KINETICS OF FIRST ORDER REACTIONS:

A chemical reaction is said to be of first order reaction if its rate is determined by the change of one of the concentration term only.

Consider a general chemical reaction its follow first order kinetics

Let [A] ₀ =initial concentration of reactant A

[A]_t = concentration of after time t

[B]_t = concentration of product B after time t

On Integration of above equation

On rearrangement equation (1) give equation of straight line

We can also write equation (1)   as  

Case (1): 

# On increasing angle (slop) the value of reaction constant increases hence k3>k2> k1

Case (2):    

       

Case (3):   

           

Case (4):           

[A]t/[A]0  Vs  t :

 Variation o f concentration with time:

Characteristic of 1^st order:

(1) Concentration of reactant left after regular time interval of time will constitute a geometrical progression (GP).

(2) A first order reaction takes infinite time for completion.

(3) All radioactive disintegrations are examples of first order reaction
(4) Decomposing of H₂O₂ , Ester and Inversion of sugar are examples of first order reactions

(5) Half life time of first order reaction does not depend upon initial concentration.

Similarly concentration of product B after time t 

Graph show increase in concentration  of [B] and [A] both as exponential manner.

First Order Parallel Rreactions

Half life time of first Order reaction:

Natural life time of first order reaction:    

KINETICS OF ZERO ORDER REACTIONS:

Consider a general chemical reaction its follow zero order kinetics

[A] ₀ =initial concentration of reactant A

[A]_t = concentration of after time t

[B]_t = concentration of product B after time t

On Integration of above equation:

On rearrangement equation (1) give equation of straight line

Note: Concentration of reactant after regular interval of time will constitute an arithmetical progression (AP) 

Similarly concentration of product B after time t

Unit of rate constant:    K= Mol/litre second

Half life period:  Time required converting half of the reactant to product i.e. life of zero order reaction may give as

Imp note: In zero order reaction average rate of reaction is equal to instantaneous rate of reaction

100% completion of time: It is time in which reactant completely converted into product.

ILLUSTRATIVE EXAMPLE (1): The graph show decomposition of Ammonia  on Pt surface it initial concentration of ammonia is 0.1 M then calculate the time required for the 40% completion of reaction.

SOLUTION:   

ILLUSTRATIVE EXAMPLE (2): A certain zero order reaction has k=0.025 M /S for disappearance of A what will be the concentration of  A after 15 second if initial concentration is 0.5 M?

SOLUTION: concentration of A after time of t is [A]_t

KINETICS FOR nth ORDER REACTION:

Consider a chemical reaction have one reactant only

Differential rate expression may be written as:

Separating same variable same side

On integrating by rule

By equation (1) and (2)

Graphical representation:

Half life period:

Graphical representation:

Note : This formula do not valid for n=0 and n=1

ILLUSTRATIVE EXAMPLE (1) :  A graph plotted between log  t₅₀   Vs log conc. (a)  is a straight line what conclusion withdraw from the given graph?

SOLUTION: for a given reaction

ILLUSTRATIVE EXAMPLE (1) :  What  will be the order of reaction and rate constant for a chemical change having log  t₅₀   Vs log conc. (a)  curve as

SOLUTION: for a given reaction

Case (1) n=2 i.e.    2^nd order chemical kinetics:

Graphical representation: 

Half life period:

Graphical representation:

Case (2) n= 3 i.e.    3^nd order chemical kinetics:

Graphical representation:

Half life period:

Graphical representation:

Important kinetic expression for reaction of type as:

Graphs of various order:

W h e r e

[A]₀ = initial concentration

[A] = concentration at time t

t_1/2 = time taken for initial concentration of reactant to finish by 50%

t _3/4 = time taken for initial concentration of reactant to finish by 75%