BASIC PRINCIPLES OF CHEMICAL KINETICS

where j is the stoichiometric coefficient with minus sign for reactants and plus sign for products

k is the kinetic rate constant (always lower case) a, b, … are not necessarily the stoichiometric coefficients are not necessarily integers The reaction order is the sum of the exponents of concentration factors in an experimental rate law a + b +….. The reaction order is an experimental result

The reaction is first-order with respect to [BrO 4 - ] and [Br - ] and second order with respect to [H + ]. Overall, the reaction is fourth order

Molecularity : number of molecules that react in a single step (elementary step or elementary reaction). For an elementary reaction reaction order = molecularity but this is not true for reactions occurringin many steps. A bimolecular elementary reactions has second order kinetics, but a reaction showing second order kinetics may be complex

Zero order reaction First order reaction Second order reaction

Determination of order of reaction b) The differential method: the velocity is measured at various values of the reactant concentration. a) The method of integration: the concentration of a reactant or product is determined at various times

Method of integration First-order reactions

The half-time (or half-life), t 1/2 For a first order reaction t 1/2 is independent of [A] 0

Use of physical properties in kinetic studies The rate of a reaction can be determined by removing samples at various times, quenching the reaction, and then carrying out a chemical analysis. The method is quite tedious and instrumental determinations have supplanted direct analysis. Lambert-Beer law Consider a property which is linearly related to concentration, as the absorbance or optical density,D

For first-order kinetics The value of D at the start of the reaction The value of D at the end of the reaction

For any general reaction, which proceeds to completion, the concentration of A, the limiting reagent at any time t is given by

Second-order reactions

or

If the reaction is studied by UV-vis spectroscopy We can substitute whitin We need to know [A] 0 to calculate k

Method of flooding or pseudo-order reactions

In general

Zero-order reactions A reaction rate cannot be independent of the concentration of all the species involved, but can be independent of the concentration of one reagent. If this species is used in deficiency, the reaction results to be pseudo zero-order

Differential methods (or initial rate) method) The initial rates (i.e. the slope of the concentration-time curves) are measured are measured at various initial concentrations

The slope of the double-logarithmic plot is the order with respect to the substance whose concentration is being varied

Reversible reactions At equilibrium

The influence of temperature on rate constants Reaction rates are profoundly influenced by temperature Temperature must always be controlled in kinetic studies Rates of many reactions approximately double for each 10 °C rise in temperature

2 ln RT H dT Kd r   Arrhenius developed his theory by comparing kinetic observations with the known properties of equilibrium constants van’t Hoff equation

Arrhenius equation (empirical) E a activation energy

Transition-state theory(Eyring, 1935)

A bimolecular reaction can be represented Where X ‡ is the activated complex, which corresponds to the configuration of the system in the state of maximum energy (the transition state). The activated complex must be distinguished from an intermediate, which represents a minimum on the reaction profile.

Equazione di Eyring The concentration of X ‡ is assumed to be in equilibrium with those of the reagents From quantum-mechanical considerations

Remembering that at p = constant ln(k/T) 1/T

Consecutive reactions

Steady-state approximation

Consecutive reactions with elements of reversibility

Step 1 is rate-determining Step 2 is rate-determining

Pre-equilibria

If kinetics are first-order with respect to [B] If kinetics are zero-order with respect to [B]