J. Phys. Chem. 1903, 87, 841-844
to determine kl/kz. The method used to generate H02and OH was the same as that used in the present study. However, Hack et al. used larger concentrations of atomic oxygen (2 X 1013 < [O] < 3 X 1014 ~ m - and ~ ) chose to measure kl/k2 by observing [OH]/[H02] only a t the point where [OH] reached its maximum. They did not observe ratios in the quasi-steady-state region. Their result was kl/k2 = 0.86 f 0.4. Computer simulations of these experiments using conditions given in their Table 3 show that maximum [OH] occurred a t 1 ms or less and that a t this time [HO,]was falling rapidly. Thus, it was very difficult to accurately determine [OH]/[H02] in this way. In addition, an estimate of the mixing time in their system using the relation t = R2/2D, with R = 1.5 cm and D = 170 cm2 s-l (diffusion coefficient of atomic oxygen in helium a t 4.5 torr)21results in 6-7 ms. This suggests that (21)Marrero, T.R.; Mason, E.A. J. Phys. Chem. Ref. Data 1972,1, 3.
041
mixing may not have been complete at the time the [OH] maximum was observed.
Conclusions The rate constant ratio, kl/k2, was found to be 1.7 f 0.4 which is in excellent agreement with the ratio calculated by using earlier independent determinations of kl and k2. This confirms the absolute rate constant measurements which required experimentally difficult determinations of absolute radical or atomic oxygen concentrations. These results are expected to have a significant effect on predicted concentrations of atomic oxygen, 03,and HO, in the mesosphere and upper stratosphere above 35 kmS7p8 Acknowledgment. The research described in this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Registry No. Atomic oxygen, 17778-80-2;hydroxyl, 3352-57-6; hydroperoxo, 3170-83-0.
Muonium Addition to Cyanides J. M. Stadlbauer,* B. W. Ng, Y. C. Jean,? and D. C. Walker Department of Chemlstry and TRIUMF, Unlverslty of Brnish Columbia, Vancouver, British Columbia V6T IY6, Canada (Received September 14, 1982)
Muonium, the light radioactive isotope of hydrogen, was found to add to the CEN bond of acetonitrile, cyanoacetate, cyanide, and tetracyanocadmate(I1)with room temperature rate constants, k,, of 5.1 X lo7,7.7 x lo7,3.0 X lo9,and 1.7 x 1OO ' (all M-' s-l), respectively. While Cd(CN)42-is diffusion controlled with a critical energy of 15 kJ/mol, the others appear to be activation controlled as with cyanoacetate's activation barrier of -35 kJ/mol. Kinetic isotope effects range from 0.7 to 24.
-
Introduction Muonium (Mu) is an atom-like particle consisting of a positive muon nucleus &+)with a bound electron. Though the mass of Mu is 1/9 that of H the reduced masses are nearly equal giving Mu an ionization potential and Bohr radius similar to H. Because the muon nucleus is a radioactive particle with an intrinsic lifetime of 2.2 X lo4 s, muonium can be used as a probe to directly observe hydrogen-atom reactions. Due to the factor of 9 difference between the masses of Mu and H, Mu should be an excellent particle to study kinetic isotope effects. Muonium is formed when an energetic muon (4.1-28 MeV) enters the target and abstracts an electron from the stopping