In the Laboratory edited by
Topics in Chemical Instrumentation
David Treichel Nebraska Wesleyan University Lincoln, NE 68504
Photoacoustic Calorimetry An Undergraduate Physical-Organic Experiment Beth Fletcher and Joseph J. Grabowski* Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260; *
[email protected] The variety of chemical information that can be accessed through the application of laser technology is evident by the abundance and diversity of recent literature. As a result, and as noted in a recent article published in this Journal, the use of lasers in undergraduate chemistry laboratories has burgeoned in the past few years (1). For example, nitrogen and nitrogen–dye laser systems now offer an affordable means of introducing undergraduate students to an effective tool for investigating molecular photophysical properties, as well as thermodynamic or kinetic data for discrete reactions. Thermodynamic and kinetic information can be simultaneously determined by the relatively new technique of photoacoustic calorimetry (PAC), which can be described as “listening to molecules” as they decay from energetically excited states. Simply stated, PAC provides a direct measurement of the energy that is released nonradiatively following photostimulation. It can therefore be used to quantify the amount of energy released by luminescent pathways or the heat of reaction of photostimulated chemical events. The apparatus is similar to that employed for nanosecond fluorescence spectroscopy, with a transducer monitoring the acoustic wave rather than a photomultiplier tube analyzing the incident light (1). While more rigorous PAC data acquisition and reduction techniques are commonly employed in research laboratories (2), we describe a simple approach that requires only a nitrogen laser, a transducer, a joulemeter (or second transducer), and a digital oscilloscope. The majority of the equipment is similar to that described in recently published undergraduate spectroscopy experiments (1, 3), and PAC is readily developed as a complementary exercise or an accessible alternative. The time response of a PAC transducer can be divided into three regimes (Fig. 1), though the exact partitions depend
"Too fast"
"TimeResolved"
"Too slow"
on the transducer and apparatus geometry employed. Signals generated by heat-release pathways characterized by lifetimes less than 10 ns are “too fast” for the dynamics of the heat deposition to be resolved. However, for such signals the integrated heat release of the pathways is readily measured (as described herein). Events that occur with characteristic lifetimes slower than about 20 µs are “too slow” to be detected by the transducer and are therefore unimportant. Heatreleasing events that occur between these two limits produce waveforms that include information regarding the energy and lifetime of the transient intermediates. Although a timeresolved treatment of the photoacoustic wave has been established (4), we demonstrate the utility of PAC data to measure photophysical properties (e.g., ET1, the energy of the first excited triplet state) and chemical reaction enthalpies (∆Hrxn) while operating within the constraints of the experimentally much simpler “too-fast” regime. This manuscript describes two distinct studies that demonstrate different interpretations of data collected by identical laboratory procedures and hardware for discrete chemical systems; additional examples can be found in the primary literature or created as appropriate (5). Each project illustrates the underlying principles of PAC and is suitable as an independent laboratory exercise. The projects and principal outcomes can be summarized as follows. 1. Determination of the triplet energy of C60 demonstrates the ability to characterize short-lived reactive intermediates. A secondary outcome is achieved through examination of the wave profiles as reaction conditions are systematically altered (oxygenated versus deoxygenated). 2. Determination of the enthalpy of the photodissociation of diphenylcyclopropenone (DPCP) demonstrates the ability to extract thermal and reaction volume contributions to an observed photoacoustic signal, all within the constraints of “too-fast” PAC. A secondary outcome may include a comparison of ∆H in various solvents by assuming ∆Vrxn is constant.
Theoretical Background 10-15
10-12
10-9
10-6
10-3
100
Time / s
Figure 1. The time scale of molecular events as examined by PAC. Heat-releasing events with characteristic nanosecond (or shorter) lifetimes are only integrated, whereas events occurring between the nanosecond and microsecond limits require a time-resolution analysis. Events occurring with lifetimes beyond the slow limit are not detected by a PAC apparatus.
