The Journal of
Physical Chemistry
0 Copyright, 1986, by the American Chemical Society
VOLUME 90, NUMBER 5 FEBRUARY 27,1986
LETTERS Photochemical Generation of the Optoacoustic Effect: An Acoustic Analogue of the Method of Intermittent Activation M. T. O’Connor, R. B. Stewart, and G. J. Diebold* Department of Chemistry, Brown University, Providence, Rhode Island 0291 2 (Received: October 8, 1985; In Final Form: December 26, 1985)
When a mixture of H2 and C12is irradiated with 488-nm radiation, the evolution of heat in the gas is governed by the rate of chain reaction. The optoacoustic effect, produced by modulating the amplitude of the radiation and recording the resulting acoustic signal, thus acts as a monitor of the chemical reaction rate in a manner analogous to the technique of intermittent activation. NO is shown to act as a potent inhibitor of the H2-CI2 reaction by rapid reaction with CI radicals.
The gas-phase optoacoustic effect is produced when radiation is absorbed to liberate heat thereby giving a sound wave which can be detected with a microphone. The most frequent application of this effect has been for spectroscopic or analytical measurements where an infrared laser is tuned to excite a molecular vibrational energy level.’ When short wavelength radiation is used, the primary effect of light absorption is to break chemical bonds introducing radicals into the system that may undergo subsequent chemical reaction. Depending on the composition of the gas, it is possible for more energy to be liberated from the ensuing chemical reactions than is absorbed from the radiation beam thereby giving a greatly amplified optoacoustic effect.2 As a consequence, the properties of the optoacoustic effect are governed by the reactive mechanisms for heat generation in the gas. This permits the optoacoustic effect to be used as an experimental method for determining kinetic mechanisms. Here we show that the measurements of the acoustic amplitude and phase can be used (1) For reviews, see Y. H. Pao, Optoacoustic Spectroscopy and Detection, Academic Press, New York, 1971; A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy, G. A. West, J. Barrett, D. R. Siebert, and K. V . Reddy, Rev. Sci. Instrum., 54, 797, (1983); C. K. N. Patel and A. C. Tam, Reu. Mod. Phys., 53, 517 (1981). (2) M. T. OConnor and G.J. Diebold, Nature (London), 301, 321 (1983).
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to elucidate the mechanism for inhibition of the H2-C12 reaction by trace amounts of NO and that the photochemically generated optoacoustic effect is directly analogous to the method of intermittent a ~ t i v a t i o n a, ~technique that has long been used to investigate photochemical reactions. The chain reaction of H2 with C12 is known to be extremely sensitive to trace amounts of impurities.&’ This follows both from the long chain length of the two-center chain reactions that produce HCI kl
C1+ H,
k-I
-
HCl
kl
+H
(1)
+
H + C12 HCl C1 (2) and from the high reactivity of the inhibitors themselves: introduction of any chemical species that reacts with either C1 or H (3) G. M. Burnett and H. W. Melvill, Techniques of Organic Chemistry, Vol. 8, Peterson, New York, 1983. ( 4 ) J. C . Morris and R. N. Pease, J. Am. Chem. Soc., 61,391, 396 (1939). ( 5 ) S. Benson, The Foundations of Chemical Kinetics, Maraw-Hill, New York, 1960. (6) K. J. Laidler, Chem. Kinetics, McGraw-Hill, New York, 1965. (7) J. W. Moore and R. G. Pearson, Kinetics and Mechanism, Wiley, New York, 1981.
