SF Chemical Kinetics.

Transcription

1 tins de Paula P Chem, 9 th Edition, Chater 3,Catalysis, SF Chemical inetics. Lecture 3-4 Catalysis: Heterogeneous Catalysis & iocatalysis. Lecture review. In this lecture we focus attention on the catalysis of chemical reactions. We consider: Heterogeneous catalysis on solid surfaces Enzymatic bio-catalysis. Michaelis-Menten single enzyme/substrate inetics. Common concet: dduct formation / inding Interaction between catalyst and reactant.

2 Catalysis. Catalysis involves the enhancement of the rate of a reaction by a substance, which is not consumed in the reaction. It turns out that the vast majority of all industrial chemical reactions involve surfaces as the catalysts. The ind of rocesses involved range from hydrogenation of hydrocarbons to detoxification of exhaust gases. The catalytic converter in an automobile is a classic examle. The image resented across illustrates the general rinciles: a articular metal surface (in this case, a Pt-Rh alloy) is nown to catalyze the desired reaction. In order to maximize the surface area of the metal er weight, small articles are used. You can almost count the atoms in the article shown, which was from a real catalyst and was studied by Scanning Electron Microscoy. The article shown has atoms, based on a rough estimate from the number of atoms at its circumference. Oxide substrates are also a general characteristic of such catalysts. htt://

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5 Catalysis: general comments. Catalysts come in a variety of forms varying from atoms and molecules to large structures such as enzymes and zeolites. The catalyst offers an alternative low energy athway for the reaction, which is erhas more comlex, but energetically more favourable. The activation energy for the catalytic reaction is significantly smaller than that of the uncatalyzed reaction. Hence the rate of the catalyzed reaction is much larger. Sabatier Princile: The successful combination of catalyst and reaction is that in which the interaction between catalyst and reacting secies is not too wea but also not too strong. The overall change in free energy G 0 for the catalytic reaction equals that of the uncatalyzed reaction. Hence the catalyst does not effect the equilibrium constant (recall that G 0 -RT ln ) for the reaction + P. Thus if a reaction is thermodynamically unfavourable, a catalyst cannot change the situation. catalyst changes the inetics but not the thermodynamics of a reaction. The catalyst accelerates both the forward and the reverse reaction to the same extent. If a catalyst accelerates formation of roduct P from reactants and, it will do the same for the decomosition of P into and. Catalysis. catalyst accelerates the rate of a reaction without itself being consumed in the rocess. The catalyst achieves its function by forming bonds with the reacting molecules and allowing these to react to form a roduct, which detaches from the catalyst, and leaves it unaltered such that it is available for the next reaction. Hence the elementary stes involved in a catalytic rocess involve: Chemical bonding Chemical reaction Searation Catalysis is subdivided into 3 subareas: Homogeneous catalysis iocatalysis Heterogeneous catalysis. searation catalyst bonding catalyst P P catalyst reaction 5

6 energy Non-catalytic athway G NC P + ctivation barrier G C Potential energy Diagram for Heterogeneously Catalyzed reaction. Catalytic athway catalyst catalyst P catalyst P catalyst bonding reaction searation Reaction co-ordinate 6

7 Surface reactions. Diffusion of reactants to the active surface. dsortion of one or more reactants onto the surface. Surface reaction. Desortion of roducts from the surface. Diffusion of roducts away from the surface. Catalysis at solid surfaces gas hase athway E G energy E gas hase reactants E D surface catalysed athway adsorbed reactants E S adsorbed roducts gas hase roducts E j activation energy for ste j. Reaction intermediates stabilized via bonding to catalytic surface sites. G : gas hase reaction : adsortion S : surface reaction D : desortion 7

8 The Metal-Catalyzed Hydrogenation of Ethylene H C CH (g) + H (g) H 3 C CH 3 (g) C H 4 ads H ads reaction between adsorbed secies surface migration H ads dissociative adsortion H C CH 3ads H ads 8

9 How do molecules bond to surfaces? Two rincial modes of adsortion of molecules to surfaces. Physical dsortion : the only bonding is by wea Van der Waals - tye forces. There is no significant redistribution of electron density in either the molecule or at the substrate surface. Chemisortion : a chemical bond, involving substantial rearrangement of electron density, is formed between the adsorbate and substrate. The nature of this bond may lie anywhere between the extremes of virtually comlete ionic or comlete covalent character. 9

