J. Phys. Chem. 1995,99, 11350-11356
Bond Dissociation Energies of PbBr2(g) and the Dye Laser-Induced Fluorescence Excitation Spectrum of PbBr(A-X) Lawrence R. Drake and John W. Simons* Department of Chemistry and Biochemistry, New Mexico State University, Las Cruces, New Mexico 88003
Richard C. Oldenborg Chemical Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Received: January 4, 1995; In Final Form: April 3, [email protected]
An equilibrium thermodynamics determination of the individual bond dissociation energies in PbBrz(g) is presented, yielding 66.5 f 3.5 and 59.4 f 3.5 k c d m o l for the successive removal of Br atoms. These results are based on atomic absorption measurements of Pb(g) number densities and laser-induced fluorescence measurements of relative PbBr(g) number densities in equilibrium with PbBrz(g) at temperatures between 700 and 850 "C. The laser-induced fluorescence excitation spectrum of PbBr(A-X), excited between 467 and 485 nm and observed between 516 and 536 nm, is reported. Lifetime measurements of PbBr(A) at various PbBrZ number densities yielded a collision-free lifetime of -200 ns and a PbBr2 collisional quenching cm3 molecule-' s-I. constant of 1.42 x
Our interest in the thermochemistry of PbBrz(g) results from studies of the photochemistry of the lead halides. UV and visible atomic lasing transitions have been observed through photodissociation of the lead halides, and the development of a practical photodissociation laser is possible.' In addition, coherent blue-green light can be generated in Pb vapor by Raman shifting the 308 nm radiation of the XeCl excimer laser to 459 nm via the Pb[6p~(~Po-?P2)]~ p l i t t i n g . ~Sufficient ,~ concentrations of Pb(g) atoms to serve as a Raman shifter can be produced from the lead halides through photodissociation. Since the lead halides have high vapor pressures at relatively low temperatures: the use of the lead halides as a source of Pb atoms lowers the operating temperatures so that simple quartz cells may be used in the Raman shifter design. The energies required for the successive dissociation of Br(g) atoms from PbBrz(g) are uncertain by as much as 10 k c d mol4 These dissociation energies are important fundamental quantities in evaluating and understanding the efficiencies and kinetics of the Pb(g) production and removal in the PbBrz(g) photodissociation process. In the hopes of reducing the uncertainty in the energy required for the successive removal of Br(g) atoms from PbBrz(g), thermodynamic studies similar to those carried out for PbIz(g)5,6have been undertaken here. One method of determining the energetics of PbBr2(g) dissociation is through measurements of Pb atom concentrations in equilibrium with PbBrz(g) at various temperatures. The Pb atom concentrations are monitored by absorption of the 283.3 nm resonance line from a lead hollow cathode lamp. Another method which complements the Pb atom concentration measurements are laser-induced fluorescence (LIF) measurements of the relative concentrations of PbBr(g) in equilibrium with PbBrz(g) at various temperatures. In this work bond dissociation energies of PbBr2(g) are determined via lead atom concentration measurements and via LIF measurements of relative PbBr(g) concentrations. The laser-induced fluorescence excitation spectrum of PbBr(A-X) and PbBr(A) lifetime measurements are also reported. @
Abstract published in Advance ACS Abstracts, May 15, 1995.
Figure 1. Schematic of apparatus for determining (Pb) in equilibrium with PbBrz(g): HCL,hollow cathode lamp; S , splitter; L, lens; Mono, monochromator; DO, digital oscilloscope; Comp, computer.
