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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.    2nd order chemical kinetics:
Graphical representation: 


Half life period:
Graphical representation:

Case (2) n= 3 i.e.    3nd 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
t1/2 = 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%

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