Question

A complex reaction takes place in following steps:
$NO_{2}Cl_{(g)} \longrightarrow NO_{2(g)} + Cl_{(g)}$ (slow)
$NO_{2}Cl_{(g)} + Cl_{(g)} \longrightarrow NO_{2(g)} + Cl_{2(g)}$ (fast)
Identify rate law equation for this reaction.

• A. $r=k[NO_{2}Cl]$
• B. $r=k[NO_{2}][Cl]$
• C. $r=k[NO_{2}]^{2}$
• D. $r=k[NO_{2}Cl]^{2}$

Hint:

Rate is always determined by the slowest step of the mechanism.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
For a complex (multi-step) reaction, the overall rate of the reaction is determined by the slowest step in the mechanism.

Step 2: Key Formula or Approach:
Rate law \( = \) Rate of the slow step.

Step 3: Detailed Explanation:
The given mechanism is:
Step 1 (Slow): \( \text{NO}_2\text{Cl} \rightarrow \text{NO}_2 + \text{Cl} \)
Step 2 (Fast): \( \text{NO}_2\text{Cl} + \text{Cl} \rightarrow \text{NO}_2 + \text{Cl}_2 \)
Since the first step is the rate-determining step (RDS), the rate of the reaction depends only on the concentration of the reactants in this step.
The reactant in the slow step is \( \text{NO}_2\text{Cl} \) with a stoichiometric coefficient of 1.
Therefore, the rate law is \( r = k [\text{NO}_2\text{Cl}]^1 \).

Step 4: Final Answer:
The rate law equation is \( \text{r} = \text{k} [\text{NO}_2\text{Cl}] \).