Experimental Section Reagent. PbBrz(s) was obtained from Johnson and Mathey, Ltd., and is Puratonic Grade 1. Apparatus. The design and use of quartz cells for these hightemperature measurements have been described p r e v i o ~ s l y . ~ - ~ The cell windows allowed the passage of light both horizontally and vertically through the cell. For Pb atom absorption measurements the light was passed horizontally through the cell where the path length is 11.5 cm. A magnetically activated valve allowed for the evacuation of the cell as well as the addition of Br2 vapor. Br2 pressures were monitored with a Baratron head and a digital display unit (MKS Instruments, Types 310CHS-1000 and 170M-27E). The sample reservoir and the cell were independently heated and controlled as described p r e v i ~ u s l y . ~The - ~ sample reservoir and the cell were enclosed in a fumace constructed of firebrick which was surrounded with fiberfax insulation. The schematic of the apparatus for the Pb atom absorption measurements is shown in Figure 1. The source lamp was a lead hollow cathode lamp, HCL (Photon Superlamp, Serial No. 7668). The HCL beam was split before entering the cell which 0 1995 American Chemical Society
Dye Laser-Induced Fluorescence of PbBr(A-X)
J. Phys. Chem., Vol. 99, No. 29, 1995 11351
in the dye laser intensity, the dye laser intensity was monitored with a 1P28 PMT powered by a Power Designs Model 3K10B high-voltage supply. The PMT was placed behind the first prism and detected the scattered dye radiation escaping the prism. A small blackened tube was placed between the prism and the PMT to eliminate stray room light and to attenuate the intensity of the laser light reaching the PMT. This signal entered boxcar 2 (Par Model 162 with 164 plug in) through a 1 kohm terminator. The boxcars were triggered simultaneously from the sync out of the nitrogen laser. The settings for the two boxcars were identical and optimized. The outputs from the boxcars were connected to channels A and B of a digital oscilloscope peripheral (Rapid System datalogger). This peripheral was interfaced to a PC compatible computer where the signals were stored and analyzed.
Theory Figure 2. Schematic of the apparatus for determining LIF spectrum of PbBr(g): Dye, nitrogen pumped dye laser; sync out, synchronized trigger pulse from dye laser; P, prism; Trig. in, sync out trigger pulse to boxcars A and B; PMT, photomultiplier tube; Ref. Out, output from boxcar B to AID; AID, analog to digital converter; Ref. Sig., reference signal input to boxcar B; XT, computer; Sig. Out, output from boxcar A to AID;Mono., monochromator; Sig. in, fluorescence signal input to boxcar A; L, lens; F, filter.
allowed for the simultaneous collection of the transmittance and reference signals. Thus, variations of the lamp intensity with time were corrected for in the ratio of the transmittance to reference signals. The lamp was operated between 7 and 8 mA by a high-voltage source (Power Designs, Model 2K20). Wavelength selection was accomplished with two Jarrell-Ash ‘/4 m monochromators equipped with 250 p m slits. The transmittance and reference beams were detected by 1P28A photomultiplier tubes (PMTs) powered by separate high-voltage sources (Power Designs, Models 3K10B and 2K20). The PMT currents were monitored on channels A and B of a digital oscilloscope (Tektronix 2440) using 10 kohm terminators. The resulting signals were analyzed using a PC compatible computer. The schematic of the apparatus used for the production of thermal PbBr(g) and its detection via laser-induced fluorescence (LIF) is shown in Figure 2. A tunable dye laser (Molectron DLII) served as the excitation source. Coumarin 480 is the laser dye used to probe the A-X transitions of PbBr(g) between 467 and 485 nm. The dye laser was pumped by a pulsed nitrogen laser (Molectron W 1 2 ) operating at 10 Hz. The dye laser’s monochromator, operating in the sixth order, was scanned at a constant rate of 1 d 3 5 s in order to obtain the fluorescence excitation spectrum. The high-temperature quartz cell and furnace were the same as described above for the Pb atom measurements. For the LIF studies of PbBr(A-X) the dye laser beam passed vertically through the cell as shown in Figure 2 and was focused into the detection area with a 1 M lens. The fluorescence of PbBr was detected perpendicular to the excitation source with a 1P28A PMT powered by a high-voltage supply (Power Designs, Model 2K20). Before reaching the PMT, the PbBr fluorescence first passed through a 515 nm cutoff filter to eliminate detection of scattered dye radiation. This filter was followed by a ‘/4 m Jarrell-Ash monochromator tuned to 526 nm. This monochromator had the slits removed which allowed for a band-pass of -20 nm; thus, detection was in a band from 516 to 536 nm. The signal from the PMT was passed through a 1 kohm terminator to a differential amplifier (Tektronix, Ah4 502) where the signal was amplified 20x before entering boxcar 1 (Par Model 162 with Model 164 plug in). In order to correct the fluorescence intensity for variations