10 Potential energy versus distance curves for hysisortion and chemisortion. The wea hysical adsortion forces and associated long-range attraction will be resent to varying degrees in all adsorbate / substrate systems. However, in cases where chemical bond formation between the adsorbate and substrate can also occur, the PE curve is dominated by a much deeer chemisortion minimum at shorter values of d. Combine hysisortion and chemisortion curves. The deth of the chemisortion well is a measure of the strength of binding to the surface - in fact it is a direct reresentation of the energy of adsortion, whilst the location of the global minimum on the horizontal axis corresonds to the equilibrium bond distance (r e ) for the adsorbed molecule on this surface. The energy of adsortion is negative, and since it corresonds to the energy change uon adsortion it is better reresented as E(ads). However, you will also often find the deth of this well associated with the enthaly of adsortion, H(ads). Terminology. Substrate - frequently used to describe the solid surface onto which adsortion can occur; the substrate is also occasionally (although not here) referred to as the adsorbent. dsorbate - the general term for the atomic or molecular secies which are adsorbed (or are caable of being adsorbed) onto the substrate. dsortion - the rocess in which a molecule becomes adsorbed onto a surface of another hase (note - to be distinguished from absortion which is used when describing utae into the bul of a solid or liquid hase) Coverage - a measure of the extent of adsortion of a secies onto a surface (unfortunately this is defined in more than one way! ). Usually denoted by the lower case Gree "theta", q Exosure - a measure of the amount of gas which as surface has seen; more secifically, it is the roduct of the ressure and time of exosure (normal unit is the Langmuir, where L 0-6 Torr s ). 0

11 Tyical Characteristics of dsortion Processes Chemisortion Physisortion Temerature Range (over which adsortion occurs) dsortion Enthaly Crystallograhic Secificity (variation between different surface lanes of the same crystal) Nature of dsortion Virtually unlimited (but a given molecule may effectively adsorb only over a small range) Wide range (related to the chemical bond strength) - tyically J mol - Mared variation between crystal lanes Often dissociative May be irreversible Near or below the condensation oint of the gas (e.g. Xe < 00, CO < 00 ) Related to factors lie molecular mass and olarity but tyically 5-40 J mol - (i.e. ~ heat of liquefaction) Virtually indeendent of surface atomic geometry Non-dissociative Reversible Saturation Utae Limited to one monolayer Multilayer utae ossible inetics of dsortion Very variable - often an activated rocess Fast - since it is a non-activated rocess Irving Langmuir (88-957) Emloyed at General Electric (industrial research). Examined oxygen adsortion on tungsten filaments of light bulbs. 93: Nobel Prize in Chemistry. g surface dynamic equilibrium ads 95. Langmuir adsortion Isotherm. +

12 dsortion at gas/solid interface. dsortion. Term used to describe the rocess whereby a molecule (the adsorbate) forms a bond to a solid surface (an adsorbent). Fractional surface coverage N S N Langmuir dsortion Isotherm. number of sites occuied by adsorbate When, N S N and an total number of adsortion sites adsorbed monolayer is formed. The fractional coverage deends (g) on ressure of adsorbing gas hase secies. This () relationshi is called an adsortion dynamic isotherm. equilibrium surface ads Simle aroach to quantitatively describe an adsortion rocess at the gas/solid interface. N N S + N V ssumtions : solid surface is homogeneous and contains a number of equivalent sites, each of which is occuied by a single adsorbate molecule a dynamic equilibrium exists between gas hase reactant and adsorbed secies no interactions between adsorbed secies adsorbed secies localised, H ads is indeendent of coverage Number of Vacant sites

13 associative adsortion (g) + S (g) + S D D ads ads surface adsortion site dissociative adsortion Rate of adsortion : R ressure ( ) N N V Rate of desortion : R D N N D S fractional coverage of vacant sites D adsortion rate constant desortion rate constant t equilibrium : R R D ( ) + fractional surface coverage + D measures affinity of a articular molecule for an adsortion site. D Langmuir adsortion isotherm : associative adsortion. sloe / similar analysis can be done for dissociative adsortion. dsortion rate Desortion rate R R D D N ( ) N t equilibrium : R R D ( ) D S dsortion isotherm for dissociative adsortion. ( ) D + + 3

