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The photodissociation processes of ketene at 3130 A, 3340 A and 3650 A Taylor, Gladstone Altamont 1961

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THE PHOTODISSOCIATION PROCESSES OF KETENE O O O AT 3130 A, 3340 A AND 3650 A by GLADSTONE ALTAMONT TAYLOR B.Sc, McMaster University, 1958 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 1961 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia, Vancouver 8, Canada. Date i i ABSTRACT Previous research on the photolysis of ketene has shown that the kinetics of photodissociation processes were not f u l l y understood and that more accurate data were needed to evaluate the mechanism of the rate of dissociation of the electronical ly and vibrat ional ly excited molecules. There was some evidence that the primary quantum y i e l d s at shorter wavelengths extrapolated to a value greater than unity at zero pressure, i f t h i s were not within experimental error, i t would provide evidence for a process of multistage deactivation of the excited ketene molecules. In the kinetic studies of the dissociation of excited molecules, intersystem crossing to the t r i p l e t state had been included to account for phosphorescence. Theoretical consideration from t h i s had led to predictions of the effect of dissociation from the t r i p l e t state on the quantum yields of carbon monoxide on the photodissociation of ketene. Experimental v e r i -f i c a t i o n was now needed to determine the effect, i f any, derived from t r i p l e t dissociat ion. Previous attempts have been made to apply the unimolecular theory of dissociation to the photodissociation of excited molecules, but the data available yielded physically impossible results . Hence, only reasonable theoretical values of the parameters involved are given. This research attempted to obtain more accurate data on the quan-tum yields of ketene at 3130 $, 3340 A and 3650 A at various temperatures. From the results i t i s now possible to differentiate within the l i m i t s of the experiment, between the various theories of the dissociation process. It i s established that t r i p l e t dissociation i s either not a real effect or i s small enough to be undetectable under the experimental conditions. i i i It is possible to discount a theory of a cascade collisional deactivation process involving more than three collisions of the excited molecules, but differentiation is not made between one, two and three collisions under experimental conditions. The unimolecular theory of dissociation is applied to the results of the photodissociation process and values determined for the parameters involved. Reasonable agreement with the theoretical predictions is obtained. TABLE OF CONTENTS i v Page INTRODUCTION» o « e o e * e « « « 9 e » « * o » » « o e o o * « « X 1 • EO.I*ly Work o « o » o o o « » « « a * o » « « o o « « « e o X 2. Later Work. 2 3» Recent Work 5 4.0 Object of Present Investigation . . . . . . . . . . . . . 8 1. Light Source 11 2. C e l l Housing 11 3» Drying System 12 4.. Temperature Control System 13 5. F i l t e r s . . o . • © . . • • • • « • • • • . . « . « « . . 13 6 . Preparation and P u r i f i c a t i o n of Ketene 1L 7. Photolysis of Diethyl Ketone. . . . . . . . . . . . . . . 14 8. Gas Analyses. 15 9* Actinometry 15 REaSULTS . • • • • « • • • • • • • • . • • • • • « . . . o . « . © 19 3130 A 19 33^.0 A • • © • © • • • • © © • • » » © * o ° * * * o 9 # * * 20 3650 1 • 20 DISCUSSION 3 0 1. Theory. . . . . . . . . . . . . . . . . . . . . . . . . . 30 2. Experimental Data and Conclusions 39 BIBLIOGRAPHY 4-5 V LIST OF FIGURES Page Figure 1. C e l l Housing 11a Figure 2. Baffle System 12a Figure 3« Preparation of Ketene Figure 4» Calculated Curve 38a Figure 5. Calculated Curve 38b Figure 6. Calculated Curve 39a 0 o Figure 7. Quantum Yield vs. Pressure at 3130 A and 23 C . . . . 39b Figure 8. Quantum Yield vs. Pressure at 3340 £ and 23°C . . . . 39c Figure 9. Quantum Yield vs. Pressure at 3650 £ and 23GC . . . . 39d o o Figure 10. Quantum Yield vs. Pressure at 3130 A and 0 C 40a o o Figure 11. Quantum Yield vs. Pressure at 3340 A and 0 C 40b Figure 12. Molecular Energies at Tj and T 2 ( T 2 >^ Tj) 41a v i LIST OF TABLES Page Table 1. Molar Extinction Coefficients 21 o „ Table 2. Quantum Yields at 3130 A and 23 C 22 Table 3. Quantum Yields at 3130 A and 0°C 23 Table 4» Quantum Yields at 3340 I and 23°C 25 Table 5. Quantum Yields at 3340 A and 0°C 26 o Table 6. Quantum Yields at 3650 A and 23°C 27 Table 7. Rate Constants 28 Table 8. Calculated Values of £ m and £ q - 0 29 ACKNOWLEDGMENT The author wishes to express sincere thanks to Dr» G o B o Porter under whose supervision this investigation was carried out and whose unselfish help and guidance made this investigation f r u i t f u l * My sincerest thanks go to my wife for her co-operation and encouragement throughout this researcho My appreciation also goes to Mrs, E . Hinke who was remarkably patient i n typing and proof-reading this thesis. 1 INTRODUCTION l a Early Work The earliest photochemical decomposition of ketene was done by Norrish, Crone and Saltmarsh"1". These workers showed that carbon monoxide and ethylene were produced in a ratio of 2:1 and postulated the reaction as K + h|/ > K (la) K * > CE°Z + CO (2a) K + CH2 > C^ H + CO (3a) where K is the ketene molecule and K the excited state. Ethylene was formed by reaction between methylene radical and ketene rather than by association of methylene radicals. 2 This mechanism was disputed by Ross and Kistiakowsky who suggested because of the large amount of activation energy probably required, reaction 3a did not occur to any extent and that the ethylene formed was then due to the combination of methylene radicals. On this basis, the quantum yield would then be unity instead of 2 as from Norrish and co-workers. 3 Further work by Pearson, Purcell and Saigh seemed to confirm this view as they found that a) each methylene radical survived A x 10 collisions with ketene molecules in the quartz reaction vessel, and b) the mean value of 1.08 as found by Kistiakowsky and Ross could not be safely assumed to exceed unity in view of the experimental errors involved. Hence i t was likely that, the reaction between methylene and ketene being slow^ methylene was removed by association* 2 I t had also been observed that i f the photolysis and consequent dissociation was done i n the presence of ethylene, a non-volatile polymer was formed, presumably by attack of CH 2 radicals on the ethylene. The work of Rosenblum^ further supported methylene association. Methylene radicals had been known to react with other methylene radicals^' 1,6 to form ethylene, and with ethylene i t s e l f to y i e l d polymeric unsaturated hydrocarbons. The absence of methylene during thermal decomposition of methane was attributed to r a d i c a l combination. Also methylene r a d i c a l combination with carbon monoxide had long been known^. Rosenblum showed that photolysis of ketene i n the presence of methane, ethane and ethylene, increased polymer formation. Photolysis i n the presence of hydrogen also yielded a condensed polymer and higher satur-ated hydrocarbons, and no reaction occurred when hydrogen and ethylene were irradiated together. This indicated that methylene radicals could polymerize hydrocarbons. 