Pb(g) Measurements. The method used for determining the successive bond dissociation energies for PbBrz(g) using Pb(g) measurements is similar to that used for the PbI2 s t u d i e ~ .For ~ PbBrz(g) the following equilibria are considered. Parentheses represent equilibrium pressures in units of atmospheres: PbBr, = Pb
PbBr, = PbBr -tBr PbBr = Pb
K , = (Pb)(Br)2/(PbBr,)
K2 = (PbBr)(Br)/(PbBr,)
K3 = (Pb)(Br)/(PbBr)
The predominant thermal dissociation channel of PbBrz is via eq 2. This leads to the simplifying assumption that (PbBr) (Br), which gives K3 (Pb). Thus, the absolute measurement of (Pb) gives K3. The value of K2 is obtained from the expression, K2 = K1IK3. Values for K I ,at various temperatures, are taken from the JANAF tables4 These K I values are reasonably accurate. A 2-fold uncertainty in K I values results from a reported 1.5 kcdmol uncertainty in the value of The K2 and K3 values at various temperatures can be used to determine the successive bond dissociation energies for PbBrz(g) by both the second law method and the third law method. The second law method utilizes van’t Hoff plots, Le., In K vs UT, and gives values for A H 2 and AH3 from the slopes of the plots. The K values can also be combined with third law entropies, as shown in the equation
AHi = -RT In K, -t TAS,
to yield values for AH2 and AH3 that are independent of the temperature dependence of K2 and K3. PbBr Measurements. The LIF of PbBr is used as an alternative method of determining the successive bond dissociation energies of PbBr2(g). The equilibria of interest are the same as in eqs 1-3. If the approximation is made that (PbBr) (Br), then eq 2 gives
K2 = (PbBr)2/(PbBr,)
These K2 values combined with the K1 values obtained from the JANAF tables4 determine the values for K3. The successive bond dissociation energies are then obtained from the slopes of van’t Hoff equation plots. The relative PbBr(g) concentrations can be determined from the relative LIF intensity of the PbBr(A-X) transition at various temperatures. The fluorescence intensity is proportional to (PbBr) at low laser intensities, where the proportionality is a complex function of various molecular parameters such as the
11352 J. Phys. Chem., Vol. 99, No. 29, 1995
Drake et al.
line strengths of the various transitions. Also included in this proportionality are instrumental factors such as geometric and light detection parameters.8
Results Pb(g) Measurements. Pb atom number densities were determined from the absorption of the 283.3 nm resonance line from a calibrated lead hollow cathode lamp. The calibration of these lamps has been approached both theoretically and experimentally in previous studies.9-" The high-intensity lamp used for these measurements was previously ~ a l i b r a t e d . The ~,~ absorption due to lead atoms, (It/h))pb, was monitored at the resonance line of 283.3 nm. In order to obtain the absorption due solely to lead atoms, a correction to the overall absorption at 283.3 nm was made. This correction was accomplished by making the approximation that the absorption due to PbBr2(g) at 283.3 nm is the average of the absorption at the two nonresonance lines, 280.2 and 287.3 nm, from the hollow cathode lamp. The UV absorption spectrum for PbBrz(g) indicates that this is a reasonable approximation.I2 This correction should also apply to any other band absorber in this region. Thus, the absorption due to lead atoms is given by the following equation:
where (7) In these equations, It represents the transmittance with absorber in the cell, ZO is the transmittance with no absorber in the cell, and Z, is the reference signal. Each is measured at wavelengths i = 280.2, 283.3, and 287.3 nm. For these studies the hollow cathode lamp was warmed and allowed to stabilize. The measurements of (ZJZ0)i were made with the sample reservoir at 300 "C and the cell at 600 "C. To simplify the calculations, this value was set to unity at each of the wavelengths by supplying a constant high voltage to the reference PMT and adjusting the voltage supplying the signal PMT. The voltages required at the three wavelengths were recorded and used throughout the experiment. To ensure (ZJZ0)i had remained constant throughout the experiment, the voltages required to give (Z1/Zo)i = 1.00 were rechecked after the cell and sample regions had cooled to their original temperatures. Values for (It/Z0)i were determined with the sample reservoir held at a constant temperature of 470 "C, corresponding to a PbBrz(1) vapor pressure of 0.247 Torr.4 The Pb(g) atom absorption measurements were made in altemate heating and cooling cycles where the cell temperature was varied from 700 to 840 "C in increments of 20 "C. Prior to the measurements, Br2 vapor was added through the magnetically activated valve and then removed by pumping through a liquid N2 trap. Measurements made without prior addition, and removal of Br2(g) to the cell were not reproducible. The values obtained for (It/ZO)Pb were typically smaller during the cooling cycle, which were made at later times, than the values obtained at the same temperature during the heating cycle. This was thought to be due to a slow adsorption of Pb atoms on the cell walls and windows. The adsorption of Pb atoms on quartz surfaces has recently been reported by Rupkus et al.I3 In order to remove the Pb atoms from the walls and windows, 1-2 Torr of Brdg) was introduced into the cell before each absorption measurement. This initially disturbs the equilibrium by decreasing the concentration of Pb atoms in the cell. This procedure also removes Pb atoms that have adsorbed to the quartz
c I 'y
Figure 3. Cell transmittance as a function of time after Brz addition
TABLE 1: Equilibrium Values Obtained from Pb Atom Absorption Measurements 695 715 735 755 775 795 815 835
0.852 0.743 0.597 0.428 0.275 0.158 0.084 0.048
1.82 3.47 6.16 10.7 18.3 32.4 57.3 90.1
2.40 4.59 8.28 14.7 25.9 46.8 84.4 135
1.64 3.23 6.39 12.2 22.5 38.7 63.8 114
2.40 4.59 8.28 14.7 25.9 46.8 84.4 135
a The average temperature over the length of the cell. The average value for (It/Zo)m obtained from four altemate heating and cooling cycles. Pb atom number densities in units of 1Olo atoms/cm3obtained from (IJZo) and the calibration of the HCL. The partial pressure of Pb in units of atm. e The equilibrium constant, K2, in units of atm, obtained from the expression K2 = KI/K3. fThe equilibrium constant, K3, in units of atm, obtained from the expression K3 (Pb).
windows. The combination of these two effects results in a greatly increased throughput of the HCL beam. The absorption of the 283.3 nm resonance line was monitored as a function of time after the introduction and subsequent removal of Br2(g). The results of these measurements are shown graphically in Figure 3. The initial introduction of Br2 vapor gave a large increase in the throughput of the HCL beam. After evacuation, the absorption due to Pb atoms quickly increased. After a period of 15-30 min the absorption of the HCL beam leveled off, which was followed by a slow increase in the absorption at longer times. The period of time when the absorption measurements had leveled off was thought to be when the Pb(g) were in equilibrium with PbBrz(g). The increase at longer times was thought to be the result of Pb atoms adsorbing to the cell windows. The values for (It/& were determined during the time the system was at equilibrium. This was tested by opening and closing the valve between the sample and gas handling system. A return to the (&/10)283.3value obtained prior to manipulation indicated the system was at equilibrium. The time for equilibration after the addition of Brz(g) was typically 15-30 min. The average value of (&/IO)Pb obtained through four alternate heating and cooling cycles was used to calculate the Pb atom number density at the corresponding temperature. The average values for the absorption, the concentration of the Pb, and the K values obtained from these Pb atom absorption measurements are shown in Table 1. The van't Hoff plots of the K2 and K3 values are shown in Figure 4. The AH values obtained through a linear least-squares fit of these lines gave the first set of A H 2 and A H 3 values in
Dye Laser-Induced Fluorescence of PbBr(A-X)
J. Phys. Chem., Vol. 99,No. 29, 1995 11353 o'6
Figure 4. In K2 and In K3 vs 1000/T from Pb(g) number density measurements: 0, In 4 vs 1OOO/T; 0, In K2 vs 100OlT.