14 Langmuir dsortion Isotherm..0 high limit : monolayer formed >> + Low limit : Henry Law << + Surface coverage large P/atm small dsortion Energetics dsortion of a gas on a solid is an exothermic rocess : H ads is negative. oth adsortion and desortion rocesses follow the rrhenius equation. D adsortion re-exonential factor D E ex RT E D ex RT E (g) H ads activation energy for adsortion desortion re-exonential factor activation energy for desortion temerature () R gas constant 8.34 J mol - - H ads E D ads ex D E D E D H RT ads 4

15 How is H ads measured? G 0 ads RT ln H 0 ads T S entroy of adsortion 0 ads entalhy of adsortion Gibbs energy of adsortion Langmuir adsortion assumed ln + ln ln ln ln + 0 T T ln ln T T constant surface coverage T T 0 H ads S ln + RT R 0 ln H ads T RT ln 0 ads constant surface coverage 0 ln H T RT ads 0 H R ads Determine adsortion Isotherm curves at Various temeratures. T T Measure values of and T at a constant surface coverage. Using this idea,,, T and T can be measured so H ads can be determined. constant Ln ln H ( / T ) R ads Read off,t data at constant coverage. High T Determine adsortion isotherm at various temeratures. Low T /T Plot of ln versus /T at constant surface coverage is linear. Sloe of lot enables one to evaluate H ads. This can be reeated for various set values of the surface coverage, to enable H ads to be determined over the entire range of surface coverage. 5

16 inetics of surface reactions We robe the reaction inetics of surface rocesses assuming Langmuir adsortion isotherm. Two rincial tyes of reaction mechanism are usually considered: Langmuir- Hinshelwood Eley- Rideal. In the Langmuir-Hinshelwood mechanism the reactants are all adsorbed on the surface and react at the surface. In the Eley-Rideal mechanism one has reaction between a reactant in the gas hase and a reactant adsorbed on the surface. Θ Α fast RDS RDS het fast Θ Α het fast Langmuir - Hinshelwood inetics 95 Langmuir Isotherm 97 inetics of Catalytic Reactions Cyril Norman Hinshelwood Nobel Prize 956 Irving Langmuir Nobel Prize 93 6

17 Langmuir-Hinshelwood P Eley-Rideal P inetics of surface reactions. Langmuir-Hinshelwood Mechanism Unimolecular: single molecular secies adsorbs on surface, reacts and the roduct P does not adsorb. Reaction rate R Limiting situations. R + Surface coverage of adsorbed gas Surface coverage related to gas ressure via + ( g) P( g) Langmuir adsortion isotherm Examle: decomosition of NH 3 on W surfaces. Rate st order at low, while as ressure increases it changes to zero order corresonding to saturation inetics. ads High ressures. >> R Rate indeendent of Gas ressure Zero order inetics. dsortion rate very large when is high. Decomosition ste rds. Low ressures. << R Rate deends linearly on gas Pressure First order inetics. dsortion rocess is rate determining when is low. Decomosition is fast. 7

18 8 R + Cometitive adsortion and bimolecular surface inetics. (g) + S ads (g) + S ads - - different gas hase reactants comete for adsortion sites S. ssuming an adsortion/desortion equilibrium for each gas we get: ads ads ads C + imolecular surface reaction ( ) dt dc R + + Catalyst surface

19 LH model bimolecular reaction Maximum rate occurs where 0.5 R dc dt ( + + ) For constant P Rate limited by surface concentration of rate Rate limited by surface concentration of Θ Β >> Θ Α Θ Β << Θ Α Eley-Rideal Mechanism. Mechanism describes a surface reaction in which one reactant is adsorbed while the other is in the gas hase. ( g) ads + ( g) P( g) ads n adsorbed molecule may react directly with an iminging gas molecule by a collisional mechanism Θ Α RDS het fast Reaction rate R is deendent on the ressure of, and the surface coverage of. We assume that and roduct P do not cometitively bind for surface sites with. R + Rate always st order wrt. limiting cases for reaction order wrt. When ( H ads ) is small or is small then << and R. Rate is st order wrt. When ( H ads ) is large or is large then >> and R. Rate is zero order wrt. Cometitive adsortion of roducts can comlicate the inetics. 9

