Question

Determine the predicted rate law expression for the following radical-chain reaction

A2 -> 2 A^. k₁

A^. -> B^. + C k₂

A^. + B^. -> P k₃

A^. + P -> B^. k₄

Answer 1

initiation    A2----> 2A.   K1     rate = K1[A2] ...1

propagation A.----> B. + C K2 rate= K2[A.] ....2

inhibition A.+ P ---->B. K4        rate= K4[A.] [P] ...3

terminationA.+ B. ---->P   K3    rate= K3[A.][B.] ...4

The rate equation can be derived on the basis of steady-state approximation.The rate of change of intermediates may be set equal to zero.

d[A.]/dt =2K1[A2]-K2[A.] -K3[A.][B.]-K4[A.][P]=0 ....5

d[B.]/dt=K2[A.] -K3[A.][B.]+ K4[A.][P]=0 ......6

d[P]/dt= K3[A.][B.] - K4[A.][P]=0......7

K3[A.][B.]= K4[A.][P]

putting these value in eq.6&5

d[A.]/dt =2K1[A2]-K2[A.] -2K4[A.][P]=0

d[B.]/dt=K2[A.] =0

adding above reaction

2K1[A2] = 2K4[A.][P]

The steady-state concentration of A. radicals is

K1/K4 [A2]/[P]=[A.]

If follows that the rate of formation of C is

d[C]/dt= K2 [A.] = K2 xK1/K4 [A2]/[P]