Question

How to set up the rate expressions for the following mechanism?

Answer 1

Answer:

Explanation:

From the given information:

A → B k₁

B → A k₂

B + C → D k₃

The rate law = $\dfrac{d[D]}{dt}=k_3[B][C] --- (1)$

$\dfrac{d[B]}{dt}=k[A] -k_2[B] -k_3[B][C]$

Using steady-state approximation;

$\dfrac{d[B]}{dt}=0$

$k_1[A]-k_2[B]-k_3[B][C] = 0$

$[B] = \dfrac{k_1[A]}{k_2+k_3[C]}$

From equation (1), we have:

$\mathbf{\dfrac{d[D]}{dt}= \dfrac{k_3k_1[A][C]}{k_2+k_3[C]}}$

when the pressure is high;

k₂ << k₃[C]

$\dfrac{d[D]}{dt} = \dfrac{k_3k_1[A][C]}{k_3[C]}= k_1A \ \ \text{first order}$

k₂ >> k₃[C]

$\dfrac{d[D]}{dt} = \dfrac{k_3k_1[A][C]}{k_2}= \dfrac{k_1k_3}{k_2}[A][C] \ \ \text{second order}$