Chemistry

Chemical Kinetics – 1

Session Objectives Rate of reaction Factors affecting rate constant Molecularity Order of a reaction Kinetics of zero order reaction Kinetics of first order reaction Pseudo first order reaction

Rate of reaction For a reaction, The rate may be expressed as Unit of rate of reaction =

Rate of reaction For general reaction Rate of reaction According to law of mass action Where k is rate constant.

Rate constant Measure of rate of reaction Different for different reactions Independent of concentration of reactants Depends on the temperature

Graphical representation of rate The slope of graph at any instant gives us the rate of reaction at that moment and is called instantaneous rate of the reaction. The average of these slopes over a period gives us rate of the reaction which is called as average rate of the reaction.

Illustrative Example The reaction, 2N2O5(g)  4NO2(g) + O2(g), takes place in a closed container, it was found that the concentration of NO2 increases by 1.6 x 10-2 moles/litre in four seconds. Calculate the rate of the reaction and the rate of change of the concentration of N2O5. Solution: 2N2O5(g)  4NO2(g) + O2(g) rate of change of concentration of N2O5

Rate law It is a mathematical expression that gives the true rate of reaction in terms of concentration of the reactants which actually influence the rate. Rate expression is experimentally determined. Consider a general reaction

Molecularity For an elementry reaction, molecularity is the total number of molecules taking part in reaction. It has no significance for complex reaction

Order of reaction The number of molecules which actually react and undergo a change in concentration is known as order of reaction. For example,the dissociation of N2O5 is a first order reaction There can be a reaction of fractional order Consider a general reaction

Molecularity of Reaction Molecularity vs. Order Order of reaction is for overall reaction. The overall molecularity of complex reaction has no significance. Individual step has its own molecularity. It can even have fractional values. It is always a whole number. It is determined experimentally. It is a theoretical concept. Order of reaction can be zero. Molecularity of reaction Cannot be zero. It is the sum of the power of concentration terms on which the rate of reaction actually depends or it is the sum of powers of the concentration terms in the rate law equation. It is the number of atoms, ions or molecules that must collide with one another simultaneously so as to result into a chemical reaction. Order of Reaction Molecularity of Reaction

Illustrative Example For a reaction, aA + bB + cC  proucts, rate expression can be expressed as rate = k[A]1[B]-3/2[c]1/2, Write the order of the reaction with respect to ‘A’ , ‘B’, and ‘C’. What is the overall order of the reaction? Solution : Order of the reaction w.r.t. ‘A’ = 1 Order of the reaction w.r.t. ‘B’ = -3/2 Order of the reaction w.r.t. ‘C’ = 1/2 Overall order of the reaction = 1 + (-3/2) + 1/2 = 0

Illustrative Example The rate of the reaction, A  P, increases by a factor of 5.18 when the concentration of A is tripled. What is the order of A? Solution: Assuming the order of the reaction w.r.t. ‘A’ is n, then the rate expression can be written as or n = 1.5

Illustrative Problem For the reaction A + B Products The following initial rates were obtained at various given intial concentrations S. No [A] [B] Rate (mol lt–1 sec–1) 1. 0.1 0.1 0.05 2. 0.2 0.1 0.10 3. 0.1 0.2 0.05 Write rate law and find the rate constant of the above reaction.

Solution

Zero order reaction A Product Rate of reaction where k = rate constant for zero order reaction [A] =- kt + C where C = Integration Constant. When t = 0, then [A] =A0 hence C = A0

Zero order reaction Half life of a reaction :- Time taken for the reactant concentration to decrease to one half of its initial value Half life a initial concentration

Zero order reaction Half life a initial concentration

Zero order reaction

First order reaction A Product Unit of rate constant is time-1

First order reaction Half life of first order reaction does not depend upon initial concentration Amount of substance left after n half lives

First order reaction For 75% completion of reaction

First order reaction Slope of line =

Illustrative Example For a first order reaction, A  P, half life is 69.3 min. Calculate the time taken to decay the amount of ‘A’ to 80%. Solution:

Alternate Solution

Illustrative Example The half-life of a substrate in a certain enzyme-catalyzed first order reaction is 138 s. How long will it require for the initial concentration of substrate, which was 1.28 mmol/L, to fall to 0.040 mmol/L? Solution:

Pseudo - first order reaction Reactions which are not truly of the first order but under certain conditions reactions become that of first order are called pseudo unimolecular reaction. For example: Hydrolysis of ester in presence of acid CH3COOC2H5 + H2O  CH3COOH + C2H5OH From this reaction, the rate expression should be r = k [ester] [H2O] Since, hydrolysis takes place in the excess of H2O and concentration change of H2O is negligible practically. therefore, r = k’ [ester] Where k’ = k[H2O].

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