2. Later Work 7-10 Subsequent evidence , however, confirmed the scheme f i r s t proposed by Norrish, Crone and Saltmarsh^. In one work by Kistiakowsky and 7 Rosenberg , the reaction was studied by i r r a d i a t i n g mixtures of ethylene and ketene. With methylene-ethylene reaction there would be no pressure r i s e , with the result that as the ethylene/ketene r a t i o i n the reaction c e l l i s increased, the rate of pressure r i s e i s lowered. By using a large excess of ethylene, i t was insured that the methylene formed by decomposition of ketene would react almost exclusively with the ethylene. Under these conditions the pressure of the system remained constant indicating l i t t l e i f any polymerization of ethylene. The reactions could then be written K + h i> 2CH2 K + CH2 C2 H4 + CE2 From steady state assumptions, i f reaction 3 was neglected, we have \f CH2 + CO (lb) k 2 (2b) C ^ + CO k3 (3b) C3 H6 k4 (4b) R = 1-Z / l + 2 j where Z = k^ 2(C^) (i) and R is the ratio of the rate of pressure change on irradiation of a given mixture of ethylene and ketene to the rate of pressure change in pure ketene at the same pressure as the ketene in the mixture« If reaction 2b was neglected rather than reaction 3b we have 1 R » ! + k4 ( c2 H4 ) (2) k3(K) Thus the effect of light intensity offered a basis for neglecting one of the two reactions. A plot of R as a function of ethylene/ketene ratio at two different intensities showed no effect of different intensities. An important difference in reactions 2b and 3b also is embodied in the rate of carbon monoxide production. If reaction 2b predominates, the rate should be independent of the ethylene/ketene ratio. If reaction 3b predominates the rate should decrease at higher ethylene/ketene ratios, approaching a limit of one half of that obtained for pure ketene. Investi° gation showed that the rate of carbon monoxide production does f a l l off with increasing ethylene/ketene mixture, although not to the extent pre-dicted from reactions lb, 2b, and 4-b. A This evidence definitely established that reaction 2b did not occur and i t was concluded that methylene radicals did not undergo an association reaction but reacted with ketene or with ethylene under the conditions of the experiment. In pure ketene the ratio of moles of carbon monoxide formed to the moles of ethylene formed from reaction 3b was 2 .19 - 0.02. The temperature independence of ratio R indicated that the activation energies of the reactions of methylene with ketene and with ethylene were nearly identical. The ratio of these rate constants (k./k„) 4 3 had the value 2«5« The same ratio was obtained for the reaction of propylene with methylene. Thus not only the activation energy of the three reactions but also their frequency factors were the same. This was improbable i f the products were as simple as reactions 3b and Ab suggested. This led 7 Kistiakowsky and Rosenberg to propose diradical formation in the f i r s t elementary steps of a l l three cases: CH^ CH^ CO*, CHgCHgCHg and CHgCHCH^ , a conclusion which was further supported by a) the imperfect agreement between predicted and observed effect of ethylene/ketene ratio on the rate of carbon monoxide formation, and b) inconstancy of the ratio of rate constants k^/k-j which varied from 2*3 to 3*1. Later work by Kistiakowsky and co-workers^0 showed that methylene radicals reacted with ethylene and with carbon monoxide to form propylene and ketene respectively. The formation of ketene from methylene radicals and carbon monoxide explained the pronounced drop of rate of pressure rise on protracted irradiation of ketene. Kistiakowsky and co-workers , A had also shown that quantum yields in ketene decomposition increased with decreasing wave length. At 2700 I Strachan and Noyes11 found that within experimental error the primary 5 quantum yield was unity and there was no significant variation with temper-ature or pressure. At 3650 A* there was a marked dependence of the primary quantum yield on pressure and temperature, decreasing with increasing pressure and increasing with increase in temperature, and was much less than unity when extrapolated to zero pressure of ketene. At 2700 1 the quantum yield of carbon monoxide formation was 2.12 - 0.15* This was to be expected i f reactions l a , 2a and 3a were the sole ones. In agreement with the value of 2.19 obtained by Kistiakowsky and co-workers^, they found that the average ratio of carbon monoxide to ethylene in the products was 2.20. This difference from the expected value of 2 from reactions l a , 2a and 3a was due to additional reactions whose rates were essentially independent both of ketene pressure and temperature. These reactions could be of the form K + CH2 > CH2) 2C0* (lc) M + CH2) 2C0* > polymer + CO + M (2c) where M could be either ketene or ethylene. r O . . At 3650 A the low quantum yields observed were attributed to (a) internal conversion and (b) collissional deactivation between ketene molecules occurring along with the primary dissociation process. K* (excitation) (Id) 2K (collisional deactivation) (2d) products (dissociation) (3d) K (+ hV ?) (internal conversion) where K is a ketene molecule and K the excited state. 3. Recent Work A more extensive study of photochemical processes was done by Noyes, Porter and Jolly-^ and by Porter^ who investigated the internal K + hV K* + K K K 6 conversion process and the possibility that a radiationless transition occurred from the excited electronic state to an upper vibrational level of the ground electronic state, followed by rapid collisional deactivation because no fluorescence as suggested by reaction 4d had been observed. The mechanism for a photochemical reaction that proceeded via excited molecules could be represented by the following reactions, consid-ering only one excited electronic state. X + h V » *n (le) Y N + II =• X + M (2e) \ — > D (3e) *n > m^ (4e) *m > Yn (5e) *m )• % (6e) * i > (7e) Xj + M - > X + M (8e) X is a molecule, e.g. ketene in i t s ground state in thermal equilibrium with surrounding moleculesj Y N is a molecule in upper vibronic state reached by absorption of radiationj D represents the dissociation products (in this case carbon monoxide and methylene radicals). M i s a molecule capable of degrading vibrational energy by collision: X^  represents those molecules in higher vibrational levels of the ground state having the same total energy as Y N . There would be many degenerate states corresponding to XJL, but only a few designated by XJJ w i l l have a configuration such that a radiationless transition to Y N has a high probability. A molecule Xj w i l l spend only a small fraction of its lifetime in configuration XJJ. 1^ i s the state formed when a molecule Y N makes a transition to the ground electronic state (reaction