Types Of Rate Of Reaction

As per the general definition ,the rate of chemical reaction is defined as a speed with which a reactant is converted into product or a speed at which a reaction takes place. The rate of reaction is generally seen to be influenced by the composition of the reactant molecules and the energy of the reactant molecules (Energy generally means temperature). 

Types Of Reaction Rate
The rate of reaction is divided into two ways:
a) Instantaneous reaction rate
b) Average reaction rate

AVERAGE REACTION RATE
Average reaction rate is similar to the reaction rate which is defined for the entire time interval. Let us consider a reaction to understand more clearly the average reaction rate;
                     A ➞ B
      at t=0,  only A present [A]
      at t=t₁, both A and B present [A]₁&[B]₁ 
      at t=t₂, Both A and B present [A]₂&[B]₂
Now, The rate of disappearance of reactant is given by;  
             -rA = [A]₂ - [A]₁ / (t₂ - t₁ )
                 ➩ -rA = -∆[A] /∆t
The rate of formation of product is given by; 
               rB = [B]₂ - [B]₁ / (t₂-t₁) 
                    ➩ rB = ∆[B] / ∆t
Here, 
        [A]₁ > [A]₂ ➝ rate of disappearance of reactant is negative 
        [B]₁< [B]₂ ➝ rate of formation of product is positive

Since, only one reactant (A) and one product (B) is present in this reaction and as the mass is conserved during the reaction, therefore the amount of 'A' disappeared in the time interval 't₂–t₁' will be same as the amount of 'B' formed during the same time interval.
Therefore, 
➩ ravg = Rate of disappearance of A = Rate of formation/appearance of B
➩ ravg = -∆[A] /∆t =∆[B] / ∆t 
➩ ravg = -rA = rB
These rate gives the rate of reaction for the entire time interval "∆t ", hence are called as 'Average Reaction Rate'.
           
INSTANTANEOUS REACTION RATE
As the word pronounce instantaneous which means at a particular instant of time. Therefore when a rate of reaction is defined at a particular instant of time the then the rate of reaction is called 'Instantaneous Reaction Rate'. 
               Average rate of reaction remains constant for a given time interval and do not give any idea about a reaction at a particular instant of time. This is where the instantaneous rate of reaction comes into the picture. 
           Instantaneous rate of reaction is the rate at which the reaction is proceeding at a particular instant of time. Here, the time interval "△t" tends to zero and the average rate of reaction is converted into instantaneous rate of reaction.
For the above reaction,  
                                  A ➞ B
                ➩ ravg = -∆[A]/∆t =∆[B]/∆t 
          If, ∆t ➝ 0 then, 
                ➩ rInst = - d[A]/dt = d[B]/dt 
          Here,  
                 rIns = instantaneous reaction rate 
                 ravg = average reaction rate

For Example
2HI ➞ H₂ + I₂
➩ r inst  = - d[HI]/ 2dt= d[H₂]/dt = d[I₂]/dt
➩ ravg = - Δ[HI]/ 2Δt = Δ[H₂]/∆t = ∆[I₂]/∆t

Important Note
One more thing is that we can find out both the rate of reaction by using "Concentration Vs time" curve of reactant and product. 
The slope of the "Concentration Vs Time" curve at any point gives the average reaction rate while the tangent on the "Concentration Vs Time" curve at that point gives the instantaneous rate of reaction. 
For all "Practical Purposes, The Instantaneous Rate Of Reaction Is Used" because average rate of reaction doesn't give the exact information in most cases about the completion of the reaction.


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