2nd Order Type Parallel Reactions Case I

2^nd Order Type Parallel Reactions Case I

2nd Order Type Parallel Reactions Case I

Second order type parallel reactions case I refers to those reaction in which concentration of both reactants are same. Consider

                                                            A  +   B       ⇄       P1    +     P2

At time t=0                                        a     +    a                  0            0

At time t                                           a-x      a-x                   x           x

Rate of formation of P1 is             R1 ∝ [A] [B]            R1 = k1 (a-x) (a-x)            

                                    R1 = k1 (a-x)²             eq.17.1

Rate of formation of P2 is             R2 ∝ [A] [B]            R2 = k2 (a-x) (a-x)            

                                    R2 = k2 (a-x)²             eq.17.2

Net rate will be the sum of both reactions.

As k1 + k2 = Kt so,                                 

Rearranging                                              eq.17.3

Integrating the above equation,            

 eq.17.4

To find the value of z, consider that x=0 and t=0 and put in eq.17.4.

z = 1/a

Putting this value of z in eq.17.4 we got,         

Simplifying,                                                

  eq.17.5        

OR                                                            

 eq.17.6

Eq.17.5 is the  rate equation while eq.17.6 is the equation for rate constant of 2nd order type parallel reactions having same initial concentration.

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