Ae)» Internal conversion was considered to have occurred when 7 reaction 8e had removed sufficient energy from ^  to prevent i t s return to Yn. Primary quantum yields calculated from the above was the same as the simpler mechanism suggested by reactions Id, 2d, 3d and 4d as long as the concentration was high enough such that kg(M)^ k^ . Since the relationship was not valid in the low concentration region, the quantum yield should increase with decreasing concentration, and should be unity on extrapolation to zero pressure, lc^ was also assumed to be small compared to kg(M) since the quantum yield was found independent of concentration. Thus a l l excited ketene molecules that made the transition from Y n to were subsequently deactivated by collision even at the lowest concentration studied. Since no fluorescence had ever been observed, i t must be assumed that the energy in the internal conversion and collisional deactivation pro-cesses was lost as heat. Extrapolation to zero pressure gave a carbon monoxide quantum yield of about 0.06. The low quantum yield values obtained suggest that internal conversion is more rapid than dissociation. With increase of pressure collisional deactivation becomes the more dominant o process. At 3650 A i t appears that dissociation occurs only after a finite time interval long enough for the ketene molecule to be deactivated. o o The variation of quantum yield with pressure at 3130 A and 334-0 A was investigated by Connelly and Porter 1^' 1 9. At 3130 1 i t was found that 15 the conclusion of Kistiakowsky and Mahan that the quantum yield was independent of pressure and possibly equal to unity applied only to low pressure measurements. A plot of the reciprocal of the primary quantum yield against pressure revealed a positive slope. The primary quantum yield was 1.0 at pressures up to 60 mm but decreased to 0.59 at 750.7 mm 8 pressure. At low pressures, the ketene molecule dissociated to form products, but at higher pressures collisional deactivation became a noticeable factor. The ratio of quantum yield of carbon monoxide to ethy-o o ° lene was found to be approximately 2.14 at 2700 A, 3130 A and 3650 A. o At 334-0 A the quantum yield was found to be 0.72 at 26 mm and 0 0.21 at 384. mm. A similar plot to 3130 A yielded a much steeper slope indicating considerable collisional deactivation. A larger intercept was also obtained, which was interpreted from the mechanism as evidence that internal conversion was also a contributing factor. The slope and inter-cept decreased with increase of temperature and the activation energy of dissociation was found to be about 2 k cals/mole. At 3650 A, the inter-cept and slope also decreased with increase of temperature and the activation energy was about 4«5 k cals/mole. 4« Object of Present Investigation As more accurate data were needed to evaluate the photochemical processes involved, i t was decided to investigate the photolysis of ketene using experimental technique which would give more accurate measurements of quantum yields than had previously been obtained. It was hoped that this data would lead to a better understanding of the collisional deactivation process. In the dissociation process 19 discussed by Porter and Connelly - i t was shown that i f the collisional deactivation process involved a "strong collision" i.e., each excited mole-cule was deactivated by a single collision with an unexcited molecule the plot of the inverse quantum yield against pressure would be a straight line and the data assumed to f i t the equation 1/4) = 1 + (k 2 n/k l n)K 9 or at longer wave lengths, the equation 1/43 = 1 + (k 3 n/k l n) + k2n(K) k l n where k^ = rate constant for dissociation k^ = rate constant for collisional deactivation k^n = rate constant for internal conversion (j) - quantum yield of carbon monoxide However, i f the collisional deactivation process was a "weak collision" process i.e., a cascade collisional process in which each excited molecule lost i t s energy by a series of collisions, a plot of l/ <p against pressure from the equations derived for the process, would, at low excitation energies yield linear curves. At higher excitation energies, the curves would l e linear only in the high pressure regions and would be concave upwards at low pressures. As the number of degradational collisions increased, aside from the increased quantum yields, departure from linearity would increase and a higher extrapolated quantum yield to zero pressure obtained. If the process also involved a single collisional degradation, the simple Kassel theory of unimolecular dissociation could be applied to the photodissociation. Hence from the results i t would be possible to evaluate in reasonable terms the parameters J/ , £ m and £ 0„ G involved. However, i f the process was a cascade one, application of the simple uni-molecular theory would be impossible as more parameters would be needed. Finally i t was felt that an investigation of the effect of temperature variation would also be valuable. The variation observed, i f any, would give information as to the extent of triplet dissociation, this interstate crossing from singlet to triplet, having been introduced in the 10 kinetic study of excited molecules to account for the observation of pho sphore s cence. From the theory, at low pressures a plot of the inverse quantum yield against pressure should be linear and correspond to singlet dis-sociation because collisional excitation and consequent dissociation in the triplet state would be negligible. With increase of temperature and consequent increase in the number and energies of molecular collisions, collisional excitation, and conse-quently dissociation from the triplet state should become increasingly important. The plot of l/ (ft against pressure then should begin to depart from linearity and become concave downward. 11 EXPERIMENTAL 1. Light Source A B.T.H. medium pressure mercury arc lamp was used in a l l the runs. The divergent beam was passed through a combination of two quartz plano-convex lenses to produce a parallel beam. The beam was then passed through a circular aperture 2 cm in diameter, which could be closed by a shutter when desired, and into a f i l t e r c e l l . This cel l , was kept f i l l e d with dis-t i l l e d water by means of two side arms. At one end was a quartz window, and at the other a 3 mm Corning 9863 f i l t e r glass to exclude visible radiation. The beam was then passed through a circular aperture similar to the f i r s t , into the cell housing. 