0 1986 American Chemical Society
Letters
712 The Journal of Physical Chemistry, Vol. 90, No. 5, 1986
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MOLE FRACTION NO Figure 1. Optoacoustic signal amplitude vs. NO mole fraction for a laser power of 7 mW. The inset shows the phase lag as a function of incident laser power for a NO mole fraction of 10". atoms eliminates these radicals from further chain propagation thus terminating the sequence of reaction 1 followed by reaction 2. The fact that the chain length for the reaction of H2 with C12 is so long (the chain length can approach lo6 depending on the conditions') and that the reactions are highly exothermic (the enthalpy change for the sum of reactions 1 and 2 is 44.1 kcal/mol) means that production of the optoacoustic signal is completely dominated by release of heat energy from the chain reactions and that other mechanisms for sound production such as photofragment recoil, mole number increase, and termolecular recombination of radical^^^^ can be ignored. Experimental data were taken by recording the amplitude and phase of the acoustic signal in H2-CI2 mixtures at 1 atm irradiated with 488-nm radiation from an Ar' laser. Radiation a t this wavelength is known to excite 35C135C1 and 37C137Clto vibrational levels of the B311(0,+) state which predissociate to give two 2P3/2 atoms.8 The laser beam was amplitude modulated and then expanded in a Galilean telescope to illuminate uniformly a cylindrical (1.75 cm diameter, by 3.8 cm long) Teflon cell. The low-frequency of modulation (25-50 Hz) relative to the first acoustic resonance of the cell ensured that the measured phase lags were independent of acoustic cell resonances. Acoustic signals were detected with an electret microphone mounted in the cell. To protect the microphone from chemical attack, a sheet of Teflon was placed directly in front of the microphone; both the microphone and the Teflon sheet were sealed in place with Viton 0rings. The output from the microphone was fed to a vector lock-in amplifier that simultaneously determines the amplitude and phase of the acoustic signal. For measurements of the signal amplitude as a function of NO concentration, static gas mixtures were made barometrically in an all stainless steel and Teflon vacuum system. This method of preparing low mole fraction mixtures of N O proved to be more accurate than dilution in a flowing stream with the apparatus available. The H 2 was ultrapure grade (99.999%) with less than 0.5 ppm of 02.The C12 was electronic grade (99.99%) with maximum impurities of H 2 0 and O2 of less than 3.5 ppm. The NO was specified as 99% pure or better. After a few cycles of evacuation and flushing with N2,the acoustic cell was filled with a H2-C1,-NO gas mixture, the laser beam was switched on, and the signal was recorded as a function of time. Data were taken after a steady acoustic signal was generated. Figure 1 shows the amplitude of the acoustic signal vs. the mole fraction of N O for stoichiometric H2-C12mixtures. The data show the acoustic signal to follow a [NO]-' dependence. The dependence of the acoustic amplitude and phase on radiation intensity can be a sensitive indicator of reaction For experimental measurements of these quantities it is essential (8) M. T. O'Connor and G. J. Diebold, J . Chem. Phys., 81, 812 (9) G. J. Diebold, J . Phys. Chem., 84, 2213 (1980).
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L A S E R POWER (mW) Figure 2. Acoustic signal amplitude as a function of incident laser power A, low4. for different mole fractions of NO: 0,lod; 0, TABLE I: Rate Constants for Reactions 1-5"
rate constant, cmg/(molecule.s) k , = 1.6 X
ref 11, 15, 16 1 1 , 15, 17 11 12 11, 13
k-, = 5.1 X k , = 1.7 X lo-" k , = 1.0 X lo-'* k4 = 7 X lo-" k, = 1.4 X
13
"The value of k listed is taken from the first entry in the reference column. Rate constants for k3 and k , are reduced to equivalent bimolecular constants at a concentration of M equivalent to 1 atm. that the gas composition remain fixed while the laser intensity is varied.I0 Thus, the acoustic cell was fitted with narrow-bore inlet and outlet ports so that flowing gas mixtures could be used. or the phase lag At fixed mole fractions of NO was recorded as a function of laser power. The phase lag data mole fraction mixture show the plotted in Figure 1 for the acoustic phase to be constant with a standard deviation of 1' over the range of 0.75 to 75 mW incident laser power. The amplitude of the optoacoustic signal shown in Figure 2 is seen to be linear in laser power for several different NO concentrations. With a knowledge of previously measured rate constants (see Table I), it is possible to construct a model of the optoacoustic effect to explain the experimental data. For even small concentrations of NO, the reaction sequence
CI + N O
+M
C1 + NOCl
~ N O +C M~ k4
+
NO
+ C12
(3)
(4)
is much faster than the termolecular recombination of C1
+M
k5
+
C12 M (5) (see Table I); termination of the chain reaction of C12 with H2 is thus controlled by the N O concentration through reactions 3 and 4, as opposed to the three-body recombination of C1 atoms. Since the termination reaction sequence is fast compared with reaction 1, and since reaction 2 is also fast compared with reaction 1, the induction period for establishing steady-state concentrations of radicals is short and the stationary state approximation can be e ~ n p l o y e d . ~ As J ~ a~ ~result, ~ the rate equation for the con2C1
(10) Flowing gas mixtures give the most stable and reproducible data; ideally both amplitude and phase measurements would be made in a flowcell. Unfortunately, apparatus for accurate mixing of gases over large concentration ranges was not available for these experiments. (11) K. Kita and D. H. Stedman, J . Chem. SOC.,Faraday Trans. 2, 78, 1249 (1982). (12) H. Hippler and J. Troe, Int. J . Chem. Kinet., 8, 501 (1976). Note the M in this reference is He. Since empirically only small changes in the termolecular constant are found on changing M, the value of k , in He is used here.
