determine the rate law of the following reaction that occurs by the proposed mechanism.\n2w + x → y +…

determine the rate law of the following reaction that occurs by the proposed mechanism.\n2w + x → y + z\nstep 1 w + w ⇌ w₂ (fast, equilibrium)\nstep 2 w₂ + w → w₃ (slow)\nstep 3 w₃ + x → w + y + z (fast)
Answer
Explanation:
Step1: Identify the rate - determining step
The slow step (Step 2: $W_2+W\rightarrow W_3$) 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 ($W + W\rightleftharpoons W_2$), 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:
$rate = k[W]^3$