2« Cell Housing The housing consisted of a brass box (see Fig. I), mounted by two supports on an optical bench on which the lamp and lens system were also mounted. The cell housing was divided into four main compartments. The f i r s t contained the f i l t e r cell and interference f i l t e r mentioned previously. It had a removable light tight cover. The next compartment was further sub-divided into two sections, the dividing wall having a circular aperture 2 cm in diameter. The larger section contained a quartz plate 3.8 cm in diameter at an angle of 45° to the path of the light. Most of the incident beam was transmitted into the reaction vessel but part was reflected into the smaller compartment which contained a mount for the actinometer cell immediately behind the aperture in the dividing wall* FIGURE 1. Diagram of Cell Housing a. light source bo plane—convex lenses Co f i l t e r cell with water do Jena-Schott Interference f i l t e r e> quartz window b ft a f 8 actinometer cell (R) g. temperature control housing for reaction vessel ho quartz reaction vessel k° actinometer cell (M) R reflected beam M transmitted beam 12 The transmitted beam then entered the next compartment through a circular aperture behind which the reaction vessel was placed. This compartment had a removable light-proof l i d as previously described, to which the photolysis cell holder was fixed thus enabling the cell to be lifted out of the housing for cleaning and spectrometric measurements. The brass cell holder consisted of an inner and an outer shell, the thickness being about 1 cm. The space between the shells consisted of a series of baffles (see Fig. 2). Water was passed through this system, thus giving temperature control of the reaction vessel, which was fitted exactly in the inner shell. The cell holder was made in two halves and soldered around the ce l l . To reduce heat transfer the cell holder was wrapped with glass wool. The quartz reaction vessel, was placed as accurately parallel as possible in the path of the beam. Its sidearm was blackened to exclude external radiation and attached by means of a hollow bore high vacuum stop-cock to the vacuum system. The fourth compartment contained a holder for the second actinome-ter c e l l , placed exactly behind a 2 cm hole, through which the beam after passage through the reaction vessel, entered the compartment. 3' Drying System For runs at temperatures below room temperature condensation of moisture on the cell windows was prevented by ensuring that the air in this compartment was dry. A large aluminium tray was f i l l e d with Drierite and placed in this compartment. A constant circulation of dry air, entering through an inlet in the aluminium cover of the second compartment, and at the temperature of the reaction vessel, was kept up through this compartment. FIGURE 2. Baffle System of Water Circulation in Cell Temperature Control Housing 13 For this purpose, nitrogen from a cylinder was used in some of the shorter runs. For long runs pressurized air was passed through a series of large glass tubes with different drying agents—calcium chloride, Drierite and Anhydrone respectively. The air was then passed through another tube packed tightly with glass wool and then through a sintered glass disc to ensure that no dust particles entered the compartment. The air was cooled by allowing i t to pass through a series of glass coils immersed in water at the same temperature as the reaction vessel. U» Temperature Control System small circulating pump was fixed to a wooden base placed on the top of the Dewar, with the inlet well below the water level. The outlet was attached by a short piece of plastic tubing to the inlet pipe of the beffle circu-latory system of the cell holder described previously. After circulation through the system, the water was returned through the outlet tube of the baffle system to the Dewar for cooling and recirculation. Runs at tempera-tures below 0°C were attempted, but were abandoned because of difficulties with the circulating system. 5. Filters The various wavelengths used for photolysis were obtained by the use of Jena-Schott interference fil t e r s placed in a holder behind the f i l t e r c e l l . For runs at 3130 1 the interference f i l t e r had a X mfl_ = 310.5 p, and This consisted of a 4-»5 l i t r e Dewar vessel containing water whose temperature was kept to within - 1°C by adding either ice or tap water. A u prevented from getting too hot during long periods of exposure by the water in the f i l t e r cell mentioned earlier, which absorbed the infra-red ratiation. 6. Preparation and Purification of Ketene Ketene was prepared on the vacuum system by pyrollzing acetic anhydride , as illustrated in Figure 3« By pumping on the acetic anhydride in the storage bulb, a slow stream of the vapor flowed through the oven, which was heated to 50A°C* The acetic acid produced and the unused acetic anhydride were collected in a dry-ice-acetone bath on the low pressure side of the oven. The ketene was collected in a liquid nitrogen trap. When enough ketene had been collected, i t was purified by trap to trap distillation, the middle third being retained, then stored in a bulb immersed in liquid nitrogen to prevent polymerization. Before each run a quantity of ketene was transferred from the storage bulb, condensed by liquid nitrogen on a portion of the vacuum line, and outgassed three times, thus ensuring that a l l non-condensable or low boiling gases were removed. 7» Photolysis of Diethyl Ketone Diethyl ketone was used as a primary standard to check the quantum yields obtained. A blackened bulb containing pure diethyl ketone was put on the vacuum line, outgassed as before, and by successive conden-sation on the side arm of the reaction vessel enough was transferred to the reaction vessel to give an absorption of about A0% of the incident light. Photolysis was done at 3130 1 and at 100°C, where the quantum yield of 17 carbon monoxide is known to be 1.0 . This temperature was obtained by substituting the water in the circulating system by linseed o i l , which was heated to the desired temper-ature by an electric coil inserted in the storage Dewar* FIGURE 3. Preparation of Ketene by Pyrolysis of Acetic Anhydride at 504°C Cr y -M A. r 1b slbrtigebulb JL a. acetic anhydride b. pyrolysis vessel c. aluminium furnace at 504- C d. dry ice trap e. liquid nitrogen trap for ketene 0\ 15 8. Gas Analyses After photolysis, the gases were analysed in an all-glass vacuum system evacuated by a standard o i l pump and a single stage mercury diffusion pump. The analyses of carbon monoxide were performed by allowing the gases from the reaction vessel to flow through traps cooled to -196°C and -211°C (liquid nitrogen and solid nitrogen respectively). The solid nitrogen trap was obtained by pumping on fresh liquid nitrogen for about twenty minutes. Ketene was condensed in the f i r s t trap and ethylene in the solid nitrogen trap. The carbon monoxide was not condensed at these temperatures and was measured by a McLeod-Toepler gauge similar to that used by Strachan and Noyes^". 9» Actinometry The intensity of the absorbed radiations at the various wave-lengths was determined by the use of the potassium ferrioxalate actinometer 18 as described by Hatchard and Parker . The optical densities of the exposed o solutions were carefully determined on a Unicam spectrometer at 5100 A using 1 cm cells and were corrected for the 'blank' of the unexposed solution. During exposure about 5 ml of the ferrioxalate solution were put in the actinometer cells, and with the beam cut off, the cells were placed in position and then exposed by use of the lever mentioned earlier. The actinometer cells were about 2»L cm in diameter and 1.5 cm in path length. They were blackened on a l l sides except the quartz window facing the incid-ent light. After exposure the solutions were removed from the cells, the cells washed out three times with water and the washings added to the solution. 