Table 3. The error reported is the average deviation of the slopes obtained from four separate heating and cooling cycles. Third law values for A H 2 and A H 3 were calculated at each temperature using eq 4. The averages over the range of temperatures gave the second set of values for AH2 and A H 3 in Table 3. The uncertainty here was taken to be the same as that in AH,reported in the JANAF table^.^ LIF Excitation Spectrum of PbBr(g). The LIF studies for PbBr(g) were carried out under the same pressure and temperature conditions as the Pb atom measurements. The excitation dye laser using Coumarin 480 dye was scanned in the wavelength range 467-485 nm. The resulting fluorescence was passed through a monochromator in order to decrease the blackbody radiation detected by the PMT. This monochromator was operated without any slits and was tuned to 526 nm, giving a band-pass between 516 and 536 nm, where the fluorescence was most intense. Fluorescence measurements were first made with the sample reservoir at 470 "C and the cell at a relatively low temperature of 600 "C where very little dissociation of PbBr2 has occurred. A continuous unstructured fluorescent excitation spectrum, presumably due to PbBr2, was observed under these conditions. Further measurements were made in alternate heating and cooling cycles with the cell varying from 700 to 800 "C in increments of 20 "C. These higher temperature measurements gave structured spectra that were reproducible and with fluorescence intensities that increased with increasing temperature, consistent with the expected increase in PbBr(g) due to increased dissociation of PbBr2 at higher temperatures. These PbBr(g) spectra are superimposed on the continuous spectrum of PbBr2(g) observed with the cell at 600 "C. It was necessary to subtract out the 600 "C spectrum from the higher temperature spectra in order to obtain the spectra due to PbBr(g) only. These corrected fluorescence spectra for PbBr were obtained from the following equation
F = ( A - B)/(C - 0 ) - [(A' - B')/( C' - D') x 873.15 WT](8) where A is the fluorescence intensity during irradiation with the dye laser, B is the intensity collected with the dye laser blocked from the cell, C is the intensity of the dye laser signal collected at the reference PMT, and D is the signal collected with the laser blocked from the reference PMT. The primed quantities refer to the 600 "C data. The 873.15 WT ratio corrects the 600 "C data for the number densities at T for a constant pressure. The LIF excitation spectra of PbBr(A-X) in equilibrium with PbBrz(g) at several temperatures between
Figure 5. LIF spectra of PbBr(g): (A) 800 "C spectrum; (B) 780 "C spectrum; (C) 740 "C spectrum; (D) 700 O C spectrum.
