Question

The ozone layer in the earth's upper atmosphere is important in shielding the earth from very harmful ultraviolet radiation. The ozone, O${}_3$, decomposes according to the equation $2O_3\left(g\right)\to 3O_2\left(g\right)$. The mechanism of the reaction is thought to proceed through an initial fast, reversible step and then a slow second step.
Step 1 : Fast, reversible, $O_3\left(g\right)\rightleftharpoons O_2\left(g\right)+O\left(g\right)$
Step 2 : Slow, $O_3\left(g\right)+O\left(g\right)\to 2O_2\left(g\right)$
Then which of the following is correct?

• A. Step 2 is rate determining step
• B. The rate expression for step 2 is $-\frac{d}{dt}\left[O_3\right]=k\left[O_3\right]\left[O\right]$
• C. Molecularity is 1 for step 1
• D. Molecularity is 2 for step 2

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A The rate expression for step 2 is $-\frac{d}{dt}\left[O_3\right]=k\left[O_3\right]\left[O\right]$
B Molecularity is 2 for step 2
C Molecularity is 1 for step 1
D Step 2 is rate determining step

Step 1 is the fast step and step 2 is the slow step. Slow step is the rate determining step. Hence, step 2 is the rate determining step.

The rate of the reaction is the rate of the slow step. $-\frac{d}{dt}\left[O_3\right]=k\left[O_3\right]\left[O\right]$.

In step 1 only one molecule participates in the reaction. In step 2, two molecules collide to form the product.

Hence, the molecularity for step 1 is 1 and for step 2 is 2.