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After a typical organic molecule has been energized by absorption of incident light, the excited singlet state (S1) may relax to its ground state (S0) by a variety of pathways (Fig. 2). Decay from S1 to S0 with concomitant emission is the fluorescence pathway. Molecules in S1 can undergo internal conversion (IC) to a high vibrational level of S0 and quickly cascade down the vibrational levels of the S0 state by consecutively depositing small amounts of energy into the envi-
Journal of Chemical Education • Vol. 77 No. 5 May 2000 • JChemEd.chem.wisc.edu
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Φ ISC{S1
Φ IC
incident light pulse, and the quantity (1 – 10A ) is the fraction of the light pulse that is absorbed. K is an instrumental sensitivity constant dependent on the geometry of the cell with respect to the excitation beam and the sensitivity of the microphone employed. As the photoacoustic cell remains undisturbed throughout the entire experiment, K is a constant that is readily calibrated for each experiment. Χs, the solvent expansivity, is determined as shown in eq 2, where α, MW, Cp , and ρ are, respectively, the adiabatic expansion coefficient, molecular weight, molar heat capacity at constant pressure, and density of the solvent (all at the same temperature).
T1}
S1
ΦISC {T1
T1 So} Φ fl
Φp
Eexc
Χs = αMW C pρ
So
Figure 2. Jablonski diagram of transitions considered important with respect to PAC. Radiative processes are shown by straight lines, nonradiative processes by wavy lines. IC is internal conversion; ISC is intersystem crossing; fl is fluorescence; p is phosphorescence; Φ is quantum yield.
ronment. Alternatively, the S1 state may undergo intersystem crossing (ISC) to yield the lowest-energy triplet state, T1. Although ISC itself takes place without the loss of energy, T1 is usually of lower energy than S1; S1 molecules initially cross isoenergetically to a high vibrational level of T1 and a subsequent energy release occurs as it cascades to the lowest vibrational level of T1. Finally a molecule in the T1 state can relax back to S0 by two pathways. First, the T1 state can phosphoresce, releasing its excess energy as light. The second pathway is another ISC route in which the energy released during return to S0 is in the form of heat. Since both phosphorescence and ISC are “spin-forbidden” pathways, they are slow. In general, upon excitation by a photon of sufficient energy, an organic molecule will only utilize a subset of the decay routes previously mentioned (Fig. 2). All energy released as heat is commonly referred to as nonradiative relaxation energy. This heat is deposited into the surrounding environment (solvent) causing a local temperature increase, which induces an adiabatic, isobaric expansion of the solvent (i.e., a volume change). This expansion generates an outwardly propagating pressure wave, called the acoustic (or photoacoustic) wave, traveling at the speed of sound in that medium. The pressure wave is readily detected by a transducer (microphone), which converts the acoustic wave into a voltage signal for easy observing and recording. Comparison of the amplitude of the pressure wave of reference compounds (whose physical properties are known) against those of sample compounds (whose photophysical properties are unknown) allows for the quantification of heat deposition concurrent with relaxation. The amplitude of the voltage wave observed on an oscilloscope is directly proportional to the amplitude of the pressure wave, which, in turn, is directly proportional to the amount of heat generated as a product of nonradiative relaxation processes. The energy released as heat is dependent on the number of molecules excited and the fraction of these that decay by heat-releasing processes. For a collection of molecules each absorbing a single photon, the amplitude of the voltage wave, S, will be described by eq 1, S = K Χs f hEp(1 – 10A )
(1)
where f h is the fraction of the absorbed photon energy that is returned to the environment as heat, Ep is the energy of
(2)
Several considerations inherent in the derivation of eq 1 should be explicitly considered. First, it is assumed that during a PAC experiment, each molecule will absorb only one photon (this condition is met by setting the energy of the incidence pulse to ≤ 40 µJ for a pulse ca. 2 mm in diameter using the lowest optical density attenuator; see Experimental Procedure) (6 ). A second consideration applies to K; the optical density of each solution is adjusted so that the distance the wave propagates before reaching the transducer is constant for each discrete sample of the experiment. This condition is also easily met by obeying two empirical rules: (i) the absorptivity at the excitation wavelength should be ≈0.2 for a 1-cm path length, and (ii) the absorptivity of all samples in one experiment should be similar, but need not be identical. Finally, photoexcitation is assumed to be instantaneous—that is, occurring on a time scale much faster than the response time of the detector (also easily met by typical N2 lasers). The unitless parameter f h is the immediate target of an actual PAC experiment; it depends on the photophysical (e.g., E S1, Φfl, ΦISC, ET1, and E fl1) or photochemical (e.g., Φdiss, the quantum yield of photoinduced dissociation) properties of the molecule of interest. By consideration of energy balance for a specific chemical system, one can define what f h is in terms of the fundamental properties of the molecule. For example, eq 3 describes the behavior of a molecule that partitions between all three decay pathways described in Figure 2 within the 10-ns time limit of “too-fast” PAC. Equation 3 also assumes that the populated triplet state is longer lived than the slow time limit of instrument resolution. For these reasons, eq 3 is readily applied to numerous organic molecules.