20 Diagnosis of mechanism If we measure the reaction rate as a function of the coverage by, the rate will initially increase for both mechanisms. Eley-Rideal: rate increases until surface is covered by. Langmuir-Hinshelwood: rate asses a maximum and ends u at zero, when surface covered by. The reaction + S -S cannot roceed when blocs all sites. Catalyst Prearation For a catalyst the desired roerties are high and stable activity high and stable selectivity controlled surface area and orosity good resistance to oisons good resistance to high temeratures and temerature fluctuations. high mechanical strength no uncontrollable hazards Once a catalyst system has been identified, the arameters in the manufacture of the catalyst are If the catalyst should be suorted or unsuorted. The shae of the catalyst ellets. The shae (cylinders, rings, sheres, monoliths) influence the void fraction, the flow and diffusion henomena and the mechanical strength. The size of the catalyst ellets. For a given shae the size influences only the flow and diffusion henomena, but small ellets are often much easier to reare. Catalyst based on oxides are usually activated by reduction in H in the reactor. 0

21 mmonia synthesis : Steam reforming : High temerature water-gas shift C: Low temerature water-gas shift D: CO absortion E: Methanation F: mmonia synthesis G: NH 3 searation. mmonia Synthesis Fe/ catalyst exothermic

22 Mechanism N (g) + * N * N * + * N* 3 N* + H* NH* + * 4 NH* + H* NH * + * 5 NH * + H* NH 3 * + * 6 NH 3 * NH 3 (g) + * 7 H (g) + * H* Ste is generally rate-limiting. Volcano curve is therefore aarent with d-bloc metals as catalysts. Ru and Os are more active catalysts, but iron is used. iocatalysis: inetics of enzyme reactions. Enzymes are very secific biological catalysts. catalyst is a substance that increases the rate of a reaction without itself being consumed by the rocess. This material is described in most iochemistry texts. catalyst lowers the Gibbs energy of activation G by roviding a different mechanistic athway by which the reaction may roceed. This alternative mechanistic ath enhances the rate of both the forward and reverse directions of the reaction. The catalyst forms an intermediate with the reactants in the initial ste of the reaction ( a binding reaction), and is released during the roduct forming ste. Regardless of the mechanism and reaction energetics a catalyst does not effect H or G of the reactants and roducts. Hence catalysts increase the rate of aroach to equilibrium, but cannot alter the value of the thermodynamic equilibrium constant. energy thermodynamics unchanged E lowered E reactants H reaction coordinate catalyst absent catalyst resent roducts reactant molecule acted uon by an enzyme is termed a substrate. The region of the enzyme where the substrate reacts is called the active site. Enzyme secificity deends on the geometry of the active site and the satial constraints imosed on this region by the overall structure of the enzyme molecule.

23 Enzyme loc/ey mechanism : natural molecular recognition. Sace filling models of the two conformations of the enzyme hexoinase. (a) the active site is not occuied. There is a cleft in the rotein structure that allows the substrate molecule glucose to access the active site. (b) the active site is occuied. The rotein has closed around the substrate. hexoinase glucose 3

24 Classification of enzymes. merometric Glucose Sensors Enzymes are very secific biological catalysts. They interact with substrates via the Michaelis/Menten mechanism. If enzymes can be incororated and immobilized within a matrix located next to an electrode surface, then it is ossible to combine the secificity of enzyme catalysis with the many advantages of amerometric detection. We focus attention of glucose oxidase and the amerometric detection of blood glucose, since the glucose sensor is well develoed commercially.. Heller,. Feldman, Electrochemical glucose sensors and their alications in diabetes management. Chem. Rev. 008, in ress. J. Wang, Electrochemical glucose biosensors. Chem. Rev., 08 (008) J. Wang, Glucose biosensors: 40 years of advances and challenges. Electroanalysis, 3 (00) J. Wang, In vivo glucose monitoring: towards sense and act feedbac loo individualized medical systems. Talanta, 75 (008)