700 and 800 "C as calculated from eq 8 are shown in Figure 5. Spectra obtained at 720 and 760 "C are not shown. The observed transitions are in good agreement with previous absorption and emission studies.I4-I6 Using known spectroscopic constant^,'^-'^ we calculated that there are more than 100 possible (A, v' X, v") transitions with v" < 10 and 'v < 30 within the region being studied. These calculations as well as the observed peaks and valleys in the spectrum indicate that these transitions occur in groups. These groupings are determined by the energy level spacings, ground state Boltzmann populations, and the relative transition probabilities. PbBr(A) Lifetime Measurements. The PbBr LIF signal could be detected using the standard 50 ohm termination of a digital oscilloscope (Tektronix 2440). This allowed for a determination of the lifetimes for PbBr(A) at various PbBr2(g) vapor pressures. The determinations were made at cell temperatures of 800 "C and PbBrz(g) vapor pressures between 0.18 and 0.60 Torr. The dye laser was tuned to 479 nm, which corresponds to a peak in the PbBr(A-X) LIF excitation spectrum. Decay plots obtained under these conditions consisted of two simultaneous exponential decays. Fluorescence was observed at low cell temperatures where no thermally produced PbBr(g) was expected. (This was suspected to be fluorescence from PbBr2(g) as discussed previously.) In order to obtain the fluorescence due to the excitation of PbBr(g) only, a correction to the overall high-temperature fluorescence was made by subtracting out the fluorescence signal obtained at lower cell temperatures (530 "C) from the fluorescence obtained at higher cell temperatures. This is a viable means of obtaining the fluorescence due to the excitation of PbBr(g), since the fluorescence from PbBr(g) dominates at higher cell temperatures. Figure 6 is a typical plot of the fluorescence decays obtained at both a high and low cell temperature. The difference in these curves (with the low-temperature fluorescence corrected for the difference in the high- and low-temperature PbBrz number densities) which represents the fluorescence decay due to the excitation of PbBr(g) only is also shown. In Figure 6 zero time 'was considered to be at the signal maximum. Figure 6 shows decay times after 20 ns delay so as to eliminate the influence of the temporal profile of the laser pulse. As shown in Figure 7, logarithmic plots of the corrected decay signal vs time consisted of a single-exponentialdecay. The rate constant, k, for each experiment was determined from the slopes of these logarithmic plots. The rate constant, k, obtained in this manner, can be expressed as
Drake et al.
11354 J. Phys. Chem., Vol. 99, No. 29, 1995 18.
ma) Figure 6. High- and low-temperature PbBr2 cell fluorescence decay curves at 479 nm: 0, fluorescence decay with the cell at 800 "C; 0, fluorescence decay with the cell at 530 "C; A, the 800 "C fluorescence minus the 530 "C fluorescence corrected for the reduced number density at 800 "C, resulting in the fluorescence due to PbBr(A-X).
[PbBr2] (10*15 molecule$ cm*-3)
Figure 8. Stern-Volmer plot of PbBr(A-X) fluorescence decay rate vs PbBr2 number density. TABLE 2: Temperature Dependence of PbBr(A-X) Fluorescence Intensity t ("C)
700 720 740
760 780 800
2.73 f 0.32 3.52 i 0.46 4.69 i 0.63
1.47 f 0.216 1.99 f 0.17
a FdF7m is the ratio of the fluorescence intensity at each temperature to that at 700 "C. These uncertainties represent average deviations
from the average for eight experiments.
FT is the fluorescence intensity at a particular temperature, Q",T is the vibrational partition function for PbBr(X), and 593 is the vibrational s p a ~ i n g ~ , ' ~in- ' 'c d m o l for PbBr(X). The level the transition originates on is represented by v". Due to the near coincidence of many of these transitions, it was not possible to accurately identify transitions originating on a particular v" level. An examination of the previously published ~ t u d i e s ' ~indicates -'~ that the most intense transitions in this region occur around v" 3. In addition, the average thermal vibrational energy for PbBr(X), Le., RT, at these temperatures is close to 3 x 593 callmol. Therefore, a value of v" = 3 was used in eq 10 to represent the ground electronic state vibrational level for each transition. An uncertainty of 2 in v" introduces -1.2 kcallmol uncertainty in A H 2 and A H 3 . The ratio of the LIF intensity at each temperature to the intensity of the LIF signal at 700 "C, FTIFT, was taken at each point of the spectrum in the range from 467 to 485 nm and was found not to be wavelength dependent over this range; consequently, the ratios were averaged over the entire wavelength range. This was repeated for eight separate spectra at each temperature from four separate heating and cooling cycles. The average ratios from these eight individual experiments are shown in Table 2. These average values are then used in eq 10 to determine the ratio of (PbBr) at T to PbBr at T = 700 "C, (PbBr)T/(PbBr)T. The relative concentrations of PbBr(g) obtained from eq 10 can be substituted into eq 5 for a constant (PbBr2) to obtain the ratio of K2 at T to K2 at T. A plot of ln[Kz,~/K2,~] as well as ln[K3,~/K3,r]vs 1/T is shown in Figure 9. From the slopes of these plots, the third set of values for A H 2 and A H 3 reported in Table 3 were found. The error reported is the standard deviation from the average for the eight separate determinations. Combining (Pb) and (PbBr) Measurements. A combination of the Pb atom measurements and the LIF PbBr measurements can be used to determine the successive dissociation energies of PbBr2(g) without making the assumption that (PbBr) (Br). The Pb atom measurements can be combined with the L F measurements by using the KI expression from eq 1 to solve
Figure 7. Natural logarithm of PbBr(A-X) fluorescence at 479 nm vs decay time.
