The rate of reaction

Rate Law Relation between rate of reaction and concentration of the reactants

Three important problems Determination of rate law and rate constant from experimental data. Construct reaction mechanism that are consistent with rate law. Value of rate constant and their temperature dependence

Determination of rate law Isolation method: Add large excess Methods of initial rate: measurement of rate of reaction for several different initial concentration of reactants.

Integrated Rate Laws Consider a simple 1st order rxn: A  B Differential form: How much A is left after time t? Integrate:

Integrated Rate Laws The integrated form of first order rate law: Can be rearranged to give: [A]0 is the initial concentration of A (t=0). [A]t is the concentration of A at some time, t, during the course of the reaction.

Integrated Rate Laws Manipulating this equation produces… y = mx + b …which is in the form y = mx + b

First-Order Processes If a reaction is first-order, a plot of ln [A]t vs. t will yield a straight line with a slope of –k.

Second-Order Processes Similarly, integrating the rate law for a process that is second-order in reactant A: Rearrange, integrate: y = mx + b also in the form

Second-Order Processes So if a process is second-order in A, a plot of 1/[A] vs. t will yield a straight line with a slope of k.

Half-Life Half-life is defined as the time required for one-half of a reactant to react. Because [A] at t1/2 is one-half of the original [A], [A]t = 0.5 [A]0.

Half-Life For a first-order process, set [A]t=0.5 [A]0 in integrated rate equation: NOTE: For a first-order process, the half-life does not depend on [A]0.

Half-Life- 2nd order For a second-order process, set [A]t=0.5 [A]0 in 2nd order equation.

Outline: Kinetics First order Second order complicated Rate Laws Integrated Rate Laws complicated Half-life

Reaction order and reaction mechanism Most important application of studying the order of a reaction is to establish the mechanism of reaction. Reactions proceed in one or more elementary steps. In elementary step molecularity = order of reaction

Overall order of reaction corresponds to stoichiometric equation => The reaction mechanism most probably involves one elementary step that is identical to stoichiometric equation. When the reaction order does not corresponds to the stoichiometry of the reaction, the reaction certainly involves more than one elementary reaction.

When the reaction order does not corresponds to the stoichiometry of the reaction, the reaction certainly involves more than one elementary reaction. Elementary Reaction Reversible elementary reaction A  B (ii) Consecutive elementary reaction A  B  C (iii) Parallel Reaction: A B C

Consecutive Reaction

Consecutive Reaction

Consecutive Reaction

Consecutive Reaction Rate of formation of the final product P depends on only the smaller of two rate constants.

Consecutive Reaction This is the basis of steady-State approximation. Conc A I Time

Consecutive Reaction

Case II: when [I] [P]

[P] [I]

When are consecutive and Single-Step reactions distinguishable ? Rate of formation of product is different from rate of decay of A Rate of formation of product is same as rate of decay of A

Parallel Reaction

Parallel Reaction

Thermodynamic vs. Kinetic Control k2 >k1, K2>K1 k2 < k1, K2>K1 k2 >k1, K2<K1 k2 < k1, K2 < K1 A B C

Parallel Reaction

Reversible Reaction

Reversible reaction

Reversible reaction

Higher order reversible Reaction