Transition State Enthalpy and Entropy Effects on Reactivity. and Selectivity in Hydrogenolysis of n-alkanes

Transcription

1 Transition State Enthalpy and Entropy Effects on Reactivity and Selectivity in Hydrogenolysis of n-alkanes David W. Flaherty, Enrique Iglesia * Department of Chemical Engineering, University of California at Berkeley, Berkeley, CA 9470, United States Target Journal: Journal of the American Chemical Society Supporting Information. * Corresponding author, Fax: address: iglesia@berkeley.edu S1

2 Scheme 1 leads to hydrogenolysis rates proportional to the concentration of the reactive unsaturated intermediate ([*C n H n+-y *]): r k C H * (S1) R * n n y In which k R is the C-C bond cleavage rate constant. The pseudo steady-state hypothesis (PSSH) for [*C n H n+-y *] species leads to the rate equation: y [*] r krkd, y KA, y PRH PH [ L] (S) in terms of H and alkane pressures (P H, P RH ). This equation contains the equilibrium constants for alkane dehydrogenation and for adsorption (K D,y, K A,y ) of species with y H- atoms removed from the alkane. Here, [*] denotes the number of unoccupied sites and [L] the total number of active surface sites equal to the number of Ir s atoms. Equation S depends on [*] because α,β-coordinated reactive species occupy two vicinal sites 1 and the C-C cleavage fragments each require a separate site for stable binding.,3 A site balance then leads to: 1 n z [*] [ L] [*] KH P [*] H KD, zka, z PRH PH [ L] z1 (S3) S

3 The summation accounts for all co-adsorbed equilibrated intermediates, each with z H-atoms removed from the reactant alkane. The number of sites occupied by H* is 1 H given by the P [*] K term in Equation 4. Substituting [*] from Equation S3 into H Equation S leads to the full expression for the hydrogenolysis turnover rate equation that has a complex form given as: y Dy, Ay, RH H z 1 (S4) z1 r K K P P kr [ L] n 1 PRH [*] KD, z KA, z PH KH PH Although the form is complete and accurate, the complex nature of the denominator when surface species of all categories (unoccupied site, hydrocarbons, and hydrogen) are present precludes the interpretation of kinetic measurements in chemical terms that can be related to thermodynamic properties of the catalyst or reactants. Moreover, unbounded analytical solutions of Equation S4 can lead to non-physical (imaginary) coverages of hydrocarbons, hydrogen, and empty sites, because these different surface intermediates occupy different ensembles of sites (e.g., *C n H n+-z * and H*). 4 S3

4 Table S1. Activation enthalpies [kj mol -1 ] and entropies [J mol -1 K -1 ], and λ values for ethane and n- hexane hydrogenolysis on Ir, Rh, and Pt clusters at 593 K. A Measured value from Eyring-Polanyi plot. B Calculated entropies of gas-phase species from published partition functions. 5 C Changes in S H reflect differences between H pressures used for each n-alkane. D Determined using Equation 15 with S A,H equal to 7 J mol -1 K -1. Catalyst Alkane H A S A λ S H B,C S RH B Experimental S D 1.3 nm Ir Ethane nm Ir n-hexane nm Ir Ethane nm Ir n-hexane nm Rh Ethane nm Rh n-hexane nm Pt Ethane nm Pt n-hexane S4

5 Figure S1. Representative image and cluster size distribution of 1.3 nm Ir-SiO as obtained by transmission electron microscopy, 1,048 clusters were counted to determine <d TEM >, the surface- averaged diameter. S5

6 Figure S. Representative image and cluster size distribution of.7 nm Ir-SiO as obtained by transmission electron microscopy, 1,75 clusters were counted to determine <d TEM >, the surface- averaged diameter. S6

7 Figure S3. Representative image and cluster size distribution of 0.9 nm Rh-SiO as obtained by transmission electron microscopy, 1,04 clusters were counted to determine <d TEM >, the surface- averaged diameter. S7

8 Figure S4. Representative image and cluster size distribution of 0.6 nm Pt-SiO as obtained by transmission electron microscopy, 1,055 clusters were counted to determine <d TEM >, the surface- averaged diameter. S8

9 Figure S5. Moment of inertia for calculated for the one-dimensiothe alkyl chain is determined using equilibrium gas- phase alkane geometries where C-H and C-C bond lengths are nm and nm, respectively, and H-C-H and C-C-C bond angles are 109.5º. 6,7 The alkyl chains are assumed to exist as all-trans conformers. rigid rotation of alkyl chains about the surface normal. The structure of 8,9 S9

10 Citations (1) Bond, G. C. Metal-Catalysed Reactions of Hydrocarbons; Springer: New York, 005. () Chen, Z.-X.; Aleksandrov, H. A.; Basaran, D.; Rosch, N. J. Phys. Chem. C 010, 114, (3) Flaherty, D. W.; Hibbitts, D.; Gürbüz, E. I.; Iglesia, E. in preparation. (4) Clark, A. The Theory of Adsorption and Catalysis; Academic Press: New York, USA, (5) McQuarrie, D. A. Statistical Mechanics; University Science Books: Sausalito, CA, 000. (6) CRC Handbook of Chemistry and Physics; CRC: Boca Raton, FL, 011; Vol. 9. (7) Tait, S. L.; Dohnalek, Z.; Campbell, C. T.; Kay, B. D. J. Chem. Phys. 005, 1, (8) Ilharco, L. M.; Garcia, A. R.; Lopes da Silva, J. Surf. Sci. 1997, 371, 89. (9) Yang, M.; Somorjai, G. A. J. Am. Chem. Soc. 004, 16, S10