fh =
E exc – ΦISCE T – Φfl E fl 1
E exc
(3)
The standard approach is to use compounds that have accurately known heat-release properties (specifically, f h = 1.0) to calibrate the instrument and thereby determine the experimental parameter K. Having established the constant K, the f h of a compound of interest is readily calculated from eq 1 and the experimentally determined A, S, and Ep values (the former via any standard UV–vis spectrometer, the latter two via the PAC experiment).
Triplet State Energy Since the report by Kratschmer and Huffman in 1990 regarding the macroscopic synthesis of fullerene compounds
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(7 ), many articles concerning the characterization of C60 have appeared in this Journal (8–10). C60 is an excellent example of a compound whose photophysical properties are uniquely determined by PAC (11). The energy of a triplet state is normally determined by an examination of the phosphorescence spectrum and assignment of the phosphorescent onset. However, since C60 does not luminesce (i.e., it is neither phosphorescent nor fluorescent), the traditional method fails. The short lifetime of the S1 state (τS 1 = 33 ps) (12) and the high quantum yield for singlet oxygen production (0.94 ± 0.04) (13) are strong indicators that ΦISC{C60} = 1.0. Thus it can reasonably be anticipated that photoexcitation of a dilute solution of C60 results in production of one triplet state for each molecule that absorbs a photon. Further, in the absence of quenching agents (e.g., O2), the triplet state of C60 is longlived (τ > 10 µs) (11) with respect to the detection limit of a typical PAC apparatus. Thus, if C60 is examined in a PAC experiment in dilute solution and in the absence of oxygen (an efficient quencher of organic triplets), the simple (too-fast) form of the analysis applies and f h = (Eexc – Φ ISC E T1{C60})/Eexc. Experimental determination of f h and combination of that value with Φ ISC = 1.0 and the energy of the excitation photon returns ET1{C60} (12).
Simultaneous Determination of Reaction Enthalpy and Volume PAC can also be utilized to determine the reaction enthalpy and reaction volume of a photoinitiated process. An example is the photofragmentation of diphenylcylopropenone (DPCP) to diphenylacetylene (DPA) and carbon monoxide (eq 4). O Φdiss = 1.0
Ph
Ph
C
C
Ph
+
CO
(4)
Ph
The C 60 PAC experiment discussed earlier focused on photophysical properties of molecules that underwent no net chemical change (starting and ending states differ only in electronic configuration). DPCP undergoes an irreversible chemical reaction immediately upon absorbing a UV photon (14 ). As the PAC experiment uses a volume change as the physical observable, all processes that induce a macroscopic change in volume are integrated into the recorded signal. For the C60 experiment, the only volume change was due to heat deposition. In the DPCP experiment, the observed acoustic wave is the sum of two terms, a term dependent on the heat deposition (and consequent expansion of the solvent), Stherm, and a second term arising from differences of partial molar volumes of the solvated reactants and products, Svol (eq 5) (15, 16 ). Just as the sum of the heats of formation of the products may be different from the sum of the heats of formation of the reactants, the sum of the partial molar volumes of the products may be different from the sum of the partial molar volumes of the reactants. The difference in heats of formation is the reaction enthalpy; the difference in partial molar volumes is the reaction volume (∆Vrxn). The reaction volume may provide unique insight into differences in reactants and products (changes in charge distribution, conformation, etc.) (17, 18). Equation 5 can be further expanded, after application of eq 1, as eq 6, where ∆Vchem represents the observed volume change due to chemical reaction 642
and Ep (1 – 10A)/h ν is the number of photoexcited molecules. Sobsd = Stherm + Svol A
S obsd = Kf h Ep 1 – 10
(5) A
Χs + KEp 1 – 10
∆V chem hν
(6)
After combining eq 6 with the observed photoacoustic signal given as eq 1, the observed f hobsd can be shown to be dependent on both the reaction volume and f h as described in eq 7. By measuring f h obsd as a function of the expansivity of the solvent, Χs, an accurate determination of f h and ∆Vchem is possible (NOTE: eq 7 is the equation of a line). f h obsd h ν Χs = f h h ν Χs + ∆Vchem
(7)
Since Χs is a solvent-specific parameter, its variation is accomplished by using a closely related series of solvents (15) or one solvent with temperature-dependent Χs. The reaction enthalpy is obtained from eq 8 and the reaction volume from eq 9, which account for the efficiency of the photon-induced fragmentation reaction (Φdiss ).
