Question

Deduce the rate law from the mechanism below

A2L2 = 2 AL (fast)

2 AL + Q = A2L2Q (fast)

A2L2Q + Z --> ZL2 + A2Q (slow)

A) Rate = k3[A2L2Q][Z]

B) Rate = (k3k2k1)/(k-2k-1)[A2L2][Q][Z]

C) Rate = (k3k2)/k-2[A2L2][Z]

D) Rate = (k1k2k3)/(k-3k-2k-1)[A2L2] 2[Q][Z]

E) none of the above

Answer 1

rate law depends on the slowest step.

Here slowest step is:

A2L2Q + Z --> ZL2 + A2Q (slow)

so,

rate law is:

rate= k3*[A2L2Q]*[Z]

Here A2L2Q is an intermediate

So, use steady state approximation is step 2:

K2 [AL]^2 [Q] = K-2 [AL2Q]

so,

[AL2Q] = (K2/K-2)* [AL]^2 [Q]

rate law now becomes:

rate= k3*[A2L2Q]*[Z]

rate= k3*(K2/K-2)* [AL]^2 [Q] *[Z]

AL is still an intermediate

So, use steady state approximation is step 1:

K1 [A2L2] = K-1 [AL]^2

so,

[AL]^2 = (K1/K-1)*[A2L2]

rate law now becomes:

rate= k3*(K2/K2b)* [AL]^2 [Q] *[Z]

rate= k3*(K2/K-2)* (K1/K-1)*[A2L2] [Q] *[Z]

Answer: B