16 o Because of the intensity of the radiation at 3130 A, exposure times were short and the exposed actinometer solution in the main beam •was- diluted to five times the volume of the other to obtain an optical density within an accurately determinable region on the spectrometer. At pressures of ketene greater than 10 cm, where absorption of the incident radiation was great, no dilution was made. o For runs at 3340 A, longer periods of exposure were made and dilutions were made as before. , o For runs at 3650 A, where exposure times were very long, i t was necessary to do two or three different actinometer exposures during one run and dilutions were made to f a l l within an accurate region on the spectrometer. Before each run was performed, the photolysis cell was thoroughly evacuated. The actinometer cells were then f i l l e d , placed in position, and after exposure, developed, and the optical densities determined. The results were expressed in a ratio of the form B _ O.D. (M)xF " O _ : O.D. (R) where O.D. (M) = optical density of solution in beam M (see Fig. l ) O.D. (R) = optical density of solution in beam R F = dilution factor. The cells were refilled with ferrioxalate solution and placed in position. Ketene was then introduced in the reaction vessel at the desired pressure, which was determined on a manometer, and photolysed. The optical densities of the actinometer solutions were again determined and expressed as a ratio 17 _ P.P. (M)xF * O.D. (R) The ratio of Ro/Rp was proportional to I 0 / l - t where I Q was the intensity of the incident beam in the reaction vessel and 1^. of the transmitted radiation. These ratios were plotted against the pressure in cm. and the data from the absorption coefficient curve obtained expressed in the form Log 1 0 I 0 / I t = where Z = slope P = pressure (in cm. of Hg) of ketene in the reaction vessel. From this the amount of light transmitted could be determined. IS The quantum yields of Hatchard and Parker were used to determine the absorbed intensities. Because of the large amount of reflection from the glass-air interfaces of the reaction vessel and the actinometer cells, i t was necessary to apply a correction factor to obtain the absolute intensity of the absorbed radiation. Using the refractive index of quartz, and considering only f i r s t order reflections, the correction factor had the form I a/3 = 1.112 x ( i - ^  ) (1 + 0.1006 ) where I = intensity absorbed by ketene in the reaction vessel E = optical density of actinometer solution in beam M "X = fraction of light transmitted. Whenever the RQ ratio varied too widely from a certain mean, indicating a build up of polymer formation, the cell was removed, it s transmission determined on the Carey Spectronmeter, cleaned with alcoholic 18 KOH, and its transmission redetermined. A correction factor was then applied to the results. 19 RESULTS Values were obtained for the molar extinction coefficient of ketene at the various wavelengths. These are shown in Table 1. The value o at 3650 A is much smaller than at the other wavelengths, and the maximum shows a shift towards shorter wavelengths as the temperature is decreased. For pressures below 10 cm the extinction coefficient curves were linear with pressure. Above 10 cm pressure however, especially for 3130 I there was a marked departure from linearity. Consequently, the quantum yields in the region above 10 cm are the average of the experimental and the calculated results from the curves. 3130 A From determinations at 0°C and pressures about 2 cm, a carbon monoxide quantum yield 1.78 was obtained. At pressures in the region of 20 cm the quantum yield decreased to 0.758. At 23°C the quantum yields were correspondingly higher and decreased from 1.87 at about 2 cm pressure to a value of 1.17 at about 20 cm pressure of ketene. The results are given in Tables 2 and 3« The time of each photolysis varied from 13 minutes at lower pressures to 18 minutes at higher pressures. With the cell empty the ratio of the beams stayed fairly constant for about four photolyses. With more than four runs, however, the ratio would decrease quite rapidly due to a build up of polymer formation. The cell would then be removed and cleaned with alcoholic potassium hydroxide. During each photolysis only a small fraction of the ketene was allowed to decompose (about 5-7 per cent) to ensure that the reaction of methylene radicals with ethylene would be small. The quanta absorbed varied 20 from 0.650 ;a-Einsteins at about 1 cm. pressure to 3.78 ju-Einsteins at 20 cm. pressure. 3340 A o The carbon monoxide quantum yields were determined at 23 C (Porter, G.B., personal communication), and at 0°C. The data are summarized in Tables 4 and 5» Exposure times were much longer than at 3130 2, varying from two to three hours. The quantum yields of carbon monoxide are lower o than at 3130 A and likewise decrease with pressure, varying from 1.25 at low pressures to O.48 at high pressures at 23°G. The quantum yields at 0°C were lower than at 23°C. o 3650 A (Porter, G.B., personal communication) Because of the very small amounts of decomposition products 11 obtained at this wavelength by previous workers , i t was decided to photo-lyze for periods of from four to six hours to give accurately measurable quantities within the limit of experimental determination. Because of the long exposure times, i t was necessary to use three or four different actin-ometer solutions during each run. The quantum yields are given in Table 6. As can be seen, they are very much lower than at 3130 I and 3340 A* decreasing from a value of 0.0334 at 2 cm. pressure to 0.00516 at 24 cm. pressure. The intensities absorbed were correspondingly 2.91 ^ i-Einsteins and 14.85 ,u-Einsteins. 