E exc – ∆V rxnΦdiss E exc
(8)
∆Vchem = ∆VrxnΦdiss
(9)
fh =
Experimental Procedure
Apparatus A basic photoacoustic calorimeter is illustrated in Figure 3. The nitrogen laser (LS) we have used is a Laser Photonics LN1000 with maximum pulse energy of 1.4 mJ and a pulse duration of approximately 600 ps; it typically operates at a repetition rate between 1 and 2 Hz. The laser pulse is directed to an optical trigger, OT (e.g., PRA Model L-OT), containing a photodiode that senses the photon pulse and sends an electronic signal (to a digital oscilloscope) to synchronize data collection. Next, the laser beam passes through
LS
OT
AT
AP
BS
SC
N2 JM
OS
Figure 3. Schematic diagram of the photoacoustic calorimeter. The dashed lines indicate the light path. The components, in the order that the light or signal passes, are tank of gaseous nitrogen (N2), nitrogen laser (LS), optical trigger (OT), energy attenuator cuvette (AT), aperature (AP), and beam splitter (BS) that directs approximately 50% of the beam to (i) a joulemeter (JM) where an energy reading can be made via an oscilloscope (OS) or read digitally, and (ii) the sample cuvette with transducer (SC), which sends the signal to an oscilloscope.
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In the Laboratory
a standard quartz UV–vis cuvette (1 × 1 cm) containing solutions of ferrocene in ethanol with optical densities at 337.1 nm ranging from 0.00 to 0.60 (AT); this cell serves as a simple way to vary the energy of the pulse incident on the sample cuvette. After the light beam passes through the attenuator solution, a circular aperture, AP (≈2 mm), both reduces the energy in the pulse and shapes the beam. Next, the light beam passes through a beam splitter (e.g., MellesGriot, UV-fused silica, 25-mm diam, Model BSQ003/803), BS, and is divided into roughly equal components. One component of the beam is directed to a pyroelectric joulemeter (e.g., Molectron Detector, Inc., Model J3-09), JM, which allows absolute measurement of Ep. The other component is focused onto the sample cuvette (SC), a standard quartz 1 × 1cm cuvette, which contains the organic molecule of interest dissolved in a solvent (any solvent can be used, including water, provided there is no absorptivity at 337.1 nm). The optical density of the sample solution is ca. 0.20 and must be accurately known. The maximum pulse energy incident on the sample should be limited to 40 µ J (≈2 mm diam) to ensure that no multiphoton events are occurring. The sample cuvette is secured in a spring-loaded assembly to achieve good contact between the cuvette and the transducer (aided by a small amount of silicon grease), as shown in Figure 4. The transducer is a custom-built unit modeled after Tam and Patel (19), with minor modifications such as the elimination of grease within the transducer casing and the inclusion of brass cups on both ends of the spring inside the casing. The piezoceramic crystal (the sensor) is made of a lead zirconate–lead titanate crystal (Transducer Products, LTZ-2) measuring 4 mm in diameter, with a 500-kHz fundamental frequency. The operating frequency of the transducer depends on the apparatus geometry and is expected to vary slightly from the fundamental frequency.2 The photoacoustic signal generated by photolysis and measured by the transducer can be captured by a digital oscilloscope. As necessary, the signal can be conditioned by preamplifiers (e.g., Panametrics, Model 5660B). The amplitude of the observed signal is typically averaged over 30 to
Quartz Cuvette, can be sealed with a septum
Spring
Common Problems The most common problem experienced during PAC data collection is due to changes in the apparatus geometry. The distance between the light beam and the transducer will determine, in part, the experimental constant K and must not be altered during the collection process. For this reason, the sample cuvette should remain within the spring-loaded assembly for the duration of the experiment and the various standard and sample solutions should be carefully transferred by pipet. Rinsing the cuvette with the appropriate solvent will also decrease error associated with impure samples and consequent faulty data. The third complication is that as the optical density of the sample appears in the exponent of the too-fast PAC equation (eq 1), the quantitative comparison of the signal of one compound to that of another demands accuracy in the measurement of A values. The fourth common problem, that of multiphoton effects due to too many photons in too small a time or volume, is readily apparent as curvature in the data plotted according to eq 1. Standard Compounds In principle, any compound with accurately known photophysical properties can be used as a photoacoustic standard. However, it has been found that the most convenient standards are those that return all the photon energy “instantly” as heat. Therefore, standards are chosen that have short excited-state lifetimes and significant extinction coefficients at 337.1 nm. Tetraphenylethylene (TPE), ferrocene (FER), and o-hydroxybenzophenone are readily available compounds commonly employed as PAC standards. The use of two different standards in any one experiment increases accuracy and allows for internal consistency checks (the slopes of the two standards, for data plotted according to eq 1, must be identical). Once the apparatus has been assembled and the samples prepared, a typical PAC experiment should be easily accomplished within a 4-hour undergraduate lab. Results and Discussion
Silicone grease at interface Transducer Mount BNC Connector
Laser Beam
50 laser pulses for each optical density of the attenuating solution. Data collection usually includes measuring the signal amplitude for 10 different AT solutions.
