Chemical Kinetics Rates of chemical reaction － definition of reaction rate － integrated and differential rate law － determination of rate law Mechanism of chemical reaction － activated complex theory － model for chemical kinetics － Arrhenius equation

Rate Law Rate=k[NO 2 ] n The concentration of the products do not appear in the rate law. The value of the exponent n must be determined by experiment; it cannot be written from the balanced equation.

2N 2 O 5 →4NO 2 +O 2

Types of Rate Laws Integrated Rate Law: how the concentration of species in the reaction depend on time Differential Rate Law: how the rate of a reaction depends on concentrations Determine the differential rate law for a given reaction, the form of integrated rate law can be automatically known, and vice versa

Initial-Rate method To determine the instantaneous rate before the initial concentration of reactants have changed significantly. Several experiments are carried out using different initial concentrations. The initial rate is determined for each run.

ExperimentsInitial Rate 10.1M0.005M1.35X M0.01M2.70X M0.01M5.40X10 -7

Integrated Rate Law － first order

Plot of N 2 O 5 vs. time

Half-Life of a First Order Reaction The time required for a reaction to reach half of its original concentration is called half-life of a reaction and id designated by t 1/2.

Plot of N 2 O 5 vs. time

Integrated Rate Law － second order

Plot of C 4 H 6

Integrated Rate Law － zero order

Pseudo-Order Reaction Law

Arrhenius Postulations Collisions and Rate － the rate of reaction is much smaller than calculated collision frequency. A threshold energy (activation energy) － This kinetic energy is changed into potential energy as the molecules are distorted during a collision, breaking bonds and rearranging the atoms into product molecules.

Collisions Frequency and Molecular orientations Experiments show that the observed reaction rate is considerably smaller than the rate of collisions with enough energy to surmount the barrier. The collision must involve enough energy to produce the reaction. The relative orientation of the reactants must allow formation of any new bonds necessary to products.

BrNO collision

Potential energy graph for 2BrNO → 2NO+Br 2

Temperature Dependence of Rate Constants The order of each reactant depends on the detailed reaction mechanism. Chemical reaction speed up when the temperature is increased. － molecules must collide to react － an increase in temperature increases the frequency of intermolecular collisions.

T 1 /T 2 graph

T(K) and k

Ea: activation energy A: pre-exponential factor Arrhenius Equation

Plot ln(k) vs. 1/T

Reaction Mechanism Most chemical reactions occur by a series of steps called the reaction mechanism. The sum of the elementary steps must give the overall balanced equation for the reaction. The mechanism must agree with the experimentally determined rate law.

Step (1): rate-determining-step

Treatments 1. Rate-Determining Step Approximation 2. Steady-State Approximation 2 NO N 2 O 2 fast N 2 O 2 +H 2 N 2 O+H 2 O slow Overall: 2NO+H 2 N 2 O+H 2 O R=[NO] 2 [H2] k1k1 k -1 k2k2

Rate-Determining Step Approximation

Steady-State Approximation

Overall reaction H + +HNO 2 +C 6 H 5 NH 2 →C 6 H 5 N H 2 O Proposed mechanism H + +HNO 2 H 2 NO 2 + rapid equilib. H 2 NO 2 + +Br - →ONBr+H 2 O slow ONBr+C 6 H 5 NH 2 →C 6 H 5 N 2 + +H 2 O+ Br - fast k1k1 k -1 k2k2 k3k3

Activated Complex Theory The arrangement of atoms found at the top of potential energy hill or barrier is called the activated complex or transition state. △ E has no effect on the rate of reaction. The rate depends on the size of the activation energy E a

Catalysis A substance can speed up a reaction without being consumed itself. The catalyst is to provide a new pathway for the reaction and to decrease activation energy.

Effect of a catalyst

Heterogeneous Catalysis Adsorption and activation of the reactants Migration of the adsorbed reactants on the surface Reaction among the adsorbed substances Escape, or desorption, of the products.

Hydrogenation of ethylene

Exhaust gases