21 TABLE 1 MOLAR EXTINCTION COEFFICIENTS FOR VARIOUS WAVELENGTHS a) Reaction Vessel Temperature: 23«0°C Wavelength Extinction Coefficient 3130 A 81 3340 1 111 3650 A 31 b) Cell Temperature: 0°C Wavelength Extinction Coefficient o 3130 A 82 3340 A 103 22 TABLE 2 PHOTOLYSIS OF KETENE AT 3130 A Reaction Vessel Temperature 23«0°C Run Pressure of Intensity absorbed . , A Ketene in mm. Einstein x 106 <P = 1 ' 2 { j -14 22.0 0.744 0.935 - 0.005 15 53.8 1.803 0.836 - 0.004 16 96.8 2.598 0.752 ± 0.004 17 152.3 2.786 0.631 - 0,030 18 198.0 3.080 0.586 - 0.003 19 10.2 0.554 0.956 t 0.005 20 35*2 1.492 0.863 - 0.024 21 130.2 2.322 0.687 - P.004 22 164.3 3.424 0.635 - 0.003 23 TABLE 3 PHOTOLYSIS OF KETENE AT 3130 A Reaction Vessel Temperature 0.0°C Pressure of Intensity absorbed Ketene in mm. Einstein x 10" C)> =1/2 CO 11.2 0.650 0.941 - 0.054 20.3 0.968 0.863 - 0.005 29*4 1»262 0.836 - 0.016 42.2 1.678 0.771 - 0.011 47.0 2.021 0.776 t 0.014 96.1 3.495 0.666 * 0.018 150.0 2.363 0.570 1 0.048 199.0 3.291 0.430 - 0.008 23.1 ' 0.888 0.893 = 0.024 39.0 1.480 0.798 t 0.006 247.4 6.381 0.334 i 0.009 (continued on next page) 24 TABLE 3 (continued) Run Pressure of Intensity absorbed (4> _ - j / 2 (L)q< Ketene in mm. Einstein x 10° i ' I 48 11.2 0.407 0.841 - 0.048 49 22.6 0.854 0.798 1 0.040 50 33.0 1.222 0.763 t 0.042 51A 43.0 1.516 0.772 - 0.008 51 52.7 1.879 0.725 i 0'028 52 99.7 3.203 0.578 i 0.028 53 151.8 2.807 0.499 - 0.003 $4 199.8 3.788 0.379 - 0.012 25 TABLE 4 PHOTOLYSIS OF KETENE AT 3340 I Reaction Vessel Temperature 23«0°C Intensity absorbed L fh Einstein x 106 <P = l/2 Run Pressure of Ketene in mm. Einstein x 10° 0^  = 1/2 H^ CO 9P 40.1 1.834 0.556c - 0.010 10P 140.1 3.128 0.32?5 - 0.021 IIP 278.8 4.025 0.241 - 0.005 12P 21.7 1.131 0.626 - 0.012 13P 186.9 3.998 0.2955 - 0.006 26 TABLE 5 PHOTOLYSIS OF KETENE AT 3340 1 Reaction Vessel Temperature 0.0°C Run Pressure 0 f Intensity absorbed J* Wo(7)n, Ketene in mm* Einstein x 10 b Y " ^  * Y c ' 40 17.2 1.032 0.668 - 0.003 41 12.8 0.734 0.6997 - 0.004 42 24.2 1.462 0.611 - 0.006 43 34*2 1.551 O.565 - 0.003 44 44.8 1.613 0.527 - 0.003 45 87.0 2.087 0.4445 * 0.017 47 196.0 3.907 0.249 - 0.002 27 TABLE 6 PHOTOLYSIS OF KETENE AT 3650 A Reaction Vessel Temperature 23«0°C Run Pressure of Ketene in mm. Intensity absorbed A _ ./,([) Einstein x 106 T V 2 ^ C 0 x 10 2 IP 68.4 6.52 0.975 - 0.099 2P 244.0 14.85 0.288c - 0.003 3P 162.4 10.02 0.410^ ~ 0.008 4P 148.0 7«22 O.46O i 0.009 5P 28.3 2.91 1.670 - 0.032 6P 39.4 8.92 1.230 - 0.072 7P 68.4 4.88 0.942 5 - 0.063 o o TABLE 7 RATE CONSTANTS FOR KETENE -1 k l n <sec~ ) moles l i t e r 3130 A 23 1.524 x 10"2 2.523 x 109 1.189 x 10~2 1.885 x 109 3340 A 23 5.373 x 10°3 8.893 x 108 0 4.175 x 10"3 6.618 x 108 3650 A 23 4.029 x 10°5 6.750 x 106 TABLE 8 CALCULATED VALUES OF V, £ AND Degrees of £ g Freedom s c m - l _^  cm 3,980 22,990 4,860 21,260 4,746 21,980 Predicted values of Porter and Connelly 9 2,360 24,000 30 DISCUSSION 1. Theory The reactions of excited molecules e.g. ketene, can be repre-sented by the modified Jablonski diagram below. o »-O Ui -©-This illustrates the relative energies of the ground electronic state (K), the f i r s t excited singlet state ( Kn) and the f i r s t triplet state ( K n indicating the vibrational energy level. The reactions can be shown as: 31 K + .hy ^ rate « I & (0) 1 u l K n ^ products rate = k l n( K ) (l) hn + K > + K rate = k^cV^K) (2) 1K n > K rate = k 3 n( 1K n) (3) V » K rate = k ^ V ) U ) V > &° r a t e = k / l f t (5) 3K° » K rate = k6(3K°) (6) 3K° > products rate = k^K 0) (7) Reaction (0) depicts absorption and consequent excitation by the incident radiation up to the vibronic state n. In reaction (l) the excited molecule (e.g. ketene) decomposes into products (carbon monoxide and methylene radical^ Reaction (2) is a collisional degradation step in which the molecule i s degraded in energy to vibronic state 0 and is in vibronic equilibrium, but not electronic, with the surrounding gas. In some primary quantum yields, extrapolation to zero pressures are less than unity, and hence reaction (3), in which some of the excited molecules in vibronic state n revert to the ground state (an internal conversion process), is included. Reaction (4.), a radiation process e.g. fluorescence, is similar to reaction (3) with reversion from vibronic, but not electronic equilibrium state 0 to the ground state. Reaction (5) is an inter system crossing from the singlet to the triplet state. It might not be a simple process as shown, but could be a 32 sequence V + K the second reaction being very much faster than the f i r s t . Reaction ( 6 ) accounts for phosphorescence, but internal conversion is also included. Except at very low pressures fluorescence and phosphorescence spectra are known to be independent of the exciting wavelength in the vapor phase, and hence are shown as originating from low vibrational levels of the corresponding excited electronic states. Increase in primary quantum yields with temperature increase has also been observed and reaction (7), a dissociation from the triplet state, accounts for this. Dissociation from the ^"K^  is excluded as this state (from fluor-escence data) has been shown to have a very short lifetime, and so would not exist long enough to be energised by collision and then dissociate. Conversely, however, since phosphorescence is a forbidden transition, the o 0 triplet state "iv has a long enough lifetime to achieve vibrational equili-brium and dissociate thermally. If the assumption be made that in a collisional degradation reaction in which a l l of the effective vibrational energy i s removed in one collision i.e. the only vibronic states that dissociate are those reached by an absorption of radiation, a quantum yield relationship may be derived in the following manner. Rate of product formation = k l n( 1K n) + k^K 0) (l) 33 Rate of formation of l R n " J a " W 1 ^ ) - k 2 n ( l K D ) ( K ) " k 3 n ^ K ^ ^ Apply steady state conditions, the right hand side of equation (2) i s equal to zero. Hence ( 1 k 1 1 ) s s = "kin + kJ K ) - k 3 n ( 3 ) Rate of formation of V . k5(V> - Hih°) - *7<V> u> At steady state conditions (3K°) -k6 + k? Rate of formation of At steady state conditions (5) 1 K ° = k^cV1) (K) - k4(V) - ^ (V) (6) (V) , . - J * L _ (V)(K) (7) k4 + k 5 J?-Substituting equation (7) in (5), we have < 3 K ° ) S S • r-^ir ' "T~TT" tow (8) S S k4 + k5 k6 + 7^ Substitution of equations (3) and (8) in equation (l) gives 34 Rate of product formation = kln \ + k ? e k5 ^ k2n V K > . k ^ l o + V,. k. + k k,_ + k/,_(K) + ko_ Rate of product formation = <n k l n + k 7 ^ K 5 ^ k^K) k l n + k2n<K> + k3n k 6 + *7 ' k 4 + k 5 k l n + k2n<K> + k3n (10) <f>=[kln + ^ ^ W j / f c + k 2 n ( K ) + k3n] <u> where a = k 5 and b = k 7 k^ + k 5 k 6 + ^ a is then seen to be the fraction of "*"K^  molecules which cross to the trip-3 0 let state and b the fraction of K molecules which dissociate. 20 If the simplifying assumption of Ayscough and Steacie be made that k^n is zero, from equation 11 we get ( j > - + a b k f | K ) ( 1 2 ) k l n + k^CK) - (J) k l n + k 2 n(K) - k x - abkgjK)  k l n + k2nW k2n(K) (1 - ab)  k l n + k2n<K> (13) From equations 12 and 13 35 = kln + abk^CK) k l n + k^K) \~(p k l n + k2nCK) W K ) (1 - ab) JL - — = L + J*2 ( U) |_<£ 1 " ab (1 - ab) k^CK) Hence from equation 14- a plot of A V S t h e r e e i p r o c a l o f t h e pressure (or concentration) should give a straight line from which ab and k2 n can be evaluated. k2n Another approximation by Strachan and Noyes"'""'' neglects reaction 7, triplet dissociation. Hence we have from equation 10 k l n + k2n( K) + k 3n and hence — T — - 1 + j p 5 + |2n ( K ) ( 1 6 ) m K l n *ln 1 ko A plot of —— vs (K) should then be linear and give values for _JS and <f> k l n k2n kln Deactivation by:aPaLy-collisional Process. If the deactivation process involves more than a single collision, the following mechanism may be postulated K + h V > 1K n rate = I a l K n > products rate = kn^K11) 36 V + K l K n - l l K m + 1 + K l Km 1 n-1 -» K + products 