Transducer
Post
Figure 4. Schematic diagram of our custom-built cuvette/microphone unit. Because amplitude diminishes with distance traveled, the optimal signal-to-noise is achieved when the laser beam passes through the cuvette near the microphone face. A thin layer of silicone grease enhances coupling between the quartz cuvette and the microphone.
Photofragmentation of DPCP Figure 5 displays data collected during the DPCP experiment. Regardless of the specific experiment, the data in Figure 5 represent typical PAC waveforms and, consequently, several observations are worth noting. First, all photoacoustic waves (standard and compound of interest) are “in phase”. This indicates that no heat-releasing processes are occurring on the time-scale concurrent with instrument resolution and that these data fit the too-fast PAC time regime. Second, the DPCP waves have a larger amplitude than TPE even when normalized for Ep and A, a consequence of releasing comparatively more nonradiative energy after photoexcitation. Third, a plot of the acoustic wave amplitude normalized by (1 – T ) and plotted against Ep (inset, Fig. 5) results in the expected linear relation defined by eq 1. The ratio of the slopes of the standard (TPE) and compound of interest (DPCP) determines f hobsd{DPCP}.
JChemEd.chem.wisc.edu • Vol. 77 No. 5 May 2000 • Journal of Chemical Education
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In the Laboratory 0.7
600
DPC O
TPE
0.5
fh hνΧs / (cm3 mol−1)
500 0.3
Ph
0.1 -0.1
Laser Spike 1.0
-0.5 -0.7 -0.9
DPCP
0.8
400
300
obs
-0.3
S /(1-T ) (relative)
Signal (relative)
Ph
0.6
TPE
0.4 0.2
200
100
0.0 0.0
0.2
0.4
0.6
0.8
1.0
∆V
E p (relative) -1.1
0
0
1
2
3
4
5
6
7
8
9
10
0
1
2
Time / µs
As noted above, the value of f hobsd{DPCP} is a combination of thermal and reaction volume contributions (eq 5), since a photofragmentation reaction is occurring. The value of each component is extracted by plotting the experimentally determined f hobsd{DPCP} versus Χs for different alkane solvents as shown in Figure 6. The slope gives the correct f h{DPCP} and the intercept is the observed volume change due to the chemical reaction, ∆Vrxn, as predicted by eqs 7 and 9 (∆Vchem = ∆Vrxn, since Φdiss = 1.0). The reaction enthalpy and volume are then determined by eqs 8 and 9, respectively. We determined that ∆H rxn = 6.7 ± 1.2 kcal mol1 and ∆Vrxn = 23 ± 4 cm3 mol1 (15). (In a previous study that related the entire signal to heat deposition to the solvent, benzene, ∆Hrxn was measured as 9.9 ± 2.1 kcal mol1 [20].) As shown in Figure 6, eight different alkane solvents were used. Although this may seem difficult to achieve within the time constraints of most laboratory courses, two remedies are suggested: (i) data for just one solvent can be collected and compared to the value obtained when ∆Vrxn is assumed insignificant, or alternatively (ii) an individual team can collect data for one solvent while other teams in the class do this for different solvents, thus collectively determining the ∆Hrxn and ∆Vrxn.