medium into a bound state. The muon itself is a product of a positive pion ( T + ) decay which in turn is a product of a proton capture by 9Be. When the muon decays it ejects a positron which can be easily observed and counted by using nuclear physics counting techniques. More detailed descriptions of the particles and techniques are available Muonium was originally observed to form in gases.3 Later, pure liquids such as water,4 alcohols>6 and certain hydrocarbons7p8were found to produce usable amounts of muonium with long enough lifetimes (up to 20 ps in watel.9) to be useful as solvents to study a diverse number of solutes more reactive toward muonium. In water such re+ Department of Physics, University of Missouri-Kansas Kansas City, MO 64110
City,
0022-3654/83/ 2087-084I$Ol.50/0
actions as addition, abstraction, oxidation-reduction, and spin conversion can be observed and measured.2 When analogous hydrogen atom reactions have been measured the kinetic isotope effect can be calculated. In a previous study we observed the addition reactions of Mu with several vinyl monomerslO reporting isotope effects of 1.1 and 2.8 for acrylamide and acrylonitrile, respectively. In an effort to obtain a better understanding of muonium addition reaction isotope effects we selected cyanide, both organic and inorganic forms, as the reactive solute. ESR studies11J2have established that both organic and inorganic cyanides undergo addition by H; therefore Mu should also add across the C s N bond of cyanide. ~
~
~~
(1)D. G. Fleming, D. M. Garner, L. C. Vaz, D. C. Walker, J. H. Brewer, and K. M. Crowe, Adu. Chem. Ser., No. 175, 279 (1979). (2)D.C. Walker, J. Phys. Chem., 85, 3960 (1981). (3)V. W. Hughes, Annu. Reu. Nucl. Sci., 16, 445 (1966). (4)P. W. Percival, H.Fischer, M. Camani, F. N. Gygax, W. Ruegg, A. Schenck, H. Schilling, and H. Graf, Chem. Phys. Lett., 39, 333 (1976). (5)P.W. Percival, E.Roduner, and H.Fischer, Adu. Chem. Ser., No. 175. 335 (1979). (6) P. W. Percival, E. Roduner, H. Fischer, M. Camani, F. N. Gygax, and A. Schenck, Chem. Phys. Lett., 47,11 (1977). (7) Y. Itq B. W. Ng, Y. C. Jean, and D. C. Walker, Can. J. Chem., 58, -2.795 _ _ _ (19ROl. ~
(8)B. W. Ng, J. M. Stadlbauer, Y. C. Jean, and D. C. Walker, Can. J. Chem., in press. (9)K. Nagamine, K.Nishiyama, J. Imazato, H. Nakayuama, M. Yoshida, Y. Sakai, H.Sato, and T. Tominaga, Chem. Phys. Lett., 87,186 (1982). (10)J. M.Stadlbauer, B. W. Ng, D. C. Walker, Y. C. Jean, and Y. Ito, Can. J. Chem., 59, 3261 (1981). (11)P. Neta and R. W. Fessenden, J. Phys. Chem., 74,3362(1970). (12)D.Behar and R. W. Fessenden, J.Phys. Chem., 76,3945(1972).
0 1983 American Chemical Society
042
The Journal of Physical Chetnistty, Vol. 87,No. 5, 1983
Stadlbauer et al.
I
O2@t
I
-0 7
0 30
20
I S
I
I
I
1
1
1
I
I
.
c
-0 I O 0 0
3 0
I
I O
I
.
2 0
30
I
0 20
t
c i I
4 n n
1’1
20
T I M F I N uSFC I 1 6
0 10 O D
30
NSEC/BINI
I
I
1 0
I
i
‘A
I
2 0
T I M E IN uSEC I16
30
N5EC/BlNI
Figure 1. Typical MSR histograms: (a) raw data for pure water in an 8 4 field: (b) the data in (a) fitted to eq 1 with muon decay and background subtracted out; (c) and (d) are the data for 0.23 and 0.46 mM CN- fitted to eq 1 as in (b).