1 m •» K + K rate • Z^K11) (K) rate = k ^ V " 1 ) rate = ZC 1^ 1) (K) -> deactivation The indexes m and n are measures of the vibrational energy of the excited singlet state, m + 1 being the lowest state from which dissociation w i l l take place. For simplicity i f reaction 3 is omitted and steady state treatment be applied, the concentrations of the various states are = n (17) ss = (K) 1 + &± ( 3 where a^ = k^  and then 4>j = kjM = i = n i = 3 1 + ^ (18) The sum of contributions from each vibronic state would then be the primary quantum yield of dissociation (with dissociation from only the singlet state). j = n n &* ~1 I i (19) j = m + 1 00 1 + a± (T) 37 Since the total quantum yield cannot exceed unity, equation (19) can then be written 4> = 1 m + 1 1 + r% (20) where m + 1 1 + 5i 00 is the quantum yield from the m + 1 vibronic state. If thermal dissociation from the triplet state is now included, the total quantum yield for dissociation is now given by = 1 (1 - ab) n m + 1 1 + a± (Kl (21) where a and b are the quantities defined in equation ( l l ) . In order to evaluate equations (20) and (21) the unimolecular 21-23 theory of dissociation is assumed to apply to photochemical processes, since experimental data have indicated that the rate of dissociation of excited vibronic states i s a function of their energy content. The rate constant for dissociation from each vibronic state is then expressed as M i - 17) _£m s-1 1* (22) where )J , evaluated from its value kT in Eyring's theory, or the h weighted root-mean-square of the normal mode frequencies of vibration in Slater's theory, has the approximate value of 10"*"3 sec""'". and 8 are the vibrational energies corresponding to states of index m and i respectively. 38 s i s the nondegenerate modes of vibration in the molecule and i s the specific rate constant of vibrational state i of energy Z±- From this the quantity a± can be calculated. In order to simplify the calculations, i t is assumed that each collision results in the loss of a constant amount of vibrational energy, hence, that the vibrational energy is proportional to the indexes n, m etc. In ketene the maximum degrees of freedom is 9 and hence s = 9« Assuming V= 10^ sec ^  and Z= lO"^ mole ^  l i t e r sec""1", V_ is equal to 100 mole l i t e r . Values of k^  can then be calculated. T When values of (j) are calculated from equation (20), i t is found that with excitation energies only slightly greater than the minimum energy required for dissociation, the reciprocal of the primary quantum yield i s linear with pressure. For higher energies e.g. n^ LU and m = 30 the curves were linear only at very high pressures. At low pressures they were concave upwards and had a zero slope at zero pressure. If the relative number of collisions i s varied i.e. i f calcu-lations are made with different values of m, the results are as shown in Figure 4.. It can be seen that an increase in the number of collisions requir-ed for degradation, i.e. a decrease in the vibrational energy removed in each collision, greatly increases the primary quantum yield. There is a marked departure from linearity of the reciprocal quantum yield vs. pressure, and also a higher extrapolated quantum yield at zero pressure. Variation of the degrees of freedom s causes the primary quantum yield to change as illustrated in Figure 5, the slope increasing with an increase of s« FIGURE Ao Calculated quantum yield, s = 9, n/m = 1.5, m = 2, 5, 10, and 15. 38b FIGURE 5= Calculated quantum yield, n = 41, m = 30, s = 7, 9, and 11» (M) x 10 moles/liter 39 If calculations are made using equation (21), i.e. i f thermal dissociation from the triplet state is included, the results are as i l l u -strated in Figure 6. A radical change is observed in the curves. They are concave downward, becoming "S" shaped with larger values of ab, an effect which appears even at low pressures. 2. Experimental Data The calculations from the above theories can now be compared with the experimental data. o o At a wavelength of 3130 A and T = 23 C, the variation of quantum yield with pressure is shown in Figure 7. The curve is seen to be linear over the range of pressures used and extrapolation to zero pressure yields an intercept of 1.00 within the experimental error. This data can then be assumed to f i t the equation 1/4) = 1 + J^n. ( K ) ( 2 3 ) ^ k l n and the kinetics then be represented by equations ( 0 ) , ( l ) y (2) . It is likely then within experimental error, that at 3130 £ internal conversion and collisional deactivation of the excited molecule are, i f any, very small contributing factors. o o o For 334-0 A and 3650 A at 23 C results from the data In Tables L o and 6 are shown in Figures 8 and 9« From Figure 8 i t is seen that at 3340 A o , o the intercept is I.4.5 and the slope is greater than at 3130 A. At 3650 A the intercept is 19.70 and the slope is about thirteen times as much as at 3340 A. (M) x 10 moles/liter 0 5 1 0 1 5 2 0 2 5 Pressure in cm. Hg. 0 5 10 15 20 25 30 Pressure in cm. Hg-40 o o The data at 3340 A and 3650 A can then be assumed to be repre-sented by the equation - i • r 2 + P* « y In K l n which is equation (16) and hence the kinetics could be approximately represented by reactions (0), ( l ) , (2), (3). The increase of intercepts and slopes of the curves with increase of wavelength indicates that at longer wavelengths, internal conversion and collisional deactivation of the excited molecules are of increasing impor-tance. Apparently at the longer wavelengths the lifetime of the excited state is longer than at shorter wavelengths, so that deactivation rather than dissociation can take place. From the quantum yields at the various wavelengths, i t can be seen that there i s a marked decrease with increasing wavelength. Examination of Figures 7, 8, and 9 which give plots of the inverse quantum yields vs. pressure at 23°C and Figures 10 and 11 which are for 0°C, also shows a decided variation in the slopes of the curves. For 3130 A at 23°C the slope i s 0.656 x 10 2 l i t e r moles"1. At o ? -1 0 C i t has increased to 0.841 x 10* l i t e r moles «. For 3340 t at 23°C the slope is 1.861 x 10 2 l i t e r moles"1 and 2.395 x 10 2 at 0°C. For 3650 I at 23°C i t i s 2.482 x 1 0 ^ l i t e r moles"1. From this i t can be seen that the effect of temperature variation follows the opposite pattern of the effect of varying the wavelength. Thus low temperature effects can be compared with the effects of longer wave-lengths, while high temperature effects on the quantum yields are similar to the effects of shorter wavelengths. The quantum yields are lowered as FIGURE 10. Dependence of Primary Quantum Yield on Pressure at 3130 1 and 0°C. 41 the wavelength is increased or as the temperature is decreased, and are greater with shorter wavelengths or higher temperature. This relationship can be interpreted by reference to Figure 12 where the various energies are qualitatively related. Curves I and II represent the distribution of the energies of the molecules at temperatures T^  and T2, T 2 being greater than Tj. Curves I and