25 Redox enzymes. Redox enzyme contains tightly bound redox active rosthetic grou (e.g. flavin, haem, quinone) that remains bound to the rotein throughout redox cycle. Prosthetic grou non amino acid comonent of conjugated rotein. Redox enzymes exist in both oxidised and reduced forms. Redox enzymes can be subclassified in terms of the redox centres resent in the enzyme. Flavoroteins are most often studied. They consist of ca. 80 different enzymes containing either Flavin adenine dinucleotide (FD) Flavin mononucleotide (FMN) at the active site. The flavin unit is strongly associated with the rotein structure and is sometimes covalently bound to the amino acid residues in enzyme. Glucose oxidase b-d-glucose: oxygen -oxidoreductase EC..3.4) : GOx. Dimeric structure of glucose oxidase GOx. GOx is a dimeric rotein with MW 60 Da. Contains one tightly bound flavin adenine dinucleotide FD unit er monomer as cofactor. FD is not covalently bound and can be released from the holo rotein following denaturation. FD exhibits redox activity. Gox exhibits a very high degree of secificity for β-d-glucose. monomeric unit 5

26 redox active region rotein sheath FD active site Structure of FD redox site in GOx. 6

27 Time course of enzyme catalyzed reaction. ssume that [S] >> [E] Note logarithmic timescale. Note linear timescale. Enzyme catalysed reaction: Variation of reaction rate with substrate (reactant) concentration. Rate variation adots shae of rectangular hyerbola...0 Normalized rate ΨR / c e Unsaturated enzyme inetics Saturated enzyme inetics 0. Normalized substrate concentration uc/ M In electrochemical biosensor outut have current (rate) vs substrate concentration. This is an examle of a comlex rate equation, where the reaction rate varies with reactant concentration in a non linear way. 7

28 Single substrate Michaelis-Menten inetics. Rate Enzyme-substrate comlex lso termed c or turnover number max number of enzymatic reactions catalyzed er second. c / M measures catalytic efficiency of enzyme. Maximum value corresonds to Diffusion control reaction between S and E in solution (0 0 M - s - ). Note: iochemistry texts use ν as symbol for reaction rate (velocity). 8

29 inetics of enzyme reactions : Simle Michaelis-Menten Mechanism. R reaction flux (rate) x [ ES] c [ S] e [ E] E + S ES E + P - dx dt ss ec x x ss ss 0 e e + x ( ) e x c x x ss ss ss 0 R ce xss + + c e c ce C + M + c + c e E x ss ce + + c R x ss R Enzyme catalysed reaction: Variation of reaction rate with substrate (reactant) concentration. e E..0 c >> R E c M e c E Cc + c c << M M c E c U c M R ce U ΨR / c e Unsaturated enzyme inetics st order wrt substrate Saturated enzyme inetics Zero order wrt substrate uc/ M Rate variation adots shae of rectangular hyerbola. R u Ψ e + u c 9

30 Determination of inetic arameters M and c for enzyme catalysis. otions: Fit raw rate vs concentration data to MM equation using Non-Linear Least Squares (NLLS) fitting. Transform rate vs concentration data into suitable linear format such as Hanes lot or Lineweaver-ur lot. Lineweaver-ur equation Cec + R,0 R,0 ( c M ) e c ce M + c S c + I L L Michaelis-Menten equation S L M e C I L e C R I L S L c Plot recirocal initial reaction rate Versus recirocal substrate concentration. Measure sloe S L and intercet I L of lot. Michaelis constant (units mol dm -3 ) C + M Catalytic rate constant (unit: s - ) c + c + E C M C U C τ τ c + τ E U C u catalytic efficiency of enzyme c / M Enzyme rate constant (unit : s - ) E Cc + c M Unsaturated enzyme inetics U C M + Unit: dm 3 mol - s - Saturated enzyme inetics Time taen for E and S to combine to form roductive comlex ES Time taen for comlex ES to generate and release roduct 30

31 Catalytic efficiency Catalytic efficiency η reaches its max Value of when >> -. Since defines the rate constant for the formation of a comlex ES from two secies E and S that are diffusing freely in solution, the maximum efficiency is related to the maximum rate of diffusion of E and S in solution. Tyically for molecules as large as enzymes D has values around M - s -. η U C M + 3