Experimental Section Chemicals. The cyanoacetic acid used was 98% pure while the acetonitrile was spectroscopic grade. Certified ACS KCN was used directly and with reagent grade 3CdS04.8H20in the preparation of aqueous K2Cd(CN)4 following the standard pr0~edure.l~However, since K+ and S042- do not react appreciably with dilutions of the prepared K2Cd(CNI4solution were used directly without first recrystallizing the cadmium complex as a further purification step. With an overall formation constant of p4 = 1.5 X lola, the tetrahedral Cd(CN)4z’-was the predominant structure. The water used throughout was deionized and doubly distilled from chromic acid and potassium permanganate solutions. MSR: Muonium Spin Rotation Measurements. Under a transverse magnetic field the so-called “triplet” Mu (both particle spins parallel) has a precession frequency of 1.39 MHz/G while the free muon and other diamagnetic muonic species have a precession frequency of 13.6 kHz/G. It is, therefore, relatively easy to distinguish Mu from other muonic species in solution. When the muon decays the decay positron is ejected in the direction of the muon spin. The data are collected in a muon lifetime histogram with the muonium precession signal superimposed on the muon signal. Figure l a shows a typical data histogram for water. These histograms are computer analyzed by using a floating parameter x2-minimization program (MINUIT) to fit the equation N ( t ) = No exp(-t/7,)[1 + AD COS ( U D ~+ 4 ~ +) A M exp(-Xt) COS ( u M t - @M)] + BG (1) where N ( t ) is the signal amplitude at time t , No a normalization factor, T~ is the muon lifetime, AD and AMare (13) G. Brauer, Ed.,‘Handbook of Preparative Inorganic Chemistry”, P. G. Stecher, transl. Ed., Academic Press, New York, 1963, p 1106. (14) Y. C. Jean, J. H. Brewer, D. G. Fleming, D. M. Garner, R. J. Mikula, L. C. Vaz, and D. C. Walker, Chem. Phys. Lett., 57,293 (1978).
the diagmagnetic muon and muonium signal amplitudes, w D and W M their precession frequencies, &, and 4 M their initial phases, X is the muonium decay constant, and BG is the background count rate. This decay constant is a measure of the damping of the Mu precession signal as Mu reacts with the selected concentration of solute. Having obtained values for X for several concentrations of solute, [SI, the Mu bimolecular rate constant, k ~ can , be calculated from x = Xo + k , [ S ] (2) where Xo is the observed decay constant for the pure solvent (&, = 2.4 f 0.6 X lo5 s-l at TRIUMF’4J5). The slope of the best straight line in a plot of X vs. [SI is taken as kM*
To obtain these data a 4.1-MeV muon beam from the M20 channel at TRIUMF (Tri University Meson Facility in Vancouver) was made to strike a shallow Teflon cell (with thin mylar windows) containing approximately 80 mL of sample solution. Target solutions were bubbled with high-purity He before and during the experiment to remove dissolved oxygen. Water prebubblers were used to wet the gas and in the case of acetonitrile the prebubbler contained a portion of the working solution to minimize loss of solute through volatilization. Magnetic field coils, held transverse to the beam and centered on the target, provided an external field of 8 G to give a Mu precession frequency of 11.1MHz. A schematic of the experimental setup is given in Figure 2. The temperature dependence studies of cyanoacetate and tetracyanocadmate(1I) were done in a similar manner with a copper-backed temperature cell as described e1se~here.I~
Results Table I lists the solutes studied, their concentrations, decay constants (A), and calculated rate constants ( k M ) . (15) B. W. Ng, Y. C. Jean, Y. Ito, T. Suzuki, J. H. Brewer, D. G. Fleming, and D. C. Walker, J . Phys. Chem., 85,454 (1981).
The Journal of Physical Chemistry, Voi. 87, NO. 5, 1983
Muonium Addition to Cyanides
=
Y
v
c -
:I: 14 0
1
12 0
2 60
-1
i I
I
I
3 00 (l/T)/
Flgure 2. Schematic diagram of the MSR experimental apparatus. A and B are lead shielding and collimation for the muon beam. C is a thin scintillator muon (start) counter. D represents the shallow Teflon target in which the sample is bubbled continuously with high-purity He. E and E, separated by a carbon absorber (F), represent one set of two posibon telescopes which provide a stop signal when a decay poskron is emitted in their direction. G indicates a set of Helmhokz coils which provide a field perpendicular to the paper causing the muon to precess in the plane of the paper.
