SecondOrder Reactions 
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Secondorder reactions are VERY common. There are two types of secondorder reactions ... the simplest (the kind in most chemistry courses) is when two molecules of A collide together to form a new product. Another kind (not covered in firstyear chemistry classes but in upperyear ones) is when two different molecules (A and B) collide to form new product(s).
The Rate EquationSecondorder reactions mean the exponent on the reactant concentration is 2:

How Concentration Changes with TimeJust like with zero and firstorder reactions, you can integrate the rate equation to determine how the concentration of the reactant changes with time. If you know a little calculus (antiderivatives) you'll be able to follow the integration that I've put on the right. If you can't, just skip to the last line.
If the reaction is firstorder, a graph of 1/[A] vs. t will give a line! Remember (from grade 9) how y=mx+b is the equation of a line? Well here, y is 1/[A], the ln of the reactant concentration. x is t, the time elapsed. m (the slope) is k and b (the yintercept, where t=0) is 1/[A]o, the ln of the initial reactant concentration. 