Triplet Energy of C60 Representative photoacoustic waves of the C60 PAC experiment are shown in Figure 7. The observed “wave shift” for the oxygen-containing sample with respect to the deoxygenated and standard samples is evidence of chemical events occurring within the time-scale of instrument resolution. Therefore, the data shown in Figure 7 for C60 in the pres-
644
4
5
Figure. 6. Plot of f hobsd{DPCP} hν Χs vs Χs for the photodissociation of DPCP in linear alkanes. Eight alkane solvents were used (pentane to hexadecane). The slope gives f h{DPCP} ; the intercept is the ∆Vchem. The data shown are from ref 16.
0.8
FER 0.6
C60 w/O2
0.4
Signal (relative)
Figure 5. Plot of several photoacoustic waves as directly observed in decane. Two waves each are shown for tetraphenylethylene (TPE) and diphenylcyclopropenone (DPCP); each corresponds to a different laser energy (Ep of eq 1). The “laser spike” is due to noise generated by the actual discharge of the laser (in this case, the recording of the waveforms began before the laser fired). Note that the exact shape of the wave depends on the transducer employed and the specific geometry of the cell. Inset: The data for these and additional waves plotted according to eq 1. As the slope of each line is (Kf h) for that compound, and f h TPE = 1.0, the ratio of the two slopes is f hobsd{DPCP} (in this solvent at this temperature). For the experiment shown, the acoustic waves were obtained at 8 different laser energies achieved by using eight different attenuator solutions.
3
Χs / (cm3 kcal−1)
C60 w/Ar
0.2
Laser Spike
0.0 0.5
-0.2
0.4
C60 w/O2
0.3
-0.4
0.2 0.1
-0.6
0.0 -0.1
-0.8
C60 w/Ar
-0.2 4.5
5.0
5.5
6.0
-1.0 0
1
2
3
4
5
6
7
8
9
Time / µs
Figure 7. Plot of several photoacoustic waves as directly observed for the C60 experiment in toluene. One wave each, normalized to Ep and (1 – 10A) as described by eq 1, is shown for the standard ferrocene (FER) and C60 in the absence and presence of O2. Inset: Enlarged view of the central portion of the wave plot demonstrating the noticeable “delay” in the C60 with O2 wave as compared to the other two waves.
ence of oxygen illustrate the type of experiment that would require a time-dependent analysis. In the absence of O2, however, the observed acoustic wave can be analyzed via the much simpler too-fast approach: normalization of the signal by (1 – T ) plotted against Ep determines f h. Utilization of eq 3 (along with the assumptions outlined in the theoretical discussion, that is, ΦISC = 1.0) readily permits determination of ET1{C60}. We found ET1{C60} = 36.0 ± 0.6 kcal mol1 (11), which has been confirmed by independent measurements (21). In the presence of O2, two sequential events contribute to the observed wave: the production of triplet state C60 and its quenching by O2. The former occurs in the too-fast PAC time regime; the latter, within experimental constraints— hence, the noticeable shift of the acoustic waves.
Journal of Chemical Education • Vol. 77 No. 5 May 2000 • JChemEd.chem.wisc.edu
In the Laboratory
Suggested Alternative Studies
Literature Cited
Photoacoustic calorimetry is a technique widely applicable to chemical subjects. Its flexibility has been demonstrated herein with the organic photofragmentation reaction of DPCP and the measurement of photophysical properties of C60. C70 can and has been explored in an analogous fashion (22). Alternative PAC projects are abundant throughout the primary literature and are diverse in their subject areas (5). For example, in biochemistry, PAC can examine the energetics of CO dissociation from carboxymyoglobin (23) and the enthalpy and volume changes associated with the formation of triply ligated carboxyhemoglobin from carboxyhemoglobin (24 ). In the area of organometallics, bond dissociation energies of several alkyl- and aryl-substituted germanium hydrides have been measured (25), as have a number of metal–carbonyl (e.g., Ru– CO) and metal–ligand (e.g., Ru–N2) bond energies (26 ). In all these cases, the equipment and approach described above can be used, demonstrating the extreme versatility of PAC for determining reaction energetics and dynamics of interest.
