Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

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Chemistry : Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

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Reversible reactions and Equilibrium 

Consider the following reaction in which the forward reaction is first order in A, and the back reaction is first order in B :

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

The forward and back rate constant are kA & kB. Then rate law are 

Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev
Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Only reactant is present at t = 0 and the concentration of reactant and product for t > 0 must be equal to the initial concentration of reactant. [A]0 = [A] + [B]
then
 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

= –kA[A] + kB[B]
= –kA[A] + kB([A]– [A])
= –[A] (kA + kB) + kB[A]0

Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev
Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Using this relationship we get

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev
Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev
Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev
Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

[A] (kA + kB) – kB[A]0 = k[A]0 e-( kA+ kB)t

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Then

As t → ∝, the concentration reach their equilibrium values then

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev
Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

It follows that the equilibrium constant of the reaction is

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev
i.e  Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

kC is equilibrium constant in terms of concentration.
At equilibrium, the forward and reverse rates must be same so,

KA[A]eq = kB[B]eq

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Problem.  Using the following equation
A → C

 mechanism,

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev  Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

(a)  Find rate of reaction ?
(b)  Find rate of reaction when (i) is fast.
Sol. (a) From the rate law

Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev
Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

[B] is intermediate then we apply SSA then we get

0 = k1[A] – k2[B] – k3[B]

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

then

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

(b) When (i) is fast then

k1[A] = k2[B]
i.e.Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

 & Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Problem.  Using the following equation 
 2NO2 + F2 → 2NO2F
 Mechanism

 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev
Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Find the rate of reaction.
 Sol.
From the rate law

Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRevReversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

= 0 (F is intermediate)


 Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

Reversible Reactions And Equilibrium - Chemical Kinetics Chemistry Notes | EduRev

= 2k1[F2][NO2]

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