Question

determine the rate law of the following reaction that occurs by the proposed mechanism.
2w + x → y + z
step 1 w + w ⇌ w₂ (fast, equilibrium)
step 2 w₂ + w → w₃ (slow)
step 3 w₃ + x → w + y + z (fast)

Explanation:

Step1: Identify the rate - determining step

The slow step (Step 2: $W_2+W
ightarrow W_3$) is the rate - determining step. So the rate law is initially $rate = k_2[W_2][W]$.

Step2: Express $[W_2]$ in terms of $[W]$

For the fast - equilibrium step 1 ($W + W
ightleftharpoons W_2$), the equilibrium constant $K_1=\frac{[W_2]}{[W]^2}$, so $[W_2]=K_1[W]^2$.

Step3: Substitute $[W_2]$ into the rate law

Substitute $[W_2]=K_1[W]^2$ into the rate law from Step 1. We get $rate = k_2K_1[W]^2[W]=k[W]^3$, where $k = k_2K_1$.

Answer:

$rate = k[W]^3$