REACTION IN SOLUTIONS - BIERRUM BRONSTED ( EFFECT OF IONIC STRENGTH ON THE RATE OF THE CHEMICAL REACTION)

Let us consider a chemical reaction between ' A' and ' B' obeying second order kinetics, the rate depends on [ A]  [B ]

           Let us imagine 'A' and 'B' react in the solvent medium ( pure water) it's rate constant is k₀.

                  If the same reaction happens in pressure of the added electrolyte.

                                 Let the rate constant is kz. 

(ie), kz is transfer the rate constant when

μ ≠ 0 and

       k₀ is transfer the rate constant when

μ = 0.

A + B → product  [ n= 2]

Rate = kz [ A] [ B]................. (1)

According to Eyring equation :-

A + B ⇔ AB ≠ → .............product

    Rate ∝ [ AB ] ≠

   Rate = C [ AB]...................... (2)

FOR THE CHEMICAL REACTION :-

                                      It's happening in presence of electrolyte, instead of concentration activity [a] should be used in the law of mass action applied to the formation of AB≠

       k≠ =    aAB ≠ 

                  aA.aB

k≠ =   [ AB ] ≠     .    ʋAB ≠   

         [A] [B]             ʋA.ʋB

(or)

AB ≠ = k≠ [A ] [B ]   .   ʋA . ʋB       .......(3)

                                      ʋAB ≠

Substituting equation (3) in (2)

 Rate = e  k≠  [A ] [ B] .       ʋA . ʋB   .....(4)

                                             ʋAB ≠

Comparing equation (1) and (4)

kz [ A] [ B] = C.k ≠ [ A] [ B]     ʋA.ʋB  

                                                 ʋAB≠

   kz =  C.k ≠    ʋA.ʋB      ............(5)

                         ʋAB≠

According to Deben Huckel limiting law,

log ʋi = − Az i² √μ  

⇔log ʋA = − AZ A² √μ

log ʋB =− Az B² √μ

loɡ ʋAB≠ =− ( ZA + ZB)² √μ

Taking log the equation (5)

log kz = log C.K ≠ + loɡ ʋA + loɡ ʋB − loɡʋAB≠

log kz = log CK≠ − Az A² √μ − A zB² √ μ+A

(zA +ZB)²

(a+b)² = a² + b² + 2ab)

= loɡ Ck≠ − AzA² √μ − AzB² √μ + AzA² √μ

   + AzB² √μ + 2A. ZAZB √μ

log = log Ck ≠ + 2A zA.ZB √μ

log kz = log k₀ + 2A zA zB √μ .....(6)

If the solvent is pure water, 

        A = 0.509

Therefore, 

log kz = log k₀ + 2 (0.0509) ZA ZB √μ

log  kz    =  1.02 ZA ZB          √ μ ...... (8)

        y                m                       x

Equation (6) or (7) or (8) are known as

BIERRUM - BRONSTED EQUATION. 

Equation (8) can be converted into graph as follows.

SIGNIFICANCE :-

(1) If the reactive species are of similar changes, the rate constant will increase on increasing the ionic strength of the medium ( solution).

(2) If the reactive species are of different charges, the rate constant will decrease on decreasing the ionic strength of the medium.

(3) If the reactive species involves dipole(s) the rate constant will not change on changing the ionic strength of the medium.