1. Van Dyke, D. A.; Pryor, B. A.; Smith, P. G.; Topp, M. R. J. Chem. Educ. 1998, 75, 615–620. 2. Grabowski, J. J.; Bertozzi, C. R.; Jacobsen, J. R.; Jain, A.; Marzluff, E. M.; Suh, A. Y. Anal. Biochem. 1992, 207, 214–226. 3. Allen, H. C.; Brauers, T.; Finlayson-Pitts, B. J. J. Chem. Educ. 1997, 74, 1459–1462. 4. Rudzki, J. E.; Goodman, J. L.; Peters, K. S. J. Am. Chem. Soc. 1985, 107, 7849–7854. 5. See our Web page for a PAC bibliography: http://www.pitt.edu/~joeg/ pacref.html (accessed Dec 1999). 6. Song, X.; Endicott, J. F. Inorg. Chem. 1991, 30, 2214–2221. 7. Kratschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. M. Nature 1990, 347, 354–357. 8. Ball, D. W. J. Chem. Educ. 1994, 71, 463. 9. Hildebrand, A.; Hilgers, U.; Blume, R.; Wiechoczek, D. J. Chem. Educ. 1996, 73, 1066–1067. 10. West, S. P.; Poon, T.; Anderson, J. L.; West, M. A.; Foote, C. S. J. Chem. Educ. 1997, 74, 311–312. 11. Hung, R. R.; Grabowski, J. J. J. Am. Chem. Soc. 1991, 95, 6073– 6075. 12. Wasielewski, M. R.; O’Neil, M. P.; Lykke, K. R.; Pellin, M. J.; Gruen, D. M. J. Am. Chem. Soc. 1991, 113, 2774–2776. 13. Arbogast, J. W.; Darmanyan, A. P.; Foote, C. S.; Rubin, Y.; Diederich, F. N.; Alvarez, M. M.; Anz, S. J.; Whetten, R. B. J. Phys. Chem. 1991, 95, 11–12. 14. Fessenden, R. W.; Carton, P. M.; Shimamori, H.; Scaiano, J. C. J. Phys. Chem. 1982, 86, 3803–3811. 15. Hung, R. R.; Grabowski, J. J. J. Am. Chem. Soc. 1992, 114, 351–353. 16. Zimmt, M. B.; Vath, P. A. Photochem. Photobiol. 1997, 65, 10–14. 17. Isaacs, N. Physical Organic Chemistry, Second Edition; Longman: Essex, UK, 1995; pp 113–116. 18. Le Noble, W. J.; Asano, T. Chem. Rev. 1978, 78, 407–489. 19. Tam, A. C.; Patel, C. K. N. Rev. Mod. Phys. 1981, 53, 517–550. 20. Grabowski, J. J.; Simon, J. D.; Peters, K. S. J. Am. Chem. Soc. 1984, 106, 4615–4616. 21. Zeng, Y.; Biczok, L.; Linschitz, H. J. Phys. Chem. 1992, 96, 5237–5239. 22. Hung, R. R.; Grabowski, J. J. Chem. Phys. Lett. 1992, 192, 249–253. 23. Leung, W. P.; Cho, K. C.; Chau, S. K.; Choy, C. L. Chem. Phys. Lett. 1987, 141, 220–224. 24. Peters, K. S.; Watson, T.; Logan, T. J. Am. Chem. Soc. 1992, 114, 4276–4278. 25. Clark, K. B.; Griller, D. Organometallics 1991, 10, 746–750. 26. Belt, S. T.; Scaiano, J. C.; Whittlesey, M. K. J. Am. Chem. Soc. 1993, 115, 1921–1925.
Conclusion The breadth and diversity of experiments potentially explored by PAC allows attention to be directed to many fields in chemistry. Since instrumentation is similar to that already employed in many undergraduate laboratories, PAC can be developed as an accessible undergraduate physical-organic laboratory exercise without much expense. A variety of important chemical concepts (reactive intermediates, lifetimes, photochemistry, energetics, and dynamics) are illustrated via PAC and a new experimental technique is added to the curriculum. By allowing students to address minor variations in the experimental procedure (e.g., changing the solvent for each experimental team in the DPCP project), group efforts to address more complicated issues (∆Vchem and ∆H rather than only ∆H) can be utilized. Notes 1. ES1 is the energy of the first excited single state; Φfl is the quantum yield of fluorescence; ΦISC is the quantum yield of intersystem crossing; E T1 is the energy of the first excited triplet state; Efl is the energy of fluorescence. 2. Blueprints of the custom-built transducer used in these experiments are available if needed; similar units are obtainable commercially (e.g., Panametrics, V110-RM).
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