A
7.7 x
lo'
19.7 25.2
1.26 1.93 2.70
acetonitrile
10.0
0.81
5.1
10'
18.0 24.0 0.23 0.46 0.69 0.05 0.10 0.21 0.30
1.18 1.29
cyanide tetracyanocadmate(I1)
0.81 1.85 2.40 0.92 1.90 3.18 5.96
X
2.0
3.0 X 10'
0 00 1.7 x 10"
/'
1
oc
2 00
ni ." 3 00
(1/7)/1U'poises
With two separate sets of positron detectors, left and right, each particular experiment yields two data histograms and hence two decay constants. The decay constants listed in Table I are the average of the separate left and right values obtained for each solute concentration. Statistically the errors on kM values average & l o % , but because MSR measurements are subject to experimental irreproducibilities (from beam structure and electronics to target concentrations and geometries) a more realistic error of 2~25%is reported.15 From collision theory the temperature dependence can be expressed in the modified Arrhenius equation (3)
Therefore, in determining the critical reaction energies and frequency factors for the reactions of Mu with cyanoacetate and tetracyanocadmate(I1) In (kM/PI2)was plotted against 1/T (see Figure 3) to fit eq 4. The critical energy for In (kM/T1Iz) = In B - E / R T
t \
_ .
a Statistical errors on these decay constants are 10% or less. Realistic error o n reported rate constants is t 25%.
k = B(T1/2)exp(-E/RT)
.
I
3 0 -
\
17.0
10-?r(
85 OC for the cadmium cyanide complex is due to thermocouple failure during that experiment.
t-
cyanoacetate
1
3 80
Flgure 3. Modified Arrhenius plots of eq 4 for tetracyanocadmate(I1)
c
solute
I
1
3 40
(A)and cyanoacetate (0). The large error in temperature value at
m
TABLE I : Reaction Rate Data for the Addition of Muonium to Organic and Inorganic Cyanides
a43
(4)
cyanoacetate was found to be 35 f 2 kJ/mol and that for the cadmium cyanide complex to be 15 f 2 kJ/mol. This
Figure 4. Inverse viscosity plot showing diffusion control for tetracyanocadmate(1I) (A)and nondiff usion control for cyanoacetate (0). Left vertical scale used for the cadmium complex data while the right vertical scale is used for the cyanoacetate data.
latter value, being close to the diffusion energy of water, suggests a diffusion-controlled reaction. However, because water structure and diffusion energy vary with temperature, it is necessary to examine the effect of viscosity on the rate constant as demonstrated by Lazarinni.16 From Smoluchowski's equation (eq 5), where K is the Boltzmann (5) constant, T i s absolute temperature, 11 is viscosity, and PA and rBare the effective radii of the reacting species, it can be seen that for a diffusion-controlled process the plot of k / T vs. 1/11 should be a straight line. Figure 4 shows such a straight line for the o b s e r v e h u o n i u m rate data for tetracyanocadmate(I1). Table I1 lists the parameters used in Figures 3 and 4 as well as the calculated energies, E, and frequency factors, B. Table I11 lists the room temperature rate constants for the Mu and H reactions with the four cyanides and the calculated kinetic isotope effects, kM/kH. Also listed here are the kM blank values for acetic acid and (16) A. L. F. Lazzarini and E. Lazzarini, J.Inorg. Nucl. Chem., 42,953 (1980).
844
The Journal of Physical Chemistry, Vol. 87, No. 5, 1983
Stadlbauer et al.
TABLE 11: Temperature and Viscosity Parameters for Mu Addition to Cyanoacetate and Tetracyanocadmate(I1) solute
TrC
T/K
cyanoacetate
0 23 62 80
273 296 335 3 53
0 23 71 80
273 296 344 353
Cd(CN),Z-
kM/(M-' S-') 6.7 x 107 7.7 x 10' 5.4 x l o 8 1.6 x 10'
1.0 1.7 3.8 5.6
x 1O'O X X X
10'" lo1"
lo1"
In (kM/TI") 14.62 15.31 17.20 18.25 20.22 20.7 1 21.44 21.82
TABLE 111: Muonium and Hydrogen Rate Constants with Calculated Kinetic Isotope Effects and Some Associated Muonium Rate Constants solute cyanoacetate 7.7 x 10' 3 . 2 ~l o 6 acetonitrile 5.1 X l o ' 2.7 X 1 0 " cyanide 3.0 x 109 4.1 x 1 0 9 tetracyanocadmate(I1) 1.7 X lo1" >2.4 X l o 9 acetic acid -3.8 x 10" cadmium(I1) 8.5 x 10' hexacyanoferrate(I1) 3 x 10' a
24 19 0.7
