To obtain the dependence of λ on Ν we plot λ vs. λ (β — 1), and this is shown in Figure 5. This plot is suggested by the fact that according to Equation A-8 Ν is proportional to λ ( β — 1). Experimental results using the approximate Equation 7 indicated that the range of λ ( β — 1) was between 0 and 48, corresponding to a range of β between 1 and 2. A quadratic fit over this range was computed by the method of least squares. The results are expressed by the empirical relation 2

2

2

2

2

2

2

λ = λ 2

0

2

+

€ ι

λ (/? 2

2

-

1) - e A (/? " I ) 2

4

2

2

2

(A-ll)

with λ

0

2

= 7.3428

ci = 0.2372 C2

= 0.001150

The standard deviation of the empirical curve from the actual curve is 2.29%. Using Equation A-8, Equation A - l l becomes λ = λ 2

kr

0

2

kr

2

2

+ ci -jy Ν — t

2

4

Ν

2

(A-12)

Substituting Equation A-12 into Equation A-4, we obtain the desired axial dependence of n, denoted by n(x), as shown by Equation A-13.

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9.

CHER AND H O L L I N G S W O R T H

Chemiluminescent Reactions

131

·-·* Η ΐ Η ^ - ' ΐ Η ^ "

(A 13)

Here n is a constant obtained by formally averaging out the r dependence of n(r,x). Using Equations 5 and 6, taking logarithms and computing S == 0

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we arrive finally at Equation 8.

Figure 5. Plot of λ vs. the function (β - 1)λ . See the appendix for explanation. Note that the points are not experimental points; they are calculated from the data in Table II and are shown only to aid in the plotting 2

2

2

Literature Cited (1) (2) (3) (4) (5) (6) (7)

Andersen, J. W., Friedman, R., Rev. Sci. Inst. 20, 61 (1949). Bennett, R. G., Dalby, F. W., J. Chem. Phys. 31, 434 (1959). Collins, C. B., Robertson, W. W., J. Chem. Phys. 40, 701 (1964). Ibid., 40, 2202 (1964). Ibid., 40, 2208 (1964). Coster, D., Brons, Η. Η., Z. Physik. 73, 747 (1931). Fehsenfeld, F. C., Evenson, K. M., Broida, H. P., Rev. Sci. Inst. 36, 294 (1965). (8) Fehsenfeld, F. C., Schmeltekopf, A. L., Goldan, P. D., Schiff, Η. I., Ferguson, Ε. E., J. Chem. Phys. 44, 4087 (1966). (9) Ferguson, Ε. E., Fehsenfeld, F. C., Goldan, P. D., Schmeltekopf, A. L., Schiff, Η. I., Planetary Space Sci. 13, 823 (1965).

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(10) Goldan, P. D., Schmeltekopf, A. L., Fehsenfeld, F. C., Ferguson, Ε. E., J. Chem. Phys. 44, 4095 (1966). (11) Herzberg, G., "Spectra of Diatomic Molecules," 2nd ed., p. 204, D. Van Nostrand Co., Princeton, N. J., 1950. (12) McDaniel, E. W., "Collision Processes in Ionized Gases," p. 503, John Wiley and Sons, Inc., New York, 1960. (13) Ibid., p. 516 (1960). (14) Murphy, G. M., "Ordinary Differential Equations and their Solutions," p. 342, D. Van Nostrand Co., Princeton, N. J., 1960. (15) Nusselt, W., Z. Ing. 54, 1154 (1910). (16) Schmeltekopf, A. L., Broida, H. P., J. Chem. Phys. 39, 1261 (1963). (17) Sholette, W. P., Muschlitz, Ε. E., J. Chem. Phys. 36, 3368 (1965).

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RECEIVED June 5, 1967.

Blaustein; Chemical Reactions in Electrical Discharges Advances in Chemistry; American Chemical Society: Washington, DC, 1969.