Chemistry Assignment Help with Kinetics of First Order Reaction

4.5 Kinetics of First Order Reaction

A first order reaction is one whose rate varies as 1st power of the concentration of the reactant i.e. the rate increases as number of times as the number of times the concentration of reactant is increased.

Let us consider a uni molecular first order reaction represented by the general equation.

A ___________ Product

A x = 0 … t = 0

Chemistry Assignment Help Order Now A – x x = x … t = 0

The initial concentration of A is a mole L–1 and its concentration after any time t is (a – x) mole L–1. This means during the time interval t, x mole L–1 of A has reacted.

The rate of reaction at any time t is given by the following first – order kinetics.

         Kinetics of First Order Reaction  or   Kinetics of First Order Reaction µ (a – x)

         or           Kinetics of First Order Reaction= k (a – x)

         (Kinetics of First Order Reaction Kinetics of First Order Reaction a has a given value for a given expt.)

where k is the rate  constant of the reaction.

         Kinetics of First Order Reaction

This is differential rate equation and can be solved by integration.

         Order of a reaction

or     – ln (a – x) = k.t + C                                                     …(1)

The constant C can be evaluated by applying the initial condition of the reaction i.e. when t = 0, x = 0. Putting these in equation 1, we get

         C = – lna

Putting the value of C in equation 1, we get

         – ln (a – x) = k.t. – lna or rate-of-reaction           …(2)

If [A0] and [A] be the concentrations of reactant at zero time and time t, respectively then Eq. 2 may be put as

         graphical representation

The rate constant units for nth order reaction is as follows.

Kinetics of First Order Reaction or radioactivity = conc. 1–n . time–1

4.5.1 Half-time or half-life period of a first order reaction

The half-time of a reaction is defined as the time required to reduce the concentration of the reactant to half of its initial value. It is denoted by the symbol t1/2. Thus,

When Half-time or half-life period of a first order reaction t = t1/2

Putting  these in equation 2 mentioned above, we get

         Half-time or half-life period of a first order reaction

         (log 2 = 0.30103)

         t1/2 = Half-time or half-life period of a first order reaction                                                                               …(3)   

         Since k is a constant for a given reaction at a given temperature and the expression lacks any concentration term so from equation 3 it is evident that half-time of a 1st order reaction is a constant independent of initial concentration of reactant.

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