1Chemistry 2C Lecture 22: May 21 th, )Arrhenius Equation 2)Transition State Theory 3)Molecularity 4)Rate limiting steps 5)Reaction mechanisms 6)Catalysis 7)Nuclear Introduction Lecture 22: Kinetics

2Chemistry 2C Lecture 22: May 21 th, 2010 Temperature Effects on Reaction Rate “Normal”Catalyzed reaction (inactivation of catalyst) rare Chain reaction (Explosion) Not every reaction follows the Arrhenius equation. But most!

3Chemistry 2C Lecture 22: May 21 th, 2010 Activated Complex-Transition States The potential energy of the system increases at the transition state because: 1)The approaching reactant molecules must overcome the mutual repulsive forces between the outer shell electrons of their constituent atoms 2)Atoms must be separated from each other as bonds are broken In the transition state theory, the mechanism of interaction of reactants is not considered; the important criterion is that colliding molecules must have sufficient energy to overcome a potential energy barrier (the activation energy) to react.

4Chemistry 2C Lecture 22: May 21 th, 2010 Activated Complex-Transition States This increase in potential energy corresponds to an energy barrier over which the reactant molecules must pass if the reaction is to proceed. The transition state occurs at the maximum of this energy barrier.  The transition state is an unstable transitory combination of reactant molecules that occurs at a potential energy maximum The combination can either go on to form products or fall apart to return to the unchanged reactants.  The energy difference between the reactants and the potential energy maximum is referred to as the activation energy: E a or  G ‡

5Chemistry 2C Lecture 22: May 21 th, 2010 Energy barrier from reactants to products (forward direction) Reaction Profile Energy barrier from products to reactants (reverse direction)  G for reaction Since  G is negative, this is a spontaneous reaction, although its timescale for occurring is dictated by the energy barrier

6Chemistry 2C Lecture 22: May 21 th, 2010 Arrhenius Equations How is E a measured? The rate constant is a function of temperature, but E a is considered to be a constant and depends only on thermodynamics k=Ae -Ea/RT This is the form of a line!

7Chemistry 2C Lecture 22: May 21 th, 2010 Arrhenius Equations How is E a measured (measure two rates at two different temperatures? ln k 2 = –E a /RT 2 + ln T T 2 ln k 1 = –E a /RT 1 + ln A Subtract the two equations: ln k 1 - ln k 2 = –E a /RT 1 –E a /RT 2 ln (k 1 / k 2 ) = –E a /R (1/T 1 -1/T 2 ) Can just substitute into this equation! Make sure temperature is in Kelvin!

8Chemistry 2C Lecture 22: May 21 th, 2010 Chemical Kinetics Molecularity of a Reaction The reaction order refers to the concentration dependence of the reaction rate and can be an integer or a non-integer and even negative! The molecularity of a reaction refers to a definite molecular encounter during the course of the reaction. The molecularity has to be an integer (there are no partial atoms/molecules!) Unimolecular Reactions: One reactant molecule undergoes transformation into the product(s). Examples are racemizations, thermal decomposition, or isomerizations. Bimolecular Reactions: Two reactant molecules collide in one elementary step. Most common type of reaction molecularity. Termolecular reactions: Three reactants have to collide to lead to an reaction. Extremely rare. No reactions of molecularities higher than 3 are known.

9Chemistry 2C Lecture 22: May 21 th, 2010 Reaction Mechanism A mechanism describes in detail exactly what takes place at each stage of a chemical transformation. It describes the transition state and which bonds are broken and in what order, which bonds are formed and in what order, and what the relative rates of the steps are. A complete mechanism must also account for all reactants used, the function of a catalyst, stereochemistry, all products formed and the amount each. For example: CO + NO 2 → CO 2 + NO In this reaction, it has been experimentally determined that this reaction takes place according to the rate law R = k[NO 2 ] 2. Therefore, a possible mechanism by which this reaction takes place is: 2 NO 2 → NO 3 + NO (slow) NO 3 + CO → NO 2 + CO 2 (fast) Each step is called an elementary step, and each has its own rate law and molecularity. All of the elementary steps must add up to the original reaction.

10Chemistry 2C Lecture 22: May 21 th, 2010 Intermediates & Rate Determining Steps Reactions may have intermediate species that don’t show up in the final reaction equation, but play a role in the mechanism. Kindah like electrons in REDOX reactions. For example: 2 NO 2 (g) + F 2 (g) → 2NO 2 F (g) The first step is slow (k 1 >1), the rate determining step NO 2 + F 2 → 2NO 2 F + F Overall Rx. Step one: k 1 F + NO 2 → NO 2 F Step two: k 2 rate = k[NO 2 ][F 2 ] The experimentally determined rate law is:

11Chemistry 2C Lecture 22: May 21 th, 2010 NO 2 + F 2 NO 2 F + F F + NO 2 NO 2 F k1k1 k2k2 Slow Fast 2NO 2 + F 2 2NO 2 F rate = k[NO 2 ][F 2 ] according to the elementary reaction, with a rate limiting step Intermediates & Rate Determining Steps Each of these steps is an elementary process. That means that those two species must collide for a reaction to occur. In this example, each step is bimolecular.

12Chemistry 2C Lecture 22: May 21 th, 2010 Energy Diagram for a two-step Reaction Reactants -> transition state -> intermediate Intermediate -> transition state -> product

13Chemistry 2C Lecture 22: May 21 th, 2010 Chemical Kinetics: Enzymes and Catalysis General principles of catalysis: A catalyst works by lowering the Gibbs energy of activation. This enhances the rate of forward and backward reaction. The catalyst forms an intermediate with the reactant(s) in the initial step of the reaction and is released in during product formation. A catalyst can not affect the enthalpies or the Gibbs energies of the reactants and products.It increases the rate of the approach to equilibrium, but can not change the change the equilibrium constant.

14Chemistry 2C Lecture 22: May 21 th, 2010 Chemical Kinetics: Enzymes and Catalysis General principles of catalysis: Uncatalyzed ReactionCatalyzed Reaction

15Chemistry 2C Lecture 22: May 21 th, 2010 Types of Catalysis Homogeneous Catalysis – The interaction of reactants and catalysts in the same phase. – e.g., CFC’s (gas/gas) Heterogeneous Catalysis – The interaction of reactants and catalysts in different phases. – e.g., catalytic converters (solid/gas) Enzymes in the body are biological catalysts!

16Chemistry 2C Lecture 22: May 21 th, 2010 Reaction Profile for Enzyme The catalysed reaction pathway goes through the transition states TS c1, TS c2 and TS c3, with an energy barrier  G c *, whereas the uncatalysed reaction goes through the transition state TS u with a barrier of  G u *. In this example the rate limiting step would be the conversion of ES into EP.

17Chemistry 2C Lecture 22: May 21 th, 2010 Reaction Profiles The catalysis of H 2 O 2 decomposition by Br - 2H 2 O 2 -> 2H O 2 Overall net Rx. When Br - is added, the reaction goes 2Br - + H 2 O 2 +2H + -> Br 2 + 2H 2 0 Br 2 + H 2 O 2 -> 2Br - + 2H + + O 2 Step 1 Step 2 Br 2 is an intermediate because it is produced and then consumed! Br - is a catalyst because it speeds up the reaction and is neither and is unchanged during the net reaction!