Kinetics : Integrated Forms of the FirstOrder 
Integrated Form of the FirstOrder Rate LawThe original firstorder rate law equation is:
The integrated form of the firstorder rate law equation is:
Where X is the concentration of a reactant at any moment in time, (X)_{o} is the initial concentration of this reactant, k is the constant for the reaction, and t is the time since the reaction started.
This equation is useful in calculating how much of a substance remains after a certain amount of time has passed, or to calculate how long it takes until the concentration is at a certain point.

If the rate law of a reaction is first order
with respect to [A], then the graph of ln[A] versus time (t) creates a straight line with a negative slope. The value of the slope of the line is equal to the negative value of the rate constant (k). 
Integrated Form of the SecondOrder Rate Law
The original equation for a secondorder rate law with a single reactant is:
The integrated form of the secondorder rate law equation is:

If the rate law for a reaction is second order
with respect to [A], a graph of 1/[A] versus time (t) creates a straight line with a positive slope. The value of the slope of the line is equal to the value of the rate constant (k). 