II represent the distribution of energy after absorption of the exciting radiation by the molecules. From curves I and II i t can be seen that the average energy of the molecules E 2 a V g o at temperature T 2 i s greater than the average energy % avg. a* temperature T-j_« Examination of the excited curves I and II shows the average energy E 2 a V g # at T 2 greater than E-^ a V g e at T-^. This means that £ 2 (see Figure 12), which represents the average energy of the excited state above t h e f o - o energy at T 2 is greater than £ p t n e average energy above £Q=0 energy at Tj. Both £-j. anf* ^ 2 c o r respond t o <^ i i n t n e Kassel unimolecular theory of dissociation as given by equation (22). The greater the value of £^ the greater w i l l be k i s the rate of dissociation. Consequently, because of the difference in ^  and £ 2 ( £ 2^ £]_) "the quantum yield from the higher temperature T 2 w i l l be greater (indicated by a smaller slope of l/ (j) vs. pressure), than at T^ « If the temperatures Tj and T 2 are decreased, both the excited curves I and II wi l l be compressed towards the left, thus decreasing £ ^  and £ 2, and a smaller quantum yield is to be expected since k^ from ki = y d - 4s-)8"1 C i \ 42 w i l l be smaller, i.e. less dissociation occurs. The effect of wavelength i s similarly related. Since the 6 0-0 e n e r g y Is independent of wavelength the values of f a n d ^ depend on hy , the energy of the exciting radiation. Consequently, with longer wavelengths, i.e. excitation with lower energy radiation, the values of £ and £ 2 w i l l be smaller (the excited curves I and II w i l l shift towards the l e f t ) , than with shorter or more energetic wavelengths (the excited curves I and II , then shifting towards the right, thus increasing C ^  and 6 2)• Hence, there w i l l be a decrease in the rate of dissociation k^  from the above relationship, and smaller quantum yields at longer wavelengths are to be expected. Examination of a l l the plots of l/ (p vs. pressure, shows the curves to be a l l linear within the limit of experimental error. Consequently, the kinetics of equation (21) do not seem to be applicable. The curves do not show the "SM shape as predicted from triplet dissociation contribution to the quantum yields* Hence i t can be concluded that dissoc-iation from the triplet state does not play a significant part in the photo-dissociation process. From Figure 4 which is predicted by equation (20) involving a cascade collisional degradation process i t can be seen that for m - 2 or less the curves of l/ (j) vs. pressure are linear while at m = 5 or more, there is a decided departure from linearity. The concavity effect between m = 2 to 4, i s small. Consequently within the experimental limits, i t i s not possible to distinguish between the kinetics of a 1, 2 or 3 collisional degradation process. However, i t can be qualitatively stated that there are not more than about 3 collisions involved in the deactivation process. In Table 7 are the inverse slopes ( = kln) obtained from the k 2 n curves l/(t) vs. pressure at the different wavelengths and temperatures. 43 o If A A is chosen as the collision diameter of ketene and k^ = Z the values of k l n in column A of Table 7 are found. The value of Z obtained from Z - <S 2 ^STTkT ^ ^ where (J = collision diameter MW U^ = reduced mass of ketene = — was 1.655 x 1 0 1 1 l i t e r mole"1 sec" 1 at 23°C and was 1.585 x 1 0 1 1 l i t e r mole"*1 sec ^  at 0°C. These values can now be applied to the unimolecular theory of dissociation given by equation (22). Calculations of the quantities \j , and £n-0 give the values shown in Table 8 for various degrees of freedom s (maximum value = 9 ) . These show very good agreement with the theoretical values of 19 c Porter and Connelly . The total energy, electronic and vibrational ( c 0 - o + EJJP which is virtually independent of parameters in the theory i s 25970 cm"1 (s = 9 ) , 26120 cm"1 (s = 7) and 26726 cm"1 (s = 5)* which corre= spond to 74.2 k cals/mole, 74*6 k cals/mole and 76.3 k cals/mole respect-ively, in good agreement with the value of 76.3 k cals/mole obtained by 19 Porter and Connelly . As the carbon-carbon bond energy in ketene i s about 55 k cals/ mole, the photodissociation must lead to excited products. Since the vibrational frequencies of ketene are known, i t is possible to calculate the heat capacity, C v i b < > The value is 210 cm™1 for 27° to 154°C or 4°72 cals. deg."1 mole"1. From the photochemical data the effective heat capacity, C Q ; f f e can also be calculated. The values obtained are 74..3 cals. deg. mole"-1 with 3130 A and 42.9 cals. deg. mole with 3340 A. It is seen that the C e f f o is very much greater than C y i b e obtained from thermochemical calculations* This restilt is not unexpected. The thermochemical calculations concern average energies of molecules, but the photochemical data are based on energies weighted with respect to dissociation. Hence for the latter, the molecules having high energies are more important than those with aver-age energies. This is analogous to a thermal dissociation in which the rate constant is an exponential function of temperature, while the average energy is approximately a linear function of temperature. 45 BIBLIOGRAPHY 1. Norrish, R.G.W., Crone, H.G. and Saltmarsh, O.D., J o Chem. Soc. 1533 (1933). 2. Ross, W.F. and Kistiakowsky, G.B., J. Am. Chem. Soc. J56, 1112 (1934.). 3. Pearson, T.G., Purcell, H. and Saigh, G.S., J. Chem. Soc. 409 (1938). 4. Rosenblum, C , J . Am. Chem. Soc. 6^ ,3322 (1941). 5. Burton, M., Davis, T.W., Gordon, A. and Taylor, H.A., J. Am. Chem. Soc. 63, 1956 (1941). 6. Rice, F.O. and Glasebrook, A.L., J. Am. Chem. Soc. j>6, 2381 (1934). 7. Kistiakowsky, G.B. and Rosenberg, N.W., J. Am. Chem. Soc. 72, 321 (1950). 8. Vanpee, M. and Grard, F., Ann. Min. Belg. 42, 701 (1950). 9. Vanpee, M. and Grard, F., Bull. Soc. Chim. Belg. 60, 208 (1951). 10. Kistiakowsky, G.B. and Marshall, W.L., J . Am. Chem. Soc. 7Jt» 88 (1952). 11. Strachan, A.N. and Noyes, W.A., J. Am. Chem. Soc. 76, 3258 (1954). 12. Noyes, W.A., Porter, G.B. and Jolley, E . J . , Chem. Revs. j>6, 49 (1956). 13. Porter, G.B., J. Am. Chem. Soc. 72, 827 (1957). 14. Connelly, B.T. and Porter, G.B., Can. J. Chem. J36, I64O (1958)% 15. Kistiakowsky, G.B. and Mahan, B.H., J. Am. Chem. Soc. 72, 2412 (1957). 16. Fisher, G.J., MacLean, A.F. and Snizer, &.W., J. Org. Chem. 18, 1055, (1953). 17. Davis, W., J. Am. Chem. Soc. 70, 1868 (1948). 18. Eatchard, C.G. and Parker, C.A., Proc Roy. Soc. (London) A235_, 518 (1956). 19. Porter, G.B. and Connelly, B.T., J. Chem. Phys. 22> 8* (i960). 20. Ayscough, P.B. and Steacie, E.W.R., Proc. Roy. Soc. (London) A234« 476 (1956). 21. Kassel, L.J., Kinetics of Homogeneous Gas Reactions. (Chemical Catalog Company, New York, 1932). AS BIBLIOGRAPHY (continued) 22. Glasstone, S., Laidler, K.J. and Eyring, H., The Theory of Rate Processes. (McGraw-Hill Book Company, Inc., New York, 1941)* 23» Slater, N.B., Proc. Roy. Soc. (London) A194. 112 (1948). 

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