32 When >> -, ES comlex decomosition to form roducts is faster than ES decomosition bac to reactants. The rds will involve the rate of combination of E and S to form the ES comlex. The ES comlex will be short lived since it does not accumulate to form roducts. Unsaturated enzyme inetics. τ + U + U RDS - RDS - E + S ES ES E + P E + S E + P Have a fast re-equilibrium followed by a slow rate determining decomosition of the ES comlex to form roducts. U C M ( ) We consider two sub cases deending on the value of. >> scenario. + U Unsaturated rate constant reflects Rate determining substrate binding to enzyme. RDS E + S - ES U E + P 3

33 U C M ( ) << scenario. + U RDS - Fast re-equilibrium followed by a slow rate determining decomosition of the ES comlex to form roducts. E + S ES E + P U Cometitive Inhibition In classical cometitive inhibition the inhibitor occuies the active site on the enzyme, blocing out the substrate. If the enzyme has already bound with a substrate the inhibitor is bloced out. Hence the inhibitor secies I reacts with the free enzyme E but not with the enzyme- substrate comlex ES. Hence both Substrate S and inhibitor I comete for same active site. E + S ES E + P E + I EI Total enzyme concentration [ E] [ E] + [ ES ] + [ EI ] + [ ESI ] Equilibrium constant for formation of EI comlex I EI does not react with S to form Products. [ EI ] [ E][ I ] Lineweaver-ur Plots are linear. Sloe and intercet deend on [I]. Sloe increases with increasing [I]. Net rate equation M J.Chem. Ed. 77 (000) c [ ] [ ] { I [ ]} E S R + I + + R E S E ( )[ ] (Derived using QSS) { I [ I ]} [ ] [ ] c M c R [ ] [ ] R M I large I + + R + S S + I [ I ] SL c [ E] ( c M )[ ] E [ S ] M [ ] [ ], inh M I I I To overcome cometitive inhibition we need to increase [S] relative to [I]. [I] increasing [I]0 [ S] Net rate equation 33

34 Noncometitive Inhibition Net rate equation Derived via QSS) noncometitive inhibitor binds to the enzyme at a site that is distinct from the substrate binding site; therefore it can bind to both the free enzyme and the enzyme/substrate comlex. The enzyme s function is inhibited by inhibitor binding by erturbing the 3-D structure of the rotein so that the active site does not catalyze the substrate reaction. Inhibition occurs both at E and ES sites, and S and I bind indeendently to E. ecause I does not interfere with ES formation, noncometitive inhibition cannot be reversed by increasing substrate concentration. R I c [ E] [ S] { + [ ]} + { + [ ]}[ ] I I S M I I I M [ ] [ ] { I [ ]} c E S R ( + [ S]) + I c [ E] ( [ ]) [ S ] + I I + [ S] M Note that R m c [E] is reduced by the factor (+ I [I]) but M is unchanged R E S E [ ] { I [ I ]} { [ ]} [ ] [ ] I I c M c E + S ES E + P E + I EI ES + I ESI I [ EI ] [ E][ I ] I R R, inh [ ESI ] [ ES ][ I ] + I [ I ] I L R max - (+ I [I]) - M - R [I] increasing [ S ] [I]0 Uncometitive Inhibition In uncometitive inhibition the inhibitor I binds to the ES comlex only to form the adduct ESI. Inhibition occurs because ESI reduces concentration of active adduct ES. ecause I does not interfere with the formation of ES, uncometitive inhibition cannot be reversed by increasing substrate concentration. E + S ES E + P ES + I ESI Equilibrium constant for formation of ESI comlex I [ ESI ] [ ES ][ I ] R Net rate equation M c [ ] [ ] { I [ ]}[ ] E S R + + I S (QSS) c [ E] ( [ ]) [ S ] + I M ( + I [ I ]) oth M and R max c [E] are reduced by the factor + I [I]. [ ] [ ] [ ] c M c + [ S] { I [ ]} S + + I R E E I L R max - (+ I [I]) [I] increasing [I]0 L sloe indeendent of [I]. - M (+ I [I]) S L /( c [E] / M ) [ S ] 34

35 Very useful chater on enzyme inetics. 35