k = kf kc(PbBr2)
where kf is the collision-free rate constant, kc is the quenching rate constant, and (PbBr2) is the concentration of PbBrz(g) in units of molecules/cm3. A Stem-Volmer plot, Le., k vs (PbBr2), was linear as shown in Figure 8. The collision-free lifetime was determined from the intercept of Figure 8. The values obtained for the collision-free lifetime were between 170 and 235 ns. The slope of the plot yields a value for the quenching rate constant of 1.42 x cm3/(molecule s). This value is of the same order as the gas kinetic collision rate constant. The values obtained for kf and k, seem reasonable since they are of similar magnitude to the values obtained in similar experiments for PbI(A).5 (PbBr) Measurements. In order to relate the temperature dependence of the intensity of the fluorescence excitation spectrum to the temperature dependence of (PbBr), a correction is required for the temperature dependence of the Boltzmann population of the ground electronic state vibrational level, v", for each observed transition. The following equation gives the result in terms of ratios at two different temperatures, ln[(PbBr)dU'bBr)~l = l n [ ( T F ~ V , T > / ( T F r e V+ ,r)l (593v"/R)( 1/T - UT)(10) In this equation, T and
T are the two temperatures of interest,
J. Phys. Chem., Vol. 99, No. 29, 1995 11355
Dye Laser-Induced Fluorescence of PbBr(A-X)
TABLE 3: Successive Bond Dissociation Energies ( k c d mol) Determined for PbBrz(g) method
Pb atom meas (2nd law) Pb atom meas (3rd law) LIF meas of PbBr (2nd law) Pb atom meas and LIF meas average values JANAF values
64.3 68.7 67.3 65.8 66.5 68.7
61.6 51.2 58.6 60.1 59.4 57.2
f2.2" fl.5b 1t5.2~ f5.2d
"The uncertainty for the Pb atom measurements is the standard deviation from the average value for eight experiments. The uncertainty is taken to be that reported for the AH,values in the JANAF table^.^ This is the standard deviation from the average values for eight experiments. The uncertainty for the combined measurements is taken to be that of the LIF measurements.
for the (Br) ratio at two temperatures, T and (PbBrz), Le.,
(Br)d(Br)r = IK,,~Pb),tK,,,(Pb),11/2
K z . l j K 2 ,= ~ (PbBr)~Br)lj(PbBr).(Br),
Substitution of the expression for the (Br) ratio from eq 11 into eq 12 yields '"/(PbBr),[(Pb>rK1,~l"2 (13)
Values for K1 at T and T = 973.15 K were interpolated from the JANAF table^.^ The (Pb) ratios are interpolated from the values obtained in this work (Table 1). The (PbBr) ratios are determined from our LIF measurements by eq 10. Substituting eq 10 into eq 13 for (PbBr)T/(PbBr), and using the van't Hoff equation for the ratio of the K2 values at two temperatures yields the following equation In[ ( K ,,+Kl '"(PbTEb,) 1'2(TF&!V,+TF~QV,~)I = -(AH2 593v")tRT (AH2 593v")tRT (14)
Figure 10. Left-hand side of eq 14 vs 1OOO/T.
