Question

Nitric oxide and nitrogen dioxide are found in photochemical smog. Nitrogen dioxide is formed from nitrogen monoxide in the exhaust of automobile engines. A possible mechanism for this reaction is given below. What is the rate law predicted by the mechanism?

Reaction:
2NO(g) + O2(g) → 2NO2(g)
Step 1 (fast): NO + NO → N2O2
Step 2 (slow): N2O2 + O2 → 2NO2

A. Rate = k[NO]2
B. Rate = k[NO2]2
C. Rate = k[NO][O2]
D. Rate = k[NO]2[O2]
E. Rate = k[No2]^2/[No]^2[o2]

Answer 1

(D) Rate = k[NO]²[O₂]

Step-by-step explanation:

The rate law predicted by the mechanism

Reaction:

2 NO(g) + O₂(g) →2 NO₂(g)

Step 1 (fast): NO + NO → N₂O₂

Step 2 (slow): N₂O₂ + O₂ → 2 NO₂

According to rate law

rate of reaction is measured from slowest step

`Rate = K[N_(2)O_(2) ] [O_(2) ]` ------------------ (i)

Since N₂O₂ is an intermediate

So we replace intermediate from rate law equation

From step 1 we can write

`k=([N_(2)O_(2) ])/([NO]^(2) ) \\{[N_(2)O_(2) ]=K[NO]^(2)`

From equation (i)

∴ Rate = k[NO]²[O₂]