Before discussing the Rate law we have to understand that what is the rate of reaction?
⦁    Rate of reaction
Reaction rate is increase in concentration of product or decrease in concentration reactant of a reaction as a function of time. 
Rate of reaction =    =   -
     Unit: mol 
⦁    Expression of rate

For the reaction  2⇨  4N+

-   ,     +∆ ,  + ∆

⦁    RATE LAW
Rate law is experimental determined expression which relates the rate of reaction with the concentration of reactants.
A     +   B  ⇨ PRODUCTS
Rate   ᾱ   
Rate=k
Where  k  is the rate constant.
If   [A]   =  [B]   =  1 mol Than Rate= k
“Thus rate constant is the rate of a reaction when concentration of each reactant is unity.”
⦁    Characteristics of rate constant
⦁    Each reaction has a definite value of the rate constant at a particular temperature.
⦁    The value of the rate constant for the same reaction changes with temperature.

⦁    K is large if the product form quickly ;
⦁    K is small if the products form slowly 
Rate =  k  

Rate law and rate constant must be determined experimentally.

There are two types of reactions:
⦁    Elementary reactions
⦁    Complex reactions 
⦁    Elementary reaction:
    A chemical reaction that takes place in one and only step called complex reaction.
Example:
p⇨ p + 

⦁    Complex reaction:
    A chemical reaction occurring in sequence of two or more steps called complex reaction.
Example:
2N +  ⇨ 2N

⦁    The rate law of elementary reaction can be determined from the equation of that elementary reaction.
⦁    The rate law for the complex reaction will depend on which elementary reaction is slowest.

⦁    Order of reaction:
Order of a reaction can be determined by rate law .
aA   +   bB ⇨   cC  +   dD
Rate = k 
⦁    x and y indicates that how sensitive the rate is to change in concentration of A and B.
⦁    x and y are the order of the reaction with respect to A and B respectively.
⦁    Overall order of reaction  =  x+y 
⦁    The sum of the powers of the concentration of the reactants in rate law expression is called the order of that chemical reaction.
⦁    Types of rate law:
         There are two types of rate laws

⦁    Differential rate laws
⦁    Integrated rate laws

⦁    Differential rate laws: 
This law express the rate of reaction as a function of change in concentration of one or more reaction over a period of time . they are used to describe what is happening in molecular level during a reaction.
This rate law helps us to determine the overall mechanism of reaction by which the reactants turn into products.

Rate = -  = K 

⦁    Integrated rate law:
It expresses the rate as a function of initial concentration and a measured concentration of one or more reactant after a specific amount of a time has passed 
They are used to determine the rate constant and the reaction order from the experimental data 

ln[A] = -Kt  + ln

Where is the initial of reactant and [A] IS The concentration after a time t has passed.

⦁    Method of determing  Order in RATE LAW
             Rate law can be determined by intial rate method.
A sample data set from an “Initial rates experiment”

For the reaction     A   +   B  ⇨  C
Experiment            Observed rate
1        0.01    0.20    5
2    0.02              0.20    10
3    0.04    0.20    20
4    0.20    0.03     15
5    0.20    0.06    30
    
⦁    Determining the orders for rate law    
STEP 1: identify two experiments where one reactant is held at a constant concentration while other is varied.
STEP 2: Determine the amount of concentration was changed by i.e. , doubled and tripled etc.
STEP 3: Determine how the rate of reaction is changed.
STEP 4:Find the relationship between the change in reaction rate and change in concentration rate.
 
⦁    EXAMPLE:
Find the order of A

Experiment            Observed rate
    1    0.01    0.20    5
          2    0.02    0.20    10
3    0.04    70.20    20
4    0.20    0.03    15
5    0.20    0.06    30

Findings the orders in rate
 
For reactant A 
STEP 1-  Expts  1 and 2 vary A and keep B constant.
STEP 2-  Reactant  A was doubled in concentration.
STEP3-  the rate of reaction doubled.
Step 5- find the relationship between the change in reaction rate and change in concentration of reactant.
What happened to reaction rate  2=     n  = 1

⦁    Determine the order of  B 

Experiment             Observed rate
1    0.01    0.20    5
2    0.20    0.20    10
3    0.20    0.20    20
4    0.03    0.03    15
5    0.06    0.06    30

Findings the order for rate law
For reactant B 
Step 1: Expects 4 and 5 vary b and keep a constant.
 STEP 2: Reactant B was doubled in concentration .
STEP 3: The rate of reaction doubled.
STEP 4: Make the statement true. 
2 =       m = 1
In this way we can find order from rate law by initial rates method.

 Conclusion:

⦁    Rate law and orders determined by experiment.
⦁    Order of a reaction can be find from rate law through initial rates method.
⦁    The value of rate constant for the same reaction changes with temperature