J. Phys. Chem. 1986, 90, 7 13-7 15 centration of C1 radicals is given by (2k3[NO])x = 2pB(1 dx/dt
+
+ d sin wt)
(6)
where x = [CI]/[Cl,], d is the modulation depth of the radiation, w is the modulation frequency, p is the radiation density, B is the Einstein coefficient for absorption and dissociation, and t is the time. The solution to eq 6 (disregarding the transient solution) is given by x(t) =
pBd sin (wt - 4) k3[N0](1 + A2)’/2
713
(7)
where the phase lag 4 and the parameter A are defined by
Although the termination reactions 3 and 4 liberate an amount of heat equal to the bond energy of C12, when the lengths of the chain propagation reactions 1 and 2 are large, the production of HCI easily dominates the energy release in the system. From a consideration of the rate of HCl production in the steady-state approximation, the rate of energy release per unit volume into translational heating can be shown to be dt/dt = k2[H2][Cl,]AU,, x ( t ) (9) where AUrxis the combined energy release from reactions 1 and 2, and where the back reaction of HCl with C1 has been neglected (i.e. the HCI concentration is taken as zero in the initial stages of the reaction). Now, for a perfect diatomic gas, the pressure p is related to the translational energy per unit volume c through the relation p = 2t/5. If this relation is differentiated and combined with eq 7 and 9, the alternating component of the pressure is easily found to be (13) M. A. A. Clyne and D. H. Stedman, Trans. Faraday SOC.,64,2698 (1968). (14) M. A. A. Clyne and W. H. Cruse, J . Chem. SOC.,Faraday Trans. 2, 68, 1281 (1972). (15) A. A. Westenberg and N. S . de Haas, J . Chem. Phys., 48, 4405 (1968). (16) G. C. Fettis and J. H. Knox, Prog. React. Kine?., 2, 1 (1964). (17) J. H. Lee, J. V. Michael, W. A. Pyane, L. S. Steif, and D. A. Whylock, J . Chem. SOC.,Faraday Trans. 1 , 73, 1530 (1977). (18) S.W. Benson, J . Chem. Phys., 20, 1605 (1952). (19) J. C. Giddings and H. K. Shin, Trans. Faraday Soc., 57,468 (1961). (20) H. Shin, J . Chem. Phys., 39, 2937 (1963).
The inverse signal amplitude dependence on N O concentration shown by the data for the range given in Figure 1 is clearly consistent with eq 10. As the concentration of N O is reduced further this dependence changes as a result of the (1 A2)1/2 factor, and by a change in the mechanism of chain termination. For very high N O concentrations, the photochemical chain length becomes short and eq 9 must be modified to include the contribution of reactions 3 and 4 to the overall energy release. The linear amplitude dependence of the acoustic signal on light intensity (Figure 2) as well as the absence of any dependence of the phase lag on radiation intensity even at N O mole fractions of strongly contrasts with the nonlinear dependences seen when termolecular recombination determines the concentration of C1 radicalss,21and serves to point up the potency of N O as an inhibitor for the homogeneous reaction of H2 with C12. As indicated by eq 8, it is, in principle, possible to determine k3 from an absolute measurement of the acoustic phase lag. In the present case, however, there is little reason to expect the optoacoustic technique to provide a more accurate value for this constant than is presently available. Rather, the salient feature of the acoustic method (as well as the method of intermittent activation) appears to be its capability for delineating reaction mechanism. Of further note is the value of the method for in situ detection of small variations in reaction rate caused by changes in light intensity, gas composition, temperature, or other parameters. Although the photochemically generated optoacoustic effect is analogous to the technique of intermittent activation (also known as the rotating sector method) in that the two techniques share in common a measurement of reaction rate as a function of modulation frequency, there are significant advantages to the acoustic method: the reaction rate is monitored directly through the evolution of heat, the response to changes in reaction rate is rapid, and measurements are made with extremely high sensitivity.
+
Acknowledgment. The authors are grateful to the office of Basic Energy Studies of the US. Department of Energy for support of this research. (21) J. G. Choi and G. J. Diebold, Anal. Chem., 57, 2989 (1985).
A Modification of the Born Equation Takehiro Abe College of General Education, Tohoku University, Kawauchi, Sendai 980, Japan (Received: October 18. 1985)
The familiar Born equation for solvation free energies of ions has been modified by considering a distance-dependent relative permittivity of solvent. The modified equation better reproduces observed solvation free energies of ions than does the Born equation.
Introduction The Born equation’ has long been widely applied in many fields regarding solvation free energies of ions. The Born equation is easily derived2 for 1 mol of ions of point charge Z e (where 2 is
the formal charge and e the charge of proton) embedded in a continuous medium Of
(1) Born, M.Z . Phys. 1920, I , 45. (2) For example. see: (a) Laidler, K. J. “Reaction Kinetics: Volume 11-Reactions in Solution”; Pergammon Press: Oxford, 1963. (b) Beveridge, D.; Schnuelle, G . W. J . Phys. Chem. 1975, 79, 2562. (c) Atkins, P. W.; MacDermott, A. J. J . Chem. Educ. 1982, 59, 359.
where AG, is the molar ionic solvation Gibbs free energy, L the Avogadro constant, e, the relative permittivity of the solvent, and a the radius of a spherical cavity in which the ion is placed. Modifications and refinements of the Born equation have been
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AGm =
=( 2a
0 1986 American Chemical Society
- 1)
(1)