TABLE 4: Comparison of Various Determinations of the Successive Bond Dissociation Energies of the Lead Dihalides (kcaYmo1) halide
refs 4, 18
ref 19 ref 20
PbI PbBr PbCl
68.9 71.5 i 12 r80.8
PbI2 53 f 9 PbBr2 6 9 % 10 PbC12 73.7 f 12
A plot of the left-had side of eq 14 vs 1/T is shown in Figure 10. The plot is linear and has as slope given by -(AH2 f 593v")lR. Using v" = 3 as discussed earlier, this slope yields the fourth value of A H 2 in Table 3. The fourth value of A H 3 in Table 3 comes from A H 3 = AH,- A H 2 using the JANAF
Doo(Pb--X) 58.6 67.1
46 f 2 59.4 6 3.5
Doo(X--PbX) 57.9,54.2 54 f 2 70.6, 63.2 66.5 f 3.5 73.6, 68.5
table value of AH,.4 An uncertainty of 2 in v" would result in an uncertainty of f 1 . 2 kcaltmol in A H 2 and AH3. Altematively, the Pb atom measurements and LIF measurements can be combined to give an independent determination for AH1 assuming (PbBr) (Br). Since K1 = K2K3, it follows that AH1 = A H 2 A H 3 . Substituting the average of the second and third law values for A H 3 obtained from the Pb(g) measurements and the second law value for A H 2 obtained from the LIF measurements gives AH,= 126.7 kcaltmol. This value is only 1.2 kcaltmol larger than the value given in the JANAF tables4 and is quite likely within the combined uncertainty of the two measurements.
The ratio of K2 at two cell temperatures for constant (PbBr2) is given from eq 2 as
Figure 9. ln(K2dK2~)and In(&/&) vs 1000/T from the PbBr(AX) LIF results: 0, ln(&d&r) vs lOOO/T; 17,ln(K2dK2~)vs 1OOO/T.
Discussion and Conclusion The four sets of values of A H 2 and A H 3 from this work (Table 3) range from 68.7 to 64.3 kcaltmol for A H 2 and from 57.2 to 61.6 k c d m o l for A H 3 . Since these ranges are relatively small (-4.5 kcaltmol) and there seems to be no bias for prefemng one set of values over another, we took averages to represent our "best" values (Table 3). These values differ from the JANAF table values by -2 kcaltmol, which is well within the uncertainty estimates. The uncertainty reported for our average values are the average of the uncertainties estimated for the individual values in Table 3. This uncertainty is about onethird that reported for the JANAF table values. In addition, we have summarized in Table 4 several determinations of lead dihalide bond dissociation energy including those given by the JANAF tables: by Huber and Herzberg,Is by Ziebarth et al.,I9 by Benavidez-Garcia and Balasubramanian,20.21and by us (ref 5 and this work). The rather large stated uncertainties in the JANAF" values are primarily the result of different interpretations of W - v i s absorption and emission spectra of PbX species. Their selected values are the same as those given by Huber and Herzberg.I8 Our results for Pbh5 and PbBrz (this work) are in good agreement with these results.
Drake et al.
11356 J. Phys. Chem., Vol. 99, No. 29, 1995 The values measured by Ziebarth et al.19 and calculated by Benavidez-Garcia and BalasubramanianZ0 for D(Pb-X) are considerably higher than those discussed above. Benavidez-Garcia and Balasubramanian21 also calculated values for D(X-PbX) by two different approximation methods which are in agreement with our measurements for PbIz5 and PbBr2 (this work) and the JANAF tables: given reasonable uncertainty estimates. It should be noted that the values of the sum D(Pb-X) D(X-PbX) for X = I or Br are accurately known," the values of which are accurately reproduced by our results but not if the high value^'^^^^ of D(Pb-X) are used. The LIF spectrum of PbBr(A-X) and the lifetime measurements of PbBr(A) have been discussed in the Results section. In addition, it is noted that the collision-free lifetime of -200 ns is not out of line with 1.17 ps found for PbC1(A)22and 5 ps found for PbF(A).22,23
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